Note: Descriptions are shown in the official language in which they were submitted.
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INTERNATIONAL PATENT APPLICATION
Mitigation of Chemical Absorption Across Multiple Robots
TECHNICAL FIELD
[0001] The present application relates to operation of large
numbers of robots that
absorb a chemical from surrounding fluid.
BACKGROUND
[0002] Large numbers of remote robots, often referred to as a
"swarm", can utilize
their collective operational capabilities to accomplish certain tasks more
readily than a single
larger robot or small number of larger robots would be able to. Such robots
may operate
within a fluid system and may absorb a chemical of particular interest from
the surrounding
fluid as part of their designed function. Such absorption could be achieved by
using one or
more chemical-extracting components (hereafter referred to as "pumps") capable
of
absorbing the chemical of interest from the surrounding fluid. One example of
such a pump is
a component that draws fluid through an intake duct, passes it through a
chemically-selective
membrane to filter out a selected chemical from the fluid flow (either
restraining the chemical
from the flow or passing the chemical through while restraining the remainder
of the flow),
and then ejects the resulting chemical-depleted fluid via an output duct.
Small-scale pumps
and valves are well-known in the art, (Zhang, Xing et al., "Micropumps,
microvalves, and
micromixers within PCR microfluidic chips: Advances and trends," Biotechnol
Adv, 5,
2007), (Nguyen, Huang et al., "MEMS-Micropumps: A Review," Journal of Fluids
Engineering, 2, 2002), (Amirouche, Zhou et al., "Current micropump
technologies and their
biomedical applications," Microsystem Technologies, 5, 2009) and some examples
are taught
in U.S. Patents 6,955,670; 8,343,425; and 10,220,004; and U.S. Publications
2008/0161779,
2008/0202931, 2010/0284924, and 2012/0015428. Alternatives to the use of semi-
permeable
or selectively-permeable membranes include passing the fluid across chemically-
selective
binding sites, and/or using Zeolites (crystal structures with holes sized to
fit certain
molecules) to separate a chemical from the flow. (Jones, Tsuji et al.,
"Organic-functionalized
molecular sieves as shape-selective catalysts," Nature, 6680, 1998; Martinez
and Corma,
"Inorganic molecular sieves: Preparation, modification and industrial
application in catalytic
processes," Coordination Chemistry Reviews, 13-14, 2011). One application for
the use of
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micro- or nano-scale robot swarms is the operation of such robots operating
inside the body
of an organism for medical or veterinary purposes.
[0003] Larger-scale robots (100mm and larger, for example) can
be fabricated using
conventional construction techniques. For smaller scale robots (such as MEMS
and NEMS
robots), such robots and their constituent parts are manufactured in a variety
of ways,
including lithography and etching, micromachining, e-beam deposition, atomic
layer
deposition, and others. These techniques and others, including the integration
of circuitry
with the robots, are known in the appropriate fields (e.g., ("Handbook of
Silicon Based
MEMS Materials and Technologies," Micro and Nano Technologies, William Andrew,
2010); (Ghodssi and Lin, "MEMS Materials and Processes Handbook," MEMS
Reference
Shelf, Springer, 2011); (Schulz, Shanov et al., "Nanotube Superfiber
Materials: Changing
Engineering Design," Micro and Nano Technologies, William Andrew, 2013);
(Morris and
Iniewski, "Nanoelectronic Robot Applications Handbook," Robots, Circuits, and
Systems,
CRC Press, 2013); (Choudhary and Iniewski, "MEMS: Fundamental Technology and
Applications," Robots, Circuits, and Systems, CRC Press, 2013); (Sharapov,
Sotula et al.,
"Piezo-Electric Electro-Acoustic Transducers," Microtechnology and MEMS,
Springer,
2013). Additionally, three dimensional printers are available which are
capable of far sub-
micron feature sizes (e.g., OWL Nano, sold by Old World Technologies, Virginia
Beach,
VA, USA; Photonic Professional GT from Nanoscribe, Germany; and the f100 aHead
from
FEMTOprint SA, Switzerland). Also falling under the category of small-scale
robots,
biorobots have been created which use, for example, flagella from micro-
organisms for
motile power, and which can be steered using electrical fields, light, or
other means. (Sakar,
"MicroBioRobots for Single Cell Manipulation," Electrical and Systems
Engineering, 284,
University of Pennsylvania, 2010); (Paprotny and Bergbreiter, "Small-Scale
Robotics From
Nano-to-Millimeter-Sized Robotic Systems and Applications," First
International Workshop,
microICRA 2013, Karlsruhe, Germany, Springer, 2013).
SUMMARY
[0004] The following Summary is provided to aid in understanding
the novel and
inventive features set forth in the appended claims and is not intended to
provide a complete
description of the inventive features. Any limitations of the following
summary should not be
interpreted as limiting the scope of the appended claims.
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[0005] Where a large number of robots operate in a fluid system
to absorb a
particular chemical (hereafter referred to as a "reactant"), they may cause
depletion of the
reactant to such a degree as to materially affect the functioning of the fluid
system. In such
case, the impact of the collective absorption by the robots effectively makes
them a part of
the fluid system that alters its operation. Where a certain concentration of
the reactant is
needed, either by the robots themselves or by other reactant-using features
associated with the
fluid system, the combined absorption capability of the robots may create
situations in which
the concentration of the reactant is insufficient for proper functioning of
the fluid system. To
prevent such situations, robots may need to limit their absorption of the
reactant to avoid
creating such depletion of reactant. In some cases, the fluid system has at
least one region
where reactant is abundant (hereafter referred to as a "high-reactant
region"); in such cases,
some or all robots may be configured to absorb and store reactant when in such
a high-
reactant region, and later release the reactant for use when in a region where
the reactant is
depleted or otherwise would become depleted.
[0006] As one example to illustrate the above concepts, the
circulatory system of an
organism can be considered as a fluid system, and a swarm of robots can be
configured to
operate in the circulatory system, absorbing oxygen and glucose from blood as
reactants to
provide power to operate. In such cases, available oxygen is frequently a
limiting factor, as
oxygen is extracted both for use as a reactant to power the robots and by
cells, and the lungs
or gills provide a high-reactant region where oxygen is readily available. The
proper
functioning of the fluid system in such case includes keeping the oxygen
concentration at any
particular location in the circulatory system high enough to provide power for
robots as well
as supplying sufficient oxygen for use by cells. If a large enough number of
robots are
present and absorbing oxygen, they can impact the ability of the fluid system
to fulfill its
function of transporting and distributing oxygen to the cells, and their
combined absorptive
capability can materially affect the function of the fluid system. Typically,
this is of greatest
concern near the "end" of the circuit, before the blood re-enters the
lungs/gills where oxygen
is replenished.
[0007] A swarm of robots that operate as part of a fluid system
in which a selected
reactant is present in the fluid can be operated so as to mitigate the impact
of their combined
absorption. In one general method for performing such operation, a large
number of robots
operate in the fluid system and can each absorb the selected reactant from the
surrounding
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fluid, with the combined absorption capability of the robots being great
enough to materially
affect the functioning of the fluid system with respect to the reactant. The
robots (or at least a
subset of the robots) can be operated to determine when a particular robot is
in an absorption-
limiting need condition. Responsive to such determination, the particular
robot can then be
operated so as to limit its absorption of reactant from the surrounding fluid.
The step of
determining when a particular robot is situated in an absorption-limiting need
condition could
make such determination based, at least in part, on sensed conditions (such as
concentration
of the selected reactant or another chemical, a related parameter such as rate
of concentration
change, a physical parameter such as temperature, pressure, etc.) at the
location of the
particular robot, and/or can include making a determination of the location of
the particular
robot in the fluid system In many cases, such determination is made in
anticipation of the
reactant level eventually becoming depleted if absorption by the robot were
not limited. In
some cases, robots may be assumed to be in an absorption-limiting need
condition as a
default, until some absorption-limiting triggering event is determined to
occur, indicating that
the robot should no longer limit its absorption (examples of such triggering
events are
discussed below).
[0008] In some cases, the fluid system has at least one region
having a high
concentration of the selected reactant (a "high-reactant region"), and the
combined absorption
capability of the robots is such that it can create a concentration gradient
of the selected
reactant that decreases in concentration with increasing distance from the
high-reactant
region. The fluid may circulate through such a high-reactant regions, or even
through
multiple such regions. In fluid systems having a high-reactant region, the
step of determining
when a particular robot is situated in an absorption-limiting need condition
can include
determining that the particular robot has exited the high-reactant region; one
scheme is to
assume that an absorption-limiting need condition exists upon the robot
exiting the high-
reactant region, until an absorption-limiting triggering event is determined
to have occurred
In many cases, such triggering event is indicative of a need for the robot to
operate in a
relatively high-energy mode of operation to perform some task, such as
computation,
communication, and/or some diagnostic or therapeutic operation. Examples of
triggering
events that could determine when a particular robot is no longer in an
absorption-limiting
need condition include making a determination that the robot has circulated a
set number of
times through the high-reactant region (which may indicate that the robot has
collected a
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sufficient amount of data to communicate), is within a specified region of the
fluid system
(which could be a region suitable for communication to a receiver, a region
where a
diagnostic and/or therapeutic task must be done, a region where significant
data collection is
required, or simply a region where it is expected that reactant levels are
sufficient that
limiting absorption is unnecessary), has stored a set amount of data, has
achieved a prescribed
mission-related task to a prescribed degree, and/or requires performing a high-
energy task.
Where the fluid system is the circulatory system of a biological organism
having capillaries,
organs, and skin, and the triggering event could be determining that the robot
is within a
specified region of the fluid system, further specifying the determination
that the robot has
passed into a capillary, is within a specified distance of the skin (and thus
positioned to
transmit data to an external receiver), and/or has passed into a specified
organ In some cases,
determining that the robot is within a vessel of a specified minimum size and
within a
specified distance of a wall of the robot can be the basis for determining
that an absorption-
limiting need condition exists, and the robot can be operated to limit its
absorption and/or
(where the robot has a locomotion capability) move away from the vessel wall.
[0009] Various approaches to limiting absorption of reactant by
a particular robot can
be employed. Typically, robots can turn off some or all of their pumps, and/or
operate some
or all pumps at a different rate (such as at a different power level and/or
different duty cycle).
One approach for a number of robots that are absorbing reactant is for them to
maintain their
position within a specified distance of one another, such that the presence of
additional robots
in close proximity limits the available reactant for each robot to absorb.
[0010] In fluid systems where the fluid has at least one high-
reactant region (hereafter
discussed in the singular, although multiple high-reactant regions could be
present), the
robots may include at least a subset of robots that can store the reactant and
later release the
stored reactant for use by themselves and/or for use by another robot. In such
cases, a
determination can be made of when a particular robot with such storage
capability is located
in the high-reactant region, and operating such robot to absorb and store
reactant responsive
to such determination. A determination can subsequently be made that a
reactant need
condition exists in the vicinity of the robot, and the robot operated to
release stored reactant
responsive to such determination Many of the criteria discussed above for
determining when
an absorption-limiting need condition no longer exists could also be employed
to determine
when a reactant need condition exists, where these criteria indicate a need
for the robot to
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operate in a high-power mode (such as to communicate data after the robot's
mission has
been completed to a prescribed degree and/or after the robot has accumulated a
prescribed
amount of data). The determination of when a reactant need condition exists
could be made
based on sensed conditions, such as sensing that the concentration of reactant
in the particular
region is (or will soon be) below a specified threshold (or by sensing a
related parameter such
as rate of decrease in concentration), and/or based on determining when a
particular robot
that can store reactant is located within a specified region of the fluid
system (which could be
a region based on absolute location, location in a specific type of region, or
a relative location
such as a specified distance away from the high-reactant region, as determined
by distance
traveled, elapsed time in circulation, etc.) For a circulating fluid system,
relative location
could be determined by elapsed time or distance as an absolute value or as a
percentage of the
circulation path, such as the time or distance equivalent to traveling 50%,
70%, 80% or 90%
of the circulation path (or average circulation path, if there are multiple
possible routes
through the circuit ¨ in such cases, the determination might be that the robot
has traveled
100% of the average, indicating that it is in a longer and/or slower route
than average). Such
reactant need condition could also be indicated by receiving a communication
from an
external transmission source, such as another robot in need of more reactant
(as discussed in
greater detail below), or by an external source (such as another robot or
other device
monitoring conditions in the fluid system) that has determined that more
reactant is needed.
When absorbing and storing reactant, a robot may remain in the high-reactant
region until a
determination is made that a specified threshold amount of reactant has been
stored. Where
the fluid system circulates through the high-reactant region, the robot could
anchor itself
within the high-reactant region, select a path through the high-reactant
region that takes the
fluid longer to circulate through, and/or could delay full-power operation
until it has passed
several times through the high-reactant region (for example, operating in a
low-power mode
of operation until it has passed 5 times, 10 times, 15 times, 20 times, or 25
times through the
high-reactant region), and/or stored a threshold amount of reactant (as
determined by
pressure, weight, etc.) Where the fluid system contains other sources of
reactant (for
example, oxygen stored in red blood cells in an organism's circulatory
system), robots could
be configured to extract the reactant from such source to store for later
release. In some cases,
robots could store a reactant, move to another location, and release it at the
new location in
order to more evenly distribute reactant through a portion of the fluid
system. Such
redistribution may help to avoid the impact of robot absorption and/or may
provide a more
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consistent distribution of reactant through vessels of the fluid system in
order to make the
actual conditions experienced by the robots conform better to generalized
models used to
design and implement robot missions.
[0011] In some situations, the group of robots can include a
subset of robots that
serve as mission robots and a subset of robots that serve as supply robots,
where the supply
robots can store the selected reactant for later use by the mission robots
(the mission robots
may also be able to store reactant, typically for their own use). In such
cases, determining
when a reactant need condition exists can (possibly in addition to one or more
of the criteria
discussed above) include determining when a mission robot in the vicinity of a
supply robot
has insufficient reactant available to perform a desired operation, and
operating such mission
robot to communicate a reactant need signal to such supply robot, in response
to which the
supply robot receiving the reactant need signal can be operated to release
stored reactant for
use by the mission robot communicating the reactant need signal. Where such a
supply robot
releases reactant, it could release stored reactant into the surrounding fluid
(to be absorbed by
the mission robot), and/or could dock with the mission robot before releasing
stored reactant
to it.
[0012] Instructions for directing a group of robots to perform
any of the methods
described above can be stored on a medium suitable for providing instructions
to direct the
operation of a group of robots. A group of robots can be configured to perform
any of the
methods described above.
[0013] A group of robots for operating as part a fluid system in
which a selected
reactant is present in the fluid can comprise a large number of robots, each
of which is
configured to absorb the selected reactant from surrounding fluid, and wherein
the combined
absorption capability of such robots is great enough to materially affect the
functioning of the
fluid system with respect to the selected reactant. At least a subset of the
robots serve as
mission robots, and each have controller housed therein and at least one
mission instruction
set for directing the controller to operate the mission robot so as to perform
the operations of
determining when the mission robot is in an absorption-limiting need condition
and,
responsive to such determination, operating the mission robot to limit its
absorption of
reactant from the surrounding fluid. The determination that the mission robot
is in an
absorption-limiting need condition could be made based on the various criteria
discussed
above with regard to methods, and could include criteria such as one or more
of the sensed
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conditions at the location of the mission robot, the location of the mission
robot in the fluid
system, and/or a determination that the mission robot has exited a high-
reactant region. In this
latter case, an absorption-limiting need condition could be assumed to exist
after exiting a
high-reactant region until an absorption-limiting triggering event is
determined to have
occurred. Examples of such triggering events include determining that the
mission robot has
circulated a set number of times through the high-reactant region, that the
mission robot is
within a specified region of the fluid system, that a set amount of data has
been stored by the
mission robot, that a prescribed mission-related task has been achieved to a
prescribed
degree, and/or that a high-energy task is required by the mission robot.
[0014] A group of robots can include robots that can absorb and
store reactant and
later release stored reactant for use by themselves or by another robot. Such
robots that store
and release reactant could be mission robots, which operate as discussed
above. Mission
robots (with or without storage capability) could be supplemented with a
number of supply
robots that are provided primarily to supply reactant to the mission robots,
each of such
supply robots having controller housed therein and at least one supply
instruction set for
directing the controller to operate the supply robot so as to perform the
operations of
determining when the supply robot is in a high-reactant region and absorbing
and storing
reactant responsive to such determination, and determining when a reactant
need condition
exists in the vicinity of the supply robot, and releasing reactant for use
responsive to such
determination (note that when mission robots store reactant, they can have a
storage and
release instruction set that operates similarly, although they may employ
different criteria to
determine when a reactant need condition exists and may only release reactant
from storage
internally, for use by the mission robot itself). The determination of when a
reactant need
condition exists could be made based on the various criteria discussed above
with regard to
methods, and could include sensed conditions, such as sensing that the
concentration of
reactant in the particular region is below a specified threshold, based on
determining when a
particular robot that can store reactant is located within a specified region
of the fluid system,
and/or based on receiving communication from a nearby robot that that robot
needs reactant.
When reactant is released from storage, it could be released into the
surrounding fluid, or the
supply robot could dock with a particular mission robot to transfer reactant
directly to that
mission robot. The composition of the group of robots may be selected such
that the number
of supply robots is at least 5x, 10x, 15x, 20x, 30x, or 40x greater than the
number of mission
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robots. The robots may be configured such that the supply robots have an
average size no
greater than half the size (by volume) than the mission robots, and may be
considerably
smaller, such as 1/4 the volume, 1/8 the volume, 1/16 the volume, or 1/32 the
volume. When
operating to absorb and store reactant, robots that are determined to be in
the high-reactant
region may make a determination of whether a reactant storage triggering event
has occurred,
and ceasing storage in response to such triggering event. Such triggering
event could be a
determination that a prescribed amount of reactant has been stored, that the
robot has spent a
prescribed amount of time in the high-reactant region or made a prescribed
number of
passages therethrough (where the fluid circulates), or similar criteria
related to the amount of
reactant that the robot is able to absorb and store while in the high-reactant
region.
[0015] A robot for operating in a fluid environment with similar
robots could have
circuitry housed in the robot at least one mission instruction set for
directing the circuitry to
operate the robot so as to perform the operations of determining when the
robot is in an
absorption-limiting need condition, and operating the robot in such a manner
as to limit its
absorption of reactant from the surrounding fluid responsive to such
determination. In some
cases, the robot has at least one fuel cell housed therein, which is
configured to consume the
reactant to generate electrical energy to power the circuitry (and frequently
other capabilities
of the robot). The robot may have at least one pump for absorbing reactant
from surrounding
fluid and supplying absorbed reactant to the at least one fuel cell. The robot
may have at least
one storage tank housed therein that is connectable to the at least one pump
to receive and
release reactant therefrom, and at least one supply instruction set for
directing the circuitry to
operate the robot so as to perform the operations of determining when the
robot is located in
the high-reactant region and operating such robot to absorb and store reactant
responsive to
such determination, and determining when a reactant need condition exists in
the vicinity of
the robot and operating the robot to release stored reactant responsive to
such determination.
Where the robot is intended for use as a supply robot, it may have only the
supply instruction
set, and not include the mission instruction set for determining when to limit
absorption.
Where the robot has one or more reactant storage tanks, such tanks may have a
volume
between 2% and 25% of the total volume of the robot. The fraction of the robot
surface may
be greater than 2% and may be about 5%. The robot radius may be greater than
0.25 p.m.
Where the robot operates in a fluid that contains other sources of reactant,
the robots could be
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configured to extract the reactant from such source for its own use at the
time and/or to store
for later release.
[0016] Where particular determinations of conditions and
corresponding responses
are discussed for apparatus, those determinations and responses discussed when
addressing
the method could be employed for such apparatus, and vice versa.
BRIEF DESCRIPTION OF THE FIGURES
[0017] FIG. 1 is a flow chart illustrating one example of a
method for mitigating the
absorption effect of a swarm of robots by determining when an absorption-
limiting need
condition exists for particular robots and operating such robots to limit
their absorption of a
reactant.
[0018] FIG. 2 is a flow chart illustrating one example of a
routine that could be
employed in the method shown in FIG. 1 to determine when an absorption-
limiting need
condition exists.
[0019] FIG. 3 illustrates one example of a static fluid system
having a high-reactant
region at its surface. Robots located near the surface are in the high-
reactant region, while
robots at greater depths may cause depletion of the reactant at such depths.
[0020] FIG. 4 illustrates one example of a fluid system where a
liquid circulates
through a high-reactant region, and robots travel in the circulating fluid
[0021] FIG. 5 is a flow chart illustrating one example of a
method for mitigating
absorption by having robots store reactant when located in a high-reactant
region, and later
releasing such stored reactant.
[0022] FIG. 6 is a flow chart illustrating one example of a
reactant storage routine
that could be employed in the method shown in FIG. 5, for the case of a
circulating fluid
system.
[0023] FIG. 7 illustrates one example of a robot suitable for
performing an
absorption-limiting method such as shown in FIG. 1.
[0024] FIG. 8 illustrates one example of a robot similar to
that shown in FIG. 7, but
which is also suitable for performing storage and release of reactant.
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[0025] FIGS. 9 and 10 illustrate a group of robots that includes
a mission robot and
multiple supply robots that can store reactant and supply it for use by the
mission robot. FIG.
9 illustrates two supply robots releasing reactant from storage tanks into the
surrounding fluid
near the mission robot. FIG. 10 illustrates one of the supply robots docked
with the mission
robot to transfer reactant directly to it.
[0026] FIG. 11 illustrates an aggregated model of a circulatory
fluid system, showing
an example where the fluid system is a circulatory system of a human.
[0027] FIG. 12 is a graph of distance over time of blood
traveling through the
circulatory system shown in FIG. 11, from the time of leaving the lung to
returning to the
lung. Vertical lines near the center indicate passage through capillaries.
[0028] FIG. 13 is a compartment model of oxygen within blood,
used when
determining changes in concentration as the blood flows through the
circulatory system.
[0029] FIG. 14 is a graph showing how robot available power
(limited by available
oxygen) varies during a circulation loop, for the case where all robots
consume oxygen as fast
as it diffuses to their surfaces, without taking any mitigation efforts.
Results are shown for
three different numbers of robots in a swarm distributed throughout the
circulatory system.
[0030] FIGS. 15A and 15B are graphs showing how oxygen
concentration in plasma
(FIG. 15A) and red blood cell saturation (FIG. 15B) vary during a circulation
loop. Results
are compared for the numbers of robots in the swarm as shown in FIG. 14, along
with the
values for a case without robots.
[0031] FIG. 16 is a graph showing tissue power (relative to its
maximum with
unlimited oxygen) over the time interval when the blood flows through the
capillaries, for
numbers of robots as shown in FIGS. 14, 15A, 8z 15B, and for the case without
robots as
shown in FIGS. 15A& 15B.
[0032] FIGS. 17A & 17B are graphs showing how robot available
power (FIG. 17A)
and oxygen concentration in plasma (FIG. 17B) decrease with distance along in
a 1mm
capillary, for a case where robots operate just in the capillaries.
[0033] FIGS. 18A & 18B illustrate two examples of placement of
five robots
anchored to the wall of a 34,um long segment of an 8,um-diameter capillary.
