Note: Descriptions are shown in the official language in which they were submitted.
SENSING AND OPERATION OF DEVICES IN VISCOUS FLOW
FIELD OF INVENTION
[0001] The present invention is directed to improvements in the decisions and
operations of devices, including robots, in viscous fluid, at least partially
through
efficient analysis of instantaneous data collected via passive sensors.
BACKGROUND
Fluid Flow Analysis and Applications
[0002] Fluid flow is important to multiple fields of technology and may be
characterized
for many reasons, including an interest in the fluid flow itself, or an
interest the effects
of the fluid flow (e.g., exerting forces on an object). To analyze fluid flow,
various
sensors may be used, and dyes or particles can help visualize flow patterns.
Some of
these sensors are microscopic or molecular in size. (Grosse and Schroder, "The
Micro-
Pillar Shear-Stress Sensor MPS(3) for Turbulent Flow," Sensors, 2009; Martin,
Brooks et
al., "Complex fluids under microflow probed by SAXS: rapid microfabrication
and
analysis," Journal of Physics: Conference Series, 2010; Mustafic, Huang et
al., "Imaging
of flow patterns with fluorescent molecular rotors," J Fluoresc, 2010).
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[0003] Fluid flow can have biological effects. For example, fluid flow is
known to affect
gene expression (Zou, Liu et al., "Flow-induced beta-hairpin folding of the
glycoprotein
lbalpha beta-switch," Biophys1, 2010), and cells that fluoresce when subjected
to shear
stress have been created for use as sensors (Varma, Hou et al., "A Cell-based
Sensor of
Fluid Shear Stress for Microfluidics," 17th International Conference on
Miniaturized
Systems for Chemistry and Life Sciences, Freiburg, Germany, 2013). Shear force
is also
believed to affect the vasculature (LUTZ, CANNON et al., "Wall Shear Stress
Distribution
in a Model Canine Artery during Steady Flow," Circulation Research, 1977).
Rheotaxis
(navigation by facing into an oncoming current) in cells has also been studied
(Kantsler,
Dunkel et al., "Rheotaxis facilitates upstream navigation of mammalian sperm
cells,"
eLife, 2014).
[0004] Fluid forces can be used for particle handling. Such techniques include
inertial
focusing, and can be used to position objects within a fluid (e.g.,
microspheres or cells in
microfluidics systems) into specific bins for sorting, or otherwise position
the objects
(e.g., for analysis in a lab-on-a-chip or assay scenario). (Sharp, Adrian et
al., "Liquid
Flows in Microchannels," MEMS Introduction and Fundamentals, CRC Press, 2005;
Petersson, Aberg et al., "Free Flow Acoustophoresis: Microfluidic-Based Mode
of
Particle and Cell Separation," Anal. Chem., 2007; Karimi, Yazdi et al.,
"Hydrodynamic
mechanisms of cell and particle trapping in microfluidics," Biomicrofluidics,
2013; Martel
and Toner, "Inertial focusing in microfluidics," Annu Rev Biomed Eng, 2014)
[0005] Software for the simulation and analysis of fluid flow is freely and
commercially
available. For example, SOLIDWORKS (Waltham, MA USA) offers a "Flow
Simulation"
module, which performs computational fluid dynamics calculations. Autodesk's
(San
Rafael, CA USA) CFD software offers similar capabilities, as does COMSOL's
(Burlington,
MA USA) CFD (Computational Fluid Dynamics) and FSI (Fluid Structure
Interaction)
modules. OpenFOAM (openfoam.com) is an open source computational fluid
dynamics
package. More general tools, such as Mathematica (Wolfram Research, Champaign,
IL
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USA) and MATLAB (MathWorks, Natick, MA USA), can also be used, and statistical
analysis of results can be done via many software packages, including some of
those
already listed, and the free R (r-project.org). These lists are only
exemplary; many other
packages are available, and custom software could also be used.
[0006] Computing means which can be used include conventional CPUs, GPUs
(graphical
processing units), FPGAs (field-programmable gate arrays), ASICs (application-
specific
integrated circuits), mechanical computers, embedded microprocessors (in which
we
include microcontrollers), and application-specific mechanical devices (for
example, a
device similar to a mechanical odometer could be used to register sensor
counts, time,
or other quantities, and such a device, being optimized for a single purpose,
can be
smaller and more efficient than general purpose computational devices). For
convenience, we may refer to all such computational means or devices as a
"CPU".
[0007] For many analysis techniques, such as FEA (finite element analysis) or
FEM (finite
element method), memory (e.g., RAM, or other memory or data storage means)
size
and memory bandwidth to one or more processors can be more limiting than CPU
speed. The storage space required for the model itself is generally not a
problem, and
models themselves can be stored on CD, DVD, thumb drives, hard drives, or
other data
storage means. However, the memory required to analyze a given model can be
problematically-large because memory requirements increase as degrees of
freedom
increase. Models with many elements or degrees of freedom may require memory
beyond the capacity of, e.g., the average personal computer. Although virtual
memory
can be used, this substantially slows down the computations.
[0008] In general, solving fluid dynamics models in real-time or near real-
time may be
challenging or even impossible, depending on factors such as the hardware
used, the
available power (e.g., the same hardware may be run at different frequencies
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depending on available power and cooling), model complexity, computations
required
and algorithms used, and acceptable delay.
Rheological Sensors
[0009] Rheological sensors can aid in measuring properties of fluid flow, and
such
sensors be anywhere from macroscopic, to micron-scale (e.g., MEMS-based) or
molecular-scale, and can measure flow, viscosity, velocity, shear and pressure
(both of
which are components of stress, and could be measured with a single type of
sensor if
desired), temperature, and other quantities (Lofdahl and Gad-el-Hak, "MEMS-
based
pressure and shear stress sensors for turbulent flows," Meas. Sci. Technol.,
1999; Akers,
"A Molecular Rotor as Viscosity Sensor in Aqueous Colloid Solutions," Journal
of
Biomechanical Engineering, 2004; Haidekker, Akers et al., "Sensing of Flow and
Shear
Stress Using Fluorescent Molecular Rotors," Sensor Letters, 2005;
Soundararajan,
Rouhanizadeh et al., "MEMS shear stress sensors for microcirculation," Sensors
and
Actuators A: Physical, 2005; Grosse and Schroder, "The Micro-Pillar Shear-
Stress Sensor
MPS(3) for Turbulent Flow," Sensors, 2009; Haidekker, "Local flow and shear
stress
sensor based on molecular rotors," US7517695, 2009; Wang, Chen et al., "MEMS-
based
gas flow sensors," Microfluidics and Nanofluidics, 2009; Haidekker, Grant et
al.,
"Supported molecular biolfluid viscosity sensors for invitro and in vivo use,"
US7670844,
2010; Mustafic, Huang et al., "Imaging of flow patterns with fluorescent
molecular
rotors," _I Fluoresc, 2010; Wu, Day et al., "Shear stress mapping in
microfluidic devices by
optical tweezers," OPTICS EXPRESS, 2010; Haidekker, Grant et al., "Supported
molecular
biofluid viscosity sensors for in vitro and in vivo use," US7943390, 2011;
Eswaran and
Malarvizhi, "MEMS Capacitive Pressure Sensors: A Review on Recent Development
and
Prospective," International Journal of Engineering and Technology, 2013;
Zhang, Sun et
al., "Red-Emitting Mitochondrial Probe with Ultrahigh Signal-to-Noise Ratio
Enables
High-Fidelity Fluorescent Images in Two-Photon Microscopy," Anal Chem, 2015).
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[0010] Although not technically falling under rheological sensors, numerous
types of
other sensors exist that could provide additional data, such as gravity-based
sensors,
magnetic field sensors, angle sensors, and accelerometers. Such sensors, and
many
more, are well-known, but for examples see (Huikai and Fedder, "Fabrication,
characterization, and analysis of a DRIE CMOS-MEMS gyroscope," IEEE Sensors
Journal,
5, 2003; Herrera-May, Aguilera-Cortes et al., "Resonant Magnetic Field Sensors
Based
On MEMS Technology," Sensors (Basel), 10, 2009; Koka and Sodano, "High-
sensitivity
accelerometer composed of ultra-long vertically aligned barium titanate
nanowire
arrays," Nat Commun, 2013; Middlemiss, Bramsiepe et al., "Field Tests of a
Portable
MEMS Gravimeter," Sensors (Basel), 11, 2017).
SUM MARY
[0011] [Intentionally left blank].
[0012] Techniques are disclosed for controlling the actions of a device
(including robots)
in fluid systems having viscous flow, based on passive sensing of fluid flow
data (for
example, pressure and shear forces), which may be analyzed using quasi-static
methods
and machine learning, to derive information relating to the position and/or
movement
of the device, other objects in the fluid, and features of the fluid systems
such as
information about the fluid flow itself, and the geometry of the fluid
boundaries.
Examples of information about the device itself include its position,
orientation, and/or
movement in the channel. Examples of information about the fluid system
include fluid
flow velocity, channel size, detection of features such as curves, branches,
and merges,
and/or the presence of additional objects in the channel besides the device in
question,
either static or moving. Time courses may be considered in that multiple
measurements
Date Recue/Date Received 2020-11-04
over time may be analyzed for trends (e.g., changes in the curvature of the
vessel as the
device moves through the fluid system ¨ this is in some sense time dependent,
but only
because the device location changes with time, not because the flow is
turbulent and
cannot be understood in an instantaneous manner), but each of these
measurements is
still typically collected instantaneously and the measurements for a
particular time are
analyzed in a quasi-static manner.
[0013] This strategy allows for advantages including faster computation,
reduced
hardware requirements, and reduced sensor usage. These techniques provide
information on the device and the fluid system that can be used to
characterize the
system, such as by mapping features of the fluid system (curves, bumps, branch
points,
merge points, areas where the flow indicates a possible leak, etc.) Maps of
the fluid
system may be created, and such maps or other models of the system can be used
to
direct devices to desired locations in the system. Information on the fluid
system
features can also be used to tell the devices when to take actions, such as
navigating
branch points, adhering to the channel walls, or removing deposits found on
the walls.
BRIEF DESCRIPTION OF THE FIGURES
[0014] Fig. 1 is a schematic view of a device, illustrating various sensors,
and power,
communication, computation, and other mechanisms that could be incorporated.
[0015] Fig. 2 is a view of a spherical device operating in a cylindrical
vessel, used for
reference discussing examples of how surface stress measurements can be
processed to
obtain information on the device position and motion, and information on the
geometry
of the vessel.
[0016] Fig. 3 is a view of the spherical device shown in Fig. 2, illustrating
an array of
stress sensors distributed across the surface of the device. Fig. 3 also shows
a direction
of movement and direction to the nearest vessel wall for the situation shown
in Fig. 2.
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[0017] Fig. 4 is a view of the section 4-4 of Fig. 2, providing a 2-
dimensional
representation of the device and vessel. Region 6 shows the bounds of the area
shown
in greater detail in Fig. 6.
[0018] Figs. 5A and 5B respectively illustrate the normal and tangential
(shear) stresses
across the surface of the device resulting from the fluid flow and the device
movement
relative to the fluid and boundaries in the situation shown in Figs. 2 and 4.
[0019] Figs. 6A and 6B illustrate a 2-dimensional representation of the flow
that causes
surface stresses on the device, corresponding to the region 6 shown in Fig. 4.
Fig. 6A
illustrates the streamlines and fluid velocities with respect to the vessel,
while Fig. 6B
illustrates the streamlines and flow velocities with respect to the device.
[0020] Figs. 7A and 7B compare results for 2-dimensional and 3-dimensional
analyses of
the stresses on the device, corresponding to the situation illustrated in
Figs. 2 and 4. Fig.
7A compares the normal and tangential stresses about the device at the
locations of
several sensors, while Fig. 7B compares the speed along the vessel and angular
velocity
for 2D and 3D cases, as the relative position of the device in the vessel is
varied.
[0021] Fig. 8A illustrates a 2-dimensional representation of the resulting
stress vectors
at the locations of 30 sensors on the device, for the situation shown in Fig.
4. Fig. 8B
illustrates the resulting first six Fourier components that result from a
Fourier
decomposition of stresses as a function of angular position.
[0022] Fig. 9 illustrates the positions of a 2D array of sensors on the device
shown in
Figs. 2-4 and an orientation line used to define a front of the device for
reference
when analyzing the stress pattern across the device surface.
[0023] Figs. 10A & 10B are plots showing how both vessel diameter (Fig. 10A)
and
relative position of the device (Fig. 10B) relate to the first two principal
Fourier
components of the stresses. For both parameters, values fall within distinct
regions,
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allowing machine learning techniques to accurately evaluate each of these
parameters
based on just the first two components.
[0024] Fig. 11 is a plot comparing actual values for the relative position of
the device to
calculated values based on machine learning samples.
[0025] Fig. 12 is a plot comparing actual values for vessel diameter to
calculated values
based on machine learning samples, indicating that the accuracy is to some
degree
dependent on the relative position of the device in the vessel, with devices
near the
center of the vessel providing less accurate values.
[0026] Fig. 13 is a plot comparing actual and calculated values for distance
from the
device to the nearest wall, derived from the values for relative position and
vessel
diameter. Again, the accuracy is dependent on relative position.
[0027] Fig. 14 is a plot comparing actual to calculated values for angular
velocity of the
device, with the calculated value being obtained by monitoring the change in
the
pattern of instantaneous stresses after a short time interval.
[0028] Fig. 15 is a plot comparing actual and calculated values for speed of
the device
along the vessel.
[0029] Fig. 16 provides a graphic representation of the calculated parameters
for
direction to the wall, vessel diameter, and distance to the wall, compared to
the actual
parameters.
[0030] Fig. 17 illustrates the path of a device traveling passively through a
vessel
containing a straight section (with a discontinuity in the vessel wall) and a
curve.
[0031] Fig. 18 illustrates the device when moving through the curve of the
vessel shown
in Fig. 17.
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[0032] Figs. 19A and 19B illustrate the difference in stress experienced due
to a
discontinuity versus a curve. Fig. 19A is a plot comparing the actual and
calculated
angular velocity of the device, while Fig. 19B is a graph comparing the
correlation
between stress patterns separated by a short time interval.
[0033] Figs. 20A-20D are plots comparing actual and calculated values of
parameters
for the position of the device as a function of time as it moves through the
vessel shown
in Figs. 17 and 18. Fig. 20A compares values for vessel diameter, Fig. 20B
compares
directions to the nearest point on the wall and direction of motion, Fig. 20C
compares
the distance from the device to the nearest wall, and Fig. 20D compares speed
of the
device along the vessel.
[0034] Figs. 21A and 21B illustrate 2-dimensional analyses which are used to
compare
the stresses resulting from a device passing through a branched vessel (shown
in Fig.
21A) versus passing through a curved vessel (shown in Fig. 21B).
[0035] Figs. 22A-22D illustrate the streamlines and fluid velocities for the
device
positioned in the branched and curved vessels as shown respectively in Figs.
21A and
21B; Figs. 22A & 22B show the region 22-1 of Fig. 21A, while Figs. 22C & 22D
show the
region 22-2 of Fig. 21B. Similarly to the representations for the straight
vessel shown in
Figs. 6A and 6B, Fig. 22A shows fluid velocity with respect to the vessel and
Fig. 2213
shows fluid velocity with respect to the device, both for the branched vessel.
Fig. 22C
shows fluid velocity with respect to the vessel and Fig. 22D shows fluid
velocity with
respect to the device for the curved vessel.
[0036] Fig. 23 illustrates the stress vectors relating to the flows shown in
Figs. 22A-
22D, in a manner similar to the stress vectors shown in Fig. 8A.
[0037] Fig. 24 is a plot that compares the correlation between stress patterns
after a
short time interval, for the device traveling through the branched vessel and
curved
vessel shown in Figs. 21A & 21B.
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[0038] Fig. 25 is a plot of minimum correlation along the path of the device
for devices
traveling in either a straight, branched, or curved vessel, starting from
different relative
positions in the vessel. Unlike the plot shown in Fig. 10, where the values
fall within
distinct regions, in this case there is some overlap for devices that start
near the center
of the vessel.
[0039] Fig. 26 is a plot showing probabilities of a branch being encountered,
based on a
classifier developed by analyzing the correlation of current stress on the
device to a
previously measured stress, the calculated relative position, and the first
Fourier
component of the stress pattern. A properly set threshold value for the
probability can
distinguish branched vessels from curved vessels.
[0040] Figs. 27A and 278 illustrate device paths through branched (Fig. 27A)
and curved
(Fig. 27B) vessels, starting from different relative positions.
[0041] Fig. 28 is a plot illustrating branch classifier performance, plotting
fraction of true
positives against the fraction of false positives as the probability threshold
value for the
classifier is changed.
[0042] Fig. 29 is a plot illustrating fractional path length required for the
classifier to
exceed a particular threshold fraction of true positives, for both forward
(from large
vessel into branch) and reverse (from branch merging into larger vessel)
paths.
[0043] Fig. 30 depicts a graphic representations of calculated values (similar
to the
graphic representations discussed with reference to Fig. 16) for four devices
in a vessel,
showing one example of how the presence of other objects can affect the
calculated
parameters, particularly for a device positioned in the middle of the group.
[0044] Fig. 31 is an illustration showing an example of a device in a vessel
with
additional objects; in this case, the vessel could be a capillary and the
additional objects
could be red blood cells (which can substantially deform in narrow
capillaries, hence
CA 3038104 2019-03-26
their geometric representation), however, as is true of all analyses herein,
size scales
and other specifics may vary greatly as long as the flow is still viscous.
[0045] Figs. 32A-32C illustrate graphic representations of values for a device
that is
ellipsoidal, rather than spherical. The calculated values change as the device
moves with
a tumbling motion, from a position with its semi-major axis perpendicular to
the vessel
wall (Fig. 32A), to a 450 angle (Fig. 328), to a position where the semi-major
axis is
parallel to the wall (Fig. 32C).
[0046] Fig. 33 is a graph evaluating the impact of signal noise on the
classifier evaluated
with reference to Fig. 28; Fig. 33 graphs the area under the curve of Fig. 28
for
increasing percentages of signal noise in the sensors used to make the
calculated
parameters used for the classifier.
[0047] Fig. 34 is a schematic illustration that shows an overview of
techniques that can
be employed to derive values of several parameters of device position and
motion, as
well as vessel geometry, according to the examples discussed with respect to
Figs. 1-
15.
[0048] Figs. 35-37 are flow charts that broadly illustrate examples of methods
for
collecting data (Fig. 35), training inference models (Fig. 36), and employing
such
inference models in a device (Fig. 37).
[0049] Figs. 38 & 39 are flow charts illustrating examples of a mapping
procedure (Fig.
38) for comparing feature data from multiple devices and constructing a map of
a fluid
system, and a procedure (Fig. 39) for a device to use such a map to aid in
performing a
prescribed mission.
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DETAILED DESCRIPTION
Terminology
[0050] "Boundaries" are divisions between the fluid and objects adjacent to
the fluid,
surrounding the fluid, or within the fluid. Examples include the wall (or
"channel,"
"vessel," or other appropriate term) surrounding a fluid a stationary object
within the
fluid, or a moving object within the fluid.
[0051] "Boundary layers" are transitions, often sharp transitions, of one or
more
properties (e.g., the velocity or vector of a fluid flow, or a chemical,
thermal, or other
gradient within the fluid) of a fluid flow. Boundary layers may be caused by
the fluid
flow itself (although at low Reynolds numbers, gradual transitions are the
norm), or
maybe caused by boundaries interrupting the natural flow of the fluid.
[0052] A "channel", unless context requires otherwise, is the boundary of a
fluid
system. Such a boundary may also be referred to as a wall or vessel, or any
other term
that conveys that it provides means for holding the fluid system in a
particular shape
(which shape is not necessarily static or rigid, though it may be). Specific
examples may
use terminology appropriate to the applicable field. For example, the fluid
boundaries in
an industrial system may be referred to as pipes, while in a biological
context, they may
be referred to as vasculature or capillaries.
[0053] "Features" of a fluid flow system include boundaries and their
properties, fluid
and its properties, fluid flow and its properties, and objects within the
fluid and their
properties. For example, features could include positions of boundaries
holding the
fluid, positions of objects within the fluid, characteristics of the fluid or
fluid flow such as
viscosity, velocity, direction, or the nature of any gradients present, such
as gradients in
temperature, velocity, or chemical concentrations. The term "feature" or
"features" is
also used in other contexts, such as using machine learning data-processing
techniques
to extract "features" from data. Context should make the intended meaning
clear.
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[0054] "Fluid flow system," "fluid system" or simply "system" when context
makes the
meaning clear, refers to any system of flowing fluid(s) (including gases) and
any
boundaries, including walls and other objects within the fluid. Examples
include, but are
not limited to, systems frequently containing water or other common solvents
(e.g.,
microfluidics or "lab on a chip" systems), biological systems (e.g., blood
flow within
vasculature, lymph flow within lymphatic channels, or gas flow within lungs),
and
industrial systems (which may deal with highly-viscous materials, from oil, to
foodstuffs
such as peanut butter, honey, ketchup and sour cream, and which, as a result,
may have
viscous flow even at relatively large sizes, providing some cases where
devices could be
at least several inches in size).
[0055] "Harmonic analysis" includes any of various mathematical analysis
techniques in
which data are represented as the superposition of basic waveforms, including
2-
dimensional and 3-dimensional Fourier transformations, spherical harmonic
techniques,
and other techniques known in the art.