FIG 18A shows
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the case where the robots are positioned on alternating sides of the vessel,
while FIG. 18B
shows the robots all positioned on the same side.
[0034] FIGS. 19A & 19B are graphs showing robot power (FIG. 19A)
and oxygen
concentration in plasma (FIG. 19B) with 25% overall hematocrit, for comparison
to the case
shown in FIGS. 14 and 15A (for normal hematocrit). The reduced hematocrit
simulates the
effect for a patient with reduced ability to store oxygen in their blood, such
as an anemic
patient.
[0035] FIG. 20 illustrates a cross section of a robot capable of
storing oxygen in a
spherical storage tank.
[0036] FIG. 21 is a graph of fraction of surface occupied by
pumps needed to collect
all oxygen molecules arriving at the robot surface, as a function of robot
size.
[0037] FIG. 22 shows three constraints on robot and tank
fractional size for supply
robots to carry enough oxygen to provide each mission robot with sufficient
oxygen.
[0038] FIG. 23 illustrates a main mission robot and an oxygen
supply robot, where
the supply robot is optimized according to the parameters shown in FIG. 22.
[0039] FIG. 24 is a graph of the power available to a robot
through the circulation
loop for three different scenarios where 1012 robots are in the swarm,
comparing available
power to a case where power is not limited (the same as the curve for 1012
robots from FIG.
14). The scenarios compared are where all robots are limited to a specified
maximum power,
and where robots are limited based on their location in the circuit.
[0040] FIG. 25 is a graph showing how oxygen concentration in
plasma varies for the
three cases shown in FIG. 24. Note that the curve for unlimited power use is
the same as the
curve for 1012 robots in FIG. 15A.
[0041] FIG. 26 is a transition graph showing a Markov stochastic
process for the
amount of data stored by robots (in numbers of capillaries for which data is
stored), where
each edge corresponds to the robot making a single circulation through the
body.
[0042] FIG. 27 is a graph showing how concentration near the
wall of a 2mm
diameter straight blood vessel changes with distance for a distributed swarm
of 1012 robots, in
three cases. In the first case, robots fully consume all oxygen reaching their
surface. In the
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second case, robots within 0.3mm of the vessel wall do not consume oxygen. In
the third
case, only half the robots consume oxygen but without regard to their position
in the vessel.
[0043] FIG. 28 is a graph showing the same three cases as for
FIG. 27, but for
merging vessels with asymmetric branching where two 2mm-diameter branches
merge into a
2.5mm vessel.
[0044] FIG. 29 illustrates five robots positioned along a vessel
similar to that shown
in FIGS. 18A & 18B, but where successive robots are offset about the
longitudinal axis of the
vessel by an angle 0, shown in FIG. 29 for the case where 9 = 30 (the
arrangements shown
in FIG. 18A& 18B respectively correspond toe = 180 and C = 0 ).
[0045] FIGS. 30A & 30B are graphs showing how average robot
power and power
for the last downstream robot vary as a function of the offset angle (- shown
in FIG. 29,
relative to the power that would be available with all robots aligned along
the vessel wall
(i.e., with C = 0 as shown in FIG. 18B). FIG. 30A shows the case for an
average fluid speed
of lmm/s, while FIG. 30B shows the case for average fluid speed of 0.2mrn/s.
[0046] FIGS. 31A & 31B illustrate five robots in a vessel
similar to that shown in
FIGS. 18A, 18B, & 29, but where the distance between successive robots
increases
quadratically. FIG. 31A shows this distribution for robots aligned along the
same side of the
vessel (i.e., C = 0 ), while FIG. 31A shows the distribution where robots are
on alternating
sides of the vessel (i.e., C = 180 ).
[0047] FIGS. 32A & 32B are graphs showing the average power for
the robots and
for the last robot as a function of the offset angle 0, relative to the
situation of uniformly-
spaced robots aligned along the vessel wall (as shown in FIGS. 30A & 30B), for
fluid flow
speeds of lmm/s (in FIG. 32A) and 0.2mm/s (in FIG. 32B).
[0048] FIG. 33 is a graph of the dimensions of blood vessels as
a function of time
through the circuit shown in FIG. 12, with the size of larger vessels ignored
to show the range
of sizes where hematocrit varies with vessel size.
[0049] FIG. 34 is a schematic view of blood vessel branching to
illustrate increased
aggregated cross section in smaller vessels.
[0050] FIG 35 is an aggregated vessel cross section showing
increased cross section
and reduced hematocrit in smaller vessels.
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[0051] FIGS. 36-38 illustrate gradients in concentration that
result in merged vessels
when the flows from smaller vessels having differing concentrations combine in
the merged
vessel.
DETAILED DESCRIPTION
[0052] When a large number of robots operate in a fluid system
and absorb a selected
chemical (hereafter "reactant-) as a function of their operation, their
combined absorption of
the chemical may potentially deplete its concentration to such a degree as to
materially affect
the function of the fluid system with regard to that reactant. As used herein,
"materially
affect" means that the concentration of the reactant can be reduced to such a
degree in some
locations in the fluid system that available reactant is insufficient for some
intended purpose.
In some cases, the operation of the robots is dependent on an adequate supply
of the reactant
(such as where the robots employ the reactant to generate operating power),
and such
insufficiency occurs when the available reactant in some location is too low
for the robots in
that location to operate as intended. In some cases, the fluid system serves
primarily to
distribute the reactant (such as in the circulatory system of an organism,
where the blood
distributes oxygen to cells throughout the body of the organism), and such
insufficiency
occurs where there is insufficient reactant in some regions compared to the
concentration that
is intended to be provided by distribution. In many cases, both of these
situations exist, and
insufficiency could be based on either or both of the intended needs of the
robots themselves
or the need of some other reactant-absorbing feature associated with the fluid
system. To
prevent such insufficiencies, the robots can be operated to limit their
absorption under
circumstances where it is appropriate, mitigating the effect of absorption of
the reactant by
such robots; in many cases, operation of the robots is adjusted in
anticipation of an
insufficient concentration of reactant that would arise later if operation
were not adjusted at
the present time. In some cases, robots can absorb and store reactant when in
a location where
the reactant is readily available (a "high-reactant region"), and later
release such reactant for
use when in a circumstance where available reactant is insufficient. While the
examples
discussed are directed to systems where the fluid is a liquid, the same
techniques could be
employed in systems where the fluid is a gas, in such cases where the
absorption action of the
robots is capable of causing material depletion of the reactant.
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[0053] FIG. 1 is a flow chart that illustrates one example of a
method 100 for
mitigating absorption by limiting the absorption of robots when circumstances
warrant such
limiting action. At the start, a large number of robots are present in the
fluid system, each of
the robots being configured to absorb a selected reactant that is present in
the fluid system,
and where the combined absorption capacity of the robots is great enough that
it can
materially affect the function of the fluid system by causing depletion of the
reactant in one
or more regions, unless absorption is limited. In normal operation, the robots
absorb the
reactant (step 102). Some or all of the robots are operated such that a
determination is made
as to whether or not each such robot is in an absorption-limiting need
condition (step 104);
that is, a determination is made as to whether the current situation of the
robot is such that it
should limit its absorption of the reactant to avoid the creation of a
depleted region.
Responsive to a determination that an absorption-limiting need condition
exists, the robot is
operated so as to limit its absorption of the reactant from the surrounding
fluid (step 106).
The determination step 104 is repeated, and if an absorption-limiting need
condition is
determined to still exist, then the robot continues to limit its absorption of
the reactant. If it is
determined in step 104 that no absorption-limiting need condition currently
exists for the
robot, then it can resume operating in a manner where it does not limit its
absorption of the
reactant.
102 ¨ Robots absorb reactant
104 ¨ Determine whether absorption-limiting need condition exists
106 ¨ Operate to limit absorption
[0054] Prior to the start of the method, the robots can be
introduced into the fluid
system in a manner appropriate to the available access to the fluid system.
Where the system
is open at some location, the robots can be introduced at such location. Where
the fluid
system is fully enclosed, the robots can be introduced through an existing
port or through a
port installed, temporarily or permanently, for the purpose of introducing the
robots. As one
example, where the fluid system is the circulatory system or organ of a living
organism, an
injection or infusion device such as known in the medical and veterinary arts
could be
employed as a port to introduce the robots at a desired location (e.g., into a
blood vessel or
into the organ of interest).
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[0055] There are various criteria that could be used in step 104
to determine when an
absorption-limiting need condition exists, and the specific criteria selected
are typically
dependent on the particular fluid system, reactant distribution, and intended
operation of the
robots. Typically, determining that an absorption-limiting need condition
exists is made
based on the anticipation that a reactant deficiency would result in some
region of the fluid
system in the future if absorption is not limited at the present time. One
parameter that might
be monitored to determine such a condition would be the rate of depletion of
the reactant. In
some cases, the location of the robot in the fluid system is one basis, or the
only basis, for
determining that an absorption-limiting need condition exists. For example, in
a case where
the fluid system has a high-reactant region, the absorption by the robots upon
leaving such
high-reactant region could create a gradient where the concentration of
reactant decreases as
the distance from the high-reactant region increases. If absorption is not
limited, the reactant
concentration at locations further from the high-reactant region may be
insufficient for the
needs of the robots and/or other reactant-using features associated with the
fluid system. In
such case, a routine 120 such as shown in FIG. 2 could be employed in
performing the step
104 of the method 100.
[0056] In the example of the absorption-limiting need condition
determining routine
120, a determination is made as to whether the robot has exited the high-
reactant region (step
122). Upon such determination, an absorption-limiting need condition is
assumed to exist
(step 124), and the robot is operated to limit its absorption of the reactant,
according to step
106 of the method 100. A determination is then made as to whether a triggering
event has
occurred (step 126), where such triggering event is indicative of the robot
being in a situation
where limiting its absorption is no longer required and/or desirable. A
typical class of such
triggering events occur when it is determined that the robot has reached a
location and/or a
stage of mission completion where it needs to use the reactant at a higher
rate than can be
supplied through limited absorption. For example, where the reactant is used
to power the
robots, a robot may need to perform a high-energy task (such as transmitting
data) upon
reaching a particular location in the fluid system, and/or upon having
completed its mission
to a particular degree. Some specific examples are determining that the robot
has reached a
particular location in the fluid system, has passed through a particular part
of the fluid system
a prescribed number of times, or that it has stored a prescribed amount of
data. Upon
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determining in step 126 that such a triggering event has occurred, the robot
returns (step 128)
to operating in a mode in which it does not limit absorption of the reactant.
122 ¨ Determine whether robot has exited high-reactant region
124 ¨ Absorption-limiting need condition is assumed to exist
126 ¨ Determine whether absorption condition triggering event has occurred
[0057] FIGS. 3 and 4 illustrate two examples of fluid systems
having high-reactant
regions. FIG. 3 illustrates a static fluid system 150 where the fluid is a
liquid 152, having a
surface 154 that is in gas exchange with an atmosphere 156 that contains a
reactant The
supply of dissolved reactant at the surface 154 creates a high-reactant region
158 near the
surface, where the reactant is abundant. Robots 160 having a locomotion
capability (such as
ability to swim and/or ability to adjust their buoyancy) are distributed in
the liquid 152, and
those located in the high-reactant region 158 can absorb reactant without
creating a
deficiency, so long as their absorption rate is less than the rate at which
dissolved reactant is
replaced by gas interchange at the surface 154. As the robots 160 move, some
exit the high-
reactant region 158 near the surface 154 to operate at greater depths in the
liquid 152. The
absorption of such robots 160 may deplete the reactant in lower depths faster
than the
reactant can be replaced by diffusion, and would create a region at some depth
where the
concentration of reactant would be insufficient for the robots 160 to operate
properly. To
avoid this, robots 160 can limit their absorption of the reactant upon leaving
the high-reactant
region 158, and only resume full absorption when it is determined that they
are in a condition,
based on location, mission profile, or other considerations, that it is
desirable for them to have
more reactant available in order to perform their desired operation (such as
to absorb a
reactant used to generate power when the situation warrants a higher rate of
power
consumption to allow the robot to perform mission tasks), or simply when they
are again in
the high-reactant region 158.
[0058] FIG. 4 illustrates a fluid system 170 where a liquid 172
circulates through a
circuit 174 that includes a high-reactant region 176 where reactant is
supplied to the liquid
172 (one of example of such a circulating system is the circulatory system of
a living
organism, discussed in greater detail below, where the lungs/gills provide a
high-reactant
region where oxygen is replenished in the blood). Robots 178 can circulate
with the liquid
172, and may be provided with a locomotion capability (allowing them to move
relative to
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the flowing liquid 172) and/or an anchoring capability (allowing them to
anchor to a wall of
the circuit 174 so as to remain in place against the flow of liquid 172). As
the liquid 172
circulates away from the high-reactant region 176, the absorption of reactant
by the robots
178 causes a reduction in the concentration of the reactant (typically
creating a gradient
where concentration decreases with increasing distance from the high-reactant
region 176),
and may result in the reactant being insufficient for its intended function in
regions of the
circuit 174 that are distant from the high-reactant region 176, such as an end
region 180
located before the liquid 172 returns to the high-reactant region 176. Again,
such an
insufficiency can be avoided if the robots 178 limit their absorption when
exiting the high-
reactant region 176, until such time as their situations are such that they
need to absorb the
reactant at a greater rate in order to perform mission tasks.
[0059] There are a number of schemes that can be used in step
106 of method 100 to
operate a particular robot to limit its absorption. One simple scheme is for
the robot to cease
the operation of the component(s) it uses to absorb the reactant. Some or all
of such
components could be deactivated, or the operation of such components could be
adjusted to
reduce their rate of absorption while they remain active (such as by reducing
the operation
rate or duty cycle). Another scheme is to operate the robot in such manner
that the reactant
available for it to absorb is limited, such as by traveling in a group with
similar robots such
that the group depletes the reactant in its close vicinity, and diffusion
limits the available
reactant for each robot in the group. Where alternative reactants are
available, such as for use
as a fuel, some robots could limit absorption of one reactant by switching to
a different one.
[0060] FIG. 5 is a flow chart that illustrates one example of a
method 200 for
mitigating absorption by having robots store reactant when located in a high-
reactant region,
and later releasing such stored reactant. Depending on the situation, a
particular robot could
operate according to this method by itself or could operate according to this
method as well
as according to a method for limiting absorption, such as the method 100
discussed above. In
some cases, some robots act as supply robots that are operated according to a
reactant storage
and release method, while other robots act as mission robots and operate
according to an
absorption-limiting method (although such robots may also employ a storage and
release
method as well).
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[0061]
At the start of the method 200, a large number of robots are operating in
the
fluid system (step 202), where the fluid system has at least one high-reactant
region and at
least some of the robots are each configured to absorb and store reactant from
the
surrounding fluid. For purposes of discussion, only those robots that are
operated to store and
release reactant are addressed when describing this method; other robots that
absorb the
reactant may also be present. Similarly, while more than one high-reactant
region could be
present, the discussion addresses the case for a singular high-reactant
region; where multiple
high-reactant regions exist, the method could be applied to any of the high-
reactant regions.
The robots are operated such that a determination is made as to whether or not
each such
robot is in the high-reactant region (step 204). Such determination could be
made based on
sensing concentration of the reactant, by sensing fluid flow parameters that
characterize the
high-reactant region, and/or by use of location determination techniques.
Responsive to such
determination, the robot is operated to absorb and store reactant (step 206).
So long as the
robot is in the high-reactant region, it may continue to absorb and store
reactant until such
time as it is determined in step 204 that it is no longer in the high-reactant
region. Optionally,
the robot may stop absorbing upon determination that a triggering event has
occurred (step
208), such as the storage capacity of the robot being reached (as determined
by time spent
absorbing, pressure, weight, etc.) When it is determined in step 204 that the
robot is no longer
located in the high-reactant region, it may optionally be operated to cease
absorbing and
storing reactant (step 210). Note that such action would also correspond to
the step of limiting
absorption in an absorption-limiting method, where an absorption-limiting need
condition can
be assumed to exist when a robot exits a high-reactant region. Alternatively,
the robot could
continue to absorb reactant normally after leaving the high-reactant region
(i.e., skipping
optional step 210).
[0062]
A determination is made as to whether a reactant need condition exists in
the
vicinity of each robot that is no longer in the high-reactant region (step
212) Such
determination could be based on criteria similar to those discussed for
determining when an
absorption-limiting need condition no longer exists, such as by concentration
sensing, fluid
flow parameter sensing, and/or location determination, but could also be based
on
communication of such condition from an outside source, such as another robot.
Upon such
determination that a reactant need condition exists, the robot is operated to
release stored
reactant for use (step 214). Such release could be release from storage within
the robot, to
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provide itself with reactant, or could be released for use by another robot,
in which case the
reactant could be released into the surrounding fluid or released directly to
the other robot
(when the two robots are docked together).
202 ¨ Robots operate in fluid
204 ¨ Determine whether robot is in high-reactant region
206 ¨ Operate robot to absorb and store reactant
208 ¨ Determine whether reactant storage triggering event has occurred
210 ¨ Operate to limit absorption
212 ¨ Determine whether reactant need condition exists
214 ¨ Operate to release reactant
[0063]
FIG. 6 illustrates one example of a reactant storage routine 230 that
could be
employed in the method 200, and which is suitable for fluid systems where the
circulation of
the fluid may pass the robot through the high-reactant region before the robot
has had an
opportunity to store a desired amount of reactant. In some cases, such
situation could be
avoided by the robot taking action to prolong its time in the high-reactant
region, such as
anchoring to a wall, actively moving against the flow of circulation, or
positioning itself
where the flow of fluid through the high-reactant region is slower. However,
in cases where
the robot flows with the fluid, the storage routine 230 could be employed. In
the storage
routine 230, after the determination has been made in step 204 that the robot
is no longer in
the high-reactant region, a determination is made as to whether or not the
robot has a
prescribed amount of reactant stored (step 232). This determination could be
made by sensing
a parameter such as pressure and/or or weight, or could be assumed from the
robot having
spent a sufficient time in the high-reactant region or made a sufficient
number of passages
therethrough (where the fluid circulates). If it is determined in step 232
that the prescribed
amount of reactant has not been stored, the robot is operated in a low-use
mode of operation
(step 234) until such time as the determination in step 204 indicates that the
robot is again in
the high-reactant region. In the low-use mode of operation, the operation of
the robot is
adjusted to reduce its need to use the reactant. In cases where the reactant
is used to generate
power for the robot, the low-use mode of operation may be provided by limiting
the function
of the robot to reduce its power consumption. When in the low-use mode, the
robot may
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ignore any determination of whether or not it is in a reactant need condition
according to step
212. When it is determined in step 204 that the robot is again in the high-
reactant region (or
in a different high-reactant region, in a fluid system where more than one
exists), the robot is
again operated to absorb and store reactant in step 206. Once it is determined
in step 204 that
the robot has exited the high-reactant region, the determination is made again
in step 232
whether or not the prescribed amount of reactant has been stored. Eventually,
after some
amount of time and/or number of passes through the high-reactant region, the
step 232
determines that the prescribed amount of reactant has been stored, at which
time the robot can
be operated in a different mode than the low-use mode, and responds to a
determination in
step 212 that a reactant need condition exists in its vicinity by releasing
stored reactant
according to step 214.
232 ¨ Determine whether prescribed amount of reactant stored
234 ¨ Operate in low-use mode
[0064] FIG. 7 illustrates one example of a robot 300 suitable
for performing an
absorption-limiting method such as the example of the method 100 illustrated
in FIG. 1;
robots suitable for practicing the methods discussed may not have all
components and
functionalities shown and described, and in some cases may have functional
equivalents to
the components illustrated. The robot 300 has a housing 302 and a controller
304 (provided
by a microprocessor or similar logic and control component) located inside the
housing 302.
The controller 304 has an associated memory 306, containing an appropriate
storage medium
for containing instructions, in which a mission instruction set 308 is stored.
A communication
transceiver 310 may be provided, which can receive inputs to the controller
304, and can be
operated by the controller 304 to transmit messages and/or data to other
robots and/or to one
or more remote receivers located within or outside the fluid system (for
simplicity, some
connections of various components with the controller 304 are not shown) The
robot 300 has
a number of intake pumps 312, which communicate with the exterior of the
housing 302 and
can absorb the selected reactant from the surrounding fluid In the particular
example of the
robot 300, the intake pumps 312 serve to absorb a reactant that is used to
generate power to
operate the robot, and provide the reactant to a fuel cell 314 (while not
shown, similar pumps
could be employed to absorb a different reactant from the fluid for supply to
the fuel cell for
reacting with the selected reactant, such as one set of pumps absorbing oxygen
and another
set absorbing glucose).
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[0065] The robot 300 may be provided with various sensors,
represented in this
example by sensors 316, 318, and 320. The type of sensors employed is
typically determined
by the intended mission, and the sensor types shown merely represent some
examples that
could be used. In this example, the sensors include a concentration sensor
316, an array of
surface stress sensors 318, and a location sensor 320. The concentration
sensor 316 provides
the controller 304 with a signal indicative of the concentration of the
selected reactant at the
location of the robot 300. The stress sensors 318 provide the controller 304
with signals
indicative of the distribution of stresses about the housing 302, which can be
processed to
provide information about relative location, fluid flow, and/or
characteristics of the fluid
system, as disclosed in US Patent 11,526,182. While the stress sensors 318
could provide
information on the location, the location sensor 320 can be provided to
supplement or replace
them and provide the robot 300 with an indication of its current location in
the fluid system.
Examples of location sensors (other than stress sensors) could include a clock
and sensors to
determine flow speed (to navigate by dead reckoning), sensors for receiving
location signals
from a network or array of transmitters, sensors capable of determining nearby
tissue, cell,
and/or microbe types, sensors for detecting specific environmental conditions
(chemical,
pressure, thermal, etc.), sensors for detecting features for comparison to a
stored map, or
other sensors appropriate for navigation within the particular fluid system.
[12]. It should be
noted that some sensors could provide the functions of others; for example, a
concentration
sensor could indicate that the robot is within a region where the
concentration of the
particular chemical being sensed is known to be high or low (such as
determining when the
robot is within a high-reactant region) and thus serve as a location sensor,
stress sensors could
be used to determine that the robot is located in a vessel of a certain size
and serve as location
sensors, etc.
[0066] The sensors (316, 318, 320) may be sufficient to allow
the robot 300 to
perform its intended mission, such as when mapping the distribution of a
chemical of interest
or mapping the vessels of a fluid system. In some cases, one or more mission-
specific
components are provided, as indicated by mission-specific component 322. The
mission-
specific component 322 can be any component designed to aid the robot 300 in
performing a
desired mission, typically in cooperation with sensors such as the sensors
(316, 318, 320) to
determine when it is appropriate for the robot 300 to take a particular
action. Examples of
mission-specific components could include a mission port to release a mission-
related
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chemical (such as a pharmaceutical agent, an agent that changes fluid
viscosity, a marker
agent that is remotely detectable, etc.), an energy transmitter to direct
electromagnetic
radiation, acoustic energy, thermal energy, etc. at a target site, an
electrode to electrically
stimulate or monitor current or voltage at a target site, a mechanical
manipulator, a diagnostic
probe, and/or a sample collector.