[0056] "Instantaneous" measurement means without the need for continuous data
collection or time-courses. No process is literally instant. For example,
sensors take
time, even if only fractions of a second, to gather data. Computing means take
time to
analyze the data. Data transmission takes time. So, by taking "snapshots" or
"instantaneous" readings, we mean that as fast as the data representing a
system
having viscous flow can be gathered and analyzed, the desired inferences can
be made.
The distinction is that static or quasi-static systems can be analyzed
"instantaneously,"
while time-dependent systems (which is almost all familiar everyday systems)
cannot
be, because even if nothing the natural flow of the fluid, the system can
change over
time due to turbulence.
[0057] "Machine learning" includes any appropriate mathematical operations or
data
analysis which allows the desired inferences or determinations to be made,
including
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quantitative (e.g., velocity, viscosity) or qualitative (e.g., classification)
analyses.
Examples include Bayesian networks, classifiers, data mining, decision trees
(and
ensembles of decision frees such as random forests), deep learning, linear
regression,
logistic regression, neural networks, statistical analysis (descriptive and
inferential), and
wavelets. Pre- and post-processing of data, including averaging, noise
reduction,
normalization, Fourier transforms and many other techniques, is assumed to be
inherent in machine learning and used as appropriate; such techniques are well-
known.
Machine learning may take place in real-time, or not, as necessary and
convenient, and
may be performed by computational means within a device inside a system,
distributed
among multiple devices in a system, offloaded to computational means outside
the
system, or a combination thereof. References to "inferences,"
"determinations," or
other terms relating to the use of data to determine system properties, where
contextually appropriate, are synonymous with machine learning. Machine
learning is a
well-developed field, with numerous publications and books on the subject. The
following are but a small sampling of books on relevant topics in machine
learning:
(Everitt and Hothorn, "A Handbook of Statistical Analysis Using R, 2nd
Edition," CRC
Press, 2010; Bishop, "Pattern Recognition and Machine Learning (Information
Science
and Statistics)," Springer, 2011; Witten, Frank et al., "Data Mining,
Practical Machine
Learning Tools and Techniques, 3rd Edition," Burlington, MA, Elsevier, 2011;
Aster,
Borchers et al., "Parameter Estimation and Inverse Problems, 2nd Edition,"
Academic
Press, 2012; Mostafa, Ismail et al., "Learning From Data," AMLBook, 2012;
Goodfellow,
Bengio et al., "Deep Learning (Adaptive Computation and Machine Learning
series),"
MIT Press, 2016; Geron, "Hands-On Machine Learning with Scikit-Learn and
TensorFlow:
Concepts, Tools, and Techniques to Build Intelligent Systems," O'Reilly Media,
2017)
Features and Position in Fluid Systems
[0058] Fluid forces are routinely used to position objects within a fluid. The
design
problem to be solved in such cases might be stated as "An object within the
fluid flow
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starts at position X, and needs to end up at position Y. How can the fluid
flow be
designed to make that happen?"
[0059] However, there is another position-related problem to be solved, and
one which,
to the best of our knowledge, has not been previously addressed for Stokes
flow (aka,
viscous flow) scenarios. This problem might be stated as "Given the ability to
gather
fluid-flow data, what information can be determined about the location,
identity, and
characteristics of system features?"
[0060] In addition to having different goals, the context of these two
problems may be
very different due to different levels of control (or lack thereof) over
various aspects of
the respective fluid flow systeMs. Diagnostic capabilities may differ greatly
as well.
[0061] For example, in microfluidics systems or other systems designed for
particle
handling, the systems are designed to achieve some goal (e.g., move an object
from
point X to point Y). In order to do this, the designer of the system has,
within the limits
of manufacturability and cost, complete control over system design. The size
and shape
of the fluid channels can be controlled, the wall material can be controlled,
the flow rate
can be controlled, valves can be added as needed, etc. In short, almost all
aspects of the
system are amenable to being engineered so that the system meets its
functional goals.
And, to ensure that this is happening reliably, diagnostic capabilities may be
built into,
or facilitated, by the system. For example, visual (including microscopic)
inspection of
microfluidics chambers can be permitted by using a transparent cover material,
and
such inspection can ensure that the objects within the fluid are being
positioned as
desired, or that the correct number of objects end up in various bins.
[0062] Further, not only are many of the features of an engineered system
optimized
for a given purpose, but the very fact that they were engineered implies that
they are
likely to be known. There is generally no need to experimentally determine,
for
CA 3038104 2019-03-26
example, the diameter of a microfluidics channel, its shape, or the path that
it takes;
even if it was arbitrary (which is unlikely), it is still known.
[0063] Such an example contrasts with a scenario where there is little or no
control over
system design, where knowledge of at least some of the system features may
range
from incomplete to non-existent, and where the system design does not
facilitate
information gathering (e.g., a transparent cover over the system allowing
visual
inspection).
[0064] As an industrial example, assume fluids (which could be anything from
gasses, to
water, to highly-viscous fluids such as oil, or foodstuffs such as peanut
butter, honey, or
sour cream) are pumped through pipes in a processing plant. It may be
desirable to put
one or more sensor-containing objects into the fluids for quality assurance or
other data
collection, either of the fluid, of the system itself (e.g., to find leaks,
cracks, temperature
variations, contaminant buildup, map the system if it has not been completely
documented, etc.), or both. The parameters of such a system, such as the
layout and
construction of the pipes, the fluid in the pipes, and the flow velocities may
not be
amenable to being changed. And, it is likely that these parameters have not
been
engineered to be able to easily determine an object's location at a given
point in time
(for example, the pipes may not be transparent, not just to light, but to
radiofrequency,
ultrasound, or other sensing modalities, and they may not be easily
accessible). Despite
this, the sensor-laden objects (aka, devices, which may also be robots) must
be able to
identify system features, including their own location at a given time if
mapping of
system features is desired.
[0065] Similar problems occur in very different contexts and at very different
scales. For
example, consider the use of a medical micro-camera or other diagnostic object
that
could be injected into the blood stream. Some diagnostic data may be useful
regardless
of knowing the object's position (e.g., blood glucose level), but for other
data (e.g., the
16
CA 3038104 2019-03-26
existence of plaques on the vasculature walls, mapping the vasculature itself,
or
determining blood oxygen levels, which vary from the arterial to venous side
of the
circulatory system), it would be useful to be able to determine the position
of the object
as it moves through the system and correlate that position with the data being
collected.
[0066] There are many ways to address the issue of position tracking of
objects. At
some scales, GPS, Wi-Fl, BlueTooth or RFID can be used for position tracking.
In other
scenarios, such as with medical applications, ultrasound, electromagnetic, or
optical
methods can be used for imaging and/or position tracking.
[0067] Despite the existence of several solutions to the problem of position
and feature
determination in a fluid system, not all solutions work well at all scales or
Reynolds
numbers. And regardless, alternative solutions can still be useful,
particularly if they
offer greater accuracy, a reduction in data processing to reduce computational
capacity
required, or allow faster processing and analysis of data with the same
capacity. Also,
alternative solutions need not stand alone, but rather data could be
incorporated from
multiple methods to refine accuracy and reliability.
Determining Feature Characteristics Using Flow Data
[0068] Some embodiments discussed herein include the indirect determination of
feature information via the measurement of fluid flow-related data. For
example,
among the possible feature data of interest, indirect position determination
is included
in some embodiments of the invention. By "indirect," it is meant that rather
than
measuring or observing, e.g., position, directly or using well-known means
(e.g., using
optical or ultrasound inspection), the desired information is inferred by
collecting fluid
flow data and computing the information of interest.
17
CA 3038104 2019-03-26
[0069] As an example of the process of indirect position determination,
consider a
device moving through a fluid system. The device may use various sensors to
gather
flow data, such as sensors capable of determining the fluid pressure and shear
forces at
multiple locations across the device's surface. Using these sensors, the
device can map,
spatially and over time, the patterns of the fluid flow which surround it.
However, this
information by itself does not provide the device's position. The patterns of
fluid flow
must be used to deduce information about the local environment. For example,
pressure and shear values which differ from one side of the device to the
other may
indicate the proximity of a wall near one side of the device and give the
device
information about its velocity relative to the channel. Different values and
patterns of
the same sensor data may indicate that the device has passed another object in
the fluid
or could indicate a change in the geometry of the fluid channel (e.g., a
curve, branch
point, merge, narrowing, widening, or some irregularity such as a plaque or
leak). Once
such features are determined, the device position can be determined, at least
relative to
the features (e.g., the position of the device relative to the local channel
geometry, or
relative to another object in the fluid).
[0070] In some cases, device position relative to some feature(s) may be
sufficient.
However, in other cases it will be useful to determine the device's absolute
position
within the system. This can be done in a variety of ways, depending on the
data
available. If a map of the system is available, the position relative to one
or more
features may be able to be translated into an absolute position. For example,
if sensors
can gather data, which is then processed using machine learning, allowing the
device to
determine the geometry of the immediate channel (and perhaps having stored the
geometry of other portions of the channel through which the device has already
passed), if the geometry is unique and overlaps with data on other regions for
which
information exists, this may be all that is required to unambiguously identify
the
position of the device within the overall fluid system (an analogy might be
made to the
18
CA 3038104 2019-03-26
way DNA fragments are assembled into the sequences of complete chromosomes
when
using shotgun sequencing). If such data are insufficient to unambiguously
identify the
device's position, it will likely at least narrow down the choices, which may
be sufficient
for a given situation. If the position of the device needs to be still further
refined,
additional data can be brought to bear on the problem. For example, if the
device has
collected additional data over time, the history of where it has been may help
to narrow
down where it could be now, given known characteristics of the system (e.g.,
approximate flow rate, or various paths that could have been taken). If such
data does
not exist or is insufficient, the device may need to make additional passes
through the
system (and multiple devices could be used to speed up the process), each time
gathering data until it is sufficient.
[0071] In addition to data directly related to the fluid flow, such as speed
and direction,
pressure, shear information, and viscosity, other ancillary data may help to
infer the
desired information. For example, data such as temperature and chemical
concentrations can also be collected and can be used to provide information to
aid
device missions, such as mapping of the fluid system. (Hogg, "Coordinating
microscopic
robots in viscous fluids," Autonomous Agents and Multi-Agent Systems, 3,
Kluwer
Academic Publishers-Plenum Publishers, 2007; Turduev, Cabrita et al.,
"Experimental
studies on chemical concentration map building by a multi-robot system using
bio-
inspired algorithms," Autonomous Agents and Multi-Agent Systems, 1, 2014) If
such
data varies across the system in known ways (such as temperature decreasing
with
distance from a heated source), or correlations can be determined, this
information may
be useful in enhancing the accuracy of inferences made using other data.
Various data
can not only be combined but can also be measured over time and in multiple
locations,
allowing spatial and time-based patterns to be analyzed. Note that this still
assumes
Stokes flow. Time-based patterns are not assumed to exist due to turbulent
fluid flow,
but rather because something that affects the system is changing over time
(e.g.,
19
CA 3038104 2019-03-26
consider variation in diastolic versus systolic blood pressure as the heart
beats, or
changes in flow rates or temperatures dictated by other equipment in an
industrial
setting).
[0072] Note that all the main sensing modalities described can be passively
implemented. They do not require sending electromagnetic waves (e.g., LIDAR,
active
electrolocation), acoustic waves (e.g., SONAR), or any other type of emission
into the
environment. Although such techniques could be used for other purposes, such
as
communication, or could be used in addition to the passive sensing modalities
described, they are not needed for, e.g., shear or stress sensing. Additional
examples of
passive sensing include viscosity sensing, heat or chemical gradient sensing,
gravitational direction sensing, gyroscopic or rotation sensing, acceleration
sensing, or
passive sensing of electromagnetic or acoustic waves (either existent in the
system or
deliberately induced to facilitate measurements).
[0073] It should be noted that passively-sensed characteristics other than
shear and
stress may be suitable for analysis techniques similar to those described in
detail with
regard to shear and stress forces. In general, such passive techniques will be
more
energy-efficient that active techniques. And, as the inventor has discovered,
even
instantaneous sampling of just a few (in some cases even one, e.g., stress)
variables, as
long as they are the right variables, and properly analyzed, can be highly
accurate and
informative, and very tractable to use in real-time or near-real-time.
[0074] Inferences made from collected data may be subject to problems like
sensor
noise or ambiguity in the data. However, it is not always necessary to obtain
exact
positions, unambiguous feature identity, or complete reliability in any
inference for the
inference to have value, either by themselves, or in combination with other
data or
inferences. Any relevant data, even if some uncertainty is present, may, to
use Bayesian
CA 3038104 2019-03-26
terminology, help refine the posterior probabilities which can be used to make
inferences about the environment.
Computational Modeling
[0075] Techniques for modeling fluid flows given the channel geometry and
fluid
properties are well-known and frequently referred to as "computational fluid
dynamics"
(CFD). Techniques for inferring channel features and other information of
interest given
only passive sensor data have not been studied nearly as much. The only work
of which
the applicant is aware pertains to the lateral lines of fish, and artificial
variants thereof,
in turbulent environments (Yang, Chen et al., "Distant touch hydrodynamic
imaging with
an artificial lateral line," Proceedings of the National Academy of Sciences
USA, 2006;
Pillapakkam, Barbier et al., "Experimental and numerical investigation of a
fish artifical
lateral line canal," Fifth International Symposium on Turbulence and Shear
Flow
Phenomena, 2007; Bleckmann and Zelick, "Lateral line system of fish,"
Integrative
Zoology, 2009; Chambers, Akanyeti et al., "A fish perspective: detecting flow
features
while moving using an artificial lateral line in steady and unsteady flow," J
R Soc
Interface, 99, 2014; Vollmayr, "Snookie: An autonomous underwater vehicle with
artificial lateralline system," Flow Sensing in Air and Water, Springer, 2014;
Liu, Wang et
al., "A Review of Artificial Lateral Line in Sensor Fabrication and Bionic
Applications for
Robot Fish," Appl Bionics Biomech, 2016; Tang, Feng et al., "Design and
simulation of
artificial fish lateral line," International Journal of Advanced Robotic
Systems, 1, 2019).
[0076] For convenience, fluid flows are often categorized as being viscous
(also called
Stoke's flow or creeping flow), laminar, or turbulent, depending on Reynolds
number.
However, the cutoffs between these various regimes are not exact.
Mathematically,
viscous flow is characterized by a low Reynolds number. The Reynolds number is
a
dimensionless number defined as: (size * speed * density) / viscosity. A "low"
Reynolds
number is frequently taken to be less than 1, but there is no sharp cutoff to
differentiate
21
CA 3038104 2019-03-26
viscous flow from laminar flow (or laminar flow from turbulent flow). Rather,
as the
Reynolds number gets higher, the behavior of the fluid gradually becomes less
viscous,
and therefore analytical techniques which assume viscous flow become gradually
less
accurate. Given the gradual decrease in accuracy as the Reynolds number
increases, if
systems are being analyzed under the assumption of Stokes flow, a Reynolds
number of
<1 is preferred, a Reynolds number of < 0.3 more preferred, and a Reynolds
number of
<0.1 even more preferred; in many cases, the number will be lower still, such
as less
than 0.03. Fluid flow systems do not necessarily have a single Reynolds
number. Rather,
depending on factors such as the local channel geometry, speed of fluid flow,
and
viscosity, different parts of a fluid flow system could have quite different
Reynolds
numbers, and the same area of a fluid flow system could have different
Reynolds
numbers at different times. The devices, methods, and techniques described
herein are
directed to parts of fluid flow systems with appropriate Reynolds numbers.
Advantages of Analyzing Viscous Flow
[0077] A substantial amount of the literature on fluid flow concerns turbulent
systems,
where quasi-static assumptions do not apply, and where an accurate analysis of
physical
systems requires gathering data over time to sample the system in its various
states.
This creates a higher computational burden and requires a non-instantaneous
data
sampling period.
[0078] On the other hand, viscous flow can be treated as being quasi-static at
low
Reynolds numbers and low Womersley numbers (which generally occur together,
unless
the system has some force which is causing it to change rapidly, such as high-
frequency
vibrations, e.g., ultrasound) because viscous forces are much more significant
than
inertial forces. In terms of data gathering from an actual system, this means
that a
snapshot in time of the fluid flow parameters suffices. And when modeling a
system, a
viscous flow system can be treated as static rather than time-dependent.
Static models
22
CA 3038104 2019-03-26
frequently solve much faster than time-dependent models. For example, using
the
commercial software COMSOL and its CFD module, static models often solve at
least 10
times faster than models solved in a time-dependent manner. The difference can
be
even more extreme depending on the time period analyzed for time-dependent
models.
[0079] For a device that is often limited in its capabilities (e.g., power
storage,
computational speed, memory, communication bandwidth) due to its size, and
functioning within what may be a relatively small, closed system, a reduction
in
computational requirements has important physical repercussions. For example,
slower
computational hardware may be used, which is often smaller and/or more power
efficient than faster computational means. Less energy devoted to computations
means,
e.g., more power is available for other systems, or the device's power
production/storage system can be smaller, or the device can run for a longer
period
without recharging/refueling, or the device can have less impact on its
environment
when its power requirements affects that environment (e.g., using oxygen
and/or giving
off carbon dioxide, or generating heat or electromagnetic interference).
[0080] Similarly, sensors need only gather data that represents a snapshot in
time,
rather than gathering a time course of data as would be required to analyze a
turbulent
(aka, unsteady or transient) system. Not only does this reduce the power
required to
run the sensors, but by reducing the amount of data that must be collected,
this affects
things such as reducing the memory requirements to store the data, reducing
the power
to write that data to memory, and reducing the communication power and
bandwidth
required to communicate the data to another device in the system, or an
external
computational resource. Also, as described herein, with proper analysis, just
one or two
measured values can provide a great deal of information about the local
system, further
cutting down on memory and communication requirements.
23
CA 3038104 2019-03-26
[0081] Given that sensors (along with other components that may be involved,
such as
acoustic transducers) may be mechanical in nature, not only is power
consumption
reduced, but so is wear on the mechanisms of the device. Computational means
may
also be mechanical. In such systems, memory may be stored by setting different
configurations of jointed connections, and logic is computed through the
movement of,
e.g., a set of links and rotary joints whose positions change as computations
take place.
The following references describe how such mechanical computational devices
can be
implemented: (Merkle, Freitas et al., "Mechanical Computing Systems," US
Patent
Application 20170192748, 2015; Merkle, Freitas et al., "Molecular Mechanical
Computing Systems," Institute for Molecular Manufacturing, 2016; "Mechanical
computing systems using only links and rotary joints," ASME Journal on
Mechanisms and
Robotics, 2018)
[0082] Even where computational means are of more traditional types (e.g.,
electronic),
physical wear and tear (and of course, power consumption) still must be
considered. For
example, even electronic memory storage devices eventually break down. In a
traditional hard drive, where bits are stored as magnetically-oriented areas
on a platter
and changing the value of the bit involves magnetizing the area in a different
direction,
the platter can be damaged, or the read/write arm can be damaged. For example,
when
a shock or vibration causes the read/write arm to hit the platter, the
magnetic media
may be damaged, as may be the read/write arm.
[0083] In solid state memory (e.g., NAND- or NOR-based flash memory, where
individual memory cells contain NAND or NOR logic gates), the gates eventually
wear
out because, for example, the voltage pulses uses to change the values stored
in the
logic gates eventually degrade the semiconductor material to the point where
some
gates no longer function correctly. Because of this apparently unavoidable
problem,
some memory devices devote extra space to spare memory cells that can be used
when
others break down. Of course, this requires extra hardware and software to
detect and
24
CA 3038104 2019-03-26
account for failed memory cells. For example, wear-leveling algorithms (or
other
techniques, such as BBM, or "Bad Block Management") can be used to try and
ensure
that, on average, each cell is used the same number of times so that none wear
out
prematurely. But that only improves the average lifetime of the device, it
does not
eliminate the damage. So, not only do such devices still fail, but in small
devices there
may not be space for optional features such as spare memory cells, or space,
time or
extra power for running wear-leveling algorithms.
Data Inferences
[0084] There are various ways in which inferences or determinations can be
made using
acquired fluid flow data (and other data as desired). For example, one way to
interpret
such data would be to develop a database of fluid data "fingerprints" or
patterns (which
could be based on raw sensor data, but more often would be based on select
data
features). This could be done, e.g., by placing sensors in known positions in
an actual
system of interest, collecting and analyzing the data, and converting the
results to
different features of the system (e.g., via machine learning). Subsequently,
new data can
be compared to the initial database to determine which pre-existing patterns
are the
closest match. This is referred to in the field of machine learning as
classification. To
avoid confusion and ambiguity, it is worth repeating that system features are
parameters of the fluid system, such as channel geometry, and characteristics
of the
fluid flow. Data features are not the same as system features. Data features
are select
data, often transformed in some manner from the raw sensor data, which are
used to
train machine learning routines. One way to think about this is that machine
learning
allows data features to be converted to system features, so that when a device
collects
data, an interpretation of the data can be provided that is easily interpreted
by a
human. For example, rather than a string of numbers, which may not be very
useful to a
human, machine learning allows the data features to be turned into inferences
such as
"the device is in a channel with a diameter of X which branches up ahead."
CA 3038104 2019-03-26
[0085] Another way in which inferences can be made using fluid flow data is to
collect
the necessary data using system mock-ups. For example, if one is interested in
being
able to identify features in a vascular system, a microfluidics device could
be created
that mimics various features of the vasculature but has the advantage that the
sensing
device can be placed and/or located to allow aliasing the collected data to
the position
of the device.
[0086] Simulations can also be used to create virtual environments which can
provide
data that is used to train machine learning algorithms which allow inferences
to be
made from the data. Such simulations offer the advantages of fast iteration
time and
can provide a large amount of data on many different scenarios without having
to build
physical mock-ups. For example, by setting up appropriate virtual systems
which contain
straight segments, curved segments, branching segments, merging segments,
other
objects in the fluid, or other scenarios, it is possible to run, e.g., Monte
Carlo simulations
as many times as needed to generate a data set that is used to provide input
to a
machine learning system and allows robust system feature determination.
[0087] If a device were to run into a scenario (e.g., a new geometry) that was
not
classifiable per the existing data, the scenario could be added to mock
systems or
simulations, and the system retrained until it could accurately distinguish
the new
scenario.
[0088] The data may be analyzed in its raw form or may be preprocessed.
Techniques
for preprocessing data for subsequent machine learning are well known. For
example,
noise can be removed, data averaged, and Fourier and other transforms
(optionally
including dimension reduction and/or feature selection techniques) can be done
on the
data.
[0089] As an example of the practical application of these techniques, using
data
obtained from simulations, the present Applicant has been able to achieve very
accurate
26
CA 3038104 2019-03-26
feature discrimination via the collection of surprisingly small amounts of
data. For
example, using computational model in two dimensions and three dimensions,
stress
and shear were measured on the surface of an object in a low Reynolds number
fluid
flow. The virtual channels used included many different geometries, and within
these
geometries, the device was placed in many different locations. The data were
subsequently subjected to a Fourier transform. Then the first few modes of the
transformed data were used for regression analysis. The regression analysis
showed that
devices in viscous flow, by collecting just these pieces of data, can make
multiple
important quantitative (e.g., velocity) and qualitative (e.g., classification
of vessel
geometry) determinations. Additionally, it has been shown that this can be
done in a
manner which is very computationally efficient where it is most important: in
a power-
and/or space-limited device. The reason for this is that most of the
processing is in the
generation of the virtual data and the training of the system (e.g., for
classification),
which can be performed by a remote device (e.g., a typical desktop computer,
workstation, or cluster of computers). Once the machine learning training is
complete,
classifying new data based on the training results is not nearly as
computationally
demanding as creating and analyzing the data initially.
[0090] Of course, the devices and methods described are only exemplary. It
will be
obvious to those skilled in the relevant arts that, given the teachings
herein, many other
combinations of devices (along with sensors), data, data processing or
preprocessing
(including none), and machine learning techniques could also be used.
Device Requirements
[0091] In one of the simplest implementations, a device for fluid flow
analysis could be
comprised of a single type of sensor, and preferably (although optional) some
way of
communicating the data gathered by the sensor to an external computer (e.g.,
RF,
27
CA 3038104 2019-03-26
acoustic, or optical communications, or some direct data transfer after the
device has
exited the fluid system) for analysis.
[0092] While some method of communication, and therefore a power source, is
preferable, it is not required in all instances. For example, molecules which
have
different fluorescent or other properties depending on shear could rely upon
external
activation or assays. For example: (Haidekker, Grant et al., "Supported
molecular
biolfluid viscosity sensors for invitro and in vivo use," US7670844, 2010;
Mustafic, Huang
et al., "Imaging of flow patterns with fluorescent molecular rotors," J
Fluoresc, 2010;
Zou, Liu et al., "Flow-induced beta-hairpin folding of the glycoprotein
lbalpha beta-
switch," Biophys J, 2010; Varma, Hou et al., "A Cell-based Sensor of Fluid
Shear Stress
for Microfluidics," 17th International Conference on Miniaturized Systems for
Chemistry
and Life Sciences, Freiburg, Germany, 2013; Zhang, Sun et al., "Red-Emitting
Mitochondria! Probe with Ultrahigh Signal-to-Noise Ratio Enables High-Fidelity
Fluorescent Images in Two-Photon Microscopy," Anal Chem, 2015).
[0093] Assuming communication hardware is built into the device, many means of
communication are possible, including wired, wireless (e.g., electromagnetic,
such as RF
or optical), or acoustic (e.g., generated by piezo-based mechanisms, which
could also
serve as pressure sensors).
[0094] A power source could also take many forms, including a battery, a fuel
cell (e.g.,
a hydrogen fuel cell, or a glucose fuel cell for medical purposes or other
environments
where a glucose supply, and potentially an oxygen supply, is available,
although any
necessary fuel could also be carried in onboard storage tanks), induction-
based power
collection, or a mechanism which uses ambient pressure changes or vibrations
to
harvest energy from the environment (including pressure changes induced by,
e.g., the
application of an external ultrasound source).
28
CA 3038104 2019-03-26
[0095] The ability of a device to actively position itself within a fluid
system could be
useful, but not required. Data could be gathered as the device passively moves
through
the system with the fluid flow, or in some cases, device position could be
externally
manipulated (e.g., magnetically). If onboard locomotion is desired, there are
many ways
of providing this. For example, traditional propellers, flagella- or cilia-
like mechanisms,
undulating surfaces, tank tread- or treadmill-like mechanisms (which, while
uncommon
in everyday experience, can be very efficient at low Reynolds numbers),
brachiation
with device arms, or mechanisms which allow the device to adhere to the
channel wall.
[0096] An onboard computer, including memory to store data, could also be
convenient, but not necessary. Where onboard computation is used, power and
space
may be limited, making efficient means of data analysis potentially more
important than
if sensor data are offloaded to external computing devices.
[0097] Note of these choices are mutually exclusive ¨ any combination could be
used, of
the above examples, or of other methods of addressing such functionality well-
known in
the arts. The size and shape of a device may be environment- and mission-
specific, and
could assume any shape, from a sphere, cylinder, or ellipsoid to much more
complex
shapes (or could change shape as needed), and could be covered with, for
example, any
number of sensors, propulsion mechanisms, energy harvesting mechanisms, and
communication equipment (e.g., antennae).
Exemplary Sensor Positioning or Integration
[0098] Sensors can be in many places, and often multiple sensors, potentially
of various
types, would be placed in one or more locations within a system or on a device
within a
system. For example, sensors could be external to the fluid system (e.g., the
Doppler
ultrasound equipment used for medical diagnostics resides outside of the
systems it
measures). Sensors could be mounted on, or an integral part of, the walls of
the fluid
system (e.g., wall-mounted or wall-integral sensors can be built into micro-
fluidics
29
CA 3038104 2019-03-26
channels). Sensors could be mounted on the surface of devices within a system
(e.g.,
pillar-type shear sensors), or within devices (e.g., pressure sensors, such as
can be
fabricated using piezoelectric sensors). Sensors could also be incorporated
directly into
the fluid itself when appropriate (e.g., molecular shear sensors).
[0099] As an example of device-mounted sensors that could be employed, Fig. 1
depicts
a device 50 having shear sensors 52 distributed across part of the surface of
a shell 54,
and a piezo pressure sensor 56 (which could also serve as an acoustic
transducer for
both communication and power harvesting) on another part of its surface. The
sensors
employed could be of various types, such as shear sensors, velocity sensors,
direction
sensors, pressure sensors, and many other types, including combination sensors
that
collect more than one type of data. Of course, Fig. 1 is a diagrammatic
representation
and the shapes, sizes, numbers, placement and types of sensors, propulsion,
power
storage, communication, and other mechanisms, can vary as desired, and some
may not
be present at all. The illustrated device 50, by way of example, employs a
battery 58 to
provide power to the sensors (52, 56) as well as to an on-board computer 60,
and a
treadmill locomotion unit 62. An antenna 64 allows the computer 60 to receive
data
from a remote site, and may allow transmission to such site, which could be an
operator
interface and/or could be other devices.
Exemplary Analysis of Non-Locomoting Device in a Vessel
[0100] To illustrate the present techniques, Figs. 2-4 illustrate a relatively
simple
situation for analysis, where a spherical device 100 moves passively through a
straight,
cylindrical vessel 102. Fig. 2 shows the device 100 and vessel 102, while Fig.
4 illustrates
a cross-section that can be used in a 2D analysis of the device motion. This
motion
results in stresses on the surface of the device 100, as illustrated in Figs.
5A and 5B (3-
dimensional analysis) and in Figs. 6A-8B (2-dimensional analysis). In the
cases
considered herein, the flow speed, vessel size and fluid viscosity result in
viscous flow
CA 3038104 2019-03-26
(also known as Stokes flow or creeping flow). (Happel and Brenner, "Low
Reynolds
Number Hydrodynamics," The Hague, Kluwer, 1983), (Hogg, "Using surface-motions
for
locomotion of microscopic robots in viscous fluids," J. of Micro-Bio Robotics,
2014). For
purposes of the present discussion, Stokes flow can be considered to exist
when the
Reynolds number:
Re = ¨ud
(1)
of the flow is small (i.e., Re < 1). In this expression, v is the fluid's
kinematic viscosity, d is
the vessel diameter and u is the flow speed. For a device moving slowly in
such flows,
the fluid motion at each time is close to the static flow associated with its
instantaneous
position, velocity, and orientation. This quasi-static approximation applies
for small
values of the Womersley number:
vv r (2)
\Flit
where r is the radius of the device and t is the time over which the geometry
changes.
As with the Reynold's number, there is no strict cutoff for values of the
Womersley
number at which quasi-static analysis is applicable; rather, such analysis
becomes less
accurate as the number increases. For many purposes, the approximation should
be
appropriate for a Womersley number of less than 1 (and like the Reynolds
number, a
Womersley number of < 1 is preferred, <0.3 more preferred, < 0.1 even more
preferred,
and some systems will have even far lower Womersley numbers, where the quasi-
static
approximation then becomes almost exact). Changes in device geometry can arise
from
and actual change in its shape (e.g., if the device were flexible or had
moveable
segments), or changes in its position and/or orientation. The time for
significant change
in the device's position is of order r/vdevice, which is larger than r/u
because a device
moving passively in the fluid moves more slowly than the fastest fluid speed
in the
vessel. Similarly, significant changes in orientation take time of order
1A0dev1ce, which is
31
CA 3038104 2019-03-26
also larger than r/u. Thus, a lower bound on the time for significant geometry
change,
at least from passive changes in position or orientation, is t> r/u.
[0101] Evaluating the flow in this example requires specifying boundary
conditions at
the ends of the vessel segment and on the wall. Specifically, the incoming
flow can be
taken to be fully-developed Poiseuille flow (Happel and Brenner, "Low Reynolds
Number
Hydrodynamics," The Hague, Kluwer, 1983). This gives a parabolic velocity
profile at the
inlet, with maximum speed u at the center of the vessel. A pressure gradient
drives the
flow, so shifting the pressure by a constant leaves the flow unchanged. For
definiteness,
the pressure can be set to zero at the outlet. The vessel walls are no-slip
boundaries,
where the fluid velocity is zero. The flow velocity matches the device's
motion at each
point on the device's surface, expressed in terms of the device's center-of-
mass velocity
and angular velocity.
[0102] Figs. 5A and 5B illustrate the resulting pattern of normal stress and
tangential
stress, respectively, on the surface of the spherical device 100, when moving
through
the vessel 102 with the geometry and viewpoint of Fig. 2 (the specific
parameters used
in generating the figures for the present discussion are described in the
numerical
example discussed herein); the size of the arrows indicates the magnitude of
the force.
The arrow 104, on the right of the spherical device as shown in Figs. 5A and
5B, indicates
the direction of motion of the device 100, as also shown in Figs. 2 and 4. The
arrow 106
indicates the direction to the nearest point on the vessel wall. Fig. 4 shows
a section of
the vessel 100, with diameter d, and the spherical device 100, with radius r,
with its
center at position ycwith respect to the cylindrical vessel axis 108, and
distance d/2 ¨
lycl from the vessel wall 110.
Comparing Two- and Three-Dimensional Flow Analysis
[0103] Fig. 5A illustrates the normal components of stress on the surface of
the device
100, where positive and negative values correspond respectively to tension and
32
CA 3038104 2019-03-26
compression. Fig. 5B illustrates the tangential components of stress on the
surface, with
arrows showing the direction and relative size of the tangential stress
vectors. The fluid
flow is driven by a pressure gradient in the vessel. Adding an arbitrary
constant to the
pressure does not change the flow but contributes to the normal force on the
device
surface. To remove this arbitrariness, the present calculations select this
constant such
that the total measured normal stress on the surface of the device is zero.
[0104] The stress is relatively large on the side of sphere facing the nearby
vessel wall.
In addition, the largest variation of the stress is in the azimuthal direction
around the
sphere's equator 112. In particular, the largest magnitude of the tangential
stress is at
the point of the sphere closest to the vessel wall 110. The sphere's direction
of motion is
nearly 90 around the equator from that closest point.
Fig. 7A compares the stress from 2-dimensional analysis of fluid flow
(indicated in solid
lines) with the stress around the sphere's equator from 3-dimensional flow
(indicated
with individual points). In the latter case, by symmetry, the tangential
stress is directed
around the equator, thereby matching the direction of the tangential stress of
the 2-
dimensional case. The normal and tangential stresses for the scenario
illustrated in Figs.
5A and 58, as a function of azimuthal angle cp from 0 to 2Tr, are measured
from the
direction of a cylinder axis 108 (shown in Figure 4), which is nearly parallel
to the
device's direction of velocity. The two vertical lines indicate the direction
of motion
(indicated by arrow 104 in Figs. 5A and 58) and the direction of the nearest
point on the
vessel wall (indicated by arrow 106). Positive tangential stress is in the
direction of
increasing cp, i.e., counterclockwise rotation. The stress components
correspond to the
stress vectors shown in Fig. 8A.
[0105] As an additional comparison between the 2-dimensional analysis and the
3-
dimensional analysis, Fig. 7B compares the device's speed through the vessel,
vdevIce, and
angular velocity, codevice, as a function of relative position in the vessel,
y, for the
33
CA 3038104 2019-03-26
geometry of Figs. 2 & 4, but varying the position of the device in the vessel
(as used
herein, "relative position" or r.p. is a measure of the center of the device
relative to the
center of the vessel, accounting for the device and vessel diameter so as to
range from
0, where the device is centered in the vessel, to 1, where the device is just
touching the
vessel wall). The resulting speed and angular velocity are calculated varying
the position,
yc, of the sphere's center within the vessel, ranging from zero (where the
sphere is in
the center of the vessel), to slightly less than d/2 ¨ r = 2m (where the
sphere is almost
touching the vessel wall). In these cases, the device's motion is very nearly
parallel to
the cylinder's axis because the transverse component of the device's velocity
is
significantly smaller than its velocity parallel to the vessel. In all
comparisons performed,
the 2-dimensional and 3-dimensional calculations give very similar results.
Thus, in the
following discussions, two dimensional examples are generally used for
simplicity.
Surface Stresses Resulting from Fluid Flow and Device Movement
[0106] In the case discussed above, where a spherical device moves passively
in a
straight vessel, such as shown in Figs. 2 and 4, and where the effects of
gravity and
Brownian motion can be considered negligible, the stresses on the device
surface can be
determined by numerically evaluating the flow and device motion in the segment
of the
vessel. Due to symmetry in this basic example, the device's velocity lies in
the cross
section of the plane shown in Fig. 4, and a simplified numerical evaluation
can be made
by using two-dimensional quasi-static Stokes flow analysis, as discussed
above.
[0107] Figs. 6A and 6B illustrate a 2-dimensional representation of the flow
and stresses
on the device surface, of the region 6 shown in Fig. 4, using an arbitrary
choice for the
orientation of the device 100, illustrated by orientation line 114 (labeled in
Fig. 8A), with
respect to the vessel 102. The fluid pushes the device through the vessel with
a
translational velocity Vdevice (from left to right as viewed in Fig. 6A) and
with an angular
velocity (t)device which is negative (i.e., clockwise rotation as viewed in
Fig. 6A). Fig. 8A
shows how resulting stresses vary over the device surface. A useful
representation of
34
CA 3038104 2019-03-26
the stress pattern is its Fourier decomposition (discussed in greater detail
herein, with
regard to determining device orientation). In this example, the largest
contribution is
from the second mode, for both normal (pressure) and tangential (shear)
components
of the stress, as shown in Fig. 8B.
Evaluating Device Orientation, Location, and Vessel Geometry
[0108] Figs. 6A, 6B, 8A, and 8B illustrate one example of instantaneous stress
measurements that can be used to calculate values of device orientation and
position in
a vessel, and the vessel's diameter; in this case, a 2-dimensional analysis is
performed.
Together, these calculated values give the device's relation to the vessel
through which
it moves. The following discussion again refers to the spherical device 100
and
cylindrical vessel 102 shown in Figs. 2 and 4 (using data generated from the
specific
numerical example discussed herein).
[0109] Figs. 6A and 6B indicate the fluid flow near the device 100, in the
section of the
vessel 102 shown in Fig. 4. The orientation of the device 100 is indicated by
the
orientation line 114 (shown in Figs. 8A & 9). Arrows show streamlines of the
flow and
the arrow size show the flow speed. Fig. 6A illustrates the fluid velocity
with respect to
the vessel. Velocity is zero at the vessel wall 110, and matches the motion of
the device
100 at its surface. Fig. 6B shows the fluid velocity with respect to the
device 100.
Velocity is zero at the device surface. Fig. 8A illustrates the stress vectors
on the device
surface. The arrow lengths show the magnitude of the stresses at the locations
of
sensors 116 distributed on the device surface at different angles 4) with
respect to the
orientation line 114; in this example, 30 sensors 116 are employed. Fig. 8B
shows the
relative magnitudes of Fourier coefficients of the first six modes of normal
and
tangential components of stress on the device's surface.
CA 3038104 2019-03-26
Device Orientation
[0110] Objects may rotate as fluid pushes them through a vessel. As seen in
Fig. 8A, the
device 100 has large tangential stress on its side closest to the vessel wall
110. This
stress arises from the large velocity gradient between the device's moving
surface and
the stationary fluid at the wall, as illustrated in Fig. 6A. Thus the location
on the device's
surface with largest tangential stress magnitude identifies the direction to
the nearest
vessel wall 110.
[0111] The simplest orientation value based on this observation would be to
use the
location of the device's stress sensor 116 with largest tangential stress
magnitude.
However, this approach is limited in resolution to the spacing between sensors
(as well
as positioning of sensors on a 3-dimensional spherical surface not aligning
with a plane
most suitable for a related 2-dimensional analysis) and is sensitive to noise
that might
be present in a single sensor 116. A more robust implementation uses the angle
i'l
¨extreme
with respect to the front of the device (as indicated by the orientation line
114), that
maximizes the magnitude of an interpolation of tangential stress measurements
around
the surface. In one example of such analysis, the interpolation is based on
low-
frequency Fourier modes. This interpolation combines information from multiple
sensors to reduce noise and can identify locations that lie between sensor
positions for
improved resolution. The calculated direction to the wal1,19,,,y, is taken to
be the
direction of the normal vector at the location t.9.,t,, on the surface. For
circular devices,
the surface normal vector aligns with the center of the device such that a
¨ extreme -= wall.
However, these angles can differ for other shapes, as discussed herein
regarding
elongated devices.
[0112] As shown in Fig. 2 and 4, the device's motion is nearly parallel to the
vessel wall
110. Thus, the device 100 can evaluate its direction of motion as being
roughly
perpendicular to its calculated direction to the closest wall 110 (indicated
in Figs. 2 and
4 by the arrow 106). More specifically, Fig. 8A shows that, near the direction
to the wall
36
CA 3038104 2019-03-26
110, the normal stress is negative in the direction of motion. This
observation allows the
device 100 to determine whether the direction of motion is +90. or ¨900 from
the
direction to the wall 110, as discussed regarding determining device motion.
Calculated Values from Stress Measurements
Fourier Coefficients
[0113] Stresses vary fairly smoothly over the device surface, as illustrated
in Fig. 7A. This
observation motivates representing the stresses by a Fourier expansion in
modes with
low spatial frequencies. Limiting consideration to these modes reduces the
effect of
noise and is computationally efficient.
[0114] The Fourier coefficient for mode k is
x-i-1
Ck _ ¨ 12,7_0 exp (27i) (3)
n
where n is the number of sensors and k ranges from 0 to n ¨ 1. To focus on low-
frequency modes, the present analysis considers only modes up to k=M, with M <
n/2.
The examples discussed herein use M= 6 and n = 30 (six modes, thirty sensors
116),
as shown in Figs. 8A and 9. In the following discussion, these coefficients
are used in
two ways.
[0115] First, the stress measurements are extended from the locations of the
device's
sensors to the full surface by interpolating the Fourier modes. Mode k is the
real part of
cke-ok, where 0 is the angle around the device's surface measured
counterclockwise
from the front of the device (see Fig. 9). The interpolated stress values are
f(9) = 91(c 0 + 2 ck e-wk) (4)
where 91 denotes the real part and the factor of 2 accounts for the symmetry
between
modes k and n ¨ k.