[0067] The robot 300 may be provided with a locomotion component
324 and/or an
anchoring component 326, either or which can be employed when it is desired
for the robot
300 to not be freely carried by the fluid. The locomotion component allows the
robot 300 to
move through the fluid, while the anchoring component 326 allows the robot to
anchor to a
wall of the fluid system so as to remain in place while the fluid flows past.
In some cases, the
anchoring component 326 could be designed to allow joining to another robot
[0068] Depending on the particular mission that the robot 300 is
designed for, some
components as described may not be present or may function differently than
described. For
example, where the robot only needs to respond to transmitted instructions,
the "transceiver"
310 could only receive, and where the robot only needs to transmit data and/or
message, the
"transceiver" 310 could only transmit.
[0069] The mission instruction set 308 can include instructions
for operating the robot
300 to perform one or more intended missions, which may make use of the
sensors (316, 318,
320) and, optionally, one or more mission-specific components 322. In addition
to whatever
instructions are needed to operate the robot 300 to perform its intended
mission functions, the
mission instruction set 308 includes instructions for directing the controller
304 to operate the
robot 300 to perform the operations of determining when the robot 300 is in an
absorption-
limiting need condition (similar to step 104 of the method 100), and
responsive to the
determination that the robot 300 is in an absorption-limiting need condition,
operating the
robot 300 in such a manner as to limit its absorption of reactant from the
surrounding fluid
(similar to step 106 of the method 100). In making the determination and
operating the robot
to limit its absorption, any of the techniques discussed above with regard to
examples of
methods for operating a swarm of robots could be employed. The determination
could be
made based on information obtained by the sensors (316, 318, 320), based on
information
stored in the memory 306, and/or messages received by the transceiver 310.
Limiting the
absorption could be achieved by adjusting the operation of one or more of the
intakes pumps
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312 and/or by changing the location of the robot 300 by operating the
locomotion component
324.
[0070]
FIG. 8 illustrates one example of a robot 350 that is similar to the robot
300,
but which is also suitable for performing storage and release of reactant,
such as discussed in
the example of the method 200 illustrated in FIG. 5. The robot 350 has a
storage and release
instruction set 352 stored in the memory 306, and a reactant storage tank 354
which can
receive reactant from the intake pumps 312 and can release the stored
reactant. The reactant
could be released to the fuel cell 314 via an optional supply duct 356, and/or
could be
released to an optional outlet port 358 (which in turn can release reactant
into the fluid
surrounding the robot 350 or could be designed to dock with another robot and
release the
reactant directly to an intake pump or other component of that robot). The
storage and release
instruction set 352 includes directions for the controller 304 to operate the
robot 350 so as to
perform the operations of, determining when the robot 350 is in a high-
reactant region
(similar to step 204 of the method 200) and, responsive to such determination,
operating the
350 robot to absorb and store reactant (similar to step 206 of the method
200), as well as
instructions for determining when a reactant need condition exists in the
vicinity of the robot
350 (similar to step 212 of the method 200), and responsive to such
determination, operating
the robot 350 to release reactant (similar to step 214 of the method 200). The
storage and
release instruction set could also be considered as a supply instruction set;
in general, where
the reactant is released from storage for use by the robot itself (such as
releasing reactant
from the storage tank 354 to the fuel cell 314 via the supply duct 356), it is
a "storage and
release instruction set", and when released for use by another robot (such as
releasing
reactant from the storage tank 354 via the outlet port 358), it is a "supply
instruction set". In
practice, some robots may include both options, releasing reactant for their
own use when
necessary for their own operation, and releasing reactant for use by another
robot when
necessary for that robot's operation. In some cases, reactant may be released
into the
surrounding fluid for the operation of some feature associated with the fluid
system which is
not another robot, to offset depletion of the reactant by robots in some
region of the fluid
system. In making the determinations and operating the robot, any of the
techniques
discussed above with regard to examples of methods for operating robots to
store and release
reactant could be employed. The determinations of when the robot 350 is in a
high-reactant
region and when a reactant need condition exists could be made based on
information
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obtained by the sensors (316, 318, 320), based on information stored in the
memory 306,
and/or messages received by the transceiver 310. The action of absorbing and
storing the
reactant is typically achieved by operating the pumps 312 and the storage tank
354, but may
also make use of the locomotion component 324 and/or the anchoring component
326 to
allow the robot 350 to remain for a longer time in the high-reactant region.
The action of
releasing the reactant operates the storage tank 354 and one or more of the
supply duct 356
and the outlet port 358, and may again make use of the locomotion component
324 (such as
to move towards another robot to dock with it to directly transfer reactant)
and/or the
anchoring component 326 (such as when it is desired for the robot 350 to
remain within a
particular location in the fluid system while releasing reactant to the
surrounding fluid).
Where the robot 350 is intended primarily for storing reactant for later
release at a different
location (i.e., a "supply robot"), it typically would not have any mission-
specific component
322, and may lack other components and/or functionalities shown.
[0071] FIGS. 9 and 10 illustrate one example of a group 400 of
robots 402 & 404
where the robot 402 is designed to perform a desired mission, and the robots
404 are each
designed to store reactant and supply it for use by the mission robot 402 (or
another mission
robot, not shown); for purposes of illustration, only the small group 400 is
shown, but in
practice a very large number of robots (402, 404) of each type would be
employed,
distributed throughout the fluid system. The robots (402, 404) can include
components as
discussed above for the robots 300 & 350, but for clarity only a subset of the
components are
illustrated in FIGS. 9 & 10.
[0072] FIG. 9 illustrates one option for releasing stored
reactant, where two supply
robots 404 in close proximity to the mission robot 402 release reactant from
storage tanks
406 through outlet ports 408 into the surrounding fluid (as indicated by the
arrows pointing
out of ports 408). This release increases the concentration of the reactant in
this region, and
the reactant can be absorbed by pumps 410 on the mission robot 402 (as
indicated by the
arrows pointing into pumps 410). FIG. 10 illustrates one alternative option,
where one of the
supply robots 404 docks with the mission robot 402 to transfer reactant
directly to it via
mating wits 412, 414 (which could also serve respectively as an outlet port
408 and a pump
410). To move together to dock, either or both of the robots (402, 404) could
employ a
locomotion component 416.
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[0073] The group 400 includes several supply robots 404 for a
single mission robot
402, and the supply robots 404 are each smaller in size than the mission robot
402. Smaller
size allows optimizing the supply robots for more rapidly absorbing and
storing reactant
while in a high-reactant region, since reactant diffuses more quickly to a
large number of
smaller robots than to a smaller number of larger robots. Additionally, as
their only function
is to supply reactant to mission robots 402, the supply robots only require
the sensors,
instruction sets, and other components to perform their storage and release
operations, and
typically require less interior space to accommodate the components needed to
perform their
function. For many situations, the number of supply robots is significantly
greater than the
number of mission robots, such as at least 5x, 10x, 20x, or 40x the number of
mission robots.
The supply robots may be no greater than half the size (by volume) than the
mission robots,
and may be considerably smaller, such as 1/4 the volume, 1/8 the volume, 1/16
the volume, or
1/32 the volume. Smaller robots have a greater ratio of surface area to
volume, and thus are
able to fill storage tanks faster than larger robots. The rate molecules
arrive at the robot is
proportional to its radius rrobot (see Eq. 1 below), while tank capacity is
related to its volume,
which is proportional to rrobot3 (assuming the tank occupies a set fraction of
the robot
volume); thus the time to fill a tank scales as rrobot2.
EXAMPLE
[0074] The particular robots to be employed and method of
employment can be
designed for a particular intended application. The following discussion
addresses one
possible example of a circulating fluid system, where oxygen is the reactant
and is used to
power the robots. The discussion addresses several considerations in limiting
absorption of
oxygen by a swarm of robots operating in the fluid system. For this example,
the fluid system
is a model of a human circulatory system, where blood flowing through vessels
of the fluid
system is recharged with oxygen in the lungs and becomes gradually depleted of
oxygen as it
flows through the body before returning to the lungs. Most of the circulation
through the
body passes through a single capillary network between arteries and veins, and
this typical
case is the basis for the model fluid system described. Other situations, such
as portal flows
where the blood flows through two sets of capillaries, require generalizing
the model
considered here This particular example illustrates the type of considerations
used for
designing and operating robots for a particular application. The general
principles for
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determining parameters, as well as particular features, behaviors, criteria
for making
determinations, and other details described with respect to this example
should be applicable
to alternative applications, modified as necessary to suit the particular
situation.
[0075] For purposes of discussion, the model assumes the use of
robots powered by
fuel cells that oxidize glucose. Oxygen is the rate-limiting chemical for this
reaction, since its
concentration in the blood is much lower than that of glucose, and the maximum
possible
power for robots is when they use all oxygen reaching their surfaces.
Throughout this
example, "power" may be used interchangeably with "oxygen" when discussing the
availability of the reactant to the robots.
[0076] When the distance between neighboring robots is large
compared to their size,
a good approximation of robot oxygen collection is that of an absorbing
sphere_ Such a robot
in blood plasma with oxygen concentration c absorbs oxygen at the rate [5]:
47D02.rrobot=C
Jrobot =
(1)
where Axis oxygen's diffusion coefficient in plasma and r
= robot is the robot radius.
Absorption can be close to this value even when only a few percent of the
robot surface
absorbs oxygen [5].
[0077] The reaction energy of glucose oxidation and rate of
oxygen absorption
determine the power generated by the fuel cell. Not all of that power is
available for robot
operations due to losses in the power system. These losses include dissipation
in wires
connecting fuel cells to loads in the robot and internal losses in the fuel
cell, e.g., due to
membrane transport and incomplete catalysis. We characterize these losses by
the fuel cell
efficiency,f robot: the fraction of the full reaction energy available to the
robot. The power
available to the robot from glucose oxidation is:
Probot =frobot --Trobot
(2)
6
where e is the energy released by oxidizing a glucose molecule and the factor
of 1/6 arises
from the need for six oxygen molecules to oxidize each glucose molecule.
[0078] A small number of robots in the bloodstream have no
systemic effect on
oxygen concentration. In that case, the normal concentrations found in the
circulation
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determine the power available to the robots and nearby tissue, whether the
robots are widely
separated or form aggregates [19]. However, large numbers of robots may
consume a
significant fraction of the oxygen in the blood. Red blood cells carry most of
the oxygen in
blood. These cells release oxygen in partial compensation for that consumed by
the robots.
This replenishment depends on the concentration of red blood cells, i.e., the
hematocrit. In
small vessels, cells typically travel a bit faster than plasma, leading to a
reduced hematocrit in
these vessels [28]. In addition, tissue consumes oxygen from nearby
capillaries.
[0079] Estimating systemic effects of robot oxygen consumption
does not require
precise vessel geometry of each of the many circulatory paths through the
body. Instead,
vessels of each size can be considered as an aggregate, with the flow through
an average
aggregated structure for a single loop around the circulation being shown in
FIG. 11,
illustrating circulation from lungs 1102 to the rest of the body 1104 and back
to the lungs
1102; the lungs 1102 in this case provide a high-reactant region that the
fluid circulates
through. This loop starts as fully oxygenated blood leaves a lung capillary
1102 via a
pulmonary vein 1106 and continues through the heart 1108, aorta 1110, body
1104, and vena
cava 1112 and back though the heart 1108, until the blood next reaches a lung
capillary from
a pulmonary artery 1114 (while passage through the lung capillary at the end
of the circuit
contributes to the total circulation time, it is not addressed in this model
as even 1012 robots
do not significantly alter the oxygen available in lung capillaries). A useful
simplification for
evaluating the typical power available to robots is to average over the vessel
cross section,
which gives a one-dimensional model of the blood flow. Further discussion of
the model used
for the present example is provided below in the section "Vessel Circuit
Model".
[0080] A circulation loop takes about one minute average (actual
time to complete a
circuit depends on where the blood goes, e.g., shorter times for transit
through the head than
through the feet). Evaluating behavior on this time scale averages over the
short-term
variations in flow speeds, particularly in arteries, due to heart beats. The
present model also
considers a fixed, resting pose for the body and does not treat longer-term
variations from
changes in activity level or environmental factors. This temporal averaging
leads to a steady-
state profile of oxygen concentration in a typical circulation loop. The
change in oxygen
concentration in each part of the circuit depends on its transit time and
hematocrit. A blood
vessel model can define both the fraction of the blood volume occupied by red
blood cells
(the "hematocrit") and the transit time (based on flow speed) as functions of
vessel diameter.
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For the hematocrit, the fluid flow in small vessels tends to push cells toward
the center of the
vessel where they move faster than the average speed of the flow. This
Fahraeus effect
decreases the hematocrit in small vessels. On average, the hematocrit in
vessels greater than
lmm varies little (h 0.45), while in smaller vessels the hematocrit decreases
with size, such
that 81..1 dia. capillaries have a hematocrit (h = 0.34). Blood flow speed is
dependent on vessel
size, and aggregated vessels provides a circuit transit time model as shown in
FIG. 12 where
the vertical Axis indicates distance in millimeters and the horizontal axis
indicates time in
seconds. The vertical lines near the center indicate passage through a
capillary. Dashed lines
show regions where interpolation is used to model arteries and veins of
changing size.
[0009] Considering a small volume of blood moving through the
circulation,
containing plasma, blood cells, and robots, a concentration model as shown in
FIG. 13
consists of four compartments. Blood vessels contain three of these
compartments: blood
plasma 1302, blood cells 1304, and robots 1306, where robots occupy a small
fraction of the
plasma volume, and are assumed to move with cells, rather than with plasma.
The fourth
compartment in this model is the tissue 1308 around capillaries. Oxygen
concentration in the
moving volume of blood changes due to the combination of consumption by robots
and
tissue, and oxygen release by red blood cells to maintain equilibrium.
Robot robot spacing
number nanocrit number large capilliaries body
density vessels
8 x 10-6 2 x 1012/m3 80pm N/A 170,um
1011 8 x 10-5 2>< 1013/m3 40pm N/A 80pm
10,, 8 x 10-4 2>< 1014/m3 20,um 100pm 40pm
Table 1
[0081] Table 1 lists some typical values for proposed swarm
applications [12] for use
in determining robot power and oxygen concentration in the model shown in FIG.
13.
Nanocrit is the fraction of the blood volume occupied by robots (in analogy
with hematocrit,
which is the fraction occupied by cells). The robot spacing is the typical
distance between
neighboring robots. The value for large vessels is the cube root of the
average blood volume
per robot. In capillaries, the spacing is from the blood volume in an 8p.m-
diameter vessel, up
to a maximum capillary length of lmm. The spacing in the body is the cube root
of the
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average body volume per robot for a nominal 50L body volume. The largest
number of robots
considered here, 1012, have a combined mass of several grams and volume of a
few
milliliters. The table gives typical spacings between robots in large vessels,
within capillaries
and between nearby small vessels. These spacings are much larger than the size
of the robots
so that the robots typically do not directly compete with neighboring robots
for oxygen, in
contrast to situations where robots operate in close proximity [19]. In large
vessels the nearest
robots are within the same vessel, but in small vessels, the nearest robot may
be in a
neighboring vessel.
[0082] Micron-size robots (i.e., robots with a radius on the
order of about 1pm) have
considerably smaller volume than red blood cells, so even the largest number
of robots
considered here occupy less than 0.1% of the blood volume, compared to 45%
typically
occupied by blood cells. This small fraction of robots does not significantly
affect blood
rheology [12], allowing the model to use typical flow speeds in the absence of
robots.
Devices are assumed to have sufficient power-generating capability to consume
all oxygen
reaching their surface, so that oxygen concentration in the plasma and its
diffusion rate to the
robot surface are the limiting factors for the power available to the robots.
[0083] To model oxygen consumption as the blood circulates, the
flow of the blood
can be considered as flowing through a single aggregated vessel consisting of
two
compartments, plasma 1302 and cells 1304, where the cross sections of these
compartments
varies along the length of the vessel as the larger vessels branch into
smaller vessels
(increasing the aggregated cross section) and then the smaller vessels join
together again into
larger vessels (decreasing the aggregated cross section), and where the
fraction occupied by
cells (i.e., the hematocrit) is smaller in smaller vessels (see FIGS. 34 &
35). Robots 1306 are
a small portion of the blood and can be ignored for purposes of determining
flow. The plasma
and blood cell compartments exchange oxygen with each other, and with robots
and tissue.
The section "Oxygen Concentration in Vessels" discusses concentration changes,
first
considering how oxygen concentration changes in vessels with variable cross
section for a
single vessel, then for an aggregated vessel having two compartments
exchanging oxygen, to
determine how concentration changes in a volume of fluid moving with the flow
in one of
these compartments. This differs from behavior in vessels of a fixed cross
section, due to the
changing cross section and fraction of the total cross section occupied by
each of the two
compartments. To determine the power available to a robot throughout the
circulation loop,
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the concentration in a volume of blood (containing the robot) moving through
the circulatory
system is determined using this compartment model.
[0084] FIG. 14 shows how robot power varies during a circulation
loop in the case
where robots consume oxygen as fast as it diffuses to their surfaces, so robot
power is given
by Eq. 2 above. FIG. 14 shows power in picowatts as a function of time in
seconds, for three
different total numbers of robots distributed through the circulation loop.
FIG. 14 shows the
power used starting when a robot leaves a lung capillary (0 seconds) and
ending just before it
next enters a lung capillary, with the light vertical lines indicating when
the robot is in a
capillary. Robot power decreases as the robot moves from the lung: hundreds of
picowatts in
the arteries, an abrupt reduction in the capillary where tissue competes with
the robots for
oxygen, and a continued gradual decrease as the robot travels through veins
back to the lung.
The consequences of this variation in power during a circuit depend on how
well it matches
the power requirements of the robots' tasks. For instance, if the robots
require a significant
amount of power to maintain their activity, the minimum power available during
the
circulation (i.e., just before returning to the lung) is a significant result
from this model. If
this minimum is below the required power, either the task needs to use fewer
robots or the
robots need sufficient onboard energy storage to support their activities
until they return to
the lung. Some applications could have flexible timing of robot power demand.
These tasks
could include computation to evaluate sensor measurements, maintenance tasks
such as
checking robot functionality, and communicating information to other robots.
In such cases,
robots could wait until there is abundant power to perform these tasks, e.g.,
while passing
through arteries. In other cases, the robots might have their highest power
demand during the
short time they pass through capillaries. For instance, robots might need to
move to cells near
the capillary that are emitting chemicals into the blood, thereby requiring
the robots to
measure, compute and propel themselves while in the capillaries [17]. In this
case, a
significant result from FIG. 14 is the power available while robots pass
through capillaries.
[0085] To further illustrate the consequences of robots using
oxygen for power, FIGS
15A and 145B show oxygen concentration (in units of 1022 oxygen molecules /
m3) in the
plasma (FIG. 15A) and red cell saturation (FIG. 15B) as a function of time in
seconds, and
compares the values shown for different numbers of robots in FIG. 14 with the
values for a
situation without robots (top line), in which case the only oxygen consumption
occurs in
tissue around the capillaries. In FIG. 15A, oxygen concentration in plasma is
expressed in
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molecules per unit volume (macroscopic studies usually express concentrations
in more
readily measurable quantities such as moles of chemical per liter of fluid or
grams of
chemical per cubic centimeter, and discussions of gases dissolved in blood
often specify
concentration indirectly via the corresponding partial pressure of the gas
under standard
conditions; as an example of these units, oxygen concentration CO2=
1022molecule/m3
corresponds to a 17,uM solution, 0.53,ug/cm3 and to a partial pressure of
1600Pa or 12mmHg,
and this concentration corresponds to 0.037cm302/100cm3 tissue with oxygen
volume
measured at standard temperature and pressure). In FIG. 15B, relative oxygen
saturation of
red cells is shown, where 1 is fully saturated cells (as they exit the lungs).
The light vertical
lines indicate when the flowing blood is in a capillary. For the cases where
the swarm
contains 1010 or 1011 robots, the diffusion limit on the rate oxygen reaches
the robot surface
(i.e., Eq. 1) prevents the robots from fully depleting oxygen in the blood.
That is, as is the
case without robots, the blood returns to the lungs with much of the oxygen it
originally took
from them. By contrast, a swarm having one trillion (1012) robots that consume
oxygen as
fast as possible completely depletes oxygen by the end of the circuit. This
would significantly
impair the ability of the fluid system to provide the intended function with
regard to
providing sufficient oxygen to power the robots. Such depletion could also
impair the
function of the fluid system in supplying oxygen to vein walls near the end of
the circuit,
before the blood re-enters the lungs.
[0086]
Values for parameters used for the present example are presented in Table
2
below. The sources for these values are given in the section "Model
Parameters" below.
Geometry
capillary radius rcap 4,um
tissue cylinder radius rtissue 40,um
robot radius rrobot 1pm
fluid
density p 103 kg/m3
hematocrit hfull 45%
blood volume Vblood 5.4L
tissue
power demand 4kW/m 3
02 concentration for half Ktissue 1021 molecule/m3
power
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power
reaction energy from one e 4 x 10-18J
glucose molecule
robot fuel cell efficiency /robot 50%
red blood cells
partial pressure for 50% 07 P50 3500Pa
saturation
02 saturation exponent I1 2.7
maximum 02 concentration in c max 1025 molecule/M3
02
cell
oxygen
02 diffusion coefficient Do, 2 x 10-9 m2/s
02 concentration in lung c0lung2 7 x 1022
molecule/m3
02 partial pressure to Ho, 1.6 x 10-19
concentration ratio Pajmolecul e/m3)
Table 2
[0087] A significant consequence of robots consuming oxygen is
their effect on
oxygen available to tissue. Robots consume oxygen in arteries bringing oxygen
to capillaries,
and compete with tissue for oxygen in the capillaries. Much of the oxygen that
robots use
comes from red cells, which limits the decrease in concentration in plasma.
Nevertheless,
robot consumption leads to some reduction by the time blood reaches the
capillaries, as
shown in FIG. 15A. The extent to which this reduced concentration affects
tissue depends on
the minimum oxygen that tissue requires to support its metabolism. Tissue
demand leads to
the abrupt reduction in concentration in capillaries seen in FIG. 15A. Even
with the largest
number of robots considered here, the concentration in capillaries is
sufficient to support
resting tissue demand. Specifically, cellular functions continue to operate
normally until
oxygen partial pressure is below 5mmHg [9], corresponding to concentration 0.4
x 1022
molecule/m3. This is lower than the capillary concentrations seen in FIG. 15A.
[0088] The conclusion of sufficient oxygen for tissue also
follows from treating the
tissue surrounding the vessel as homogeneous and metabolizing oxygen at the
rate that
produces power according to:
trrizsasux e CO2
Ptissue p
(3)
K tissue + C 02
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where 47,%, is the nominal demanded power density (i.e, power per unit volume)
of the
tissue and Ktissue -S i the concentration of 02 giving half the maximum
reaction rate. When
oxygen concentration is substantially larger than Ktissm, tissue power is
nearly independent of
oxygen concentration.
[0089] FIG. 16 shows tissue power relative to its maximum value
with unlimited
oxygen, for the time (in seconds) when the blood flows through the
capillaries, for the case of
no robots or for the three numbers of robots as in FIGS 14-15B The reduction
in oxygen in
capillaries due to robots has only a minor effect on tissue power in the case
considered here,
i.e., resting metabolic demand. Blood typically transports much more oxygen
than required
by tissue (such as to support peak metabolic rate, which can be as high as
200kW/m3 [27])
and so provides a buffer for any localized increase in tissue metabolic
demands.
[0090] While FIG. 16 illustrates power available in the
capillaries (which is most
relevant for availability of oxygen for tissues), FIG. 15A shows that the
lowest oxygen
concentrations occur toward the end of the circulation loop, as robots return
to the heart and
then to the lungs. Normally, blood returning to the lungs contains a
significant portion of the
oxygen originally collected in the lungs. Robots can make use of this oxygen
without concern
of reducing oxygen available to tissue since this blood has already passed
through capillaries
to deliver oxygen to tissue. A caveat to this conclusion is that cells
comprising the walls of
blood vessels consume a portion of the oxygen carried in those vessels.
Specifically, small
arteries and veins, and the inner portion number of walls of larger vessels,
receive nutrients
that diffuse into the wall from the blood carried in the vessel [34]. These
cells form a small
fraction of the body tissue so their oxygen use is not a significant
contribution to total tissue
oxygen consumption. Moreover, the small diffusion distance of oxygen and the
relatively
large volume of the vessels compared to capillaries means consumption by the
vessel walls
does not significantly alter the concentration in the vessels during the time
blood flows
through them, and this oxygen consumption can be ignored in the model.
[0091] However, the lowered oxygen concentration in veins due to
the robots could
be a safety issue. For example, normal leg veins have oxygen concentrations of
about 30-
40mmHg and red cell saturation 50-70% [25], where 30mmHg is 2.5 1021,,m3.
These
ranges are a bit below the values toward the end of the circulation loop with
1011 robots. This
comparison suggests lowered concentration in veins should not be an issue when
using that
many robots, but could be significant for larger numbers of robots. The oxygen
requirements
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of vein walls may place more stringent constraints on robot oxygen consumption
than the
requirements of most tissue, which receives nutrients from capillaries.
Quantifying this
constraint requires determining the minimum concentration these cells can
tolerate for
various amounts of time. An initial assessment is to assume these cells have
requirements
similar to those of resting tissue. In that case, FIG. 15A shows that 1012
robots could be
detrimental to vessel walls over the last 15 second or so of the circulation
unless their
absorption is limited.
[0092] Robot power production adds heat to the body, arising
from the full reaction
energy in the fuel cells, not just the fraction available for the robot's use.
The total dissipation
from all the robots equals the average available power over a circulation,
multiplied by the
number of robots and divided by the fuel cell efficiency. Table 3 gives values
for average
power over the circulation time, minimum power (just before returning to the
lungs), and
total energy dissipation from the oxygen consumed by all the robots, for the
three cases using
the numbers of robots in Table 1. For comparison, typical basal metabolism is
100W or
2000kca1/day. The table shows that 1010 robots, each consuming as much oxygen
as it can,
add less than 10% to basal metabolism. On the other hand, 1012 robots add more
than twice
the basal amount, thereby adding significant heat to the body. This is well
below the heat
dissipation during exercise [12], but nevertheless may be a limiting factor
during prolonged
robot operation.
Number of robots average power minimum power total
dissipation
1010 460pW 380pW 9W
10" 325pW 240pW 65W
1012 120pW none 240W
Table 3
[0093] The oxygen concentration profile produced by robots
alters assumptions
underlying some clinical measurements, particularly the relation between
direct
measurements and inferred properties based on causal relationships in the body
[4]. For
instance, normally oxygen is only removed from blood in capillaries so the
arterial
concentration is the same throughout the body. This is the basis for pulse
oximetry, a
common, noninvasive measurement of respiratory heath and oxygen supply to
organs [29].
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Large numbers of robots consume oxygen in arteries, leading to significant
concentration
reduction in the vessels between the lung and capillaries, as shown in FIG.
15A. In the
presence of such robots, pulse oximetry may require modified calibration to
account for
variation in arterial oxygen depending on body location and the time since the
blood left the
lung. These systemic changes could also affect the interpretation of other
large-scale
functional oxygen measurement techniques, such as photoacoustic imaging [6].
The model
described here indicates how oxygen varies with location and could aid in
calibrating and
interpreting these measurements.
[0094] As compensation for their alteration of conventional
clinical measurements,
robots should be able to measure oxygen concentration throughout the body at
micron length
scales, thereby far surpassing the accuracy and quantity of external
measurements.
Interpreting such measurements may need to account for the systemic changes in
concentration produced by the robots. In spite of this robot capability,
recalibrated
conventional sensors remain useful as checks on robot performance and to allow
comparison
with established clinical practice. Moreover, receiving measurements from
robots may be
delayed due to communication limits, e.g., if robots must wait until they are
near the skin to
send information out of the body. Delays or reduced information could also
occur if continual
communication takes too much power away from the robots' main tasks. In such
cases, the
improved sensing capability of robots may not be as readily available as
measurements from
conventional sensors.
Robots in Capillaries
[0095] In some applications, robots would perform most of their
tasks in capillaries,
e.g., to monitor or act on individual cells accessed from capillaries. In this
case, robots could
initially travel through the circulation until they reach capillaries, at
which point they attach
to the capillary walls to perform their primary function. Robots in lung
capillaries would have
access to the oxygen not taken by red cells, as discussed below. However,
robots in
capillaries of the systemic circulation would only consume oxygen from blood
passing
through capillaries, rather than during the entire circulation.
[0096] Applying the model described above to robots positioned
in systemic
capillaries requires two modifications First, there is no robot oxygen
consumption in arteries
or veins, since they do not contain robots. Second, since these capillaries
contain about 5% of
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the total blood volume [12], the number density of robots in capillaries is
about 20 times
larger than when they are distributed throughout the blood volume. With these
modifications,
FIGS. 17A & 17B illustrate how robot power (FIG. 17A) and oxygen concentration
(FIG.
17B) vary in a capillary with typical length of lmm (arterial flow arriving
from the left).
Since there is no oxygen consumption in arteries in this scenario, the oxygen
concentration in
blood entering the capillary does not depend on the number of robots. Oxygen
concentration
and robot power decrease through the capillary, so robots near the venous end
of the capillary
have less power. If necessary, robots near the arterial end of the capillary
could reduce their
power to leave more available for downstream robots. FIG. 17A shows the
decrease in robot
power (in picowatts) with distance (in millimeters) along the capillary, while
FIG. 17B shows
decrease in oxygen concentration (in 1022 molecules per cubic meter) in plasma
with
distance. Comparing FIG. 17B with FIG. 15A shows that the oxygen concentration
in blood
after passing through a capillary is similar to that when robots are
distributed throughout the
blood and consume all oxygen reaching their surface. In both cases, the robots
extract about
the same amount of oxygen from circulating blood, up to the time it passes
through a
capillary. The average power per robot and their total dissipation are similar
to the values in
Table 2. However, this power is entirely generated in capillaries, giving a
much larger power
density in the blood as it passes through capillaries. For example, 1010
robots heat capillaries
at an average rate of about 30kW/m3. This is several times the resting tissue
power demand
used in this model (see Table 2), and comparable to the power density for
cells with high
metabolic demands, such as heart or kidney cells [12]. Nevertheless, heat
transport by blood
and through tissue is rapid enough at these small scales that this increased
power density does
not result in much local temperature increase, even when robots are close
enough to come
into contact [19]. This indicates that even when all robots operate in
capillaries, the main
heating issue is for the body as a whole due to the large number of robots, as
discussed above,
rather than local heating in capillaries.
[0097]
While FIGS. 17A & 17B show the average behavior in capillaries, the small
blood volume in individual capillaries leads to considerable variation due to
differences in
capillary type [12], flows within a network of connected capillaries, and the
precise locations
of robots in a capillary. For instance, at the lower range of the numbers of
robots considered
here, each capillary has only a few robots, on average, so that the actual
number of robots
varies considerably among capillaries, including many capillaries with no
robots.
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[0098] The circulation model considered here does not evaluate
variation in oxygen
concentration at micron length scales, such as oxygen diffusion across a
vessel. Moreover,
the model assumes robots are sufficiently far apart that they do not compete
with neighboring
robots for oxygen. From Table 1, this is reasonable even when all the robots
are in capillaries,
up to about 1011 robots or so. However, with 1012 robots in capillaries, the
distance between
neighboring robots is only somewhat larger than their diameter, and that many
robots create
some competition for oxygen, reducing the oxygen they collect and the power
they generate
compared with the model's predictions.
[0099] To illustrate the effect of competition among neighboring
robots and diffusion
across capillaries, the effect of oxygen diffusing in the fluid moving through
the vessel can be
modeled using common software, such as Comsol, to compute the concentration
distribution
in the fluid to compare two situations, as shown in FIGS. 18A & 18B, where
robots 500 are
positioned in a small segment of a capillary 502 with the average spacing
corresponding to
1012 robots in the capillaries, where five robots 500 are anchored to the
inner wall 504 of an
8,um-diameter vessel with 5.5,um spacing along the vessel. The vessel segment
502 shown
here is 34pm long. These examples differ in the positioning of successive
robots: alternating
between opposites sides of the vessel (FIG. 18A) or all on the same side (FIG.
18B).
Modeling was conducted for each of the two robot positions shown in FIGS. 18A
& 18B, for
each of two fluid flow speeds (0.2mn-trs and lmm/s) that are within a typical
range for
capillaries [12], using the oxygen diffusion coefficient from Table 2. The
models showed
large variations in concentration along the vessel, particularly near each of
the robots. This
contrasts with the monotonically decreasing concentration from the averaged
circulation
model shown in FIG. 17B. For the slower flow speed, oxygen concentration
decreased
significantly before reaching the third robot in both arrangements, and varied
across the width
of the vessel with a lower concentration on the side nearest a robot. The
concentration
variation across the vessel was particularly large at the higher flow speed,
where oxygen does
not have enough time to diffuse throughout the vessel cross section while the
fluid passes the
robots. Robots positioned on the same side of the vessel increase the
difference in oxygen
concentration between the two sides of the vessel compared to robots on
alternate sides. An
interesting result is that robots farther downstream have more available
oxygen when the
robots are on the same side vs. on different sides, as the side opposite is
less depleted,
allowing more oxygen to diffuse across the vessel at the point where the
downstream robots
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are located. The differences in oxygen concentration around the robots leads
to variation in
the rate oxygen molecules reach the robot surface, depending on robot position
and fluid
speed.
[0100] While the large-scale model shown in FIGS. 17A & 17B
describes behavior
averaged over capillaries, the oxygen concentration and robot power may vary
considerably
from this average in individual capillaries, because of both variations in the
number of robots
in the small volume of blood in a capillary and the positions of the robots on
the capillary
walls. There could be additional variations due to features of the flow not
included in this
model of oxygen transport in capillaries. For instance, it neglects oxygen
consumption by
nearby tissue cells, the possibility of oxygen diffusing out of the vessel and
then back to the
robots due to the large concentration gradient near their absorbing surfaces.
Moreover, the
model assumes the oxygen saturation of passing blood cells remains in
equilibrium with the
concentration in the fluid. Accounting for tissue consumption, diffusion
outside the vessel,
and the kinetics of oxygen release from blood cells gives similar large
concentration
gradients near absorbing robots on a vessel wall [19]. Additional changes to
the oxygen
concentration could arise from blood cells as they distort to move past robots
anchored to the
vessel wall.
[0101] An additional consideration for robots remaining in
capillaries rather than
moving with the blood is the extent to which such robots increase the vascular
resistance of
the flow, particularly in the narrowest capillaries, since vascular resistance
of these vessels is
inversely proportional to the fourth power of their diameter according to
Poiseuille' s law
[16]. As an example, the pressure drop for a vessel without robots compared to
a vessel with
robots such as shown in FIGS. 18A & 18B indicates that the robots increase the
vascular
resistance by about 20% in each case (slightly higher for offset robots, but a
difference likely
beyond the accuracy of the model used). Robots on vessel walls may further
increase the
resistance by changing how blood cells distort as they move past the robots.
As an extreme,
robots could block passage of the cells If this increased resistance reduces
the blood flow,
robots and the tissue around the capillaries would not receive new oxygenated
blood as
rapidly as assumed by the circulation model. Alternatively, the body may
compensate for the
increased resistance by a corresponding increase in the blood pressure.
Avoiding injury from
robot blockage or increased blood pressure may limit the number of robots that
can be
stationed in capillaries, and how long they can remain there. This could be a
significant
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limitation on applications that require longitudinal data on individual cells
over an extended
period of time.
[0102] An alternative way to collect information from the same
cell over a period of
time that avoids blocking capillary blood flow is by using robots that move
with the blood, as
considered by the average circulation model, where the robots collect data
while passing
through a capillary. By collecting sufficient data to uniquely identify the
capillary and their
location within it, post-processing could match data collected by different
robots at different
times from the same capillary, thereby reconstructing longitudinal
observations with single-
cell resolution. Instead of continuously monitoring cells, this would collect
snapshots each
time a robot passes through a capillary near the cell. On average, each an
robots completes a
circulation in t = 60s and passes through about 1.25 capillaries in the
systemic flow
(including a portion portal flows that pass through more than one capillary
during a single
circuit [10]). On average, robots pass through a given capillary at the rate r
= 1.25114,AT-where
N 2x leis the number of capillaries in the systemic circulation
[12]. The average time
between successive robots is 1/r. For example, with n = 1012 robots, a robot
passes through a
capillary about once a second, though with considerable variation around this
average value.
If this is adequate temporal resolution for the task, and robots can collect
data while moving
with the flow instead of, e.g., requiring probes into the vessel wall, then
collecting data as
robots move through capillaries is a viable alternative to robots attached to
the wall. In either
case, the robots would mainly be active and consuming oxygen during the time
they are in
capillaries, so FIGS. 17A illustrates their average power. This alternative
does place larger
demands on robot data storage, since the robots need to collect not only the
cell
measurements of interest but also the data required provide the unique
identifications. On the
other hand, robots moving in capillary networks could also use their
interactions with the
flow and other robots to perform distributed microfluidic computation [31] to
provide useful
infoitilation on the microcirculation.
Patient Variation
[0103] Disease and injury could alter oxygen availability and
affect the power
available to robots treating sick or injured people. In this regard, one
relevant health status is
anemia, i.e., having lower than normal hematocrit. Such patients have less
ability to replenish
the oxygen robots remove from plasma than people with normal hematocrit. FIG.
14 shows
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power available to robots in an individual with normal hematocrit. This model
can also
illustrate the effect of low blood cell count (i.e., anemia) by reducing the
hematocrit
parameter. As an example, FIGS. 19A & 19B show robot power (FIG. 19A showing
power in
picowatts as a function of time in seconds) and oxygen concentration (FIG. 19B
showing
concentration in 1022 molecules per cubic meter) in plasma with 25% overall
hematocrit, for
the same numbers of robots as in FIG. 14. Even with this lowered hematocrit,
the available
oxygen from circulating cells provides significant power for all but the
largest number of
robots considered here. However, 102 robots remove all oxygen before blood
reaches
capillaries. For the lower range of robot numbers, anemia does not
significantly change the
situation for robots using chemical power, but the low oxygen reserve in cells
with this
reduced hematocrit significantly increases oxygen depletion with a large
number of robots.
This example shows how models developed here can not only evaluate robot
capabilities but
can also evaluate the suitability of patients for applications of microscopic
robots.
Personalized versions of such models could help develop mission plans for the
robots and
provide a baseline to compare with robot measurements during early stages of a
mission to
identify and respond to deviations from the plan before they become harmful.
This extends to
microscopic robots the current use of computational models to help plan
conventional
medical procedures [39].
[0104] As described above, conventional monitoring may have
reduced accuracy
when large numbers of robots are consuming oxygen. The variation in response
to large
numbers of robots based on the patient's health status suggests a staged
approach of gradually
increasing the number of robots in the body. Another way to achieve a similar
effect is by
having robots initially limit their power use and gradually increase that
limit to the level
required for their mission. During this initial stage, the robots could
monitor their effect on
oxygen concentration and other body processes to determine whether full power
would
exceed safety limits prior to fully activating all the robots. This evaluation
would allow
determining patient-specific trade-offs in treatment options. For example, a
treatment could
use fewer robots or have them operate at lower power with the tradeoff of
longer treatment
duration or less frequent communication with the robots. In particular,
monitoring body
function at the start, and during, a mission would allow adapting robot
behavior and mission
parameters to far more detailed measurements than would be available from
conventional
macroscopic sensors. Continual comparison with personalized versions of the
general model
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discussed here could aid in the interpretation of these measurements and
anticipate the likely
effect of increasing the number of robots and/or increasing their power use.
Mitigation Strategies
[0105] As discussed above, oxygen absorption by robots raises
concerns for
extremely large numbers (1012) of robots, and may raise concerns in some
situations even
when smaller numbers of robots are employed. To address these concerns,
various strategies
to mitigate the impact of such absorption can be employed. Broadly, these
strategies fall into
two approaches, saving oxygen for later release, and limiting absorption by
robots under
circumstances where full-power operation is not needed.
[0106]
With regard to the approach of storing oxygen for later release, oxygen in
lung capillaries is normally more than sufficient to fully saturate blood
plasma and red cells.
The amount of additional oxygen depends on the health of the lungs: patients
with limited
lung capacity may not have sufficient additional available oxygen for robots
to collect.
However, under normal conditions, robots could store some of the remaining
available
oxygen in pressure tanks without reducing oxygen collected by red blood cells.
The lungs
serve as a high-reactant region. There are several ways that stored oxygen
could supplement
the oxygen available to the robots at a particular location after circulating
away from the
lungs. Robots could also fill tanks from oxygen in vessels other than lung
capillaries.
However, this would reduce the oxygen available later in the circulation in
the same way as
robots collecting, and immediately using, all oxygen reaching their surfaces.
In addition, if
the treatment includes passing the patient's blood through an external oxygen
exchanger,
robots could remain in that exchanger as long as needed to fill oxygen tanks.
However,
typical treatments using microscopic robots would likely not need such an
exchanger.
Moreover, this external circulation would alter the typical circulation time
assumed for the
model described above. The discussion here does not include these options for
collecting
oxygen, but instead focuses on robots obtaining oxygen in lung capillaries.
[0107] A robot can store oxygen in a pressure tank [12]. FIG. 20
is a cross section of
an oxygen-storing robot 550 (which can be functionally equivalent to the robot
350 shown in
FIG. 8) having a spherical oxygen tank 552 defined by a tank wall 554 with
wall thickness t
and interior volume that is a fraction fof the robot's volume (as enclosed by
a robot surface
556). For clarity, the wall thickness is exaggerated compared to the other
dimensions, and the
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drawing is not to scale. The amount of oxygen the robot 550 can store during a
single pass
through a lung capillary (a "high-reactant region") is limited by three
factors: the rate at
which the robot 550 absorbs oxygen, the time it spends in the lung capillary,
and the capacity
of the storage tank 552. These three factors are discussed below.
[0108] Oxygen absorption rate for the robot 550 depends on how
fast molecules
diffuse to the robot surface 556 and the fraction of the surface 556 that
captures arriving
oxygen, using pumps 558 (functionally equivalent to the pumps 312 of the robot
350 shown
in FIG. 8). Eq. 1 gives the rate oxygen diffuses to the robot surface. The
corresponding flux
to the surface is -/
robot/(47Crrobot2 ). For a 1pm-radius robot .1
- robot¨ 1.8 x 109molecules/s in
lung capillaries, corresponding to a flux of 1.4 x 1020 molecules/m2/s.
[0109] For maximum absorption, the pumps 558 must have
sufficient capacity to
collect molecules as fast as they reach the pump 558. However, the pumps 558
have a
maximum operating rate (assuming sufficient supply of molecules) Jimmy ¨
(47Trrob0t2
).sFp,,," where s is the fraction of the robot surface 556 used by the pumps
558 and Fpump is
their maximum pump capacity. For molecular sorting rotors, a plausible
capacity is Fpump =
1022molecules/m2/s [12]. Capturing all the molecules requires that .J
pump .'robot. With Eq. 1,
the minimum surface coverage required is:
DO2C 1
S
(4)
Fpump rrobot
with c being the oxygen concentration in lung capillaries.
[0110] Another constraint on pump surface fraction arises from
diffusion. When
pumps do not cover the entire surface, an oxygen molecule diffusing to the
robot surface 556
does not necessarily reach a pump. Nevertheless, once a molecule reaches any
part of the
robot surface 556, it usually moves for a considerable time near the surface
556 before
diffusing away. This means that pumps 558 that only cover a few percent of the
surface 556
can collect oxygen nearly as well as a completely absorbing surface [5]. This
provides a
lower limit on the fraction of the surface 556 used by the pumps 558. An
additional constraint
arises from the multiple uses the robot 550 may have for its surface, e.g.,
for sensing,
structural support, communications, locomotion, etc., which prevent the pumps
558 from
occupying the entire surface 556.
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[0111] FIG. 21 illustrates the net effect of the three
constraints of pump capacity,
diffusion to reach a pump, and the maximum surface area available to pumps in
determining
what fraction of the surface area must be used by pumps (vertical axis) in
order to collect
nearly all available oxygen molecules while the device is in a lung capillary,
as a function of
device size (radius in in wri). The calculations use Eq. 1 for diffusion as a
function of device
size and the value for pump capacity cited above. In the shaded area 2102 on
the left,
molecules arrive faster than the pumps can collect them, even if they cover
the entire surface
of the robot. In the shaded area 2104 on the right, surface coverage is 5%,
which is sufficient
for pumps to capture most of molecules reaching the robot surface. For
intermediate sizes
between these shaded regions, the surface fraction is a function of the robot
radius from Eq.
4. In this case, the minimum fraction is 5%, which allows capturing most
arriving oxygen [5].
The maximum in FIG. 21 is for the theoretical case of pumps covering the
entire surface.
Even if the other components that the robot 550 needs on its surface 556 limit
the pumps 558
to no more than 25% of the surface, FIG. 21 shows that this limit only applies
to robots
significantly smaller (---r < 0.06 m) than those used in the scenarios
discussed herein, and
therefore pump capacity should not be a limiting factor for oxygen absorption.
[0112] For time spent in a lung capillary, blood passes through
a lung capillary in
about 0.75s [10], and this can be used as the oxygen collection time for
robots moving with
the blood, although robots might have somewhat less time as they move with
cells, due to the
reduced hematocrit in small vessels. Robots could increase the filling time in
several ways.
Robots moving passively with the blood could use several circulations through
the lungs to
fill their tanks. Active robots could extend their filling time by sticking to
capillary walls or
selecting longer routes through the lung capillary network.
[0113] The tank 552 stores oxygen at high pressure. For a
spherical tank of radius r
with a thin wall of thickness t, Laplace's law gives its maximum pressure as
[12]
2tcf
PLE1aX_ ..........................................
(5)
where a- is the failure strength of the wall 554. For a wall 554 formed of
covalently-bonded
carbon, a conservative estimate of the failure strength is o- = 1010 Pa, about
20% of diamond's
failure strength [12]. For example, a tank with radius r = 0.3,um and wall
thickness t = 5nm
has maximum pressure near 3000atm. The scenarios discussed in this example use
tanks
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storing oxygen at about one-third of this maximum pressure. At these storage
pressures and
body temperature, common gases such as oxygen deviate somewhat from the ideal
gas law.