37
CA 3038104 2019-03-26
[0116] Second, machine learning is applied to determine relations between
these
Fourier coefficients and properties of the vessel near the device. To simplify
this
procedure, the relative magnitudes of the Fourier coefficients Mk, are used,
with .
components
.i.
mks = ¨ICk sl (5)
c,
where s denotes either the normal or tangential component of the stress, and
Cis the
root-mean-square magnitude of the coefficients, i.e., C = VEkicklA2 with Ickl2
=
Esick,s1^2 . The constant mode, co, does not contribute to the variation in
stresses
around the device, so is not included in this normalization. The relative
magnitudes
simplify the evaluation because they are independent of the device's
orientation, the
overall fluid flow speed, and the fluid's viscosity. This is because 1) the
device's
orientation affects the phase of the Fourier coefficients, but not their
magnitudes, and
2) the stresses for Stokes flow are proportional to the flow speed and fluid
viscosity (Kim
and Karrila, "Microhydrodynamics," Dover Publications, 2005), so the
normalization
removes this dependence. This allows for a very efficient process from a
computational
standpoint: All that ends up being needed to accurately determine several
important
system features are the relative magnitudes of the first few Fourier modes of
the
normal and tangential components of stress.
Evaluating the Direction of Motion
[0117] As pointed out when discussing Fig. 8A, a device can evaluate its
direction of
motion through the vessel from the observation that the direction of motion is
nearly
perpendicular to the direction to the wall. Specifically, Fig. 8A shows the
derivative,
dfnormal
/d0, of the normal stress at extreme is negative. If the direction of flow,
and hence
motion, were reversed, this derivative would be positive. Thus, the sign of
this
38
CA 3038104 2019-03-26
derivative, s, identifies whether the motion is +900 or ¨90 from the
direction to the
wall, i.e., the direction of motion is wall 90' or wall+ S90 , respectively.
[0118] This evaluation technique was modeled for a sample of devices at
various
positions and orientations in vessels, using variations of the situation show
in in Figs. 2 &
4 for a range of vessel diameters and flow speeds, and the mean magnitude of
the
errors for both the indicated direction to the wall and the indicated
direction of motion
were found to be less than 1 degree (surprisingly accurate due not only to the
small
number of data features being used, but also because this resolution is far
smaller
than the spacing of the sensors, which in this example is one every 12
degrees). The
largest errors occurred for devices near the center of the vessel, where the
tangential
stresses on the sides facing the opposite walls are nearly the same. However,
for devices
near the center, the wall in either direction is at about the same distance
from the
device, so such errors have little significance at such central location.
Devices in such
locations could adopt various strategies to address the possible inaccuracy in
such
circumstances; examples include ignoring or de-weighting current readings and
relying
on previous values, or, if present, communicating with other nearby devices
(particularly
those located near the vessel wall, having a large value for relative
position) to obtain
more accurate values.
Relating Stresses to Device and Vessel Properties
[0119] The pattern of stresses across the device surface are affected by the
relative
position of the device in the vessel and the geometry of the vessel. These
differences
can allow evaluating, based on stress measurements across the device surface,
information on the position of the device in the vessel and the geometry of
the vessel.
Some of this information is available based on instantaneous measurements,
while
additional information can be obtained by monitoring how such instantaneous
measurements change over time. The discussion below describes examples of the
use of
39
CA 3038104 2019-03-26
particular machine learning techniques to obtain evaluations for parameters of
the
device position in the vessel and geometric properties of the vessel.
Relative Position in the Vessel
[0120] The patterns of surface stresses are significantly different for
devices near the
center of the vessel and those near its wall. A useful way to express this
variation
independently of vessel diameter is through the device's relative position in
the vessel,
defined as
rp = lYcl (6)
d/2-r
whereyc is the position of the device's center relative to the central axis of
the vessel, as
shown in Fig. 4. Relative position ranges from 0, for a device at the center
of the vessel,
to 1, for a device just touching the vessel wall. The relative position can be
calculated
from stress measurements with a regression model, as discussed below.
[0121] Different machine learning methods have a variety of trade-offs among
expressiveness, accuracy, computational cost for training and use, and
availability of
training data (Hastie, Tibshirani et al., "The Elements of Statistical
Learning: Data Mining,
Inference, and Prediction," Springer, 2009; Mostafa, Ismail et al., "Learning
From Data,"
AMLBook, 2012; Jordan and Mitchell, "Machine learning: Trends, perspectives,
and
prospects," Science, 2015). The following discussion describes regression
methods,
which perform well with only a modest number of training instances, and whose
trained
models require only a relatively small number of computations to evaluate. It
will be
obvious to those skilled in the art given the teachings herein, including the
data
gathered, features selected, and inference models used, that many alternative
techniques could be employed.
CA 3038104 2019-03-26
Principal Components of Fourier Coefficients
[0122] To evaluate the device's position in the vessel and the vessel
diameter, training
samples were used to fit regressions between these properties and the Fourier
coefficients of the stresses. However, these Fourier coefficients are highly
correlated in
these samples, which make regressions numerically unstable. To avoid this
problem,
these correlations were removed by using the main principal components of the
Fourier
coefficients. That is, the regressions were trained using just the principal
components
accounting for most of the variation among the modes (Golub and Loan, "Matrix
Computations," Baltimore, MD, John Hopkins University Press, 1983). With M = 6
Fourier coefficients for each of normal and tangential stresses, the first two
principal
components account for 98% of the variance among the training samples. Thus,
just the
first two principal components were used for evaluation in this example.
[0123] Figs. 10A & 10B are graphs that indicate the range of the first two
principal
components for 200 test samples evaluated in the numerical example discussed
herein.
In Fig. 10A, the disk sizes indicate vessel diameter, while in Fig. 10B the
disk sizes show
the device's relative position, given by Equation (6). The lower left portion
of the graph
in each graph shows cases with the device near the center of the vessel. The
lower right
shows devices near the vessel wall. Thus, the first component mainly varies
with the
device's position in the vessel and the second with the vessel's diameter. The
small
spread in points for devices near the center of the vessel indicates
relatively little
information on vessel geometry from pattern of stress in that case. This leads
to worse
evaluation performance when devices are near the center of the vessel.
[0124] Fig. 11 is a graph that compares predicted and actual values of
relative position
for the set of test samples discussed herein. The root mean square (RMS) error
is 0.032.
Thus, by measuring surface stress, a device can fairly accurately determine
its relative
position in the vessel. The regression is least accurate for devices close to
the center of
the vessel, i.e., with relative position less than about 0.1.
41
CA 3038104 2019-03-26
Vessel Diameter
[0125] For flow at a given speed, wider vessels have smaller fluid velocity
gradients than
narrower ones. These leads to different stress patterns for devices at given
relative
positions in those vessels, especially for devices close to the wall, where
gradients are
largest. A device can exploit these differences with a regression relating
vessel diameter
to Fourier coefficients of the stress.
[0126] Since diameter is a positive value, an evaluator can be constrained to
give
positive values. Specifically, a generalized linear model (Dobson and Barnett,
"An
Introduction to Generalized Linear Models," CRC Press, 2008) with logarithm
link
function and gamma distribution for the residual was studied. Vessel diameter
has a
strong nonlinear relation with the first two principal components of the
Fourier
coefficients, as seen in Fig. 10. A regression using only linear variation of
the principal
components gives less accurate values; depending on the accuracy requirements
of the
intended application, greater accuracy may be desirable. Including quadratic
terms
accounts for much of the nonlinear relationship, giving a value for the
diameter d, in
microns, as:
d = exP(/go + E=i)ei Pi + E1<<i<2 igPiPj) (7)
(using the parameters provided in Table 4 herein).
[0127] To evaluate the accuracy of this regression, predicted and actual
values for
vessel diameter for the test samples are compared in the graph of Fig. 12. The
straight
line in Fig. 12 indicates perfect prediction (i.e., where predicted and actual
values are
the same). The point markers group the instances by their relative positions,
as
described in the legend. The root mean square (RMS) error was found to be
within
about 10% of the actual diameters, with the largest errors being for devices
near the
center of the vessel (e.g., relative positions smaller than 0.2).
42
CA 3038104 2019-03-26
Distance to Vessel Wall
[0128] Eq. (6) defining the relative position of the device relates the
relative position of
the device, the vessel diameter, and the distance of the device's center to
the vessel
wall, such that the distance to the wall can be expressed in terms of the
calculated
relative position and vessel diameter.
d rp*d
dwall = ¨2 ¨ 7---r ¨ r (8)
Thus, combining the calculated values of relative position and vessel diameter
as
discussed above provides a value for the device's distance to the wall. An
evaluation of
this procedure for the test samples is shown in Fig. 13. Calculated values for
distance to
the wall are accurate for devices near the wall, allowing the device to
identify when it is
close to the wall. On the other hand, prediction error is particularly large
for devices
near the center of the vessel (r.p. <0.2, where "r.p." stands for "relative
position," and
is measured as distance from the center of the vessel).
Evaluating Device Motion
[0129] The above examples describe evaluation of instantaneous parameters
based on
measurements of the stresses on the surface of the device. Further analysis
can
evaluate the motion of the device in the vessel. For Stokes flow, the
stresses, and hence
the Fourier coefficients, are linear functions of the device's speed and
angular velocity.
The stresses have a more complex dependence on the geometry (i.e., vessel
diameter
and the relative position of the device within the vessel). One approach to
evaluating
motion is to train regression models of these relationships, like the
procedure discussed
for evaluating position.
[0130] An alternative approach derives a value for angular velocity from how
stresses
change with time and combines that value with a regression model to evaluate
the
device's speed through the vessel. The capability of monitoring changes in the
stresses
43
CA 3038104 2019-03-26
over time could be accomplished using an onboard timer or by receiving a time
signal
communicated from an external source.
Angular Velocity
[0131] For straight vessels, the rate of change in the direction to the vessel
wall relative
to a defined "front" of the device equals the device's angular velocity.
Because a
device's motion in the vessel is mainly directed downstream (assuming the case
of a
passively-moving device), the distance to the wall changes relatively slowly,
and thus
the pattern of stress on the device surface, measured from the front of the
device,
maintains roughly the same shape but shifts around the device due to its
rotation. Thus,
the device can evaluate its angular velocity from the angle AO that the stress
pattern
moves around its surface in a short time interval At: wdevice ¨AO/At. A device
can
determine AO from the correlation between the surface stresses at these two
times. A
device can use the shift in its surface stress pattern over a short time At to
evaluate its
angular velocity, if the device has access to a clock with sufficient
precision (as noted,
this could be either an onboard clock or an externally-provided time signal).
[0132] The analysis supposes that f(0,t) is the stress at angle 6 and time t.
If the stress
maintains its shape as the device rotates, then AO would be the value such
that f(0
+AO,t +At) = f(0,t) for all 0. However, any change in the shape of the stress
pattern will
mean there is no such constant value. A more robust approach to determine AO
is the
value maximizing the correlation between the stresses at the two times. A
check on the
assumptions underlying this method is that the maximum correlation is close to
one,
indicating that the main change in stresses is rotation around the device,
rather than,
say, significant change in vessel geometry or the device's distance to the
vessel wall
during time interval At.
[0133] This procedure must compare stresses close enough in time to avoid the
device
completing a full turn, i.e., avoiding aliasing. For instance, the device
could measure the
44
CA 3038104 2019-03-26
shift at a sequence of increasing intervals of time until there is a
sufficient change in the
angle of maximum correlation to reliably identify the change, but not so much
that the
shift exceeds a full turn. A simpler approach is to use a fixed time interval,
selected
based on the expected angular velocities such that the change in orientation
within a
measurement interval is a fraction of a full rotation (e.g., less than one
radian), thereby
avoiding aliasing.
[0134] One way to apply this method is to evaluate the correlation at shifts
of an
integer number of sensors. This is a simple computation, but limits AO to be
an integer
multiple of spacings between sensors. A more precise method, discussed herein,
has the
device interpolate its stress measurements (Eq. (4)), and determine AO as the
value
maximizing correlation between interpolated stress values at the two times.
Calculated
values based on normal and tangential stresses are similar. In the current
example, the
average from these two stress components was employed.
[0135] This method was evaluated with 100 of the test samples, where the
motion of
each sample was evaluated for small time intervals and the angle AL,
maximizing the
correlation between the stresses before and after the motion was determined.
The
maximal correlations were above 99.9% for all the samples, indicating
negligible change
in the shape of the stress pattern during this time interval. Fig. 14 shows a
comparison
of predicted and actual values of the angular velocity (in arbitrary units
since the
relationship holds for wide-ranging size and time scales as long as the flow
is viscous;
the same concept applies to Figs. 12 and 13, and other plots where specific
units are not
provided) for these samples, with the reference straight line indicating
perfect
prediction (i.e., where predicted and actual values are the same).
Relating Stresses to Device and Vessel Properties
[0136] The flow in a vessel has a parabolic speed profile (Happel and Brenner,
"Low
Reynolds Number Hydrodynamics," The Hague, Kluwer, 1983). Thus, near the
center the
CA 3038104 2019-03-26
flow is relatively fast and the gradient of speed with distance from the
vessel wall is
relatively small. Conversely, near the vessel wall the speed is low and
gradient large.
These variations mean that a device near the center moves relatively quickly
along the
vessel, but rotates slowly, since the flow on either side is fairly similar
(or identical, for a
device exactly in the center). On the other hand, a device near the wall moves
slowly
along the vessel, but the large velocity gradient makes the device rotate
rapidly. Thus,
the ratio of speed through the fluid to rotational velocity at the device's
surface:
_ I9device
Sratio (9)
wdevicer
is large for a device near the center of the vessel and small for a device
near the wall.
Since both device speed and angular velocity are proportional to overall fluid
sped and
viscosity, their ratio is independent of these factors. The speed ratio is
close to a linear
function of the odds ratio, (1¨r.p.)/r.p., of the relative position defined by
Eq. (6). Thus,
a useful model for evaluation of the speed is a least-squares fit to the
training samples,
which gives
1¨rp)
Sratio = a + D (¨ (10)
rp
with a = 3.1 0.2 and b = 5.41 0.03, where the ranges indicate the standard
errors of
the values. For the test samples of this example, this fit was found to give a
median
relative error of 8% for the speed ratio. The largest errors arise when the
device is very
close to the center of the vessel (i.e., cases with r.p. <0.01).
Speed
[0137] Combining calculated values of angular velocity and speed ratio gives a
value for
the device's speed through the vessel via Eq. (9). Fig. 15 illustrates a
comparison of
evaluated and actual speeds (in arbitrary units, for reasons described herein)
for the test
samples, with the straight line indicating perfect evaluation (i.e., where
calculated and
46
CA 3038104 2019-03-26
actual values are the same), and with the point markers grouping the instances
by their
relative positions, as described in the legend. The mean relative error is
20%. The
prediction error varies significantly with device position; specifically, mean
relative
errors are respectively 43%, 21%, and 7% for relative positions less than 0.2,
between
0.2 and 0.5, and at least 0.5. The large error for small relative positions
(i.e., when the
device is close to the center of the vessel) is due to unreliable calculated
values of the
speed ratio in such cases.
[0138] To illustrate specific calculations to evaluate the effectiveness of
the above
analysis techniques, the following discussion refers to the example of
microscopic
devices operating in human capillaries, where the vessel size, fluid velocity,
and fluid
kinematic viscosity result in a Stokes flow condition. It should be
appreciated that the
dimensions involved are related to the kinematic viscosity, and thus
significantly larger
vessel and device sizes could be used for more viscous fluids of interest. As
discussed
herein, for some industrial applications involving highly viscous fluids,
devices could be
many thousands of times larger. But, even for medical applications devices
could be
significantly larger than the example of Table 1 given the Reynolds number of
< 0.04,
and that some biological fluids, such as blood plasma and lymph, have
significantly
higher viscosities than 1mPaS.
[0139] Table 1 shows typical parameters for fluids and microscopic devices for
the
application of microscopic devices operating in capillaries. In some cases,
the last
column gives a range of values or approximate bounds rather than a single
value. Values
for the examples discussed in detail are within about a factor of two of these
bounds. In
the present example, Table 1 shows the Reynold's number for typical examples
of flow
parameters discussed in this section, which is much less than 1.
47
CA 3038104 2019-03-26
Table 1
Quantity Symbol Value
temperature Tfluid 310K
density p 103 kg/m3
viscosity 10 Pa = s
kinematic viscosity v = ti/p 10-6 m2/s
vessel diameter d 5-101.tm
maximum flow speed u 200-2000pcm/s
Reynolds number Re = ud/v <0.04
device radius r 1/./m
device speed vdevice < u
device angular velocity codevice
[0140] For the device motion considered here, with the parameters of Table 1,
the
resulting Womersley number (Eq. 2) is Wo <0.05, which is sufficiently small
that quasi-
static Stokes flow is a good approximation.
[0141] Passively-moving devices may be moved by fluid forces, gravity, and
Brownian
motion. For purposes of simplification, the devices in the present analysis
are assumed
to be neutrally buoyant in the fluid, so that the effect of gravity can be
ignored. To
evaluate the importance of Brownian motion in this example, the diffusion
coefficient of
a sphere is:
D kbTfluid 10-13 ni2/s (11)
671-(etc)r
with the parameters of Table 1, and where kB is Boltzmann's constant. The
Peclet
number:
48
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rvdevice
Pe = (12)
characterizes the relative importance of convective and diffusive motion over
distances
comparable to the device size. At the lower range of velocities for the
specific numerical
examples discussed, Vdevice 100 m/s, the resulting Pe = 1000, which is large
compared
to 1. Thus, diffusion is not important. The Peclet number represents the
gradually
decreasing importance of convective and diffusive motion for a particular
size, and thus
there is no distinct threshold at which diffusion becomes insignificant. But
for example,
for many purposes, Pe > 100 will give adequate accuracy, and in more stringent
cases,
Pe > 500 should assure that the effects of Brownian motion do not
significantly impact
the analysis. Lower Peclet numbers can be analyzed, just with the
understanding that
Brownian motion will increasingly add noise to the measurements as the number
gets
smaller (although this could be offset, e.g., by averaging multiple
measurements).
[0142] The rotational diffusion coefficient of a sphere is:
D kbTfluid ,.., 0.1 rac12/
rot (13)
87-r(eta)r3
(Berg, "Random Walks in Biology," Princeton University Press, 1993) For the
parameters
of Table 1, Wdevice 100rad/s so for a change in orientation of 9 1rad,
(Odevicee/Drot
1000, showing that rotational diffusion is not significant.
[0143] Since diffusive motion is relatively small over the times considered,
the motion
can be analyzed on the basis of assuming that such motion results entirely
from the fluid
forces on the device. For the time scales considered here, viscous forces keep
the device
close to its terminal velocity in the fluid (Purcell, ''Life at low Reynolds
number,"
American J. of Physics, 45, 1977). Thus, the device's velocity and angular
velocity can be
considered as the values giving zero net force and torque on the device.
49
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[0144] The pattern of normal and tangential stresses on the device 100 shown
in Figs.
5A, 5B, 6A, 6B, and 8A, when moving through the vessel 102, were determined
with the
geometry and viewpoint of Fig. 2 and the further parameters set forth in Table
2, for
purposes of illustration. This example, using the parameters given in Tables 1
and 2, is
comparable to that of a micron-sized device moving in a small blood vessel
such as a
capillary. With radii of curvature of tens of microns (Gunter Pawlik,
"Quantitative
capillary topography and blood flow in the cerebral cortex of cats: an in vivo
microscopic
study," Brain Research, 1981), such vessels are approximately straight over
the
distances considered in the present example.
[0145] In this example, the fluid pushes the device through the vessel at 530
m/s and
with angular velocity ¨150rad/s (i.e., clockwise rotation as viewed in Fig.
6A). The
position tic marks shown on the axes in Figs. 6A and 6B are in microns. The
arrow
lengths shown in Fig. 8A indicate the magnitude of the stresses at each of the
30
sensors, ranging from 0.8Pa to 3.9Pa.
Table 2
Quantity Symbol Value
device position yc 1.7i.tm
vessel diameter d 6,um
maximum inlet flow speed u 1000p.m/s
vessel segment length 10p.m
Direction to Wall and Direction of Motion Values
[0146] Evaluations for direction to the wall and direction of motion were
modeled for
device samples at various positions and orientations in vessels. Using
variations of the
situation show in in Figs. 2 & 4, a range of vessel diameters and flow speeds
corresponding to small blood vessels were simulated. These samples employed
parameters chosen uniformly at random according to the following criteria:
CA 3038104 2019-03-26
The maximum inlet fluid speed is between 200 and 1000 lArn/s, equally likely
flowing to
the right or to the left. The vessel diameter is between 5 and 10 pm. The
vessel segment
length is between 18 and 20 m. The position of device's center horizontally
is within 2
pm of the middle of the vessel's length. The position of device's center
vertically is
between the center of the vessel and a minimum distance of 0.5 iim from the
wall. Any
device orientation was allowed (0 to 360 degrees).
The samples tested used 800 training and 200 test samples. The results from
these
samples showed mean magnitudes of error less than 1 degree for both the
calculated
direction to the wall and the calculated direction of motion, with the largest
errors
occurring for devices near the center of the vessel.
Position and Vessel Geometry Values
[0147] Training samples were also used to evaluate the device's position in
the vessel
and the vessel diameter; in this case, the training samples were used to fit
regressions
between these properties and the Fourier coefficients of the stresses. Only
the first two
principal components of the Fourier coefficients, for each of normal and
tangential
stresses, were used for evaluation in this example.
[0148] Specifically, principal components are linear combinations of the
relative
magnitudes of the Fourier coefficients, Mk,s given in Equation (8).