To account for this deviation, the tank storage capacity is estimated using
the van der Waals
equation of state for oxygen [12].
[0114] During a 0.75s transit through a lung capillary [10], 1.3
Y 109 molecules diffuse
to the surface of a lum radius robot. For example, at body temperature and
tank pressure of
1000atm, the number density of oxygen molecules is 1.26 x 1028molecule/m3
[12], which is
far larger than the concentration in blood (see Table 2). A tank 552 with
radius 0.3,um could
store all the collected molecules. This tank 552 would occupy about 3% of the
robot's
volume, including a 5nm-thick wall 554.
[0115] From Eq 2, a robot collecting oxygen as fast as it
diffuses to its surface while
passing through a lung capillary collects enough oxygen to provide about 7pW
for the
duration of a 60s circulation loop. This is well below the power available
from oxygen in the
blood during the circulation with even as many as 1012 robots, except for the
last ten seconds
or so of the loop. If the stored oxygen were only used during the last ten
seconds of the
circulation, it would provide about 50pW. This oxygen storage is not
sufficient for robots
requiring around 100pW or so, and hence can not completely alleviate depletion
by large
numbers of robots consuming oxygen. However, stored oxygen would be useful as
a
supplemental power source for brief intervals of reduced oxygen, such as when
a robot is
next to a white blood cell moving through a capillary, so the plasma around
the robot is
temporarily not replenished by nearby red blood cells. It would also be useful
on its own for
somewhat smaller numbers of robots, and/or robots with somewhat lower power
requirements.
[0116] As another illustration of oxygen storage, suppose robots
collect enough
oxygen to provide 100pW for the 60s duration of the average circulation loop,
which
corresponds to 1.8x 101 oxygen molecules. Storing this much oxygen in a
pressure tank at
one-third its maximum pressure requires about one third of the robot volume
for a tank with
lOnm thick walls. Filling this tank requires lOs in a lung capillary, which is
much longer than
typical transit times. To fill its tank, a robot could remain in a lung
capillary rather than flow
with the blood, e.g., by anchoring itself to the capillary wall. Lung
capillaries contain 70mL
of blood [10], so if robots stay in capillaries long enough to fill their
tanks, lung capillaries
would hold about 15% of the robots in only 1.2% of the blood volume. For 1012
robots, this
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scenario gives a nanocrit of 0.01 in lung capillaries, about ten times larger
than the overall
nanocrit (see Table 1). The distance between robots in a capillary would be
correspondingly
reduced, to about 10,um. This spacing is small enough that nearby robots
compete for oxygen,
thereby somewhat increasing the filling time beyond that determined here for
isolated robots
[19]. These estimates indicate the trade-offs required for robots to carry
enough oxygen for
100pW without consuming oxygen from the blood during the circulation. In
particular, this
scenario requires a large fraction of robot volume for storage, significantly
increases robot
concentration in lung capillaries, and requires robots have the capability to
anchor themselves
in capillaries.
[0117] An alternative (or supplement) to oxygen tanks in the
robots performing the
medical mission is to use additional specialized oxygen supply robots [11], in
a manner
similar to the group 400 of robots (402, 404) shown in FIGS. 9 & 10. The
supply robots
collect oxygen while passing through the lungs and deliver it to the main
mission robots in
the systemic circulation. This oxygen delivery contrasts with transport robots
intended to
serve as artificial red blood cells that also collect carbon dioxide for
return to the lungs [11],
as such robots require power to collect and compress molecules while in the
systemic
circulation, which robots that only deliver oxygen do not need (as they only
collect and
compress molecules while in the high-reactant region of the lungs, where ample
oxygen for
power is present). Such oxygen supply robots face the same limit on extracting
oxygen from
lung capillaries as discussed above, depending on their size and tank
capacity. However, the
supply robots can be optimized to address these limitations without
compromising other
requirements of the main mission.
[0118] For example, considering the scenario where robots cannot
fill their tanks
during a single transit through a lung capillary, supply robots could be
designed to fill their
tanks in this time by exploiting the geometry of diffusion: from Eq. 1 the
rate molecules
arrive at the robot is proportional to its radius rrobot, while tank capacity
is related to its
volume, which is proportional to rroboi3when tanks use a fixed fraction of the
robot volume
and a fixed storage pressure. The time to fill a tank scales as rroboi2. This
means that instead
of a single large tank in one robot, using proportionally smaller tanks in
many robots, with
the same overall storage capacity, can collect the same amount of oxygen in a
shorter time.
For example, decreasing the robot size by a factor of two reduces the time
required to fill its
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tank by a factor of four. Increasing the number of robots by a factor of eight
gives the same
total volume of robots and the amount of oxygen they can transport.
[0119] To quantify the design trade-offs for these robots,
consider n oxygen supply
robots as shown in FIG. 20, each of radius r with a fraction f of its volume
for oxygen
storage. Scaling the entire geometry with robot size means the thickness of
the oxygen tank
wall is proportional to r. From Eq. 6, this scaling has the same maximum
pressure for the
storage tank in robots of different sizes. Specifically, the wall thickness in
this example is t =
20nm >< (r/r 1 where rrobot= 1,um is the radius of the mission robots. The
wall cannot be
robot,
less than one atomic layer, so this scaling does not apply for arbitrarily
small robots (e.g.,
with a minimum t> mm thickness, this relation applies for rrobot> 0.05,um -
the supply robots
considered here are larger than this size). As discussed above, tanks can
store oxygen at one-
third of their maximum pressure. With these specifications of the supply
robots, the number
of robots, their size, and volume devoted to oxygen (i.e., values for the
parameters n, r and])
can be selected such that the robots in aggregate carry 1.8 x 1010 oxygen
molecules for each
of the mission robots, duplicating the amount of stored oxygen as discussed
above. In
addition to this requirement, three constraints on the choice of these
parameters for supply
robots are considered.
[0120] First, the robots should be small enough so that
favorable diffusion scaling
allows them to fill their tanks with a single transit of the lung capillaries.
This includes setting
the fraction of the surface used by pumps as shown in FIG. 21 so the robots
can collect nearly
all the oxygen available to them in the lung capillary. Second, the volume of
the robot outside
its oxygen tank must be sufficient to contain its other components. These
additional
components include pumps to collect oxygen and mechanisms to control the
operation of the
robot. It is assumed here that determining oxygen concentration in the fluid
around the robot
is used to decide when to collect or release oxygen; other considerations
besides
concentration could be employed, such as location in the circulatory system
and/or receipt of
a request for oxygen from a nearby mission robot For the volume used by the
pumps, each
pump is assumed to have sized = lOnm [12] so the total volume of pumps is 47-
cr2sd. The
controller and other components are assumed to require a fixed minimum volume
v = 0.1,um3
that was estimated for transport robots delivering oxygen to tissue [11]. This
gives the
required volume for other components as:
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V + 4 7172.5'd
(6)
[0121] The third constraint is on energy required by the supply
robots. Their main
energy use is to fill their tank. This consumes part of the received oxygen
while they are in
the lung capillary, thereby increasing the filling time. Comparing the pump
energy required
to compress oxygen [12] with the rate at which the robots receive oxygen in
lung capillaries
(as discussed above) indicates that a robot should only need about 3% of the
oxygen it
collects to operate the pumps, so the energy required for filling the tank has
a negligible
effect on filling time.
[0122] Supply devices need energy for their operation after
leaving the lung. This
includes sensing when oxygen concentration is low (or other condition for
release of stored
oxygen) and determining when to release oxygen, which are tasks that do not
depend on
robot size. Supply robots could obtain energy using oxygen from the blood
outside the lung
capillaries in the same way as the mission robots. However, that would
decrease the oxygen
available to the mission robots, partially negating the benefit of using
supply robots to
mitigate oxygen reduction in the blood. Instead, the supply robots could use
their stored
oxygen to power their operation outside the lungs. For effective oxygen
transport, this
consumption should be a small fraction of the stored oxygen so that a supply
robot can
deliver almost all its oxygen to the mission robots. One measure of this power
requirement is
the average use over the 60s circulation loop. For instance, 0.1pW is an
estimate of the power
needed for computation by robots supplying oxygen to tissue [11]. After supply
robots leave
the lung, their main activity is determining when to release stored oxygen, so
computation
determines their energy demand, and 0.1pW is a plausible estimate of their
required power
for continuous operation. In practice, supply robots would only need to check
oxygen
concentrations intermittently, thereby reducing their average power use below
this value. A
reasonable requirement for a supply robot is that its tank can hold enough
oxygen to provide
at least 1pW, on average, during a circulation loop. This provides sufficient
energy for the
robot while using only a small portion (1%) of its stored oxygen.
[0123] FIG. 22 shows these three constraints on robot and tank
fractional size for
supply robots to carry enough oxygen to provide each mission robot with 100pW
for 60s, the
same oxygen requirement as discussed above; the vertical axis is the fraction
of robot volume
used for oxygen storage, and the horizontal axis is robot radius in Jim. In
the region at the
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upper right of insufficient time curve 2202, tank capacity and robot size are
such that
diffusion is too slow to fill the tanks during a single lung capillary
transit. In the region to the
left of the generally-vertical too small curve 2204 in the center, the robot
is too small and/or
the oxygen tank too large to leave enough room for other robot components.
Finally, in the
region at the lower left of insufficient power curve 2206, the oxygen tank is
too small to both
provide enough power to the supply robot during the circulation and to deliver
most of its
oxygen to the mission robots (i.e., the tank cannot store at least 1pW*60s
worth of oxygen).
The point 2208 is the design choice satisfying the constraints with the
smallest value of the
total volume of the supply robots given in Eq. 7 below. Robots satisfying all
the constraints
(i.e., the region 2210 of FIG. 22 between the insufficient time curve 2202 and
the insufficient
power curve 2206 and to the right of the insufficient room for components
curve 2204) are
feasible designs. Selecting among these designs can optimize operational or
production goals.
Operational goals include minimizing the nanocrit, i.e., the total volume of
the supply robots
and reducing their size to simplify passage through small vessels or slits of
the spleen [13].
Production cost depends on the number of robots and the manufacturing cost of
each robot. A
proxy for manufacturing cost is the number of atoms required for their
structure and
mechanisms, in analogy with 3D printing with cost dominated by time and
materials rather
than the complexity of the printed structure. This proxy is proportional to
the volume of the
robot other than the interior of the oxygen tank. This proxy for production
cost is the total
volume of all the supply robots multiplied by 1 ¨f (where f is the fraction of
each robot
volume for oxygen storage):
471 3
Vtotai n x ____________________________________________ r'
3
(7)
Vproduction ¨ (1 n Vtotal
An example of optimized parameters are those that minimize the total volume of
the supply
robots. These parameters correspond to the point 2208 in FIG. 22, where the
supply robots
have radius r = 0.32,um and an oxygen volume fraction f = 0.23. FIG. 23
illustrates this
optimized design by comparing cross sections of such an oxygen supply robot
550 and a
main mission robot 560 having a radius of 1pm (Table 2) These parameters also
minimize
Vprothiction in Eq. 7. This choice of r and f provides both an operational
benefit of minimizing
the nanocrit and a production benefit of minimizing the volume proxy for
manufacturing cost.
Table 4 shows how number and volume of the supply robots compare to the main
mission
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robots with these parameters. Carrying the same amount of oxygen per main
mission robot
(100pW for 60s) requires about 43 supply robots for each mission robot. The
mission robots
and supply robots together have a nanocrit about 2.4 times larger than for the
mission robots
alone.
property ratio to mission robots
number of supply robots 43
total volume of supply robots 1.4
total manufactured volume of supply robots 1.1
Table 4
[0124] When considering atypical placement of robots in a cube
of blood with 20pm
edge length, for the case of 1012 mission robots in a blood vessel whose
diameter is larger
than the size of the cube and where cells and robots are uniformly
distributed, such a cube
typically contains one of the mission robots (see Table 1), and 43 supply
robots (see Table 4),
while blood cells (each with a typical red cell volume of 100pm3 [12]) occupy
about 40% of
the cube volume. This is an approximation to the actual distribution, since
smaller objects
(such as the robots of both types) tend to concentrate toward the vessel wall
[12].
[0125] Due to their larger numbers, the spacing between supply
robots in capillaries
is smaller than those for the mission robots given in Table 1 However, the
supply robots are
also smaller, so their spacing measured in terms of their size is reduced to a
lesser extent. For
example, with 101' mission robots, supply robots are separated by about 8
times their radius
in straight capillaries used for the estimate in Table 1. This suggests that
neighboring supply
robots compete to some extent for oxygen in lung capillaries, which may
somewhat increase
their filling time compared to the estimate assuming independent diffusion to
each robot.
However, lung capillaries have a complex network structure [41] which could
alter the extent
of this competition, especially due to the variation in paths and transit
times.
[0126] For the supply robot 550 shown in FIG. 23, the pump
volume is a small
fraction of the component volume in Eq. 6. If pump size and surface coverage
are larger than
assumed here, an additional optimization is allowing for a smaller number of
pumps than
indicated by FIG. 21. This would trade a longer filling time due to fewer
pumps for additional
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volume for other robot components. This would give another parameter to
optimize, in
addition to robot radius and tank fractional size shown in FIG. 22. The
specific optimal robot
550 and tank 552 sizes shown in FIG. 23 depend on the robot component size and
power
requirements (i.e., the second and third constraints in FIG. 22). This example
illustrates how
multiple design constraints combine to determine the choice of robot
parameters. These
constraints arise both from the robot's external environment (e.g., the
diffusion rate of
oxygen) and the robot's internal capabilities (e.g., the power required for
its operation).
Better estimates of these parameters require more detailed design of the robot
components.
Depending on these values, there could be no feasible design (i.e., no region
in FIG. 22
meeting all three criteria) for some situations That would indicate that the
robots' component
volumes or power requirements are too large to provide this oxygen. In that
case, oxygen
supply robots could provide less than the 100pW used in this scenario, or the
mission robots
could use another mitigation strategy to avoid low oxygen concentration.
[0127] Using supply robots increases nanocrit. While likely not
a significant issue for
the scenarios of Table 1, large nanocrit from supply robots could alter blood
flow [12] or
require a compensatory reduction in the number of main mission robots.
Moreover,
increasing the number of robots collecting oxygen in the lungs eventually
extracts all
available oxygen. At this point, additional robots would not increase the
total collected
oxygen and would reduce the reserve available to the body by increasing blood
perfusion in
the lungs.
[0128] Supply robots carry oxygen from the lungs to the systemic
circulation. In the
case of passive flow, supply robots release oxygen into the surrounding blood
plasma when
deemed necessary, such as when they detect low oxygen concentrations. Some of
that
released oxygen diffuses to nearby robots. The rest remains in the blood
plasma or diffuses
into tissue or red cells. This means the blood carries some of the released
oxygen back to the
lung without providing robot power. This wasted oxygen is particularly
significant when
released in the veins, where it does not diffuse into tissue This is a likely
scenario since the
lowest concentrations occur in veins. This diffusive oxygen delivery by
specialized robots is
not as effective as when robots carry their own oxygen, as described above.
[0129] Robots could partially offset the limitation of diffusive
transport by releasing
oxygen only when they are close to a main mission robot, as determined, for
example, via
short range communication [12,20]. This proximity allows more of the released
oxygen to
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reach the receiving robot's surface. If necessary to support high burst power,
multiple supply
robots could aggregate around a mission robot and simultaneously release
oxygen (as shown
in FIG. 9). This temporarily produces a high oxygen concentration in that
region. However,
as not all of that oxygen reaches the robot, the total release must be limited
to avoid tissue
damage due to excessive oxygen, i.e., hyperoxia, which is a particular concern
in the brain
[43]. This safety limit due to released oxygen not reaching a mission robot
limits how rapidly
a group of supply robots can deliver oxygen, thereby reducing their ability to
support high
burst power that robots could obtain if they carry their own oxygen.
[0130] For greater efficiency, oxygen supply robots could
directly transfer oxygen to
the mission robots by docking with them (as shown in FIG. 10). Direct transfer
provides
oxygen in the same way as an onboard tank. In this approach, supply robots act
as external
oxygen tanks for the mission robots. Using separate robots to carry oxygen
allows them to
selectively provide power to robots that most need it. For example, this
selectivity could
allow one robot in a group to have a burst of high power for long range
communication of a
summary of data collected by the group. While this flexibility is a potential
benefit, some
amount of power variation within a group of robots can also be achieved if
most robots limit
their oxygen demands, as described below. Direct transfer requires more
complicated robots
than releasing oxygen into the blood and relying on diffusion. In particular,
docking requires
locomotion and navigation on the part of the transport or mission robots, or
both, to find each
other in the constantly changing fluid environment as the robots and cells
move. If the
mission robots need locomotion capability for their mission, they could also
use that
capability to reach oxygen supply robots. In that case, there is no need for
the supply robots
to also have locomotion capability, thereby simplifying their design and
providing more room
for them to carry oxygen. An additional issue is if a supply robot delivers
oxygen by
completely emptying its tank while docked, direct oxygen delivery would
produce a
population of supply robots with a declining fraction of those with full
tanks. Devices with
full tanks become harder to find, and the robots may need a communication
protocol to
identify those supply robots that have available stored oxygen.
[0131] FIG. 14 shows that 1012 robots deplete oxygen toward the
end of the
circulation loop, i.e., in veins. A rechargeable reservoir with control over
oxygen release
could be formed from robots small enough to travel through the circulation and
able to attach
to vein walls. These could be the same type of circulating oxygen supply
robots as discussed
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above, but used as a reservoir fixed to vessel walls rather than traveling in
the blood along
with the main mission robots. As an example of this scenario, consider a
reservoir capable of
supplying enough oxygen for 100pW to each of 1012 mission robots during the
last 20s of
their circulation. The supply robots in the reservoir could do so by releasing
oxygen into the
blood, but only a portion of that would diffuse to the mission robots, while
the rest would
return to the lung unused. Instead, circulating mission robots could find and
dock with the
reservoir supply robots to receive oxygen from them directly. With uniform
distribution of
robots, the last 20s of the circulation contains about a third of the robots.
To provide the
mission robots with sufficient oxygen to generate 100pW each during the last
20s of
circulation, the reservoir would need to supply 1020 molecules/S. To maintain
this rate for a
single circulation time, the reservoir would need to start with 6 x 1021
oxygen molecules. As
an example, if the reservoir consists of 11um-radius supply robots using 80%
of their volume
to store oxygen in tanks with 20nm-thick walls and at one-third the tanks'
maximum
pressure, each supply robot could store 4.6x 1010 molecules and the exterior
volume of the
tank (i.e., including the tank wall) would occupy 85% of the supply robot's
volume. If a
supply robot uses 10pW to support its operation, it would consume about 4% of
its stored
oxygen during a 60s operation time. With these parameters, the reservoir would
require 1.4 x
1011 supply
robots to provide oxygen to the 1012 circulating mission robots. A reservoir
supply robot with these parameters would require 26s to fill its tank in a
lung capillary,
compared to the typical 0.75s transit time through a lung capillary. If the
supply robots move
passively with the circulation rather than concentrating in lung capillaries
for the required
time, and do not use power while circulating, each would require 35
circulations through the
lung to fill its tank, which would take about half an hour. In this scenario,
using a reservoir
would provide oxygen to support 100pW for mission robots during the last third
of a
circulation loop only once in every 35 circulations. In the remaining
circulations, the mission
robots would have little power during the last third of their circulation, or
no power if they
stop using power to avoid extremely low oxygen concentration and cell
saturation toward the
end of the circulation loop.
[0132]
Robots could mitigate their effect on oxygen concentration by limiting
their
power use, particularly early in the circulation loop (i.e., in arteries)
where oxygen is
plentiful. Examples of strategies that robots could use for limiting power are
discussed below.
Since 1012 robots consuming oxygen as fast as possible leads to significant
oxygen reduction
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(as shown in FIGS. 15A & 15B), this case is used for evaluating the effects of
strategies for
limiting power use.
[0133] A fixed limit on robot oxygen consumption could be
implemented in hardware
by reducing the number or capacity of pumps on the robot surface, or limiting
fuel cells
inside the robot. This would prevent the robot from using all oxygen reaching
its surface
when the concentration is high, i.e., shortly after leaving the lungs. The
more flexible and
targeted power limitation methods discussed in this section require robots to
alter pump
capacity based on sensor measurements of quantities such as oxygen
concentration, location
in the body, or distance to vessel walls. Moreover, software-based limits
would allow some
robots to use all the oxygen when occasions arise that could benefit from high
burst power.
[0134] An alternative method for limiting oxygen collection in
large vessels is for the
robots to travel in groups, analogous to the grouping of blood cells in some
blood vessels
[12]. Such groups could form from robots waiting in moderate-sized vessels,
such as lung
veins, for a group to accumulate, or robots could search for others to form a
group while
moving with the blood; groups could be formed by robots joined together and/or
robots that
simply travel in close proximity to each other. If the group is large and
compact enough that
some robots are completely surrounded by others, the robots at the surface of
the group could
share collected oxygen with those inside, or the robots could occasionally
change positions so
each robot spends part of the time at the surface of the group. When vessels
become too small
for the group, the robots could disperse. Such grouping reduces absorption per
robot by
exploiting the competition for oxygen among nearby robots, which is the
opposite of the
improved absorption by smaller robots discussed above. For example, suppose ii
robots join
to form a spherical group of radius R. To accommodate the volume of these
robots, R rrobot
From Eq. 1, the rate this group collects oxygen is proportional to R. The
oxygen
collected per robot in the group is reduced from that of isolated robots by a
factor of
(R/rrobot)/ii n 2/3 . For example, 100 robots of radius lgm could form a group
with R
5,um and then each robot would receive about 5% of the oxygen that isolated
robots would
collect. For this method of power reduction, the groups need not all have the
same size nor
contain all the robots in large vessels. For example, if among 200 robots, 100
form a group
while the others remain isolated, the total oxygen consumed by those robots
would be about
half what they would consume without any grouping.
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[0135] The simplest approach to limiting robot oxygen
consumption is for all of the
robots to have a fixed maximum power generation rate. FIG. 24 shows one
example of this
approach for 1012 robots, comparing the cases where power is not limited
(curve 2402, which
is the same as the curve for 1012 robots from FIG. 14), the case where all
robots are limited to
a maximum of 200pW (curve 2404), and a case where robots are limited based on
their
location in the circuit (curve 2406, discussed below). As with FIG. 14, the
plot shows
available robot power in pi cowatts as a function of time in seconds as the
robots move
through the circulation loop. The light dashed curves 2408 and 2410 show the
power
available to a robot for the two power-limiting strategies, if the robot in
question were not
following the strategy and instead consumed all oxygen reaching its surface,
provided that no
more than an insignificant number of other robots exceed their limits, so
oxygen is not
significantly reduced by the few robots that do switch to maximum power. The
imposition of
a 200pW limit for all robots extends the range of a circuit throughout which
robots have
power, but power still falls to zero before returning to the lung. To provide
some power
throughout the circulation loop with this many robots would require a somewhat
lower power
limit. The dashed curves 2408 and 2410 in FIG. 24 indicate power available to
a robot from
the oxygen concentration in the plasma around that robot. This is the power a
single robot
would have if it switches from limited-power to using all available oxygen,
but while most or
all of the other robots in the fluid system operate to limit their power
consumption (applying
the 200pW limit for curve 2408 or the location-based limit for curve 2410). If
only a few
robots switch to a higher-consumption mode of operation, they do not
significantly lower the
oxygen, so the dashed curve indicates the power available to a few robots
(e.g., for occasional
burst activity) provided that only a tiny fraction of the robots make use of
that additional
power at any given time.