Specifically, the hth
component has the form:
Ph = Eli`,1.1 Es an,k,s(mks ¨ mAk,$) (14)
where m^k,., is the average of mk,s over the training samples and ah,k,., are
weights, with
values for the first two principal components given in Table 3, which provides
weights
for first two principal components (i.e., an,k,, for h = 1,2). For each
component,
weights for normal and tangential stresses are on the first and second lines,
respectively.
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Table 3
1 2 3 4 5 6
h = 1 -0.419 0.508 -0.268 0.060 0.027 0.010
-0.419 0.473 -0.298 0.047 0.018 0.006
h = 2 0.451 0.184 -0.266 -0.352 -0.181 -0.080
0.451 0.479 -0.097 -0.258 -0.132 -0.052
[0149] To evaluate relative position using the training samples, the relative
position was
related to the first two principal components of the Fourier coefficients, pi
and p2, by
( it 15)
r' P' = / 1 + exp(¨(60 + + fi'2P2))
where the Aare the fit parameters given in Table 4. These parameters were
obtained
from standard statistical models fit to the training data; such procedures are
well known
in the art, and are available in conventional statistics software (e.g., R,
Mathematica,
MATLAB).
Table 4
Parameter Value Standard Error
¨0.51 0.09
3.3 0.3
/32 ¨4.6 1.1
[0150] Using Equation 12, the vessel diameter in microns could be calculated
using the
parameters given in Table 5. The resulting root mean square (RMS) error was
0.51 m,
or within about 5-10% of the actual diameters considered in this example. The
largest
errors were for devices near the center of the vessel; e.g., the RMS errors
were 0.911m
and 0.3[im for relative positions smaller and larger than 0.2, respectively.
52
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Table 5
Parameter Value Standard Error
13o 1.66 0.01
[31 0.68 0.01
32 4.05 0.06
131,1 2.74 0.05
132,2 11.0 0.4
131,2 ¨5.4 0.2
[0151] A calculated distance to the wall can be derived from the relative
position of the
device and the vessel diameter. In this example, as shown in Fig. 13,
calculation error
was largely dependent on relative position, with devices near the center of
the vessel
(relative position less than 0.2) having relatively high errors. Note that
"high" error in
this case is about 5-10% of vessel diameter, which is surprisingly accurate,
but perhaps
no more so than the fact that at larger relative positions, the predicted
points generally
fall almost exactly on the line, having average errors of about 2% or less.
Table 6
Relative Position RMS Error in Distance to Wall
less than 0.2
between 0.2 and 0.5
at least 0.5 0.05 m
Device Motion Values
[0152] For the cases considered here, angular velocities were typically about
100 rad/s,
so a 5ms measurement interval was selected to provide a change in orientation
of less
53
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than one radian between measurement to avoiding aliasing. To evaluate angular
velocity, the method discussed above of determining the angle AO by maximizing
the
correlation between the stresses before and after the motion was used to
evaluate
angular velocity using 100 of the test samples. The motion of each sample was
evaluated for At = 5ms. The resulting predicted and actual values of the
angular velocity
for these samples is shown in Fig. 14 and the mean error for the calculated
values was
0.51rad/s (about 0.5% of the angular velocity).
Complex Vessel Geometries
[0153] The stress-based calculated values discussed above illustrate
techniques that
treat the simple case of a single spherical device moves passively with the
fluid through
a straight vessel. Using the samples of those cases as a basis, new analyses
to calculate
values for more complex situations can be created. One approach would be to
modify
the machine learning techniques described herein (many techniques would likely
produce accurate results with the teachings herein to guide) for vessels with
other
shapes. An alternative approach is to apply the evaluation methods set forth
for straight
vessel to these more complex situations. Even though the resulting calculated
values are
almost certain to be less accurate, it is of interest to see how well the
analysis process
performs in situations for which it was not trained, so this latter approach
is discussed
below.
[0154] In evaluating the use of these techniques, it is helpful to graphically
show how
inaccuracies can occur in the calculated values through the assumption of
incorrect
geometries (e.g., a straight channel being assumed when in fact it is not
straight). The
quality of the calculated values of the device's relation to the vessel can be
graphically
represented with an arrow through the device's center, as shown in Fig. 16.
The
calculated relation of a device 200 to a vessel 202 is indicated with respect
to an
orientation line 204 shows a relative "front" to index the orientation of the
device 200.
54
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Solid calculated value arrow 206 through the device's center 208 graphically
summarizes three calculated values: the direction and distance from the
device's center
208 to the nearest vessel wall 210 (the calculated distance being indicated by
the
portion of arrow 206 from the device's center to the arrowhead), and the
vessel's
calculated diameter Dcaic (the calculated diameter being indicated by the
total length of
arrow 206). The actual vessel 202 has vessel walls 212, while the calculated
values
indicate the positions of calculated walls 210 indicated in dashed lines. In
the particular
example shown schematically in Fig. 16, the device 200 slightly underestimates
both its
distance to the actual wall 212 and the vessel's actual diameter. Perfect
values would
show the solid arrow 206 directed perpendicular to the vessel walls 212 and
extending
from one wall 212 to the other.
Curved Vessels
[0155] The following discussion examines how calculated values based on
straight
vessels perform as a device 300 as depicted in Fig. 18 moves through an
exemplary
curved vessel 302, such as illustrated in Figs. 17 and 18. The vessel 302 has
two types of
curvature: a bump 304 (shown in Fig. 17) in the vessel wall 306 having a
radius of
curvature similar to the size of the device 300, occurring along a straight
section 308,
and a gradually-curved section 310, with a radius of curvature that is large
compared to
the size of the device 300. For the numerical examples discussed herein, the
values used
for analysis used a maximum inlet flow speed of li = 1000pimjs, and positions
along the
axes in Fig. 17 are represented in microns. These parameters can be
significantly greater
in scale when applying the present techniques to fluids having a higher
viscosity. In Fig.
17, the curved arrow 312 shows the path of the device's center 314 (shown in
Fig. 18),
as fluid moves it through the vessel 302. Ticks 316 along the curve 310
indicate positions
of the center 314 at various times.
CA 3038104 2019-03-26
Evaluating Angular Velocity
[0156] In Fig. 18, as the device 300 moves through the vessel 302, the
stresses on the
device 300 surface mainly change due to the device's rotation with respect to
the vessel
wall 306. In particular, the position on the surface of the maximum tangential
stress
generally faces the closest vessel wall 306. The direction to the wall 306
changes due to
a combination of the device's rotation and the vessel curvature, as shown in
Fig. 18.
Specifically,
clewan chPwall d(psi)
(16)
dt dt dt
where 1i is the device's orientation (indicated with respect to orientation
line 318,
shown in Fig. 18), and wall and (Iowan are respectively the angle to the
vessel wall
measured from the front of the device and measured from the x-axis (comparable
to the
same angles shown for the device 100 in Fig. 9). The first term on the right
is due to the
vessel curvature. The second term is ¨codevice, the negative of the device's
angular
velocity.
[0157] In general, measuring the change in stresses evaluates how rapidly the
direction
to the wall 306 changes with respect to the front of the device 300.
Alternatively,
¨dOwalVdt is how rapidly the device 300 rotates with respect to the vessel
wall 306,
giving the rate of change of the orientation with respect to the wall 306. In
a straight
vessel, ¨dOwaii/dt = COdevice so the rate of stress change is directly
proportional to the
device's angular velocity. However, in a curved vessel, Eq. (16) shows this
value has an
additional contribution from the vessel curvature.
[0158] For a device moving through the curved vessel, Fig. 19A shows a
comparison of
the angular velocity, calculated from correlation over At = 5ms, with the
actual value,
Wdevice, where the calculation of angular velocity is made as described for a
straight
vessel. While the device 300 is in the straight portion 308 of the vessel 302,
the
56
CA 3038104 2019-03-26
calculated value is close to the actual value. The angular velocity changes as
the device
300 passes the bump 304 in the vessel wall 306, and the calculated value
tracks the
change with a delay of about At. Fig. 19B shows the correlation between stress
patterns
separated by 5ms (the time interval used to evaluate the angular velocity in
this
example).
[0159] In the slowly curving portion 310 of the vessel 302 (time after 60ms),
the
calculated value for angular velocity deviates systematically from the actual
value. This
difference is because the evaluation procedure actually measures the rate of
the
device's orientation changes with respect to the vessel wall, i.e., ¨dew /dt
from Eq.
(16), rather than with respect to an external reference. To test this
relationship, Fig. 19A
also shows the average rate of change of the device's orientation with respect
to the
wall 306. This is close to the calculated value in both the straight section
308 and the
gently curved section 310 of the vessel 302. As the device 300 passes the bump
304, the
value deviates significantly from ¨dewall
/dt, in part because the direction of maximum
tangential stress deviates from the direction to the nearest point on the
vessel wall (as
seen in Fig. 20B). So in this case, large tangential stress is not an accurate
indication of
the direction to the vessel wall, and its change over At also gives an
inaccurate value for
¨dOwaii /dt. Instead, for small, high-curvature bumps in the vessel wall, the
calculated
value more closely tracks the actual angular velocity.
[0160] Fig. 19B shows the drop in correlation of interpolated stress patterns
as the
device 300 passes the bump 304, indicating that the stress pattern is changing
more
than it would just due to device rotation in a straight vessel. This is useful
information.
The decreased correlation is an indication of an abrupt geometry change in the
vessel.
While a hypothetical bump 304 may be of relatively minor interest (though it
at least
provides a system feature for mapping) in this context, if it were a bulge in
a high-
pressure industrial pipe, or plaque in pipes or vasculature, this could be
important
information.
57
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Evaluating the Device's Relation to the Vessel
[0161] Figs. 20A-20D show comparisons of actual and calculated values of
information
relating to the position of the device 300 and its relation to the vessel 302
as a function
of time as the device 300 moves through the vessel 302 shown in Figs. 17 and
18. The
graph of Fig. 20A compares actual and calculated vessel diameter at the
device's
position. Fig. 20B shows the differences between the calculated and actual
directions to
the nearest point on the wall and the calculated and actual direction of
motion. Fig. 20C
compares the actual and calculated distance between the device's center and
the
nearest point on the vessel wall. Fig. 20D compares the actual and calculated
speed at
which the device 300 moves through the vessel 302. The calculated values are
determined using the techniques discussed herein for a straight vessel.
[0162] The device 300 is in the nearly straight section 308 of the vessel 302
for the first
30ms, and the calculated values are close to the actual values. During 35-
55ms, the
device 300 passes the small bump 304 in the vessel wall 306, and the
calculated values
deviate significantly from the actual values. The fairly abrupt changes in the
calculated
values (not only alone, but in combination, since the relationships between
the
calculated values may change as well) allow the device 300 to identify when
such
changes in geometry occur. Finally, after about 60ms, the device 300 moves in
the
gently curved section 310 of the vessel 300. The direction values (as shown in
Fig. 20B)
are quite accurate despite the curvature of this section, but the other
calculated values
have somewhat larger errors than in the straight vessel section 308. Overall,
the
calculated values give the device 300 a rough idea of its relation to the
curved vessel
section 310, and a clear signal that a change has occurred.
[0163] Of course, this is using machine learning algorithms trained for
straight vessels
on curved vessels. Obviously, appropriate retraining with data gathered from
analogous
vessels would yield higher accuracy. But, there is also a somewhat different
method of
handling such situations, which is by using classification techniques.
58
CA 3038104 2019-03-26
Branching Vessels
[0164] A bump or curve is one of the simplest possible geometry changes.
Consider
more complex cases such as where the vessel branches, or multiple branches
merge.
This is a common occurrence in fluid systems from vasculature, to
microfluidics, to
industrial piping. Such changes are important to device goals such as mapping
and
navigation, given that they are the fluid system equivalent of street
intersections,
highway on/off ramps, or other features common to roads.
[0165] In biological systems, the identification of such system features could
aid in, for
example, organ detection and discrimination (Augustin and Koh, "Organotypic
vasculature: From descriptive heterogeneity to functional pathophysiology,"
Science,
2017) as well as tumor detection (Nagy, Chang et al., "Why are tumour blood
vessels
abnormal and why is it important to know?," British J. of Cancer, 2009; Jain,
Martin et
al., "The role of mechanical forces in tumor growth and therapy," Annual
Review of
Biomedical Engineering, 2014). In such cases, devices able to determine vessel
geometry
could supplement other available information, such as chemical concentrations,
to more
accurately identify different types of tissue.
[0166] Considering all these possible uses (and these are just examples,
certainly there
are more), the ability to detect branching or merging vessels is an important
device
capability. Some methods to detect where a vessel splits into branches, or
when
multiple vessels merge into a larger one, have been previously suggested. For
example,
acoustic detection seems possible (Freitas, "Nanomedicine, Volume I: Basic
Capabilities," Landes Bioscience, 1999), though interpreting reflected signals
could
require significant computation in the presence of multiple reflections,
scattering, and in
some cases, the small difference in acoustic impedance between the fluid and
walls,
among other possible issues.
59
CA 3038104 2019-03-26
[0167] The approach taken here is that the detection of branches (in which we
will
include merges, which can be viewed as branches with the fluid traveling in
the opposite
direction) can be made based on measured changes in the patterns of fluid-
induced
stresses on their surfaces when the size, fluid speed, and fluid kinematic
viscosity are
such that a viscous flow regime exists.
Geometry of Vessels
[0168] For purposes of illustration, the following discussion again employs
the
parameters of the specific numerical example discussed herein for a spherical
device of
neutral buoyancy. These examples are used to evaluate device behavior in
vessels with
geometry comparable to that of short segments of capillaries, generally having
radii of
curvature of tens of microns (Gunter Pawlik, "Quantitative capillary
topography and
blood flow in the cerebral cortex of cats: an in vivo microscopic study,"
Brain Research,
1981). Typically, such vessels split into just two branches (CASSOT, LAUWERS
et al., "A
Novel Three-Dimensional Computer-Assisted Method for a Quantitative Study of
Microvascular Networks of the Human Cerebral Cortex," Microcirculation, 2006),
and
the branches have a larger total cross section than the main vessel (Murray,
"The
physiological principle of minimum work: I. The vascular system and the cost
of blood
volume," Proceedings of the National Academy of Sciences USA, 1926), leading
to
slower flows in the branches (Sochi, "Fluid flow at branching junctions,"
International
Jounral of Fluid Mechanics Research, 42, 2015). For simplicity, the examples
discussed
focus on planar vessel geometry, where incoming and outgoing axes of curved
vessels
are in the same plane, and where branching vessels have the axes of the main
vessel
and the branches in the same plane. Obviously, in many actual scenarios, the
fluid
system would not be planar, and this would actually help with goals such as
mapping,
because the off-plane angle could serve as an additional identifier to reduce
ambiguity
of similar sections of the fluid system. Such angle changes could be detected
by the
same methods we describe for classification of planar systems, and could also
be
CA 3038104 2019-03-26
detected by additional sensors, such as gyroscopes, providing additional data
to confirm
or increase the accuracy of inferences.
[0169] Figs. 21A and 21B show examples of two vessel geometries considered,
with Fig.
21A showing a device 400 moving through a branched vessel 402 and Fig. 21B
showing a
device 410 moving through a curved vessel 412 (similar to the device 300 and
curved
section 310 discussed with regard to Figs. 17 & 18). In each case, the curved
arrow (404,
414), shows a portion of the path of the device's center as it moves through
the vessel
(402, 412) with the fluid. The ticks (406, 416) along the paths indicate times
(in
milliseconds for this example) before or after the location of the device
(400, 410). The
dashed rectangle 22-1 of Fig. 21A indicates the part of the branched vessel
402 shown in
Figs. 22A ¨ B. The dashed rectangle 22-2 of Fig. 21B indicates the part of the
curved
vessel 412 shown in Fig. 22C ¨ D. The device (400, 410) in each case for this
example has
a radius 11um and the vessel inlets, on the left side of each vessel, both
have diameters
of 7.8,um.
[0170] To simplify comparison, the fluid flow speed for these two cases is
chosen so the
devices (400, 410) have the same average stress magnitudes on their surfaces
at the
indicated position along each path (404, 414). Specifically, the maximum speed
at the
inlet is 1000 m/s for the branched vessel 402 and 530 m/s, for the curved
vessel 412.
At the position of the device 400 shown in the branch 402, the device 400
moves at
1891um/s and rotates with angular velocity ¨34rad/s, i.e., clockwise. For the
device 410
in the curve 412 these values are 186,um/s and +39rad/s. Again, the values
provided are
exemplary, and other values would be appropriate for situations that have
dynamic
similarity, including much larger values where much more viscous fluids are
considered.
[0171] Computational models of devices in branched and curved vessels were
created
to develop and test a branch classifier based on stresses on the device's
surface. These
models were used to generate data samples. Such data samples could also be
obtained
61
CA 3038104 2019-03-26
experimentally, e.g., by measuring forces on microfluidic devices (Wu, Day et
al., "Shear
stress mapping in microfluidic devices by optical tweezers," OPTICS EXPRESS,
2010). For
this analysis, models of device paths were created for a range of vessel
diameters and
flow speeds corresponding to small blood vessels, with parameters given in
Table 1.
These samples are variations of the situations shown in Figs. 21A and 21B,
with
parameters chosen uniformly at random according to: A maximum inlet fluid
speed
between 800 and 10001.lm/s. For curved vessels, a vessel diameter between 6
and
1311m, and a bend angle, between direction of inlet and outlet, between 25
degrees and
75 degrees. For a vessel splitting into two branches, diameters of the
branches, dl and
d2, were between 6 and 10 m. The diameter of the main vessel, d, is determined
from
dl and d2 according to Murray's law (Murray, "The physiological principle of
minimum
work: I. The vascular system and the cost of blood volume," Proceedings of the
National
Academy of Sciences USA, 1926; Sherman, "On connecting large vessels to small:
The
meaning of Murray's law," Journal of General Physiology, 1981; Painter, Eden
et al.,
"Pulsatile blood flow, shear force, energy dissipation and Murray's law,"
Theoretical
Biology and Medical Modeling, 3, 2006). The two branch angles were between 25
degrees and 75 degrees, and ¨25 degrees and ¨75 degrees, respectively. Vessel
segment
length extended 30 m in each direction from the curve or branch. The initial
position of
the device's center was eight times the device radius from the vessel inlet,
and
randomly positioned between the vessel's walls with minimum gap 0.2r between
the
device surface and the wall. The device orientation was between 0 and 360
degrees.
[0172] From the initial device position, the device's motion through the
vessel until it
comes within 81.tm of an outlet was solved. Boundary conditions on the flow
were a
parabolic velocity profile at the inlet, no-slip along the vessel wall, and
zero pressure at
the outlet for a curve, or at both outlets for a branch. A total of 2000
samples created
according to this procedure were studied, with 1000 for each vessel type
(i.e., curve or
branch), For each of these vessel types, 800 samples were used for training
the classifier
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and the remaining 200 were used to test the classifier performance. The paths
in these
samples are about 401.tm in length. The fluid typically moved the device along
the path
in about 100ms.
Device Stresses and Motion in Vessels
[0173] Stresses on the device surface can be determined by numerically
evaluating the
flow and device motion in a segment of the vessel. For the vessel sizes,
planar
geometries, and fluid speeds considered here, the motion and stresses can be
approximated by two-dimensional quasi-static Stokes flow. As examples, Figs.
22A-22D
show the fluid velocity near the device, in the sections of the vessels
indicated by the
dashed rectangles 22-1 and 22-2 in Figs. 21A & 21B, respectively. Despite the
different
vessel geometries, the flow near the device is similar in the two cases. In
Figs. 22A-22D,
the arrows show streamlines of the flow with the arrow size showing the flow
speed.
Fig. 22A shows fluid velocity with respect to the vessel in the branched
vessel case.
Velocity is zero at the vessel wall, and matches the motion of the device at
its surface.
Fig. 228 shows fluid velocity with respect to the device in the branched
vessel. Velocity
is zero at the device surface. Fig. 22C shows fluid velocity with respect to
the vessel in
the curved vessel. Fig. 22D shows fluid velocity with respect to the device in
the curved
vessel.
Stresses on Device Surface
[0174] The stresses on a device's surface are denoted by s(0,t) for the stress
vector at
angle 9 at time t. The angle 6 specifies a location on a device's surface,
measured from
an arbitrary fixed point on the device called its "front" (such as illustrated
in Fig. 9). A
device can evaluate s(0,t) by measuring stresses at various locations on its
surface with
force sensors, and interpolating between these locations. By measuring forces
normal
and tangential to the surface, the sensors determine the stress vector.
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[0175] The stresses depend on the vessel geometry near the device and the
speed of
the flow. However, this relationship may not be not unique: different
geometries can
produce similar stress patterns. Figs. 21A & 21B provide one such example of
similar
stress patterns, as indicated by the diagram of stresses about the device
shown in Fig.
23. Fig. 23 compares how stresses vary over the device's surface for the
branched vessel
and for the curved vessel, with the arrows indicating the stress vectors at
points spaced
uniformly around the surface (comparable to the illustration of stress vectors
for a
straight vessel as shown in Fig. 8A). The arrow lengths show the magnitude of
the
stresses, ranging up to 0.58Pa, at locations of sensors on the device surface.
The
patterns of stress on the surfaces are nearly the same for the branched and
curved
vessels. Thus, in general, the pattern of stresses at a single instant does
not reliably
identify the geometry of the vessel near the device, and in such situations it
is necessary
to analyze changes in the stress patterns as the device moves to distinguish
the cases. In
use, continuous data collection is not needed; rather instantaneous
"snapshots" of
stress data at two or more time points can be used.