[0136] By limiting their power production when oxygen is
plentiful, robots leave
more oxygen for robots later in the circulation loop. In effect, the robots
use blood cells as
external oxygen storage tanks to shift when and where robots utilize oxygen.
This is
conceptually similar to oxygen provided by additional supply robots discussed
above, without
the need for additional robots. On the other hand, specialized supply robots
could deliver
oxygen more effectively, especially if they use pumps for transfer rather than
relying on
diffusion.
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[0137] Instead of a fixed power limit, robots could use a
specified percentage of the
oxygen reaching their surface. Unlike a fixed power limit, such as 200pW, a
percentage limit
would adjust to the decreasing oxygen concentration as robots move through a
circulation
loop. For example, 101' robots using only 10% of the oxygen would have the
same effect on
oxygen concentration as 1011 robots using all available power (which would
provide adequate
power throughout the circuit, as shown in FIG. 14). The robots would have a
few tens of
pi cowatts. This would only be a worthwhile alternative to using I 011 robots
if there is a
benefit of having ten times as many robots, each with one-tenth the power. For
instance, if
the mission is to have at least one robot pass through every capillary to look
for a target
location, e.g., recognized by a rare pattern of chemicals, and this detection
can be done with
low power. In that case, a larger number of robots can complete the survey
more rapidly than
a smaller number of robots. Moreover, if the response to the detection
requires much more
power, such power should be available to the few robots finding the target due
to the higher
oxygen concentration left by most other robots using only a small fraction of
the available
power.
[0138] The above discussion of power limits supposes those
limits are always in
effect. Another possibility is limits that apply occasionally so robots
alternate between
consuming much or all of the available oxygen and limiting their consumption.
For example,
robots could consume significant oxygen only every second or third circuit. If
such duty
cycling occurs independently among robots, it would reduce the number of
active robots by
the corresponding factor, i.e, 2 or 3 in this example. On the other hand, if
robots synchronize
their schedules, oxygen in the circulation would alternate between high and
low levels. This
could be beneficial if the harm from continuous moderately low oxygen is worse
than
switching between very low and normal concentrations.
[0139] A more sophisticated limitation method is for the limits
to depend on the
robot's location rather than using a single overall limit. Such a strategy
would be particularly
useful if the main operation of a robot occurs when it is in a capillary (e g
, measuring
properties of nearby tissues). In this case, robots could reduce power use
while in arteries, to
have more available for the short time they spend in capillaries. They could
also defer some
power consumption (e.g., analyzing measurements they collected in the
capillary), until they
reach vessels with more available oxygen. This could be in veins, where
additional reduction
in oxygen saturation of red cells would no longer affect oxygen available to
tissues. This
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strategy should include some adjustment for portal flows, e.g., in the portal
vein, where blood
flows through another capillary, in the liver, before returning to the lungs.
In that case, the
robot could wait until it has passed a liver capillary before increasing its
power use
(variations in flow paths such as the portal flow are discussed in the section
"Variations in
Circulation Paths"). Location-based limit curve 2406 in FIG. 24 shows an
example for 1012
robots using this method, where robots are limited to 20pW in arteries, 200pW
while in
capillaries, and unlimited use in veins. With these parameters, this approach
provides power
throughout the circulation loop. In particular, it provides higher power when
robots are in the
veins compared to robots using all available power or using an overall power
limit. In the
arteries, additional power is available for a small number of robots that do
not follow the
location-based limit, as indicated by the curve 2410. FIG. 25 shows the effect
of this limit on
oxygen concentration by curve 2502, showing oxygen concentration (in 1022
molecules per
cubic meter) as a function of time (in seconds). FIG 25 also shows curve 2504
for the case
discussed above where power to all robots is limited to 200pW and curve 2506
for the case
where robots do not limit their power consumption.
[0140] Implementing location-dependent limits on power may
require that robots
determine the type of vessel they are in. Robots could do so in a variety of
ways, with trade-
offs between complexity for robot processing and accuracy. One approach is to
use an
onboard clock to measure the time since a robot left the high-oxygen
environment of a lung
capillary. They could use a fixed time, e.g., 30 seconds, to decide when they
have likely
reached a vein and can increase power use. This approach does not adjust for
variation in
circulation speed due to changes in heart rate, nor variations in circulation
path lengths, but is
a simple approach that avoids the need for robots to determine when they have
passed
through a capillary.
[0141] Alternatively, robots could measure oxygen concentration
in the surrounding
plasma This is high in arteries, decreases as the robot passes through a
capillary where tissue
consumes oxygen, and is relatively low in veins Concentration thresholds
required to
distinguish these types of vessels depends on the concentration of robots and
the power-
consumption method of the robots (see FIG. 25). This variation could be
predefined based on
these choices. More challenging for estimating location from oxygen
concentration is the
variation in tissue use in different organs and at different times, and
variation in hematocrit in
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small vessels. These variations limit the accuracy of using oxygen
concentration to determine
the type of vessel the robot is in.
[0142] Combining a variety of measures can identify vessel type
more accurately.
Most circuits through the body move through arteries of decreasing size,
through a capillary,
and then through veins of increasing size. Changes in pressure and how much it
varies over
the duration of a heartbeat distinguishes arteries from veins [12]. For small
vessels, changes
in fluid flow near the robot allow estimating vessel size [18]. It should be
noted that these
techniques for determining location could be used in other situations where
the operation of a
robot is to be adjusted based on its location in the circuit.
[0143] In addition to adjusting power based on the type of
vessel a robot is in, a robot
could adjust its power based on its macroscopic location in the body For
example, robots
could use information on which organ they are in [12] to set their power
limits. This would
allow robots to adjust power generation to match organ-specific tasks. As an
extreme case, if
robots only need to be active in one organ, then a number of robots large
enough to deplete
oxygen if they all use power would instead consume much less oxygen and mainly
affect that
organ and tissue downstream from that organ. This would avoid depleting oxygen
in veins
throughout the body, but could lead to significant local oxygen reductions,
particularly in the
small veins leaving those organs before the blood reaches larger veins, where
it mixes with
blood from other organs.
[0144] The most severe reduction in oxygen with 1012 robots
occurs near the end of
the circuit, i.e., after blood has mixed into large veins. For robots limiting
power use to one or
a few organs, that extreme reduction would not occur: instead, blood from
other organs
would partially restore oxygen in the vein. Organ-specific power use could
tolerate larger
numbers of robots than if all robots consume oxygen. A trade-off in this
scenario is that only
the portion of robots in the target organ at any given time would be actively
performing their
tasks while the majority of robots simply move passively with the blood.
Alternatively,
robots with locomotion could target the organs of interest, thereby providing
sufficient
concentration to perform their mission with a smaller total number of robots.
[0145] Another application for power limits based on location
within the body is to
adjust to organ-specific variations in tissue demand, beyond those compensated
for by
variation in tissue capillary density or changes in blood flow in response to
those variations.
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That is, robots may need to reduce their oxygen consumption in tissue with
higher than usual
oxygen demand. At a local scale, robots could determine such limits from
measuring oxygen
concentration. However, by the time a robot reaches the tissue, and encounters
the lowered
oxygen concentration, it may be too late for limiting power in small arteries
leading to that
tissue and where oxygen concentration may still be relatively high. In this
case, a robot could
limit power more effectively using information on which organ it is entering
and the overall
tissue demand of that organ.
[0146] Instead of a power limit on all robots, the limit could
be selective by
depending on the recent history of each robot. The benefit of a history-
dependent limit
depends on the fraction of robots requiring significant power at any given
time, as determined
by their current configuration and their local environment. For example, if
only 10% of
robots need significant power, then the effective number consuming oxygen is
reduced by
that fraction. If this reduction is, at least roughly, uniform throughout the
body, the robot
power affects oxygen according to the effective number of active robots. For
instance, if only
10% of a trillion robots generate significant power and do so at their maximum
possible rate,
the effect on oxygen concentration corresponds to 1011 robots consuming oxygen
as rapidly
as they can.
[0147] One situation leading to history-dependence arises in
robots with oxygen
storage and considerable variation in power requirements, depending on where
they travel in
the body. Such a robot could limit its oxygen intake and supplement that
intake with oxygen
from its storage tank. When the tank is nearly empty, the robot could absorb
more rapidly to
fill it. This would be useful if neighboring robots share data and only one of
them needs to
expend significant power to process or communicate the data: the robot using
burst power
would deplete its tank and need to refill it. Another case of history-
dependent power is if
robots only need high power when handling rare events. This could occur when a
robot
detects a specific chemical in the blood and needs to use locomotion
capability to move
toward its source [17], or if such a robot requires confirmation from other
nearby robots
before taking action, to reduce the number of false positives. In this latter
situation, the
detecting robot could increase its power use to communicate with nearby robots
and evaluate
their responses. In this case, the originating robot may need sufficient power
to send a
significant number of bits (e.g., a summary of the data it collected), whereas
responding
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robots could just send a short response indicating whether their information
is consistent with
that from the detecting robot.
[0148] As a quantitative example of history-dependent power,
consider robots that
measure chemical concentrations in capillaries and communicate their readings
when they are
in range of external receivers on the skin. One way in which robots could
determine they are
close to a receiver is for receivers to emit a beacon signal that robots can
detect when they
pass through nearby vessels in the skin. Suppose the relevant data for this
mission occurs in
tissue other than the lung or skin. In this case, the relevant property of
each circulation loop is
whether the robot goes to the skin, and, if not, whether it flows through a
portal system,
thereby measuring two capillaries before returning to the lung for another
loop through the
circulation. With typical resting perfusion rates [10], 8% of the blood flows
to the skin and
20% flows through the portal vein, which is the major circulation path passing
through two
capillaries. The rest of the blood flows through a single capillary that is
not in the skin before
returning to the heart. Suppose a robot can store measurements from up to 5
capillaries and
has time to transmit the data from up to 3 measurements while near the skin.
[0149] Due to the mixing of blood in the heart, where a robot
goes in the body during
each circulation loop is independent of where it went previously. This leads
to a Markov
stochastic process for the amount of data stored by a robot with the
transition graph shown in
FIG. 26. Each edge in the graph corresponds to the robot making a single
circulation through
the body. For instance, a robot with empty data storage is most likely to
store data from one
capillary during its next circulation. A robot could also go to the skin, in
which case it does
not collect data, or through a portal system, in which case it collects data
from two
capillaries. The number in each node in FIG. 26 is the number of capillary
measurements the
robot has currently stored. The thickness of the edges correspond to the
transition
probabilities. After multiple loops, the Markov process approaches its
stationary distribution,
in which about 70% of the robots have filled data storage. Such robots are
unable to collect
any additional data until they have had an opportunity to transmit, and
delete, some of their
collected data during their next passage near the skin. Moreover, most of the
robots reaching
the skin would have data on at least 3 capillaries, and hence have enough data
to transmit at
their maximum rate while near the skin.
[0150] Suppose the robots mainly require power during data
collection. The 70% of
robots with full data storage then use only a minimal amount of power. In
terms of power
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use, 1012 robots would be comparable to 3 x 1011 robots consuming oxygen as
fast as they
can. This would be similar to an overall limit of robots using 30% of
available power, but
with history dependence so that the power use is targeted to those robots that
most need it,
rather than a reduction for all robots.
[0151] Low oxygen concentrations in veins could affect cells on
the vessel wall.
Addressing this issue suggests another location-based limit, namely for robot
power limits to
apply only when a robot is close to the vessel wall. This could be useful in
vessels whose
diameter is at least a millimeter or so since, for vessels of that size,
diffusion limits oxygen
transport to a relatively small fraction of the vessel diameter during the
time a robot passes
through the vessel. Specifically, the low oxygen concentration with 1012
robots occurs during
the last 10 to 20 seconds of the circulation loop. The characteristic
diffusion distance of
oxygen during 1= 20s is _µ/2 Do2t = 0.3mm, with D02 given in Table 2. Robots
could avoid
creating low concentration near vein walls by reducing their oxygen
consumption when they
are near the vessel wall, e.g., as determined by measuring fluid stresses on
their surfaces [18].
Alternatively, if robots have locomotion capability, they could move away from
the vessel
wall. In this case, the low oxygen concentration would occur in the central
portion of the
vessel only. The effectiveness of limiting oxygen consumption based on
distance to the vessel
wall depends on how much mixing occurs during transport in moderate-sized
veins, including
the effect of merging vessels and cell motion. For veins whose diameter is
substantially larger
than the size of cells, this could be evaluated by approximating the blood as
a uniform fluid.
For smaller vessels, this evaluation may require simulations including
deformable cells, e.g.,
in vessels with diameters up to hundred microns or so [2]. The main advantage
of limiting
power use near vessel walls arises in vessels large enough that oxygen does
not have time to
diffuse across the vessel, and there is not significant mixing from the flow.
In general, mixing
is slow in laminar flow [36] found in such vessels.
[0152] As a quantitative example of this mitigation method,
consider the flow in a
40mm-long portion of a vein with diameter of 2mm. Suppose oxygen is well-mixed
through
the blood as it enters this vessel segment, has a relatively low concentration
of 0.5 x 1022/m3
and there are 10" robots in the circulation. Oxygen transport in the vessel
segment can be
evaluated assuming a parabolic (i.e., Poiseuille) flow profile with average
speed of 2.5mm/s.
Oxygen transport is a combination of convection with that flow, diffusion,
consumption by
robots and replenishment by red cells; as this vessel is a vein, there is no
significant
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consumption by tissue. In this case, the mixing due to the motion of blood
cells is a minor
addition to the diffusion of small molecules, such as oxygen, in the blood
[12]. The Peclet
number (roughly corresponding to the number of vessel diameters required for
diffusion to
spread oxygen across the vessel) for this oxygen transport is:
vd
Pe = ¨
(8)
D 02
where v is the flow speed, d a characteristic distance and Dorthe diffusion
coefficient, and
from Eq. 8 above for the case here is Pe = 2500, so oxygen mainly flows along
the vessel
with relatively little diffusion across the vessel. This leads to considerable
variation in oxygen
concentration across the vessel, as robots in the slowly moving blood near the
walls deplete
oxygen much more thoroughly than robots traveling with the faster flow near
the center of
the vessel.
[0153] Robots could mitigate the rapid concentration decrease
near the wall by
reducing their oxygen consumption. As an example, FIG. 27 shows how the
concentration (in
1022 molecules per cubic meter) near the vessel wall changes with distance
along the vessel
(in millimeters) in three cases for a straight vessel of 2mm diameter, in the
case of 1012 robots
distributed throughout the entire circulatory system. In the first case, shown
by curve 2702,
robots fully consume oxygen reaching their surface. In the second case, shown
by curve
2704, only half the robots consume oxygen (or, equivalently, each robot
consumes only half
the oxygen reaching its surface), without regard to their position in the
vessel. In the third
case, shown by curve 2706, robots within 0.3mm of the vessel wall do not
consume oxygen,
with that distance corresponding to oxygen's characteristic diffusion distance
discussed
above. This distance to the vessel wall accounts for about half the total
cross-sectional area of
the vessel, and only about half the robots are consuming oxygen (i.e., those
in the central
portion of the vessel). As seen in FIG. 27, the approach of an overall
reduction in power
(curve 2704) reduces the rate of oxygen depletion near the wall, but is much
less effective
than when robots limit power based on their distance to the wall (curve 2706).
[0154] The example shown in FIG. 27 is for flow in a single
straight vessel. The flow
from the merging of veins of various sizes could somewhat increase the mixing
and thereby
reduce the benefit provided by robots limiting consumption near the wall. To
evaluate this
effect, FIG. 28 illustrates an example of merging vessels with asymmetric
branching where
two branches, each with diameter of 2mm, merge into a vessel with diameter of
2.5mm
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(typically when blood vessels merge, the total cross section of the two
branches exceeds that
of the main vessel, so flow speed in the branches is somewhat slower than in
the main
vessel). To focus on the effect of the merging vessels, the example included
only 8mm in
each branch and in the main vessel (16mm total, compared to the 40mm-long
straight vessel
discussed with FIG. 27). Accounting for the effect of the branches required
solving for the
fluid flow through the vessels, with the flow exiting the main vessel assumed
to be parabolic
with average speed 2.5mm/s, and the inlet pressure assumed to be the same for
both branches.
The fluid flow with these boundary conditions was laminar, and the merging
flows provided
some mixing where the branches joined. The behavior of the concentration was
similar to that
seen in the straight-vessel example, with oxygen becoming depleted near the
vessel wall.
FIG. 28 shows the reduction in oxygen concentration along the upper wall of
the upper
branch and main vessels for the same three oxygen consumption cases as shown
for the
straight vessel in FIG. 27, with curve 2802 showing the case where robots do
not limit power,
curve 2804 showing the case where robots reduce their consumption by 50%
regardless of
location, and curve 2806 showing the case where robots do not consume oxygen
when within
0.3mm of the vessel wall. Even in this last case (curve 2806), the
concentration near the wall
eventually gets very small, although it does not become completely depleted as
occurs when
robots do not limit absorption (curve 2802) or where robots consume 50% of
oxygen
reaching their surfaces regardless of their location (curve 2804). In the
context of these
examples, the main benefit of this mitigation is extending the range of the
circulation loop by
a few centimeters compared to when robots consume all oxygen or limit
consumption to
50%. This increase in range could be especially beneficial in a vein just
before it merges with
other veins that contain blood from shorter circuits and hence have more
remaining oxygen
than the model estimates for an average circulation loop. In that case,
avoiding fully depleted
oxygen for a few additional centimeters could be sufficient to avoid extremely
low
concentrations near the walls of any veins, without requiring all robots in
those vessels to
reduce their power generation. Alternatively, achieving the same increase in
range with a
power limit on all robots would require a much larger reduction in power than
the 50%
reduction that corresponds to robots near the wall consuming no oxygen while
the rest of the
robots consume at their maximum rate. The usefulness of this distance-based
limit on oxygen
consumption compared to limiting all robots depends on the benefit some robots
obtain from
more power while in the veins compared to the additional complexity of robots
required to
determine their distance to the vessel wall.
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[0155] Capillaries are of particular interest, as they allow
robots to operate close to
tissues of interest while remaining in a blood vessel. The small volume of
capillaries leads to
relatively large variation in robot numbers as discussed above. Those
capillaries that contain
significantly more robots than average have less power. Robots could reduce
this variation by
moving away from particularly close neighbors, including moving to other
capillaries that
have fewer robots. Within a single vessel, robots in close proximity compete
for oxygen; such
robots could improve oxygen distribution using a small-scale version of the
power limiting
strategies discussed above. In addition, the flow of oxygen to robots depends
on their
positions along the vessel wall, which provides an additional mitigating
strategy for small
groups of nearby robots: improving power distribution by deliberately
adjusting their
positions relative to their neighbors. Computer modeling of oxygen
distribution suggests that
there are competing effects on the oxygen delivered to robots, as a robot
directly upstream of
another absorbs much of the oxygen that would otherwise go to the downstream
robot, but
where placing all robots on one side of the vessel allows more oxygen to reach
downstream
on the other side of the vessel, which can then diffuse across the vessel to
downstream robots.
The relative importance of these effects depends on the ratio of convective to
diffusive
transport of the oxygen, i.e., the Peclet number of the oxygen transport [36]
as discussed
above.
[0156] To illustrate the potential of position adjustment,
consider 5 robots 500
positioned along a vessel wall with neighbors offset by an angle 0, as shown
in FIG. 29. In
this example, five 2j.tm diameter robots 500 are arranged in a vessel 502 of
81.im diameter
(the same situation as illustrated in FIGS. I8A 8z. 18B). Successive robots
500 are offset
around the wall 504 by the angle 0 about a longitudinal axis 506 and spaced
along the vessel
by 5.511m (the arrangements shown in FIG. 18A & 18B respectively correspond to
0 = 180
and 0 = 0 ). This arrangement is analogous to the angular spacing of leaves
around the stem
of a plant, where angles related to the golden ratio can minimize the extent
to which higher
leaves cast shadows on lower ones [38]. However, unlike the direct path of
light, diffusion
allows some oxygen to reach robots that are directly downstream of others on
the vessel wall.
FIGS. 30A & 30B show curves for the average robot power (curve 3002) and power
for the
last downstream robot 500' (curve 3004) for the case of 5 robots in a vessel,
as a function of
the offset angle 0 (in degrees), relative to the power that would be available
with all robots
aligned along the vessel wall (i.e., with 0 = 0 as shown in FIG. 18B), for two
flow speeds.
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The solid curves 3002 show the average power for the 5 robots 500 with average
fluid speed
lmm/s (FIG. 30A) and 0.2mm/s (FIG. 30B) while the dashed curves 3004 show the
power
available to the fifth robot 500' for these same fluid speeds. FIGS. 30A & 30B
show that the
offset angle has a different effect on the average robot power than it does on
power for the
last robot 500', which receives the least oxygen. Specifically, offsetting
neighboring robots
500 by 180 increases the average power by a few percent, with larger effect
for faster
moving fluid. On the other hand, positioning all robots 500 on the same side
of the vessel 502
(i.e., 0 = 0) increases power for the last robot 500' even though it is
directly downstream of
all the other robots 500 in the group. Computer models show that this occurs
because robots
on one side of the vessel allow more oxygen to reach downstream along the
other side of the
vessel and then diffuse to the last robot, and that this effect is larger for
slower moving fluid
(where the upstream robots have greater opportunity to deplete the fluid of
oxygen before it
flows past). The robots could select among these placement options based on
the relative
importance of maximizing power for the group as a whole vs. ensuring that all
robots have at
least a minimum amount of power and/or depending on the size of the vessel
and/or fluid
speed.
[0157]
Robots 500 could use nonuniform positions along the vessel to provide more
power to downstream robots by having upstream robots closer to each other than
downstream
ones. As an example, in addition to the angular separation around the vessel
discussed above,
suppose the robot positions along the direction of the vessel increase
quadratically, starting
with a difference of 2.5ri0b0t for the first two robots 500 and occupying the
same total distance
along the vessel as the uniformly spaced robots discussed above. FIG. 31A
shows this
distribution for the case of zero offset angle between neighbors (i.e., 0 = 0
), where the
distance between facing surfaces of the first two robots 500 is 0.5rrobotõ
while FIG. 31B shows
the distribution for 0 = 180 , where successive robots 500 are on opposite
sides of the vessel.
The fluid flows from left to right in each case. The larger distance between
the last robot 500'
and the others allows the last robot 500' to collect oxygen from a larger
portion of the fluid
than when robots 500 are uniformly spaced (as is shown in FIGS. 18A, 18B, and
29). FIGS.
32A & 32B show the average power for the robots (curve 3202) and power for the
last robot
500' (curve 3204) as a function of the offset angle 0, relative to the
situation of uniformly-
spaced robots aligned along the vessel wall as used in FIGS. 30A & 30B, again
for the same
two fluid flow speeds (lmm/s in FIG. 32A and 0.2mm/s in FIG. 32B). The
nonuniform
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spacing has little effect on the average power, but aligned, nonuniformly
spaced robots
provide 20% more power to the last robot 500' than uniformly spaced robots.