Changing Stress Patterns
[0176] As a device moves through a vessel with changing geometry, the stresses
on its
surface change. In many cases, the stresses change significantly as a device
moves
through a branch, whereas changes are fairly small as a device moves around a
curve (as
noted in the discussion of curved vessels), allowing these two cases to be
distinguished
from each other.
[0177] One measure of changing stresses is the correlation of the stress
pattern at two
times. For example, if f(9) and g(8) are two vector-valued functions of the
angle 8
around the device's surface. The correlation between these vector fields is:
cor(f, g) = ________________________________________________________ 1 f f(e)
= g(e)de(17)
11f1111g11
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with the normilfl = 0021. f(61) = f(6) d and f = g denoting the inner product
of the two
vectors. In this case, the vector fields are the stresses on the device
surface. As an
example, the correlation between the surface stresses in the two cases shown
in Fig. 23
is 0.98. Due to the normalization, the correlation is independent of the
overall
magnitude of the stresses. In particular, this means that the correlation does
not
depend on the fluid viscosity.
[0178] As noted, the device can evaluate the stress field s(0,t) by
interpolating surface
stress measurements, and a particularly useful method is interpolating the
stress
pattern from a few Fourier modes. The correlation between two stress patterns
can be
computed directly from the Fourier coefficients, avoiding the need to
explicitly evaluate
the integrals in Eq. (17). As in the straight vessel example, the first six
modes are
analyzed, which is sufficient to capture most of the variation in stress over
the device's
surface for the cases considered herein.
[0179] When viewed from a fixed location on the device surface (such as a
specific
sensor), the stress changes both due to changing vessel geometry and due to
the
device's rotation caused by the fluid. For spherical devices, this rotation is
not relevant
for identifying vessel geometry, and thus the device must remove the component
of
change that is due to rotation of the device. One way to do so is to maximize
the
correlation over all possible rotations of the device between the two
measurements
used in the correlation. Specifically, this approach compares the stress at
time t, s(0,t),
with shifted versions of the stress at a prior time, s(0+ Aat ¨ At), and uses
the
maximum correlation over all shifts AO. That is, the device measures changes
in the
pattern of stress that are not due to its rotation by evaluating:
c(t, At) = mgcor(s(0, t), s(0 + AO, t ¨ At))
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for the correlation function of Eq. (17). Another application of this
maximization is
evaluating the device's angular velocity because the shift in angle, AO,
giving the
maximum as a value for how much the device has rotated between these two
times.
[0180] Using the example of a micron-sized device in capillary-sized vessels,
Fig. 24
shows the correlation between stress patterns separated by 10ms as the device
moves
through the branch and curved vessels shown in Figs. 21A and 21B. The times on
the
horizontal axis correspond to the tick marks along the paths shown in Figs.
21A and 21B,
with t = 0 corresponding to the device positions shown in those figures. For
the curve,
the stress pattern remains nearly the same, so correlations are close to one.
For the
branch, however, the correlation drops as the device approaches the branch,
about
30ms before it reaches the position shown in Fig. 21A. Later, the correlation
drops again
as the device moves into one of the branches. Similarly, if the device were
moving the
opposite direction, i.e., the flow was a merge of two small vessels into a
larger one, the
device would encounter these drops in correlation in the opposite order and at
times
shifted by 10ms as it compares its current stress pattern with the pattern it
had
encountered earlier along the reversed path.
[0181] For the flow speeds and vessel sizes considered here, At = 10ms is a
reasonable
choice, as it represents an interval during which a device can move a distance
comparable to the extent of branching or curving, but not so far as to
completely pass
the changing geometry. However, the precise value of At is not important. For
example,
comparing stresses separated by At = 5ms or 20ms is qualitatively similar to
the
behavior shown in Fig. 24. For definiteness, we use At = 10ms in the following
discussion. For more viscous fluids and larger device and vessel sizes,
depending on
device velocity, it is likely that substantially larger time intervals could
be used.
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Classifiers for Vessel Geometry
[0182] The results shown in Fig. 24 suggests that a device can identify vessel
branches
by checking for when the correlation of stresses separated by a short time is
sufficiently
small. This procedure should reliably distinguish branches from curves if
there is little
overlap in the distributions of minimum correlations for these two geometries.
Unfortunately, the behavior shown in Fig. 24 does not occur in all cases.
Instead, the
distributions of minimum correlation for curves and branches have considerable
overlap, especially when the device is near the center of the vessel, as shown
in Fig. 25,
which is a scatterplot of the minimum value of c(t,At) along a path (for At =
10ms) and
initial relative position; this plot quantifies the difficulty caused by
overlap in minimum
correlation values, by showing how the minimum correlation along a path
depends on
how close the device is to the vessel wall before it reaches the curve or
branch, i.e.,
while still in a fairly straight portion of the vessel. How close a device is
to the vessel wall
is given by the device's relative position (r.p.) from Equation (6), which can
be
calculated from instantaneous surface stresses when in a straight vessel. The
points on
the plot of Fig. 25 distinguish devices moving through a branch, around a
curve, or along
a straight vessel. To highlight the differences among these geometries, the
horizontal
axis shows 1¨c on a logarithmic scale. Thus, situations where the stress
pattern changes
only slightly over time At (i.e., correlations are close to 1), appear on the
left side of the
diagram.
[0183] In cases where the device starts near the center of the vessel, Fig. 25
shows that
curved paths have a wider range of minimum correlations than branches, and
this range
includes the values occurring in branches. Combined with smaller, noisier
stresses for
devices relatively far from the vessel wall, this indicates correlation is not
a reliable
identifier of branches when devices start near the vessel center.
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Identifying Branches from Stress Measurements
[0184] To improve identification for paths starting close to vessel center,
additional
information available to the device can be used. In one example of creating a
vessel
geometry classifier, a summary of the stress pattern at the time the device
evaluates the
correlation was used. That is, to identify branches, at time t, three pieces
of information
were employed in this example: the correlation c(t,At), the relative position
for the path
that was determined prior to any significant change in the stress, and the
current stress
s(0,t). Using this information, a set of training samples was generated. For
each training
sample (created as discussed above), the time t was determined along the path
with
the minimum correlation, and the three pieces of information from that time
along the
path were employed. This method is an example of off-line training; that is,
the training
samples are assumed to have measurements from a completed path (i.e., a path
starting before the device reaches the branch or curve and continuing until
the device is
well past those changes). With measurements along the whole path, the time of
minimum correlation can be obtained and values at that time used for training.
Using
such training samples from both branch and curve vessels results in the
example of a
logistic regression classifier for branches described herein. The parameters
of the
resulting model were then applied to evaluate the accuracy of the model.
Regression Classifier for Branch Detection
[0185] In the present example of a branch classifier, branches are identified
using a
logistic regression based on the three characteristics of the device's
stresses along its
path through a vessel: First, the correlation between the current stress and
that of a
short time earlier. Second, the device's relative position in the vessel
evaluated during
the device's most recent passage through a nearly straight section of the
vessel. Third, a
measure of the shape of the device's current stresses, specifically the first
principal
component of the Fourier coefficients of the stress pattern (as discussed for
analysis of
the stresses when moving through straight vessels).
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[0186] The regression model for the probability of a branch, P - branch, is
Pbranch = 1/1 exp(¨b(log(1 ¨ c), rp, pi)) (19)
where c is the correlation between changing stress patterns, defined in Eq.
(18), rp is the
relative position, defined in Eq. (6), pus the first principal component of
the stress
pattern, and
b(lc,rp,pi) [3o + /31 lc + f32 rp + flu lc' + /32,2 rp2 + P3pi
where the [3... are the parameters, given in Table 7, determined from the
training
samples.
Table 7
Parameter Value Standard Error
igo ¨0.8 0.7
¨1.7 0.6
132 9.0 1.8
/31,1 ¨0.97 0.11
132,2 6.8 2.3
193 11.6 0.8
[0187] Training this regression used stress measurements along the complete
path of
each sample to identify the time with minimum correlation along the path. This
"off-
line" training corresponds to the situation after devices complete their
paths, so stress
measurements all along the paths are available for training. Specifically, for
each
training sample, rp is the relative position at the start of the sample path
where, by
construction, the device is in a straight vessel segment prior to reaching the
curve or
branch. Moreover, c is the minimum correlation along the path, i.e., the
minimum value
of c(t,At) along a path, for At = 10ms. The branch and curve points in Fig. 25
are
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CA 3038104 2019-03-26
examples of these relative position and correlation values. Finally, the value
of pi used
for training is the principal component of the device's stress at the time of
the minimum
correlation.
Applying the Classifier to Identify Branches
[0188] The classifier described above was trained with the minimum correlation
along a
path. A device using the same method when applying the classifier would have
to wait
until it was sufficiently far past a changing geometry to be sure it had
detected the
minimum correlation along the path for that change. This off-line application
of the
classifier could be useful in reporting vessel geometry changes well after
encountering
them, e.g., to provide a description of the path leading the device to a
target location.
[0189] The discussion below addresses the more demanding classification task
of
recognizing a branch near the time the device encounters it. This on-line or
real-time
classification allows the device to take action while still near the branch.
In this case, a
device uses the classifier by repeatedly evaluating Eq. (19) as it moves.
During these
evaluations, the correlation c(t,At) is not necessarily the minimum
correlation along the
path: i.e., the device could encounter smaller values as it continues through
the vessel.
Thus, the device using this method is extrapolating beyond the values used for
training.
[0190] The classifier uses the device's relative position in the vessel before
it encounters
a branch or significant curve. Thus, the device must save its calculated value
for relative
position, updating the value only while vessel geometry is not changing. A
device could
determine when this steady behavior occurs by checking when the correlations
between
stresses at various delay times At are close to 1, and the pattern of stress
on its surface
is consistent with its presence in a straight vessel segment. When the device
encounters
changing geometry, it uses the saved value for its relative position when
evaluating the
classifier, i.e., Eq. (19). This procedure applies to typical capillaries
(Gunter Pawlik,
"Quantitative capillary topography and blood flow in the cerebral cortex of
cats: an in
CA 3038104 2019-03-26
vivo microscopic study," Brain Research, 1981) where significant geometry
changes are
separated by tens of microns, a considerably larger distance than the size of
the devices
small enough to pass through those vessels.
[0191] As an example of how the classifier applies to on-line classification,
Fig. 26 shows
the values of P - branch from Eq. (19) along the device paths of Figs. 21A &
21B. Fig. 26 plots
the calculated probability of encountering a branch (P " branch) vs. time as
the device
moves along the paths shown in Figs. 21A & 21B, based on correlation c(t,At)
with At =
10ms. The branch path (shown in Fig. 21A) has higher values than the curved
path
(shown in Fig. 21B). This example indicates how a device could use the
classifier for on-
line branch identification, such as by considering a branch to be nearby
whenever P branch
exceeds a predetermined threshold. For this example, a threshold around 0.8
serves to
distinguish the branch from the curve.
[0192] In addition to identifying whether the device passes a branch, Fig. 26
indicates
when this method detects the branch. In this case for the branching vessel, P
. branch
becomes large about 30ms before the device reaches the location shown in Fig.
21A.
This corresponds to the device entering the branch. The device slows as it
moves
through the branch, leading to a period of large correlation for about 20ms.
As the
device leaves the branch, the stress pattern changes again, leading to a
second
minimum in the correlation (see Fig. 20) and another maximum in P
- branch. In other cases,
the device moves more rapidly through the branch, so the At = 10ms time
difference
used here gives a single minimum in the correlation and, correspondingly, a
single peak
in Pbranch. A device could distinguish these cases by checking for a second
peak within a
few tens of milliseconds. Over that amount of time, the second peak indicates
the
device is leaving the branch rather than encountering a second branch. This is
consistent
with the typical spacing of branches in capillaries.
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Selecting a Threshold to Identify Branches
[0193] A suitable threshold to use for identifying branches with the
classifier discussed
above depends on the relative importance of false negatives (i.e., missing a
branch) and
false positives (i.e., incorrectly considered a curved vessel to have a
branch). The relative
importance of these errors depends on the particular application. For example,
if a
device with locomotion capability needs to move into a branch, it is better to
recognize
a branch before passing it, so the device would only need to actively move a
short
distance to reach the desired branch. This contrasts with the situation of not
recognizing
the branch until well after the device has passed it, in which case it would
need to move
a larger distance, and move upstream against the flow of the fluid, expending
greater
energy reserves. In this situation, the device could use a relatively low
threshold for
branch classification, thereby being fairly sure it will identify branches as
it encounters
them, though it may also, incorrectly, attempt to move into a branch when
passing
through some curved vessels (in which case, at worst, the device may hit the
vessel
wall). Such errors are more likely the earlier the device needs to identify a
branch
because the flow well upstream of a branch is similar to that in vessel
without branch.
[0194] Another action the device could take upon detecting a branch is to move
to the
vessel wall near the branch and act as a beacon to other devices arriving at
the branch.
The beacon signal could, for example, direct subsequent devices into one
branch or the
other to ensure roughly equal numbers explore each branch despite the fluid
flow
favoring one branch over the other. More generally, branches could be useful
locations
to station devices for forming a navigation network (Freitas, "Nanomedicine,
Volume I:
Basic Capabilities," Landes Bioscience, 1999). With a limited number of
devices to form
this network, and if it is sufficient to station devices at some rather than
all branches,
the device could use a high threshold of probability to ensure that branches
identified
by the classifier are very likely to actually be branches.
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CA 3038104 2019-03-26
[0195] Other applications have less need for identifying branches while
devices are
close to them, but instead collect information on the number and spacing of
branches
for later use, e.g., as a map or diagnostic tool at larger scales than short
segments of a
single vessel. This applies to identifying vessel geometries that distinguish
different
organs or normal tissue from cancer tissue (Nagy, Chang et al., "Why are
tumour blood
vessels abnormal and why is it important to know?," British J. of Cancer,
2009; Jain,
Martin et al., "The role of mechanical forces in tumor growth and therapy,"
Annual
Review of Biomedical Engineering, 2014). In such cases, the emphasis could be
on
identifying all branches, favoring a relatively low threshold when approaching
the
apparent branch, and then verifying detected branches with subsequent
measurements
after the device has moved past each possible branch, thereby reducing the
false
positives while keeping sensor information obtained near the branches from the
original
identification of those cases that are later verified to be branches.
[0196] When multiple devices are employed, if spaced closely enough, devices
passing a
branch could communicate verified branch detections to devices upstream of the
branch. With a message from a downstream device that it verified its recent
passage of
a branch, a device could lower its threshold in anticipation of that upcoming
branch. The
message could come from a downstream device that entered a different branch of
the
splitting vessel than the device receiving the message. For the example of
micron-sized
devices in capillaries or similarly-sized vessels, devices using acoustic
communication
could compare measurements over 100,um or so (Hogg and Freitas, "Acoustic
communication for medical nanorobots," Nano Communication Networks, 2012),
which
is farther than the typical spacing between branches in capillaries.
Verification After Passing a Curve or Branch
[0197] A device can use stresses to identify branches as it encounters them.
This
contrasts with off-line methods that collect time-stamped information before,
during
and after a device passes a branch, and later use the entire path history to
identify if and
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CA 3038104 2019-03-26
when the device passed branches. A possible combination of the two approaches
is to
use on-line classification to identify likely branches, record information
about them, and
later verify the branch detection when the device has additional information
after
passing the possible branch. Information a device could use for this
verification task
includes indicated changes in vessel diameter, relative position, and/or
device speed
before and after passing the curve or branch. Typically, these changes are
much larger
after passing a branch than a curve. Specifically, when a vessel splits into
branches, the
branches have smaller diameter than the main vessel, but the combined cross
sections
of the branches is larger than that of the main vessel (Murray, "The
physiological
principle of minimum work: I. The vascular system and the cost of blood
volume,"
Proceedings of the National Academy of Sciences USA, 1926). Thus, calculating
values
for vessel diameter before and after the branch gives a direct indication of
branching.
[0198] The increased total cross sectional area after a vessel splits leads to
slower flows
in the branches (Sochi, "Fluid flow at branching junctions," International
Jounral of Fluid
Mechanics Research, 42, 2015), whereas flow in a curve remains nearly
constant. This
means that a device could also check for changes in its speed through the
vessel before
and after passing a detected branch or curve to verify the identification.
However,
slower fluid speed in the branch does not necessarily mean that the device's
speed
changes in the same proportion, because (as discussed herein when discussing
evaluation of device speed) the device's speed depends both on the speed of
the flow
and how close the device is to the wall (i.e., its relative position). Along
with flow speed,
the relative position can change as a device passes a branch. However, as
previously
described for straight vessels, a device can normally accurately determine its
distance
from the vessel wall and its rate of rotation. Factoring these into any speed
change
detected makes this a useful test.
[0199] Figs. 27A & 27B illustrate the behavior of devices passing through a
branch (Fig.
27A) and a curve (Fig. 27B), starting at different relative positions in the
vessel. Each
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CA 3038104 2019-03-26
path shown is for a device traveling by itself through the vessel, passively
moved by the
fluid flow. Again using the example of micron-sized devices in capillary-sized
vessels, the
ticks along the paths indicate times, in milliseconds, from the start of each
path when
the maximum inlet flow speed is 1000,um/s. Devices along paths near the center
of the
vessel move more rapidly than those near the walls, indicated by the wider
spacing
between successive ticks along the central paths. The vessel inlets both have
diameters
of 7.8,um.
[0200] Devices close the wall remain close upon entering a branch or moving
around a
curve. However, devices entering a branch near the center of the vessel move
to near
the wall of the branch, and devices starting between the center and the wall
move to
near the middle of a branch. This change in relative position can distinguish
branching
from curved paths in cases where the device is not close to the wall.
Similarly, the
change in speed is particularly large for branch paths when the device is not
near the
wall, so its speed reflects the decreasing flow through the branches. When the
device is
near the wall, in either a branch or curve, it moves relatively slowly and
remains near
the wall, giving relatively little change to distinguish between a branch and
a curve.
[0201] Changes in relative position and speed are particularly useful for
distinguishing
curves and branches for paths near the middle of the vessels, precisely the
cases where
the correlation-based method (discussed with regard to Fig. 25) are least
reliable.
Moreover, the larger differences in these measures between curves and branches
for
paths near the center of the vessel could compensate, to some extent, for the
lower
accuracy when calculating position and speed from stresses when the device is
near the
center of the vessel.
[0202] Due to errors in evaluating position, speed, and vessel diameter from
surface
stresses, evaluating changes from a combination of these measures before and
after
passing a branch or curve is more robust than relying on a single method.
Similarly,
CA 3038104 2019-03-26
combinations of various sources of information are likely to be helpful in
developing
classification schemes for alternative vessel geometries.
Classification Performance
[0203] To evaluate the performance of the branch classifier example discussed
herein, a
set of test samples were studied. In the branch vessels considered in this
example, the
fluid flows from the larger vessel into the two branches, and thus testing the
classifier
with these paths evaluates how well a device recognizes when the vessel splits
into two
smaller vessels, with the device moving into one of them. The situation for
flow merging
from smaller branches into a larger vessel is similar, since a device at a
given location in
a vessel experiences stresses on the device surface that are the same for
either direction
of the flow, due to the reversibility of Stokes flow (Happel and Brenner, "Low
Reynolds
Number Hydrodynamics," The Hague, Kluwer, 1983). Thus, the stress measurements
along a path are the same for paths through merging branches, but in the
reverse order.
For merging vessels, the classification operates in the same way as for
splitting vessels,
but with a shift of time At in when the correlation is measured. For instance,
for the
device 400 at the location shown in Fig. 21A, the correlation c(t,At) compares
the
stresses at the device's indicated location with the stresses when the
device's center
was at the point along the path 404 indicated by the tick 406' for ¨10ms when
using At
= 10ms. Conversely, a device moving in the reverse direction along the path
404, i.e.,
from the branch at the upper right into the main vessel at the left, would
compare its
stress with that 10ms earlier on the reverse path, corresponding to the
location of the
tick 406" for 10ms on the forward path. Thus while stresses are the same along
the
forward and reversed paths, the comparison used for the correlation and the
initial
position in the vessel before encountering the branch are different for these
two
directions. When the device along the reverse path is at the position
indicated by the
tick 406' for ¨10ms, it would compare stresses at the same two times that the
device
400 on the forward path 404 does at the position indicated in the figure. So,
a device on
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CA 3038104 2019-03-26
the reverse path computes the same correlations as a device on the forward
path, but
with a shift of At in time. In this comparison, the devices use the same
correlation in the
classifier. But, because they are at different locations along the path when
they evaluate
that correlation, they would have different values for the other two values
used in the
present classifier example: the current stress and the initial relative
position.
[0204] The classifier training employed for evaluation only included the
forward
direction for each branch, i.e., moving from a main vessel into one of the
branches at a
split. As a test of how well the classifier generalizes, each branch test
sample was
analyzed for higher pressure on the left (causing flow from left to right,
thus
experiencing a branch) and for higher pressure on the right (causing flow from
right to
left, thus experiencing a merge). A benefit of analysis under Stokes flow
conditions is
that the fluid flows are the same except for the velocities being reversed,
and thus the
stresses at any particular point along the path are the same in both cases.