[0158] The choice of robot positions on the vessel wall alters
the power available to
downstream robots in a manner similar to that of robots limiting their power
use, as discussed
above, but without requiring the robots to continually monitor and adjust
their power
consumption. Instead, robots attaching to a vessel wall for extended operation
could
determine their positions during their setup and then avoid devoting any
computation to
maintaining power limits while they perform their tasks while attached to the
vessel wall. On
the other hand, actively adjusted power limits provide more flexibility in
distributing power
to downstream robots. Robots could adopt a hybrid approach of positioning
themselves to
best achieve their goals and having upstream robots limit their power
consumption when
downstream robots indicate they require more power.
[0159] As described above, robots moving passively with the
blood and attaching to
capillary walls can lead to significant variations in the number of robots in
each capillary. In
addition to adjusting their position in individual capillaries, robots could
alter how they
divide among nearby capillaries in a network of vessels. For example, robots
could
preferentially position themselves in some of the capillaries in a network of
vessels while
leaving others with few or no robots. In that case, the increased vascular
resistance due to
robots would tend to direct blood cells away from branches of the network
containing many
robots, thereby contributing to the heterogeneity of paths that cells take
through a network of
small vessels [37]. Provided the open paths interleave closely with the
vessels blocked by
robots, the flow through the open paths could be sufficient to support the
surrounding tissue
with less disruption to the overall flow than if robots were positioned in all
the capillaries.
The possibility of using just a portion of capillaries to perfuse tissue
arises because resting
tissue can contain more capillaries than required for adequate perfusion [10],
though with
considerable variation among locations in the body [1].
[0160] In addition to managing oxygen concentration, a concern
when large numbers
of robots consume oxygen is that they add significant heat to the body.
Mitigating oxygen
depletion by transporting more oxygen using supply robots as discussed above
does not
address issues arising from heating. Instead, providing more oxygen allows
robots to increase
their power use, and hence produce more heat. Limiting power production can
both reduce
oxygen depletion and reduce the heat generated by the robots, and is typically
the better
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approach in situations where the large number of robots might lead to
significant problems
due to both oxygen depletion and heating. Another method to mitigate heating
is to modify
the location-based power limiting strategies discussed above, to change where
the heating
occurs. In particular, robots could shift their high-power activity and the
resultant heat
production to regions of the body that readily dissipate the heat. Such
regions might be
detected by having a lower temperature than the core of the body, such as near
the skin. This
approach to heat mitigation is particularly suitable for missions where high
power demands
occur near the skin (e.g., for robots communicating information to external
receivers when
they are near the skin). An alternative communication strategy of network
message-passing
through hubs located throughout the body would distribute power use and
resultant heating
throughout the body rather than concentrating heating near the skin. With
enough robots that
heating becomes an issue, heat dissipation could constrain the choice of
communication
method, in addition to constraints on transmission rates, latency, and/or
reliability.
Vessel Circuit Model
[0161] The circuit considered for the example discussed above
starts as blood leaves a
lung capillary, where its oxygen concentration is set by that from the air in
the lung, after
which oxygen concentration decreases due to consumption by robots and tissue.
The circuit
continues through the body and back to the lung, ending as the blood is about
to enter a lung
capillary where it will be oxygenated and start a new circuit. The time to
complete a circuit
depends on where the blood goes, e.g., shorter times for transit through the
head than through
the feet. The example considers an average circulation time of about one
minute, i.e., the time
required for the resting heart rate, 5L/min, to pump the entire blood volume,
T71,100d. Oxygen
concentration in the plasma at any location determines the power available to
a robot, this
concentration being determined by the combination of oxygen removal (by robots
and tissue)
and replenishment from red blood cells. As replenishment depends on the number
of cells in
the plasma (i.e., the hematocrit), evaluating available robot power requires
characterizing the
variation in hematocrit during a typical circulation loop.
[0162] Blood carries most of its oxygen bound to hemoglobin in
red blood cells. The
number of red cells in blood is commonly expressed by the fraction of the
blood volume
occupied by cells, i.e., the hematocrit, which is typically around 45% [12].
This is the average
value over the entire blood volume. However, in small vessels the fluid flow
tends to push
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cells toward the center of the vessel where they move faster than the average
speed of the
flow. This Fahraeus effect decreases the hematocrit in small vessels. While
there is
considerable variation among such vessels, on average the hematocrit h in a
vessel of
diameter d (measured in microns) is approximately [32]
= hfull + (1 ¨ hfun) (1 1.7 e-0.35d ¨ 0.6e ¨0.01d) (9)
where kiln is the hematocrit of the entire blood volume. For example, when
overall hematocrit
is &ill = 0.45, Eq. A.1 gives h = 0.34 in a capillary with diameter d = 8,um.
Eq 9 is used to
determine hematocrit in the example, thereby treating hematocrit as only
depending on vessel
diameter.
[0163]
From Eq. 9, hematocrit only deviates significantly from //full in those
vessels
whose diameters are less than about a millimeter, so it is unnecessary to
distinguish diameters
larger than this to determine hematocrit. The model used in this example only
explicitly
accounts for vessel diameter during the portion of the circuit through small
vessels. Transport
through large-diameter vessels and the heart, which all have the same
hematocrit, can be
grouped to produce a circuit with the following parts:
1. a sequence of small veins of increasing diameters starting from the end
of a
lung capillary
2. large pulmonary veins, the heart, large arteries
3. a sequence of small arteries of decreasing diameters to the start of a
body
capillary
4. a body capillary
5. a sequence of small veins of increasing diameters from the end of a body
capillary
6. large veins, the heart, large pulmonary arteries
7. a sequence of small arteries of decreasing diameters to the start of a
lung
capillary
[0164]
Passage through the lung capillary at the end of the circuit contributes
to the
total circulation time but is not explicitly included in the model. Instead,
the concentration is
specified at the start of the circuit (i.e., just after passing through a lung
capillary) as a
boundary condition. This simplification is reasonable because the transit time
through lung
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capillaries is more than sufficient to saturate red cells with oxygen even if
they enter the
capillary with low oxygen saturation [10]. Moreover, the large spacing between
robots in
capillaries, even at the largest number of robots considered here (1012),
means that robots do
not significantly alter the oxygen available in lung capillaries.
[0165] Without consumption by robots, the change in oxygen
concentration in each
part of the circuit depends on its transit time and hematocrit. Eq. 9 gives
hematocrit equal to
Midi in the large-vessel parts of the circuit, i.e., circuit parts 2 and 6.
The transit time for these
parts is set so the total circuit time equals one minute when combined with
the estimates of
transit times through small vessels discussed below. For the capillary part of
the circuit,
typical capillary diameter and transit time are used. Eq. 9 gives the
hematocrit in the body
capillary based on its typical diameter.
[0166] For the remaining parts of the circuit, consisting of
small branching vessels,
hematocrit is estimated from the vessel diameter, d, via Eq. 9, and transit
time from vessel
geometry: diameter, d, length, 1, and number of such vessel segments,
_A/vessel. There is
considerable variation in these values. For the purpose of this model average
values are used,
analogous to using the average relation between vessel diameter and hematocrit
in Eq. 9.
These geometric parameters are related to transit time in the vessels of a
given type (i.e.,
artery, capillary or vein) and diameter. In aggregate, small vessels have
larger cross section
than large vessels, which leads to slower speeds in those vessels [24].
Nevertheless, the short
length of the small vessels more than offsets their slower flow speed, so
blood spends most of
the circuit time in large vessels. The aggregate cross section of vessels with
diameter d is
7-c(d/2)2 Nvessei The entire blood volume passes through this aggregate cross
section, when
neglecting the relatively small portion of the flow through portal systems, so
that
Tr 2 1
- d V v = -
Nvessel - blood
(10)
4
where v is the average flow speed in the vessels and T is average transit time
for the blood
volume Vblood (i.e, about one minute). This relation gives v in terms of d and
Nvessel. This
velocity determines the segment's transit time as t =
[0167] As described above, the geometric parameters of small
branching vessels are
used to quantify those parts of the circuit, using representative average
branch geometry. For
this example, vessel branching is based on branching of vessels in the lung
for which data on
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complete vascular trees is available [21, 35,40,41]. Although the structure of
capillary
networks in the lung differs from that in other parts of the body [40], the
branching of small
arteries and veins in the lung is taken as representative of such vessels for
a typical circuit
through the body. The measured geometry of arterial and venous trees in the
lungs [21]
indicates that most of the flow is through vessels of successive branch
orders. Flow that skips
a few branch orders corresponds to blood that reaches capillaries through
fewer branchings
than blood that goes through all orders. For this model of average flow,
vessel branching is
taken to follow the main flow through successive orders, giving a sequence of
vessel lengths,
diameters and number of branches at each branching order for both arterial and
venous trees
[21, Tables 2 and 5]. Doubling the number of branches to account for flow
through both
lungs, Eq. 10 determines transit speed, and hence transit time, for each level
of branching.
[0168] Large arteries branch into successively smaller vessels
until they reach
capillaries, and then merge into increasingly large veins. For circulation
through a sequence
=
of vessels i = 1,2,..., the total length is EiI, and the total passage time is
Ei which
equals the typical total transit time T. Subtracting the transit time through
small vessels from
the total time T gives the time in the circuit parts corresponding to large
vessels, i.e., circuit
parts 2 and 6 above. To partition this time between these two large-vessel
parts (i.e., arteries
and veins) to and from a capillary, respectively, the time in veins is taken
to be 1.5 times
larger than in arteries, corresponding to somewhat slower flow speed in the
veins. Combining
these vessel properties results in the circuit model as shown in FIG. 12. For
purposes of
illustration, the transit through each side of the heart is shown as taking is
to transverse
50mm. Since hematocrit is the same in the heart and in large vessels, the
precise time spent in
the heart has no effect on the model results. FIG. 12 illustrates transit
through large vessels as
an interpolation (dashed curves) between the heart and the branching through
small vessels to
and from a capillary. This interpolation matches typical average flow speed of
blood leaving
and entering the heart. Specifically, flow speed in the aorta averaged over a
heartbeat is
around 110mm/s and speed in the vena cava is around 135mm/s [14]. This
interpolation
illustrates the flow through large vessels. However, the model of oxygen
consumption only
depends on the transit time through those vessels, not the specific shape of
the dashed curves
in FIG. 12.
[0169] Fig. 33 shows the vessel diameters (in millimeters) for
the vessel circuit on a
log scale, as a function of time (in seconds) through the vessel circuit,
highlighting the
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diameters of small vessels where hematocrit deviates from its overall value.
For small
vessels, the diameters and transit times are the values described above. The
diameters for
large vessels are not shown in FIG. 33, and the diameters are not relevant for
this model as
such vessels are large enough that hematocrit equals the overall value hrun
(see Eq. 9).
[0170] FIG. 34 is a schematic illustration of vessel branching.
Smaller vessels have
larger total cross section and lower hematocrit than larger vessels; these are
illustrated in the
aggregated model of the vessels shown in FIG. 35. Such a simplified model can
be employed
because flow speed and hematocrit are relevant to robot oxygen consumption,
while the
details of vessel branching can be ignored. In this aggregated model shown in
FIG. 35, the
circulation consists of a single vessel 3500 with volumes for plasma 3502 and
blood cells
3504, where the aggregated vessel cross section is larger corresponding to
smaller vessels,
and where the fraction of volume occupied by cells (hematocrit) 3504 is
smaller relative to
the volume of plasma 3502 in the smaller vessels.
[0171] To evaluate robot oxygen consumption over a minute or so,
a one-dimensional
model of vessel flow is averaged over the variation in speed due to heart
contractions. This
gives flow speed v(x) depending on the location x along the aggregated vessel,
but not
depending on time or how close the fluid is to the vessel wall. With this time
averaging, the
total cross section A(x) is independent of time. Considering the flow in a
vessel with cross
section area A(x) and flow speed v(x) at position x, fluid flows through the
cross section at x
at a rate pv(x)A(x) where p is the fluid density. This rate is constant
throughout the vessel for
incompressible fluid, as given in Eq. 10. Speed is inversely proportional to
cross section area:
v(x) = 170/610/A(x)
(11)
where vo and Ao are the speed and cross section at an arbitrarily specified
position along the
circuit. The total cross section A(x) varies with position, as does
hematocrit, as shown in FIG.
35. Since the fraction of the total cross section corresponding to plasma and
cells varies in the
aggregate vessel a model of aggregated vessels with two compartments, plasma
and cells, can
be employed, where the relative cross sections change with the changing
hematocrit in the
vessels,
[0172] Evaluating how much cells replenish oxygen in blood
plasma requires
specifying the average speed of cells and plasma, vcell and Vplasma,
respectively. Due to
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changing hematocrit, these speeds are not the same and vary with the changing
cross section
of the vessel. One relation among these speeds is the average speed v in terms
of hematocrit:
V = (1 ¨ h) l Vn
õ..2SYna Vcell
(12)
In this expression, v is the average speed in the vessel, taken from the
parameters of the
circuit in Fig. 12. This relation assumes the addition of any robots to the
blood does not
noticeably alter the speed, which is reasonable with the small fraction of the
volume occupied
by robots [12]. This expression splits the blood volume between plasma and
cells, ignoring
the tiny volume occupied by robots.
[0173] Another relation among these speeds arises from
conservation of flow. For a
small volume of blood with hematocrit h containing plasma and cells in a
vessel with cross
section area A, the volume of plasma and cells moving across that area in a
small time At are
(1 ¨ h)A Vplasma and hA yea, respectively. Over the time of a circuit (e.g.,
about a minute),
neither plasma nor cell volumes change significantly, so the fl ow rates of
plasma and cells
must be the same throughout the circuit, i.e., equal to some constants amasma
and ace'. That is,
(1 ¨ h)Al)plasma¨ aplasma and hAv cell ¨ occell. These relations imply that
the ratio of cell speed to
plasma speed is independent of the total cross section:
Vcell = 1¨h Xcell
(13)
Vplasma cxplasma
The Fahraeus effect does not apply to large vessels, where cells and plasma
move together
with the average flow of the blood, i.e, vcdi = vpiasma and hematocrit is huh
For this case, Eq.
13 gives acell/aplasma = hfull./(1 ¨ hfull), and Eq. 13 becomes
Vcell = 1-11 /1¨ hfuii
(14)
vplasma h hfull
Combined with Eq. 9, this gives the velocity ratio as a function of vessel
diameter. For
example, with the range of hematocrits used here for large and small vessels,
Eq. 14 gives a
velocity ratio around 1.7 in small vessels, which matches reported values [3].
[0174] The aggregated vessel diameters (illustrated in Fig. 35)
and Eq. 9 give the
variation in h(x) in the aggregated vessels. This value, combined with Eq. 12
and 14, gives
the speeds vpiasma(x) and vceli(x) as a function of position in the circuit.
With these speeds,
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transit time can be calculated, and with transit time and hematocrit, oxygen
concentration at
different locations in the circuit can be determined.
Oxygen Concentration in Vessels
[0175] The aggregate vessel model shown in Fig. 35 consists of
two compartments,
plasma and cells, and the cross sections of these compartments vary along the
length of the
aggregate vessel. These compartments exchange oxygen with each other, and with
robots and
tissue. Robots are a small portion of the blood and not treated as a separate
compartment for
the discussion of this section. This section describes how oxygen
concentration changes in
vessels with variable cross section: first for a single vessel, then for two
such vessels treated
as two compartments exchanging oxygen. These behaviors determine how
concentration
changes in a volume of fluid moving with the flow in one of these vessels.
This differs from
behavior in vessels of a fixed cross section due to the changing cross section
and fraction of
the total cross section occupied by the two compartments.
[0176] A chemical in the fluid moves by convection with the
fluid's motion as well as
diffusion For the scales and flow speeds considered here, diffusion is a minor
contribution to
changing concentration. In particular, the Pecl et number (as discussed above
in Eq. 8)
characterizes the relative importance of convection and diffusion [36]. For
flow through a
vessel of diameter d, Pe roughly corresponds to the number of vessel diameters
required for
diffusion to spread the chemical across the vessel. For motion along the
vessel, the distance at
which Pe 1, i.e., d=1302/12, is the distance at which diffusion and convection
have about the
same effect on mass transport in a moving fluid. At significantly longer
distances, convection
is the dominant effect.
[0177] The distance over which diffusion is important is largest
in the vessels with
slowest flow, i.e., the capillaries. Capillary flow speeds are around lmm/s
for which Do2/1" =
2,um. This distance, comparable to the size of the robots, is considerably
smaller than a
typical capillary length, i.e., a millimeter, and the length of the full
circulation loop (e.g., as
indicated in Fig. 12) relevant for evaluating systemic effects of robot oxygen
consumption.
Moreover, the typical distance between neighboring robots is larger than Dcp/v
in the
scenarios considered here, so neighboring robots do not directly compete with
each other for
oxygen. This is unlike the case of closely spaced robots (such as aggregates
on vessel walls)
where robots significantly reduce oxygen available to their neighbors [19]. In
light of these
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observations, diffusive transport can be ignored in modeling the change in
oxygen on the
scale of the circulation loop.
[0178] For convective flow, the chemical flux at position x
along the vessel is J(x)=
v(x)c(x) where c(x) is the chemical's concentration. In a small section of
vessel between x and
x+Ax, in time At, J(x)A(x)At molecules enter that section of vessel, and J(x+
Ax)A(x-FAx)At
leave it. In addition, reactions such as release of oxygen by cells or
consumption by tissue
change the concentration at a rate R. Combining these contributions to
concentration change
gives:
Etc a
VA) R
M A ar
From Eq. 11, at position x, JA = voAoc so the rate of change of concentration
is
at: Ao t9c
¨VO ¨ -4- 11: R
at A ax
(15)
with v given by Eq. 11
[0179] As described below in the section "Processes that Change
Oxygen
Concentration", the time constant for robot oxygen consumption is less than a
minute.
Typical operations for the robots are likely to occur over time periods of at
least tens of
minutes, corresponding to many circulations, so a reasonable simplification is
to focus on the
steady-state concentration profile in the vessels, in which case Eq. 15
becomes
,
v r= f
thr
(16)
For transient operations (e g , for a few seconds after robots start consuming
oxygen) robots
will have more oxygen than indicated by the steady-state analysis considered
here.
[0180] As illustrated in FIG. 35, the aggregated vessel consists
of two main
compartments: plasma 3502 and blood cells 3504 which have separate flow speeds
(Eq. 14).
Each compartment acts as a separate vessel in terms of flow, but they can
exchange oxygen.
Generalizing Eq. 16 to account for this exchange gives the behavior of the
concentrations, Cl
and c,, in the two compartments:
c1
vi = Ri Rfrom 2
OX
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aC2
V2 - = R2+ R01 (17)
ax
where R from 2 is the change of concentration in compartment 1 due to
chemicals from
compartment 2, Rtot is the decrease of concentration in compartment 2 from
chemicals that
move to compartment 1, and R, is the rate concentration changes in compartment
i due to
production of chemical in that compartment (with a negative value for chemical
consumed).
The two compartments share the total cross section of the aggregated vessel
model, A(x).
With hematocrit h(x), the cross sections of the two compartments are Ai = (1 ¨
h(x))A(x) and
A2 = h(x)A(x) (assuming that robots occupy a negligible fraction of the vessel
volume).
Conservation of flow means vi (x)A 1(x) and v2(x)A2(x) are independent of x. R
¨from 2 and R/01 are
rates of concentration change in the two compartments from oxygen moving from
compartment 2 to compartment 1. These rates must account for different
volumes, i.e., a
given amount of oxygen makes a larger change to concentration in a smaller
volume. The
number of molecules in volume element i, extending from x to x + Ax, is
A1(x)Arc,. The rate
molecules move from compartment 2 to compartment 1 is both Rt0iA2Ax and Rfrom
2.24 1Ax.
These must be the same, so
1¨h n
RV) 1 = n
h from 2
(18)
For example, when h is small, the transfer of a given amount of oxygen has a
much larger
effect on the concentration in compartment 2 than it does on that of
compartment 1.
[0181] With the above model, a robot moving in a small volume of
fluid in
compartment 2 can be considered. Eq. 17 describes the steady-state
concentration profile in
two compartments, determining how the concentration in that fluid volume
changes as it
moves through a circuit such as illustrated in FIG. 12. In time At, the fluid
volume moves
from position x to x v2At, and the time rate of change of concentration in the
volume element
of compartment i, due to motion with the speed v2 is dc,/dt = v23ci/6x. Thus
Eq. 17 gives
dCi -,122
= (R1 Rfrom 2) ¨
u.t, V1
dcz
= R2¨ R01
(19)
dt
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for the rate that concentration changes in the two compartments from the
viewpoint of a
volume moving with the flow in compartment 2. The circulation shown in Fig. 12
starts with
blood leaving lung capillaries, so the initial condition for Eq. 19 is the
concentration in the
lung.
Processes that Change Oxygen Concentration
[0182] In this example, robots are assumed to move with cells
rather than with plasma
(i.e., flow pushes robots away from vessel walls in a manner similar to the
behavior of blood
cells [42]). This is reasonable in capillaries where cells move through single-
file: robots are
too large to fit in the gap between cells and the vessel wall, so robots move
between cells, and
hence at similar speed. In somewhat larger vessels, if robots are pushed
closer to the vessel
wall than the cells, robots would move somewhat more slowly. The difference in
speeds
between cells and the average flow rate is largest when hematocrit differs
most from its
overall value (i.e., in small vessels). Even then, the difference is
relatively minor due to the
short time (a few seconds out of the one minute circulation) that robots spend
in those
vessels, so the model results are not very sensitive to the accuracy of this
assumption.
[0183] With the assumption that robots travel with the speed of
compartment 2
discussed above, the model of concentration change requires specifying the
reaction rates
appearing in Eq. 19. During the circulation, robots and tissue consume oxygen
from the
plasma, and red cells replenish it. Fig. 13 illustrates the processes that
change oxygen
concentration. In terms of Eq. 19, Ri = Rrobot Rtissue s the rate, per unit
volume, that robots
and tissue remove oxygen from the plasma. There is no consumption within cells
so R2 = 0.
The rates R from 2 and Rto i are the transfer rates from cells to plasma that
maintains the
equilibrium of Eq. 20 below.
[0184] Oxygen removed from blood plasma is replaced by oxygen
released from
nearby red blood cells. The time scale for this process is less than 100ms
[7], which is much
shorter than the one minute circulation time considered here, and even the one
second
capillary transit time during which tissue extracts oxygen from the blood. A
reasonable
approximation is that oxygen bound inside red cells is in equilibrium with the
concentration
in the surrounding plasma. Oxygen bound in red cells is characterized by the
hemoglobin
saturation S: the fraction of hemoglobin capacity in a cell which has bound
oxygen [26]. The
oxygen concentration in the cell is C0""x2S, where C0""x2is the concentration
in the cell
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when all the hemoglobin has bound oxygen. Quantitatively, the equilibrium
saturation,
conventionally expressed in terms of the equivalent partial pressure p of 02
in the fluid
around the cell, is described by the Hill equation [15,30]:
an
Sequib (a) =
(20)
where a = p/p5ois the partial pressure ratio, 5o is the partial pressure at
which half the
hemoglobin is bound to oxygen and n characterizes the steepness of the change
from low to
high saturation. The saturation ranges from near 1 in the lungs to around 1/3
in working
tissues. Henry's Law relates the partial pressure to the oxygen concentration
in the plasma
around the cell: p = H07(707 with the proportionality constant Ho2 depending
on the
temperature. Thus, a = (Hoz/p50)CO2= CO2/Chaff where Chaff = P5 C/H02, which
is about 2.2>(
1022molecule/m3. This is comparable to lower range of oxygen concentration in
tissue. This
model does not consider deviations from Eq. 20, which mainly occur at low
saturations [15,
30], and variations in its parameters with changing blood chemistry, such as
pH and carbon
dioxide concentration.