[0205] Since the choice of probability threshold depends on the intended
application,
instead of characterizing a classifier for a single choice of threshold, a
better general
measure is the tradeoff between true and false positives over the range of
threshold
values. At one extreme, a threshold equal to one means the device never
recognizes a
branch (no true positives) but also never mistakenly considers a curve to be a
branch
(no false positives). At the other extreme, a threshold equal to zero means
the device
always considers itself to be encountering branches: this identifies all
actual branches,
but also mistakenly recognizes curves and straight vessel segments as branches
(high
false positives). For a perfect classifier, there would exist an intermediate
threshold
allowing it to identify all branches without also mistaking other vessel
geometries for
branches.
[0206] For the branch classifier example discussed herein, Fig. 28 shows the
performance as the threshold varies from 1 (at lower left, where there are no
true or
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CA 3038104 2019-03-26
false positives) to 0 (at upper right, all true and false positives).
Specifically, for each
threshold value, the figure evaluates Pbranch with Eq. (19) along the path of
each test
sample. If Pbranch exceeds the threshold anywhere along the path, that sample
is
classified as a branched vessel. The true positives are the branch samples
identified as
branches using that threshold, and the false positives are the curve samples
incorrectly
identified as branches. For comparison, the dashed diagonal line indicates how
the plot
would look if the classifier did not discriminate between paths through
branched and
curved vessels.
[0207] This example of a branch classifier performs well: with suitable
threshold, the
classifier recognizes most branches with only a few mistakes, as indicated by
the curve
in Fig. 28 passing close to the ideal behavior of recognizing all true
positives and none of
the false positives (i.e., the upper left corner of the figure). This tradeoff
curve includes
both forward and reverse paths. Examining performance separately for each
direction
(i.e., splitting or merging vessels) shows similar curves. Thus, there is no
penalty for not
including reverse paths when training the classifier. This is an indication of
the
robustness of the information used for this classifier, and the simplicity
that results from
the reversibility of Stokes flow.
[0208] A common overall performance measure for classifiers is the area under
the
curve. The area would be 50% for a classifier that made no distinction between
branch
and curve (as indicated by the dashed diagonal line in Fig. 28). 100% would be
a perfect
classifier. The area under the curve in Fig. 28 is 98.6%; this shows that the
branch
classifier performs very well for many situations, particularly in view of the
minimal data
and efficient use of CPU resources employed.
[0209] Fig. 33 shows the effect of sensor noise on classification accuracy,
showing the
reduction of the area under the curve shown in Fig. 28 for increasing amount
of sensor
noise that causes errors in measuring the stresses on the device caused by
fluid forces.
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Up to 5% error in the sensor reading due to noise, noise makes almost no
difference,
and even at 10% error, it makes little difference (accuracy still above 98%),
so these
methods should be robust even to imperfect sensor data.
When Branches Are Identified
[0210] In addition to how accurately this classifier example detects branches,
an
important performance measure is where along a path the device first detects a
branch
(i.e., whether the device detects the branch early enough to take action
before passing
the branch). One of the features this classifier uses is the correlation
between stresses
at the device's current location and those at the time At = 10ms earlier.
Typically,
stresses change the most as the device passes through the branch, and during
10ms the
device does not move significantly past the branch. This means the classifier
typically
detects the branch while the device is within the branching section of the
vessel. Again,
the time intervals selected for this example could be considerably larger when
similar
techniques are applied to larger devices and vessels employed with more
viscous fluids.
[0211] Fig. 29 shows a plot of the fraction of path length of the test sample
paths at
which P branch first exceeds the detection threshold corresponding to the true
positive
fraction (indicated on the horizontal axis). The solid and dashed curves
respectively
show forward and reverse branch paths, and the error bars show the standard
error of
the means (indicated by the points). Quantitatively, Fig. 29 shows that this
classifier
generally identifies branches near the middle of the sample paths. This
corresponds to
when the device is close to the branch, rather than well before or after
passing the
branch; thus, this classifier identifies branches while the device is close to
them, and a
device can use this stress-based classifier to identify when it is passing a
branch, well
before it passes significantly downstream of the branch. On the other hand,
branches
are not identified well before the device reaches the branch. Thus, this
particular
classifier is not as useful for applications that require significant advance
notice that the
device is approaching a branch.
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[0212] This classifier can detect most branches (high true positive fraction)
with only a
few false positives (as discussed with regard to Fig. 28). Thus, applications
will likely use
thresholds low enough to give true positive fraction above, say, 80% or so,
corresponding to the right portion of Fig. 29. With this choice for the
threshold, branch
detection will generally occur at smaller fractions of the path length for
forward paths
than for reverse paths. This corresponds to a device moving toward a vessel
split
detecting the branch just as the main vessel splits. Conversely, a device
moving in a
vessel that merges with another to form a larger vessel will identify the
branch just as
the vessels merge. Quantitatively, the difference in path fraction for these
two cases
shown in Fig. 29 (about 0.15 for thresholds giving true positives above 80% -
this is the
difference in value between reverse value and forward value at the 0.80
position on the
axis), corresponds to a difference of about 6m for the path lengths used here
(with the
parameters discussed herein). Thus the difference in where a branch is first
identified
for splitting or merging vessels is several times the device diameter.
Vessels Containing Multiple Objects
[0213] The above discussions address cases where the fluid moves a single
device
through the vessel. However, in many cases, vessels could contain additional
objects,
such as when multiple devices are employed, or when other objects are expected
to be
entrained in the fluid flow (in the numerical examples discussed herein,
addressing
vessels comparable to capillaries, blood cells would be typical objects in the
fluid). The
presence of objects in addition to the particular device under consideration
can be
considered as variation of vessel geometry. The following discussion
illustrates examples
of how the techniques described above, developed for a single device far from
any
other objects in the vessel, can be applied when other objects are nearby.
CA 3038104 2019-03-26
Vessels with Multiple Devices
[0214] In many applications, the use of multiple devices will be desirable to
provide
greater options in device operation, particularly when the devices communicate
with
each other to provide each device with more information than it can obtain
individually.
In some applications, devices could operate in close proximity, and
occasionally devices
may pass each other, such as when a device near the center of a vessel
overtakes slower
devices near the wall. Similar situations may arise in cases where other
objects besides
devices are moving in the fluid flow.
[0215] As one example, Fig. 30 shows graphic representations of the calculated
values
(as discussed for device 200 shown in Fig. 16) for four devices (500, 502,
504, & 506)
near each other in a vessel 508. Positions along the axes are in microns. Flow
is from left
to right. The solid arrows (510, 512, 514, & 516) through each device (500,
502, 504, &
506) indicate that device's calculated values, while the dashed arrows (518,
520, 522, &
524) are the corresponding calculated values that each device (500, 502, 504,
& 506)
would have at the indicated position, but if it were by itself in the vessel
508. Table 8
shows relative errors in the calculated values of speed and angular velocity
for each
device (500, 502, 504, & 506) in the group shown in Fig. 30, compared to the
case if that
device were by itself in the vessel at the same position. The angular velocity
value in this
example is from motion over ,,t = Sms leading to the positions shown in Fig.
30.
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Table 8
Speed Angular Velocity
Device Group By Itself Group By Itself
500 ¨7.7% ¨0.04% 3.6% ¨0.7%
502 ¨350/0 ¨24% 5.5% ¨1.6%
504 130% ¨40% ¨1050% ¨3.3%
506 ¨6.5% ¨2.0% 6.2% ¨3.0%
[0216] Devices 500, 502, and 506 that are near the vessel wall 526 have
similar
calculated values with or without the other devices. However, the device 504
located in
the middle of the group has significant inaccuracies in these calculated
values. The
device 504 could tell that it has inaccurate values, since the calculated
values 514
indicate the device 504 is moving quickly in a narrow vessel; however, if that
were
actually the case, the device 504 should encounter large stresses, which would
be about
40 times larger than the measured values in this case. Such small measured
stresses are
not plausible given that they would require the fluid speed or viscosity to
decrease by
that amount compared to prior measurements, before joining the group. This
discrepancy in the readings can provide an indication of a discontinuity in
the fluid flow,
which could be caused by one or more nearby objects in the fluid flow and/or
by a
discontinuity in the vessel itself; the development of further classification
options based
on the methods taught herein, or obvious extensions thereto, will help devices
to
distinguish between different situations that cause discrepancies. Optionally,
the device
504 could compare its measurements with the stresses communicated from the
other
devices (500, 502, 506), which are not consistent with high speed in a narrow
vessel.
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[0217] The devices (500, 502, 504, 506) could communicate to share calculated
values,
allowing the group to select the most reliable one, or combine calculated
values. For
example, one scheme would be to give more weight to devices that determine
that they
are close to the wall, where the evaluation methods discussed here are more
reliable.
Another scheme would be to give more weight to devices with higher correlation
in
their measurements over time.
Vessels with Cells Near the Device
[0218] Another example of additional objects in the vessel with a device
occurs in the
specific example of micron-sized devices in capillaries, where blood cells are
likely to be
encountered in the flow. Such cells typically deform as they enter capillaries
and move
through in single file. In such cases, devices will be in fluid between two
cells, as shown
in Fig. 31. In this example, a device 600 is positioned between two deformed
blood cells
602 in a small vessel 604. Positions along the axes are in microns, and flow
is from left to
right. The solid arrow 606 through the device 600 indicates its calculated
values
(direction to wall, distance to wall, and vessel diameter as described with
regard to the
device 200 shown in Fig. 16). The dashed arrow 608 shows the calculated values
that
would result for the same device 600 in the vessel 604 if the blood cells 602
were not
present.
[0219] The model for this example includes the distortion of cells 602 as they
enter
small vessels, including the resulting gap between the cells 602 and a vessel
wall 610,
but thereafter treats them as rigid bodies in their equilibrium shape, which
can take a
few tens of milliseconds to reach (Secomb, Hsu et al., "Motion of red blood
cells in a
capillary with an endothelial surface layer: effect of flow velocity,"
American J. of
Physiology: Heart and Circulatory Physiology, 2001).
[0220] The device's position and relation to the vessel are calculated using
the methods
discussed herein, which were trained on a device in an otherwise empty vessel.
The
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solid arrow 606 through the device in Fig. 31 shows that the device accurately
evaluates
the direction to the vessel wall 610 with only a small error, but
significantly
underestimates the vessel diameter, and thus also underestimates its distance
to the
wall. Table 9 compares actual and calculated device motion for the device 600,
indicating the relative errors in the calculated values of device speed and
angular
velocity for the device shown in Fig. 31 compared to the values for a device
at the same
position in a vessel without the blood cells. The angular velocity value is
from motion
over it = 5ms leading to the position shown in Fig. 31.
Table 9
Speed Angular Velocity
with cells 42% 4.9%
no cells 15% -1.3%
[0221] As indicated, angular velocity is evaluated well, but speed is
significantly
overestimated. In this case, the fluid moves the device a bit faster than the
cells, so the
device moves closer to the downstream cell. The device also moves toward the
center
of the vessel. As the device moves with respect to the cells, the errors in
the calculated
values are similar to those for the specific case shown in Fig. 31. Thus, the
presence of
cells near the device significantly affects the accuracy of the calculated
values.
Nevertheless, the calculated values remain within a factor of two of the
actual values,
thereby giving approximate values with simple analyses. Given the teachings
herein,
how to perform more accurate analyses for this, and other cases, would be
obvious to
one skilled in the appropriate arts.
More Complex Device Geometry and Motion
[0222] The discussion above addresses illustrative cases where the devices are
spherical
and move passively through the vessel. As with the more complex cases of
curved and
branching vessels, analysis of stresses may be more complicated in other
scenarios, such
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as the case where the devices are elongated rather than spherical, cases where
the
devices are actively moving rather than passively being carried by the fluid
flow, and/or
cases where the devices are not neutrally buoyant in the fluid and thus
gravitation
forces must be considered.
Elongated Devices
[0223] In the discussion of spherical devices, the stresses do not depend on
the device's
orientation. However, other shapes of devices are likely to be advantageous in
many
cases. For example, elongated shapes could be useful for detecting chemical
gradients
(Dusenbery, "Living at Micro Scale: The Unexpected Physics of Being Small,"
Cambridge,
MA, Harvard University Press, 2009) and for locomotion (Hogg, "Using surface-
motions
for locomotion of microscopic robots in viscous fluids," J. of Micro-Bio
Robotics, 2014).
The pattern of stress on an elongated device changes as it rotates, typically
alternating
between relatively long periods with its long axis nearly aligned with the
flow and short
flips (Dusenbery, "Living at Micro Scale: The Unexpected Physics of Being
Small,"
Cambridge, MA, Harvard University Press, 2009).
[0224] To apply the analysis techniques discussed herein to elongated devices,
the
interpretation of quantities involved in the evaluation procedures, which use
normal
and tangential components of the surface stress, can be generalized. For the
spherical
devices discussed previously, these components not only describe the relation
of the
stress vector to the surface, but also correspond to forces directed toward
and
perpendicular to the center of the device. Only the latter forces apply torque
around the
center. For an elongated shape, these are different decompositions of the
stress, e.g.,
stress normal to the surface is not always directed toward the center, and so
can
contribute to torque. Either of these vector decompositions, or other choices,
may
provide useful generalizations for elongated devices. For definiteness, the
analysis
CA 3038104 2019-03-26
discussed below uses both the normal and tangential components of the stress
on
elongated devices.
[0225] As one example, a prolate spheroid can be employed, as shown in Figs.
32A-
32C, which show a two-dimensional representation of a device 700. For ease of
comparison, the device 700 can be dimensioned to have the same volume as the
spherical 41m-radius devices (100, 200, 300, etc.), with its semi-major axis a
= 1.31um
and semi-minor axis b = r3/2/Va . The aspect ratio of this spheroid is a/b =
1.5. Figs.
32A-32C show the device 700 at various orientations, and how the calculated
values
(using the methods developed for spherical devices, with particular reference
to the
graphic representation of calculated values shown in Fig. 16) perform for the
elongated
shape of device 700. Positions along the axes are in microns, and flow is from
left to
right. The figures illustrate different orientations of the device 700, the
front of which is
taken to be along the semi-major axis; thus, Fig. 32A shows the device 700
when its
semi-major axis is 900 to the axis of the vessel 702, Fig. 32B shows the semi-
major axis at
450 to the vessel axis, and Fig. 32C shows the semi-major axis parallel to the
vessel axis.
Solid arrows (704A, 704B, & 704C) through each view of the device 700 indicate
the
device's calculated values, while the dashed arrows (706A, 706B, & 706C) show
the
calculated values for a spherical/circular device with 1m radius at the same
position.
[0226] In Figs. 32A-C, the calculated relative position gives the position of
the device's
center,yc, via Eq. (6), by generalizing the radius of the spherical device to
be the
minimum distance between the device's center and the wall in the calculated
direction
to the wall, i.e., the distance at which the device would just touch the wall.
Table 10
shows the relative errors in the calculated values of device speed and angular
velocity
for the device shown in Figs. 32A-C compared to a circular device at the same
position.
The angular velocity value is from motion over At = Sms leading to the
positions shown
in Figs. 32A-C.
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Table 10
shape orientation speed angular velocity
ellipse 90 ¨32% ¨0.7%
ellipse 450 ¨44% ¨1.6%
ellipse 0. ¨65% _3.3%
circle all values ¨2.0% ¨3.0%
Similar analyses could be performed for alternative device shapes.
Device Locomotion
[0227] The examples discussed above address devices that are passively moved
through
the vessel by the fluid flow. Devices with locomotion capability, allowing
them to
actively move through the fluid, may be desirable in many cases, such as to
use chemical
propulsion (Li, Esteban-Fernandez et al., "Micro/nanorobots for biomedicine:
Delivery,
surgery, sensing, and detoxification," Science Robotics, 2017) to improve in
vivo drug
delivery. Locomotion alters the stresses on the device surface compared to
passive
motion with the fluid.
[0228] To account for changes in stress due to locomotion, one approach for
locomoting devices is to directly use the stress patterns they encounter. Like
other
alternative scenarios, this may involve training new evaluators based on
stress patterns
that occur when the device activates its locomotion with various speeds and
patterns
(e.g., faster motion on one side of device to change its orientation). The
device would
select among these trained evaluators based on the current state of its
locomotion. This
state could be specified in various ways, such as by how rapidly the device
moves its
locomotion actuators (e.g., treadmills, flagella, cilia, etc.), or by how much
force or
power the device applies to its locomotion actuators. While this approach is
likely the
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most accurate, it requires extensive additional training over the range of
locomotion
patterns and values the device will use.
[0229] Another approach to handling locomotion is to vary the locomotion speed
in
such a way that the device can continue to use evaluators based on passive
motion in
the fluid. Two methods for this approach are briefly discussed.
[0230] One approach is to occasionally turn off the locomotion. The fluid
quickly reverts
to passive flow (e.g., in nanoseconds for micron-sized objects, such as micro-
devices and
bacteria (Purcell, "Life at low Reynolds number," American J. of Physics, 45,
1977). Thus,
in brief periods with no locomotion, the device can measure stresses
corresponding to
passive motion. The measurement time required with no locomotion depends on
the
stress magnitudes and sensor noise. This method is most appropriate when this
time is
short compared to significant passive drift by the device while its locomotion
is off.
[0231] Another approach is to exploit the linear relation between speeds and
stresses in
Stokes flow (Kim and Karrila, "Microhydrodynamics," Dover Publications, 2005)
when
the geometry does not change. For example, the device could measure stresses
with
locomotion at twice and at half the intended speed, and linearly extrapolate
the
stresses to obtain the values that would result for zero locomotion speed.
This gives the
device the stresses it would measure if it were moving passively with the
fluid, without
needing to turn off locomotion completely. The accuracy of this approach
requires there
to be negligible change in geometry during this procedure, both for the device
and its
environment. In particular, this requires that activating the locomotion means
itself
does not change device geometry significantly (e.g., the device could use
surface-based
motivators such as treadmills or small surface oscillations, rather than
moving extended
structures such as flagella; in this case, selection of device hardware could
be made with
the design objective of simplifying control software to reduce computational
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CA 3038104 2019-03-26
requirements, rather than focusing solely on the power efficiency or other
performance
criteria of the locomotion motivator(s)).
[0232] With both the above methods, the device can obtain stress values that
correspond to those for passive motion, and so can apply the evaluation
techniques for
passive motion discussed herein. This approach requires no additional training
with
locomoting devices.
Computational Requirements
[0233] An important metric for the analysis techniques discussed herein is
their
computational cost. Of course, each device, whether a single device, or part
of a group,
or external computation means, will have programming, which might also be
referred to
as instructions or instruction sets, that are used as part of the processes
for data
storage, data feature extraction and selection, matching data features with
system
features, and determining device actions, based at least in part on the
results of these
processes. These processes are described herein in detail, and/or represented
at a
higher level in the flow charts of Figs. 34 ¨ 39. However, as will be
appreciated by those
skilled in the arts, there are many ways to implement such programming,
including not
only a virtually infinite number of ways even in the same language, but
completely
different languages, libraries, or software packages that may be used. For
this reason,
there is no way to state absolute computational cost. However, we can describe
why
the computational costs described herein are, generally speaking, quite low.
[0234] The most basic methods discussed herein use simple functions of a few
Fourier
coefficients of stress measurements. For n sensors, a direct evaluation of M
Fourier
coefficients uses of order Mn arithmetic operations (faster methods are
available for
computing many modes, but are not necessary if M is fairly small, as in the
examples
discussed). Normalizing the Fourier coefficients involves summing the
magnitudes of the
M coefficients and then dividing these magnitudes by this sum. Principal
components
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are linear combinations of the normalized modes. Thus, the arguments used in
the
examples of regressions discussed herein involve of order Mn multiplications
and
additions. These evaluations involve a few thousand arithmetic operations for
n ==-130
sensors and M:z-- 6 modes. Based on this, evaluating stress patterns every,
say, 10ms,
would require less than 106 operations/s. Expanding the analysis from a 2-
dimensional
treatment of the stresses to a 3-dimensional analysis would square the number
of
modes, resulting in 5-10 times the number of calculations for a similar 6-mode
analysis.
The calculation requirements could be reduced by computing parameters
externally and
employing look-up tables for comparison to current stress patterns. Another
approach
may be to reduce the number of modes examined; in the techniques discussed, it
was
found that most of the information was contained in the first two modes. Also,
various
dimension reduction techniques such as are well-known in the art could be
employed.
[0235] The more sophisticated techniques discussed herein, such as using a
classifier to
detect branches in a vessel, require computational cost both to train the
classifiers and
to use them. The training can be performed off-line, from sensor measurements
collected along a sample of paths, and thus could take place on, e.g., a
conventional
computer, cluster of computers, or computers with hardware optimized for the
problem
at hand (e.g., offloading some computations onto GPUs) rather than in a device
in a fluid
system, with only the resulting regression parameters stored in the device's
memory.
Thus, the computation cost of training is not significantly constrained by the
devices' on-
board computational capabilities. Devices applying the classifier would use
their on-
board computer to repeatedly evaluate the trained classifier from their sensor
measurements. Thus, there is a computational requirement for devices using the
classifier, and a memory requirement for the device to store the parameters
obtained
from the training, but these requirements are quite small compared to the
generation
of training data and the training process itself.
CA 3038104 2019-03-26
[0236] The example of a branch detection classifier discussed herein involves
a small set
of parameters (see Table 7) and recording several sets of stress measurements
(represented by their low-frequency Fourier coefficients) to allow evaluating
correlations. This information amounts to about 100 numbers, which could fit
in a
kilobyte of memory. The regression parameters are just a few additional
numbers, so do
not add significantly to the memory requirement.