[0185] For determining oxygen removal by robots, a small volume
AV of blood with
oxygen concentration c in the plasma contains vroboiA V robots, where Vrobot
is the robot number
density in the blood. With each robot absorbing at the rate given by Eq. 1,
the total rate robots
remove oxygen per unit volume of plasma is
Rrobot = rrobotC
(21)
with rate constant 'robot = 471-Do2rioboiviobot/(1 ¨ h) . This absorption rate
assumes each robot
draws oxygen independently from a fluid with concentration c (that is, robots
are assumed to
be sufficiently far apart that they do not compete with their neighbors to
reduce the local
oxygen concentration and hence robot absorption rate [19]). Such competition
is insignificant
for robots separated by at least about ten times their size [5], which is the
case for the
numbers of robots considered here. The time constant for robots removing
oxygen from
plasma is Trobot = /Yrobot= Trobot lOs for 10' robots. Trobot i s
correspondingly smaller for the
scenarios with larger numbers of robots, so concentration changes due to
robots reach steady-
state within a single circulation time.
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[0186] Tissue extracts oxygen from blood passing through
capillaries. In terms of the
aggregated vessel model, consumption by tissue occurs over a short distance
around the peak
in total cross section shown in Fig. 35, which corresponds to capillaries. A
simple model of
tissue oxygen consumption uses a cylindrical region of tissue around each
capillary [23, 30].
The radius of this tissue cylinder, I-tissue, corresponds to a typical maximum
distance of tissue
supplied from a capillary, which is a few cell diameters. In this model, the
volume of tissue
receiving oxygen from a length Ax of capillary, with radius rcap is
7r(rtissiie2¨ rcap2)Ax, so the
ratio of tissue to vessel volume is (1tissue/rcap)2¨ 1. A consistency check on
this model is that
multiplying the total capillary volume by the tissue to capillary volume ratio
should equal the
total body volume. The total capillary volume is about 4 x 105 mm3 [12]. The
ratio of tissue to
capillary volume is about 100, giving corresponding tissue volume of about
0.04m3, which is
comparable to body volume.
[0187] Models of oxygen use and power generation in tissues can
account for tissue
structure [30]. A simpler approach [27], adopted for this example, treats the
tissue
surrounding the vessel as homogeneous and metabolizing oxygen at the rate that
produces
power according to Eq. 3 above. When oxygen concentration is substantially
larger than
Ktissue, tissue power is nearly independent of oxygen concentration, and
tissue metabolic
demand, rather than available oxygen, limits tissue power. Dividing Ptissue by
the reaction
energy per oxygen molecule consumed gives the rate of oxygen consumption per
unit volume
of tissue. Oxidizing a single glucose molecule consumes six oxygen molecules,
so the energy
per oxygen molecule is c/6, with e being the energy from oxidizing one glucose
molecule.
[0188] For the resting tissue power demand considered in this
example, oxygen
concentration in tissue is nearly constant as a function of distance from the
capillary [23],
even with additional consumption from robots [19]. For evaluating tissue
oxygen
consumption from capillaries, the oxygen concentration in the tissue is
considered to be the
same as that of the plasma in the capillary. That is, in Eq. 3 CO2 is set
equal to the oxygen
concentration in the capillary surrounded by the tissue In this case, Ptissue
is constant within
the tissue cylinder and total tissue consumption is Ptissue multiplied by the
tissue volume
around the capillary. Tissue takes oxygen from plasma in the capillary, so the
rate it reduces
concentration in the plasma is enhanced by the ratio of tissue to capillary
volume given
above, and the fraction of the vessel volume that is plasma (i.e., 1¨h).
Combining these
factors, the rate tissue reduces oxygen concentration in the plasma is
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2
Rtissue tissue (rtissue 1
¨
(22)
e/6 rcap i¨h
in the capillaries, and zero elsewhere in the circuit.
Model Parameters
[0189] Table 2 gives the parameter values used to evaluate robot
power in the
circulation in the example discussed. For tissue, Kiissue is from Ref. [27],
and the blood cell
parameters are from Refs. [7] and [30]. The oxygen concentration in the lung
corresponds to
arterial concentration [12]. Concentrations of glucose in blood plasma are in
the millimolar
range (about 1024molecule/m3), far larger than the oxygen concentrations [12].
[0190] For evaluating the rate oxygen diffuses to the robot
surface (e.g., in Eq. 1), it is
convenient to express oxygen concentration in terms of molecules per unit
volume. By
contrast, macroscopic studies usually express concentrations in more readily
measurable
quantities. These include moles of chemical per liter of fluid (i.e., molar,
M) and grams of
chemical per cubic centimeter. Discussions of gases dissolved in blood often
specify
concentration indirectly via the corresponding partial pressure of the gas
under standard
conditions. As an example of these units, oxygen concentration CO2 = 1022
molecule/m3
corresponds to a 17,uM solution, 0.531ug/cm3 and to a partial pressure of
1600Pa or 12mmHg.
This concentration corresponds to 0.037cm302/100cm3 tissue with oxygen volume
measured
at standard temperature and pressure.
[0191] Tissue power demands vary considerably, depending on the
tissue type and
overall activity level. For this example, Pit';';',e is set to a typical
resting power demand [12].
For comparison, peak metabolic rate in human tissue can be as high as 200kW/m
3 [27].
[0192] Conventional fuel cells have efficiencies around 50%
[12]. While the
efficiency of the fuel cells required for micron-size robots remains to be
determined, for
definiteness the example uses fuel cell efficiency frobot= 50%.
Variations in Circulation Paths
[0193] The above discussion addresses average circulation times.
However,
circulation paths differ depending on the length of the circuit. Paths through
organs close to
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the heart typically have shorter paths than average, while paths through the
legs typically are
longer than average. Additional variation occurs due to differences in flow
speed, such as
slow flow of blood through the spleen. Additional distance and/or time may
cause oxygen
depletion in longer/slower circuits that would not occur for the same number
of robots in
average circulation. Modeling such variation has found that the impact of such
variations is
relatively minor for numbers of robots either 1011 or fewer, or 1012 or more.
For intermediate
numbers, such as 3 x 1011 robots, variation in circulation path length and/or
flow speed can
have a significant impact on oxygen availability in the later portions of the
circuit, and it may
therefore be beneficial to adjust the operation of individual robots based on
the circulation
path they are currently in. Robots having a locomotive capability could select
an appropriate
circulation path to avoid situations where insufficient oxygen is available
(such as avoiding
longer/slower paths when an insufficient amount of oxygen has been stored,
avoiding
capillaries with a large number of other robots, etc.) or to take advantage of
shorter/faster
circuits when greater availability of oxygen would be beneficial (such as when
conducting
high-power tasks or when filling the robot's storage tank).
[0194] In general, if robots can detect that they are on a
shorter/faster circulation path
they may be able to ignore criteria that would otherwise determine that they
are in an
absorption-limiting need condition, and thus can continue to absorb oxygen to
operate in a
higher-power mode. Similarly, robots could delay high-energy tasks
(computation, long-
range communication, maintenance routines, etc.) until they detect that they
are in a short
circulation loop Information that robots could employ to determine that they
are on a shorter
circuit path could include analyzing rate of change of branch size, overall
location
information (such as external navigation information provided by acoustic
transducers or
other transmitters), elapsed time or distance before reaching a capillary,
temperature, and/or
chemical variation. [12]
[0195] Robots that can detect that they are on a longer/slower
circulation path may
apply more strict criteria to determine that they are in an absorption-
limiting need condition,
to reflect that there is a longer time before oxygen can be replenished in the
lung capillaries
(or before merging with less-depleted blood from shorter circuits in larger
veins). Robots that
store oxygen could make a determination that a reactant need condition exists
based on
detecting that they are in a longer/slower circuit, or by criteria such as
time elapsed or
distance traveled since leaving the lung capillaries. For example, since the
average circuit
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time is one minute, robots could wait one minute after leaving a lung
capillary to release
reactant (either internally for the robot's own use or externally to supply
other robots), as
such time would indicate the robot to be on a longer/slower path. Such
determination of a
reactant need condition could be combined with additional considerations
discussed above.
For example, a robot could release stored oxygen after one minute only after
already having
stored a prescribed amount of oxygen during multiple passages through the lung
capillaries.
Where the robots flow through the capillaries due to blood circulation (i.e.,
without
employing locomotion or anchoring to prolong their period in the lung) a model
of circulation
paths that accounts for variations of length and flow speed shows that a robot
of 1[1m radius
with 1/3 of its volume used for storage should have a full tank after 20
passages through the
lungs In such a case, the storage tank remains relatively full if the robot
operates at 100pW
using stored oxygen after one minute for most circulation paths, but may be
depleted on an
especially long/slow path. Alternatively, a robot could use stored oxygen
after one minute
whenever stored oxygen is available (a similar model of circulation paths
shows that robots
operating at 100pW using stored oxygen after one minute can run out of oxygen
on longer
paths, and do not fill more than 30% of their tank capacity, and thus a
smaller fraction of
robot volume may be devoted to storage when such an operation scheme is
employed).
[0196] Variation in circulation paths may result in robots in
any particular location in
the fluid system having varying amounts of stored oxygen, depending on how
much they
have been able to store and how much they have used due to their history of
traveling on
shorter or longer circulation paths. Robots may be able to take advantage of
such variation by
having those robots with ample stored oxygen undertake high-energy tasks
(computation,
long-range communication, maintenance routines, etc.) using data communicated
to them
over short range by robots with less stored oxygen, allowing those robots to
operate in a
lower-power mode.
Active Mixing
[0197] The variation in circulation paths discussed above gives
rise to another
example of robot operation to reduce the impact of a large number of robots
absorbing a
chemical of interest, when intermediate-size veins from paths of different
lengths/times
merge together. In the case where a vein carrying blood from a longer/slower
circuit path
merges with a vein carrying blood from a shorter/faster circuit path, they
blood from the
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longer path typically has a lower oxygen concentration due to consumption by
robots over a
greater time since leaving the lungs. For veins of intermediate size
(generally in the range of
millimeters), the combined flow in the larger vessel has a gradient of oxygen
concentration
across its section for some distance downstream of the merge. This gradient
results from the
time it takes for convection and diffusion to distribute the oxygen from the
oxygen-rich blood
from the shorter path vein across the vessel to mix with the oxygen-depleted
blood from the
longer path vein. As a result, when robots continuously absorb and consume
oxygen, such
continued absorption may deplete the oxygen in one region of the merged vessel
to the point
where it is insufficient for robot operation and/or be detrimental to cells in
the vessel wall in
such region. This is particularly a concern for robots located at or near the
vessel wall in such
region, where blood flow is slower and thus absorption takes place for a
longer time.
[0198] FIGS. 36 and 37 illustrate such a case, where two veins
(3602, 3604) that are
each 2mm in diameter merge together into a 2.5 diameter vessel 3606 and where
1012 robots
of 1 mm radius are distributed throughout the bloodstream and absorbing all
the oxygen that
reaches their surfaces (similar geometry to the case discussed for FIG. 28).
The axes show
dimensions in millimeters, and the gradation of shading represents the
concentration of
oxygen, ranging from the darkest shade (starting point of vein 3604)
representing 2.0 x 1022
oxygen molecules per cubic meter and the lightest shade representing no
oxygen. Vein 3602
carries blood from a longer circuit path, having a uniform concentration of
0.5 x 1022 oxygen
molecules per m3 at its start, 8mm upstream of the merge. Vein 3604 carries
blood from a
shorter circuit path, having a uniform concentration of 2.0 x 1022 oxygen
molecules per m3 at
its start. FIG. 37 shows the concentration across the merged vessel 3606 at a
location 8mm
downstream of the merge (section 37 of FIG. 36). Due to limited mixing of
oxygen across the
vessel and continued absorption by the robots, the merged flow is still
largely separated into
an oxygen-depleted region 3608 (where robots in the flow from vein 3602 have
continued to
absorb the remaining oxygen, which has not been sufficiently replaced by
diffusion or
convection) and a higher-oxygen region 3610 (where robots in the flow from the
vein 3604
have continued to absorb oxygen, but where there is still ample oxygen
available due to the
higher initial concentration). The higher-oxygen region 3610 can be considered
as a high-
reactant region.
[0199] To mitigate the impact of such gradient, robots can be
programmed to actively
transport oxygen across the merged vessel to actively distribute oxygen across
the section. In
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effect, the oxygen-rich region of the vessel serves as a high-reactant region,
and robots absorb
and store reactant when in such region, and then release such reactant from
storage when
conditions indicate that they have reached (or are statistically likely to
have reached) a
location where a reactant need condition exists. One simple operational scheme
is for the
robots to periodically store reactant when they determine that they are in a
high-reactant
region, move in series of randomly-directed segments, and then release the
stored reactant.
This would have the effect of increasing the diffusion coefficient for the
reactant. Other
schemes could be more directed to increase efficiency of redistribution (at
the expense of
requiring more complex robot behavior). Examples of such directed transport
include
detecting the reactant gradient and moving to a location of low reactant
before releasing
stored reactant, determining vessel diameter and moving along the vessel wall
to an opposite
location (based on travelling a distance of half the vessel circumference),
moving responsive
to other robots communicating that the location of a low-reactant region, etc.
[0200] As an example of the effect of increased diffusion that
could be provided by
such active mixing, FIG. 38 shows merging blood flows with similar parameters
to those
used for FIG. 36, but for a smaller vessel where the relative contribution of
diffusion to
convection in distributing oxygen across the vessel after merging is greater,
and thus the
Pecl et number (see Eq. 8) is lower. In FIG. 38, two 100[tm diameter vessels
(3802, 3804)
merge into a 125ittm diameter vessel 3806. Because of the smaller diameter,
flow speed is
accordingly lower (see Eq. 11), so the flow speed is 30% of the speed in the
vessels shown in
FIG. 36. The Peclet number for the vessels shown in FIG. 38 is 45, compared to
3000 for the
vessels shown in FIG. 36. For the vessels shown in FIG. 36, using active
transport by robots
to increase the effective diffusion rate by a factor of about 70 would result
in a distribution of
oxygen in the merged vessel 3606 similar to that seen in the smaller merged
vessel 3806 due
to increased diffusion. In this case, the gradient in the merged vessel 3806
decreases in a
small distance downstream of the merger, and there is no zone where the flow
from the
longer-path vein 3802 becomes increasingly oxygen-depleted.
[0201] Increased mixing to avoid having a reactant-depleted
region may be necessary
for proper operation of the fluid system, but could also be advantageous for
averaging the
concentration to increase the accuracy of generalized modeling of the fluid
system by making
the concentration at any particular point more consistent with the generalized
model. While
providing such active mixing may complicate the design and operation of
individual robots, it
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can provide more accurate modeling to simplify the design and implementation
of overall
robot operations and mission planning, as the actual situations encountered by
individual
robots will more closely match the generalized conditions assumed in models of
the fluid
system.
[0202] The above discussion, which employs particular examples
for illustration,
should not be seen as limiting the spirit and scope of the appended claims.
U.S. Patents
6,955,670; 8,343,425; 10,220,004; and 11,526,182; and U.S. Publications
2008/0161779,
2008/0202931, 2010/0284924, and 2012/0015428 are all incorporated herein by
reference in
those jurisdictions where such incorporation is appropriate, except where any
material
conflicts with the present text.
References
[1] Hellmut G. Augustin and Gou Young Koh. Organotypic vasculature: From
descriptive
heterogeneity to functional pathophysiology. Science, 357:eaa12379, 2017.
[2] Prosenjit Bagchi. Mesoscale simulation of blood flow in small vessels.
Biophysical
Journal, 92:1858-1877, 2007.
[3] A. C. L. Barnard, L. Lopez, and J. D. Hellums. Basic theory of blood flow
in capillaries.
Micro vascular Research, 1:23-34, 1968.
[4] Robert H. Bartlett. Alice in intensiveland: Being an essay on nonsense and
common sense
in the ICU, after the manner of Lewis Carroll. Chest, 108:1129-1139, 1995.
[5] Howard C. Berg. Random Walks in Biology. Princeton Univ. Press, 2nd
edition, 1993.
[6] Fei Cao etal. Photoacoustic imaging in oxygen detection. Applied Sciences,
7:1262, 2017.
[7] Alfred Clark, Jr. et al. Oxygen delivery from red cells. Biophysical
Journal, 47:171-181,
1985.
[8] Colin A. Cook et al. Oxygen delivery from hyperbarically loaded microtanks
extends cell
viability in anoxic environments. Biomaterials, 52:376-384, 2015.
[9] J. Ernsting. The effect of brief profound hypoxia upon the arterial and
venous oxygen
tensions in man. J. of Physiology, 169:292-311, 1963.
[10] Joseph Feher. Quantitative Human Physiology. Academic Press, 2nd edition,
2017.
[11] Robert A. Freitas Jr. Exploratory design in medical nanotechnology: A
mechanical
artificial red cell. Artificial Cells, Blood Substitutes and Immobilization
Biotechnology,
26:411-430, 1998.
- 84 -
CA 03223312 2023- 12- 18
WO 2023/229746
PCT/US2023/018787
[12] Robert A. Freitas Jr. Nanomedicine, volume I: Basic Capabilities. Landes
Bioscience,
Georgetown, TX, 1999. Available at www.nanomedicine.com/NIVII.htm.
[13] Robert A. Freitas Jr. Nanomedicine, volume HA: Biocompatibility. Landes
Bioscience,
Georgetown, TX, 2003. Available at www.nanomedicine.com/NMIIA.htm.
[14] Ivor T. Gabe et al. Measurement of instantaneous blood flow velocity and
pressure in
conscious man with a catheter-tip velocity probe. Circulation, 40:603-614,
1969.
[15] Daniel Goldman. Theoretical models of microvascular oxygen transport to
tissue.
Microcirculation, 15:795-811, 2008.
[16] John Happel and Howard Brenner. Low Reynolds Number Hydrodynamics.
Kluwer, The
Hague, 2nd edition, 1983.
[17] Tad Hogg. Coordinating microscopic robots in viscous fluids. Autonomous
Agents and
MultiAgent Systems, 14(3):271-305, 2007.
[18] Tad Hogg. Stress-based navigation for microscopic robots in viscous
fluids. J. of Micro-
Bio Robotics, 15:59-67, 2018.
[19] Tad Hogg and Robert A. Freitas Jr. Chemical power for microscopic robots
in capillaries.
Nanomedicine: Nanotechnology, Biology, and Medicine, 6:298-317, 2010.
[20] Tad Hogg and Robert A. Freitas Jr. Acoustic communication for medical
nanorobots. Nano
Communication Networks, 3:83-102, 2012.
[21] W. Huang et al. Morphometry of the human pulmonary vasculature. J. of
Applied
Physiology, 81:2123-2133, 1996.
[22] Muhammad Saad Khan et al. Oxygen-carrying micro/nanobubbles: Composition,
synthesis techniques and potential prospects in photo-triggered theranostics.
Molecules,
23:2210, 2018.
[23] August Krogh. The number and distribution of capillaries in muscles with
calculations of
the oxygen pressure head necessary for supplying the tissue. J. of Physiology,
52:409-415,
1919.
[24] Michael LaBarbera. Principles of design of fluid transport systems in
zoology. Science,
249:992¨ 1000, 1990.
[25] C. S. Lim et al. Venous hypoxia: A poorly studied etiological factor of
varicose veins.
of Vascular Research, 48:185-194, 2011.
[26] Benjamin Mauroy. Following red blood cells in a pulmonary capillary.
ESA1M
Proceedings, 23:48-65, 2008.
[27] B. J. McGuire and T. W. Secomb. A theoretical model for oxygen transport
in skeletal
muscle under conditions of high oxygen demand. Journal of Apphed Physiology,
91:2255-
2265, 2001.
- 85 -
CA 03223312 2023- 12- 18
WO 2023/229746
PCT/US2023/018787
[28] George McHedlishvili and Manana Varazashvili. Hematocrit in cerebral
capillaries and
veins under control and ischemic conditions. I of Cerebral Blood Flow &
Metabolism,
7:739-744, 1987.
[29] Meir Nitzan et al. Pulse oximetry: fundamentals and technology update.
Medical Devices:
Evidence and Research, 7:231-239, 2014.
[30] Aleksander S. Popel. Theory of oxygen transport to tissue. Critical
Reviell'S in Biomedical
Engineering, 17:257-321, 1989.
[31] Manu Pralcash and Neil Gershenfeld. Microfluidic bubble logic. Science,
315:832-835,
2007.
[32] A. R. Pries, D. Neuhaus, and P. Gaehtgens. Blood viscosity in tube flow:
dependence on
diameter and hematocrit. American of Physiology, 263:H1770¨H1778, 1992.
[33] Mohammad S. Razavi, Ebrahim Shirani, and Ghassan S. Kassab. Scaling laws
of flow rate,
vessel blood volume, lengths, and transit times with number of capillaries.
Frontiers in
Physiology, 9:581, 2018.
[34] Erik L. Ritman and Amir Lerman. The dynamic vasa vasorum. Cadiovascular
Research,
75:649-658, 2007.
[35] Siam Singhal et al. Morphometry of the human pulmonary arterial tree.
Circulation
Research, 33:190-197, 1973.
[36] Todd M. Squires and Stephen R. Quake. Microfluidics: Fluid physics at the
nanoliter scale.
Reviews of Modern Physics, 77:977-1026, 2005.
[37] Hagit Stauber et al. Red blood cell dynamics in biomimetic microfluidic
networks of
pulmonary alveolar capillaries. Biomicrofluidics, 11:014103, 2017.
[38] Soren Strauss et al. Phyllotaxis: is the golden angle optimal for light
capture? New
Phytologist, 225:499-510, 2019.
[39] C. A. Taylor and C. A. Figueroa. Patient-specific modeling of
cardiovascular mechanics.
Annual Review of Biomedical Engineering, 11:109-134, 2009.
[40] Mary I. Townsley. Structure and composition of pulmonary arteries,
capillaries and veins.
Comprehensi e Physiology, 2:675-709, 2012.
[41] Ewald R. Weibel and Domingo M. Gomez. Architecture of the human lung.
Science,
137:577¨ 585, 1962.
[42] R. L. Whitmore. A theory of blood flow in small vessels. I. of Applied
Physiology, 22:767
771, 1967.
[43] David F. Wilson and Franz M. Matschinsky. Hyperbaric oxygen toxicity in
brain: A case
of hyperoxia induced hypoglycemic brain syndrome. Medical Hypotheses,
132:109375,
2019.
- 86 -
CA 03223312 2023- 12- 18