[0237] The classifier example uses simple functions of stress measurements.
Specifically, Eq. (19) involves correlations, calculated values of a device's
relative
position, and the principal component of Fourier modes of the stresses. All
these
quantities can be computed from a few low-frequency Fourier coefficients of
stress
measurements on the device's surface. Again, a computer capable of
106operationsfs
could evaluate these values every few milliseconds. As discussed above, a 3-
dimensional
analysis is likely to require 5 to 10 times the operations of a 2-dimensional
analysis. This
is a very small, very efficient set of computations, which could be made even
smaller by
reducing the Fourier modes used, evaluating input less frequently, or using
other
techniques well known to those skilled in the art.
Applications of Techniques
[0238] The present disclosure shows examples of how devices in viscous flow
can use
solely instantaneous measurements of surface stresses to determine their
position,
orientation, and relation to the vessel through which they travel; this
information can
include, e.g., their direction and distance to the nearest vessel wall, how
fast the device
is moving, and the vessel diameter. Classification of vessel geometric
features (including
discontinuities, such as abrupt changes in vessel shape, or the presence of
other objects
in the fluid flow) can also be made accurately.
[0239] This information can then be used to build maps, navigate devices
through fluid
systems, appropriately task robots (e.g., to remove plaques, plug leaks,
adjust sensor,
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locomotion, or other duty cycles, and set up even more accurate and powerful
systems
where multiple devices can cooperate to share data or perform specialized
tasks (e.g.,
serving as branch point beacons)). These actions can all be controlled by
collecting very
small amounts of data and performing calculations that are within the reach of
virtually
any processor in real-time (once training has been completed, if appropriate).
[0240] Similar techniques should be effective for other fluid parameters that
can be
readily detected by devices equipped with appropriate sensors, such as fluid
viscosity,
flow speed, etc., and fluidic data could be combined with non-fluidic data
(e.g., external
location signals) to increase accuracy and versatility.
[0241] Note that while the examples given, where a specific physical
implementation is
referenced, tend to discuss micron-scale devices in micron-scale channels,
this is by no
means the only size scale to which these techniques apply. The determining
factor is not
size, but rather the Reynolds and Womersley numbers, which take into account
multiple
factors, including viscosity. All other things being equal, if a device is
made X times
larger, and the viscosity of the fluid is also increased X times, the
resulting system will
behave the same and can be analyzed in the same manner (i.e., systems having
the
same Reynolds and Womersley numbers have dynamic similarity). Water, and blood
(or
plasma), are not particularly viscous. Water has a viscosity of 1cp. Plasma
has a viscosity
of about 1.3cp to 1.7cp. However, there are commercially-important liquids
with vastly
higher viscosities. For example, motor oil can have a viscosity of > 1,000cp,
honey has a
viscosity of about 5,000+cp, ketchup has a viscosity of about 5,000+cp, sour
cream has a
viscosity of about 100,000cp, and peanut butter has a viscosity of about
10,000cp to
1,000,000cp. Because these liquids have viscosities ranging from about 1,000
times
higher than blood plasma or water, to over 100,000 times higher than blood
plasma or
water, devices operating in these fluids can be that many times larger and
still be
operating in the viscous flow regime. To give some exemplary size and
viscosity
comparisons, a 1um device operating in water is equivalent to a 10cm (3.9
inches)
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device operating in sour cream, or a 25cm (9.8 inches) device operating in
thick peanut
butter. So, in an industrial setting where devices could be used for tasks
such as pipe
mapping and cleaning, leak or obstruction detection, in viscous liquids the
techniques
taught herein will work exactly as they would for a device on the micron-scale
in water,
blood, or plasma.
[0242] Table 11 provides representative values for some representative
substances and
related dimensions covering a broad range of various viscosities.
Table 11
Material Viscosity Velocity Density Characteristic Reynolds
(cp) (m/s) (kg/m^3) Distance (m) Number
Peanut 10,000 to 1.0 1.08 0.1 0.01 to
butter 1,000,000 0.0001
Peanut 10,000 to 1.0 1.08 1.0 0.1 to 0.001
butter 1,000,000
Ketchup 5,000 to 1.0 1.43 0.01 0.003 to
20,000 0.0007
Honey 5000 0.1 1.45 0.2 0.04
Blood 1.3 to 1.7 0.1 1.03 0.001 0.08 to 0.06
Plasma
Olive Oil 56 0.1 0.93 0.1 0.17
Water 1 0.1 1.00 0.01 1
[0243] Note that diffusion rates are directly related to viscosity via the
Stokes-Einstein
equation, and so it will be obvious that similar comments and analysis apply
to, e.g.,
diffusion of chemicals.
[0244] Fig. 34 schematically illustrates one example of a method 800 for
determining
calculated parameters using stress measurements and various analysis
techniques, such
as discussed in the examples of 2-dimensional analysis presented above. From a
Fourier
transform 802 of the stresses across the surface of the device, the location
of extreme
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stress can be employed to evaluate the direction to the wall 804, and this
direction in
combination with the Fourier components 802 can be employed to evaluate the
direction of motion 806.
[0245] From regression analysis of the Fourier components, values can be
calculated for
the relative position 808 of the device in the vessel and the vessel diameter
810; these
two calculated values can, in turn, be used to calculate the distance to the
nearest wall
812. The distance 812 and direction 804 to the nearest wall provide a position
814 for
the device relative to the cross-section of the vessel.
[0246] The relative position 808 can also be related to a ratio 816 of speed
to angular
velocity 818. Angular velocity 818 in the examples presented is evaluated by
correlating
the current Fourier values 802 with previous values 820 determined before a
time
interval. Once an angular velocity value 818 has been calculated, it can be
used with the
speed ratio 816 to calculate a speed 822 of the device along the vessel.
[0247] Figs. 35-37 broadly illustrate examples of methods for collecting data
(Fig. 35),
training an inference model (Fig. 36), and employing such inference models in
a device
(Fig. 37). Note that all flow charts herein are merely representative of one
possible
process for accomplishing a given goal. Given the teachings herein, it will be
obvious
when some steps might be omitted, repeated, performed in a different order or
with
different triggering conditions, or where a new step might be added, and the
exact
work-flow is likely to be goal- and device-dependent.
[0248] Fig. 35 shows one example of a method 830 for collecting data, either
by use of
actual devices or by simulations. First, a scenario 832 is defined for which
data are
desired; the scenario 832 could be physically modeled, for data collection by
devices
introduced into the model, or could be constructed as a virtual model for a
simulated
scenario (one example being the situations and parameters of vessel and device
sizes,
positions, geometry, flow speed, etc.) As the device operates (either actual
devices
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operating in a physical model or simulated devices operating in a virtual
model; the
device can be moving or can remain in place while the flow passes it), sensor
readings
834 are collected (in the examples discussed herein, simulated sensor readings
are
calculated based on the parameters of virtual models and simulated device
movement)
responsive to the movement; in the simulated examples discussed herein, both
tangential and normal surface stresses across the device surface were
recorded. In the
case of physical devices, the collected sensor readings 834 are communicated
836 to a
data collector, where the sensor readings 834 are added 838 (along with the
relevant
parameters of the scenario being sensed) to a data table for analysis. Where
extremely
small devices with limited memory and computational capability are employed,
the data
collector is typically located in a remote computer. In the case of a
simulated scenario,
the virtual model and simulated devices are typically implemented on the same
data
processing apparatus as the data collector, and thus the sensor readings 834
may be
automatically sent to the data collector and added to the data table 838 as
they are
recorded.
[0249] Fig. 36 illustrates one example of a method 850 for training inference
models.
Data are collected 852, using methods which could include the generic data
collection
method 830 illustrated in Fig. 35. One or more data features of interest are
selected
854; one example of such data features are principal modes of Fourier
components, but
clearly other features of the data could be employed. The selected data
feature(s) 854
are then extracted 856 from the collected sensor data 852; such "extraction"
is normally
a definite mathematical operation on the data to obtain the selected data
feature(s) 854
(e.g., in the examples discussed herein, the Fourier coefficients for the
stress pattern
data are calculated and then the principal components are evaluated). However,
in
some cases the data may be used as is, or with simple pre-processing,
conditioning, etc.
The extracted feature(s) 856 and a selected inference model 858 are employed
to train
a model 860 for how the extracted feature(s) 856 relate to the inference model
858
CA 3038104 2019-03-26
(such as the example discussed herein where the first two Fourier mode
components
are related to vessel diameter or related the relative position of the
device). The trained
model 860 can then be tested 862 with additional extracted features 856 to
evaluate
the accuracy of how well the evaluations provided by the trained model 860
match the
actual characteristic of the fluid system. In the event that there is
insufficient data for
extracted features 856 to effectively test 862 the trained model 860, then
data
collection 852 is continued. If there are a sufficient number of extracted
features 856,
but the accuracy of the trained model 860 is not acceptable for the particular
desired
application, then the inference model 858 and/or the selected feature(s) 854
are revised
to find an inference model 858 and associated features 856 that provide a
sufficient
degree of accuracy for the intended purpose. In the case of revising the
inference model
858, such revision could include keeping the same basic technique (such as a
regression)
but considering additional terms, employing a different machine learning
technique, or
using a mix of techniques (which is well-known in the field of machine
learning and data
mining and which can involve, e.g., weighting and voting schemes to combine
the
outputs of multiple techniques). In the case of revising the extracted
feature(s) 856,
additional terms could be considered (such as considering more than the first
two
principal components, in the examples discussed herein) or alternative
dimension
reduction techniques could be employed on the sensor data. It should be noted
that the
selection of an inference model 858 could be at least partially automated,
such as by
using software that checks and compares different models for effectiveness in
classifying a particular set of data (e.g., the automated selection of machine
learning
method available in Mathematica, Weka (https://www.cs.waikato.ac.nz/ml/weka/)
or
any of numerous other such software packages). After revision, the model 860
is
retrained using the extracted features 856 (using either the same features 856
as
previously employed with a revised inference model 858, or revised features
856 used
with either the previous or a revised inference model 858). This revision
process can be
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continued iteratively until the trained model 860 shows the desired degree of
accuracy
for the intended application. When the test 862 shows the trained model 860 to
be
sufficiently accurate for the desired application, the trained model 860 can
be provided
864 to devices for use, either for further data collection, analysis, and
refinement of
analysis techniques, or for actual operation to accomplish a desired mission
(such as by
the method 870 shown in Fig. 37).
[0250] Fig. 37 is a flow chart showing one example of a method 870 for using a
trained
inference model such as the trained model 860 discussed above. First, the
device
collects sensor data 872, and then data features 874 are extracted from the
data (either
by the device or by a remote computer), according to the selection of
extracted features
856 for the particular inference model 858 employed in the trained model 860
being
used. The trained model 860 is then employed to provide an evaluation 876 of a
characteristic of the device position, movement, and/or vessel geometry based
on the
extracted features 874. The inference 876 may then be recorded 878, at least
in local
memory, for reference by the device in determining further operation (if the
inference is
that the characteristic is not important to current operations, it may be
ignored rather
than recorded). Note that recording could be transient, e.g., in RAM or the
equivalent,
or can be saved for later analysis 880, in a more permanent memory (e.g., in
traditional
non-volatile storage); it should be noted that this step is optional, and a
device could go
directly from evaluating an inference to, e.g., taking action. Subsequently,
data
collection 872 continues. Depending on the mission of the device and the
particular
inference 876, one or more of various actions can be taken, with three typical
actions
being shown in Fig. 37. As noted, the current inference 876 can be saved 880
for later
analysis (i.e., stored in the memory of the device and/or a remote computer),
possibly in
combination with the sensor data 872 and/or the extracted features 874; these
data can
then be used for later refinement of the inference model, and/or possibly in
coordination with other inferences to provide a record of inferred data that
can be used
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CA 3038104 2019-03-26
for mapping the fluid system and similar purposes. The device can take action
882, such
as moving to enter a branch or move closer to a wall, and/or may activate or
deactivate
capabilities appropriate to the particular inferred condition 876 relative to
the mission
of the device. The device can also communicate 884 the inference 876, such as
to
nearby devices or to an external location accessible to the operator. One
example of
communicating 884 to one or more other devices occurs in the situation where
multiple
devices with differing capabilities are employed together in a group to
optimize the
function of each; in a typical case, devices optimized for sensing transmit
their analysis
results to devices optimized to take a desired action at the particular
feature location
(e.g., releasing a medication at the location of a tumor, applying a sealant
at the location
of a leak, etc.)
Operation Example ¨ Fluid System Mapping
[0251] Figs. 38 and 39 illustrate two examples of operations that could be
done using
the passive sensing and analysis techniques such as discussed herein (as well
as in
combination with many other techniques discussed herein, and well-known in the
art).
Fig. 38 shows an example of constructing a map of a fluid system, while Fig.
39
illustrates an example of a device employing such a map.
[0252] Fig. 38 shows a method 900 for constructing a map, which relies on one
or more
devices operating to collect and process data using passive sensors. The
processing of
the data can be done, e.g., using a trained inference model; this operating
step 902 can
be essentially similar to the steps 872, 874, and 876 in the method 870
illustrated in Fig.
37, with the addition of recording position information. In the simplest case,
position
information can be a distance derived from elapsed time (measured by a timer)
and a
fluid speed value obtained from angular velocity and speed ratio, as discussed
in the
description of Fig. 34.
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CA 3038104 2019-03-26
L02531 When a feature of interest, such as a branch or merge is detected 904,
the
position and any available characteristics of such feature are recorded 906,
and the
steps 902, 904, & 906 are repeated until it is determined that the data
collection
procedure is completed, at which point the recorded positions and
characteristics of
features are reported 908 to one or more central databases ("database" being
used in
the general sense of any type of data storage), if offloading such functions
to an external
computer, or stored in device memory. In addition to the locations of branches
and
merges, additional data on the fluid system at a given location may be
collected and
evaluated such as changes in vessel diameter, curvature, asymmetry, etc. This
additional
data can help to distinguish the branches, such as branches having differing
diameters,
different degree of curvature, etc. When the device has additional sensing
capabilities,
additional data can be employed for further refine the position and/or to
characterize
the branches. As examples, gravity and/or magnetic field detection could
provide a
global index of direction, an on-board gyroscope could provide a consistent
local index
of direction, reception of electromagnetic or acoustic signals (either already
present in
the fluid system or deliberately induced) could provide references for
direction,
detection of chemical gradients could provide relative directions with respect
to a
source or sink for such chemicals, etc. In some cases, the "position" of a
feature may be
expressed solely in terms of some parameter of interest being sensed, rather
than
absolute location; for example, if the device senses chemical gradients, the
"position" of
a feature might be expressed solely in terms of chemical concentrations,
rather than
absolute location. While discussed in terms of branches and merges, it should
be
appreciated that other features could be mapped, such as curvature,
irregularities in the
channel, partial obstructions, points of apparent leakage, etc.
[0254] When the procedure is considered to be complete can be determined by
various
factors, such as when sufficient data has been collected to reach a desired
level of
accuracy, when the use of additional device memory is not desirable, when the
device
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CA 3038104 2019-03-26
has limited power and running the sensors is not a priority, when the device
exits the
portion of the fluid system of interest, or when the device has become
immobile. The
data-collection procedure can be done multiple times and can be done by a
number of
different devices, each reporting 908 its record of feature positions and
other data to a
central database that can be used both to offload computation, and to allow
one device
to access data acquired by another device. Because the devices can employ
relatively
simple sensors (such as stress and shear sensors) and require only modest
computational capacity, they can be fabricated more inexpensively than more
complex
devices, and a mapping operation may employ a single device, but may also
employ
dozens, hundreds, thousands, or even millions or more of devices.
[0255] Once the records of feature positions and any relevant characteristics
from one
or more devices have been reported 908, they are compared 910 to identify
areas
where the features match (including a match with overlap, which can be used to
help
combine contiguous segments of the map, similar to the way shotgun sequencing
for
DNA is performed). Where a match is detected 912, new positions and available
characteristics of one or more features are added 914 to a map stored in
memory. It
should be noted that "new" features could include duplicate reports of
features
previously added, with the additional report adding to the confidence of the
position
and characteristics, and/or refining the position and characteristics for
greater accuracy.
[0256] The steps of comparison 910, identifying matching overlaps 912, and
adding
features 914 are repeated until the map-construction procedure is considered
complete; such completion could be determined by various criteria, such as
whether the
map is considered sufficiently complete and accurate, or whether, in a multi-
device
scenario, a threshold number of devices have reported 908 their records. When
map
construction is considered to be done, the completed map is recorded 916 for
future
use (although the incomplete map can, and probably would, be recorded
incrementally
and used to aid the mapping process itself, such as by providing data that can
direct a
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device to an area that is not believed to be accurate enough, or where
coverage is
completely lacking, or to let a device know how to exit the system for repair,
recharge,
wired data downloads and uploads, etc.)
[0257] Fig. 39 illustrates one example of a device employing a map, such as
the map
recorded in step 916 shown in Fig. 38. The device performs a navigation
procedure 950,
which includes the steps of collecting sensor readings 952, extracting data
features 954
from the sensor measurements, and applying a trained model to the extracted
data
features to evaluate 956 one or more parameters of the device position and/or
movement, the fluid flow, and/or the fluid system geometry. These steps can be
essentially similar, respectively, to the steps 872, 874, and 876 of the
method 870
shown in Fig. 37, with an additional record of position (such as distance
traveled)
typically being maintained, as discussed for step 902 of the method 900. When
the
evaluation 956 indicates the presence of a feature 958 of interest in the
fluid system,
the position and any characteristics which can be evaluated (diameter,
curvature of the
branches, etc.) is compared 960 to the map to identify the particular feature.
[0258] Based on the map and the particular mission of the device, a decision
962 is
made whether or not the device should take action 964 at this particular
feature
location. The action 964 to be taken depends on the particular mission of the
device and
how the detected feature location relates to such mission. For a device with
locomotion,
the action could be to move into one branch versus the other, depending on the
desired
mission of the device. For example, the device might choose a branch in order
to reach a
particular destination, might purposefully leave known areas of a map to
gather
additional data to extend the map, might repeat a known route to refine the
map, might
choose to avoid known areas of high risk (e.g., in a biological context, the
sinusoid slits
of the spleen, might be a likely location for devices to get stuck, and in any
system,
sharp turns, reduced channel diameters, changes in heat or pressure, or other
factors,
might all put a device at risk of becoming stuck or damaged), or might simply
take a
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different route than other devices have taken, to provide more complete
coverage of
the overall fluid system.
[0259] Another option for a device with locomotion would be to move to the
nearest
vessel wall and anchor to it so as to be stationed at that location, such as
to provide a
location beacon, to detect passing objects, etc. In another example of a
possible action,
the particular mapped location may be one where there is evidence of tumor
growth,
and the device could be designed to release a tumor-killing chemical at such
location. In
an industrial setting, the device might affix itself to an area believed to be
leaking, either
sealing the leak with its own body, releasing some type of sealing material,
or being
used as a homing beacon for other devices inside, or outside, the system.
Similarly, the
device could, e.g., affix itself to an area with some type of waste or plaque
buildup, and
scrape or dissolve it off (potentially taking it into its own body so as not
to contaminate
the fluid). It should be noted that the sensing/analysis and action functions
could be
incorporated into separate physical devices, such as a multi-device group
where one or
more devices perform the sensing functions and transmit the analysis results
to one or
more other devices that take action based on the results.
[0260] Where additional sensor data beyond that used for feature
identification/
location is available, such additional data could inform the decision of
whether or not to
take action, and/or the determination of which of multiple action choices
should be
taken. It should be appreciated that the variety of possible actions is
commensurate
with the variety of possible missions to be undertaken by such devices.
[0261] Some of scenarios present options even for devices that lack
locomotion. For
example, if a device flows through a system randomly, if it is in a portion of
the system
that has already been mapped, it may elect to shut sensors down for some
period of
time to conserve power. If it randomly flows past a system feature of
interest, it may
elect to broadcast that information as a priority to other devices or to a
central
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database. It may also emit or absorb chemicals (e.g., as in the tumor killing
example ¨
locomotion would be useful, but not necessary), or affix itself to the wall.
Clearly,
depending on many factors, such as the device's mission, what capabilities the
device
has, and whether it is operating alone or in a group, with or without
locomotion, there
can be many actions to be taken.
[0262] Whether or not an action 964 is taken at the location, the sensing 952,
extraction
954, evaluation 956, feature detection 958, comparison 960 to mapped features,
determination 962, and action taken 964 (when appropriate) are repeated until
the
procedure is considered complete and is ended 966. Such end could be based on
the
device becoming inactive, the action 964 being considered to complete the
mission, the
device leaving the fluid system or having traveled a prescribed distance, or
other criteria
depending on the situation.
[0263] While the novel features of the present techniques are described in
terms of
particular examples and preferred applications, it should be appreciated by
one skilled
in the art that, given the teachings herein, which demonstrate the
surprisingly accurate
inferences that can be made from simple sensor data, and which analyzed in a
manner
that computationally allows acting on the inferences in essentially real-time,
which
greatly improves device function and versatility, the techniques discussed are
applicable
to a variety of other situations in viscous flow, and that alternative
analysis schemes
could be employed without departing from the spirit of the invention, and
which would
be apparent from the teachings herein.
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