COMPUTATIONAL SYSTEM AND METHOD FOR MODELING THE HEART

SYSTEME ET PROCEDE COMPUTATIONNELS POUR LA MODELISATION DU COEUR

English Abstract

A computational model for simulating and predicting the electrical and
chemical dynamics of the heart. The model consists of a computerized
representation of the heart anatomy and a system of mathematical equations
that describe the spatio-temporal behavior of biophysical quantities such as
voltage at various locations throughout the heart. The computer process can
present the temporal evolution of the biophysical quantities throughout the
computerized anatomical model.

French Abstract

L'invention concerne un modèle computationnel pour la simulation et la prédiction des dynamiques électriques et chimiques du coeur. Ledit modèle consiste en une représentation informatisée de l'anatomie du coeur et en un système d'équations mathématiques qui décrivent le comportement spatio-temporel des variables biophysiques, telles que la tension en différents endroits du coeur. Le processus informatique peut présenter l'évolution temporelle des variables biophysiques dans le modèle anatomique informatisé.

Claims

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What is claimed is:
1. A computational model of the heart comprising:
a space defining lattice having a set of nodes;
each of said nodes positioned in said lattice such that each node is
adjacent to neighboring nodes;
whereby said lattice and node together define a three dimensional
representation of at least a portion of the heart;
each node of said set of nodes representing a unit of the myocardium;
each node having associated with it a set of state defining node
equations for computing an action potential at the location of said node
and for computing a node potential;
each node having associated with it a set of coupling relationships
related to the anatomic structure of the heart for computing the
contribution to said node potential contributed by neighboring nodes;
whereby the total set of voltages at each of said nodes represents the
global depolarization state of the heart.
2. A computational model of the heart comprising:
a cubic lattice having a set N nodes;
each of said nodes positioned at a vertex of said lattice;
each node representing a biophysical computational unit of the heart;
each node having associated with it a set of state defining equations
expressing state variables sufficient to compute node response at time
t+deltat given node response at time t, said equations including at least
one equation selected from biophysical processes selected from the set:
i) equations for time-varying, voltage-dependent transmembrane
conductances permeable to sodium (Na), potassium (K), calcium (Ca),
and/or chloride (CI) ions, the temporal evolution of which are modeled
using ordinary differential equations;


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ii) equations for time-varying transmembrane ionic pump and
exchanger currents, properties of which are modeled using algebraic
equations;
iii) equations for time-varying Ca uptake, sequestration, and release
currents modeling the regulation of intracellular Ca levels by cellular
organelles, the properties of which are modeled using coupled systems of
ordinary differential equations;
iv) equations for total transmembrane flux of each ionic species to
which the cell membrane is permeable;
each node connection to neighboring nodes represented by a coupling
conductance, the value of which is defined by the anatomic relationship of
the two nodes;
each node having a coupling current associated with it determined by
the total current entering the node through all said coupling conductances
defined at that node;
whereby said coupling currents and node state equations may be solved
for the temporal evolution of all state variables at all nodes.
3. A process for computing a model of a heart comprising the steps of:
a) defining a set of lattice nodes;
each lattice node representing a biophysical subunit of the heart;
each node having a set of biophysical equations for computing a total
node current associated with Na, Ca and K ion transport in said biophysical
subunit;
each node associated with at least five adjacent nodes;
each node coupled to neighboring nodes;
said coupling modeled as a resistance;
b) solving said set of biophysical equations to determine said node
currents;
c) summing said node current to determine the voltage present at each
node resulting from the depolarization of each neighboring node;


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d) displaying a representation of said computed voltage.
4. A method for modeling a heart with a computer comprising:
a) defining a set of nodes;
each node representing a biophysical subunit of the heart;
each node having a membrane, defining an intracellular and an
extracellular space;
each node having a set of biophysical equations associated with it for
computing a coupling current associated with ion transport in said
intracellular space;
each node having a set of biophysical equations associated with it for
computing a coupling current associated with ion transport in said
extracellular space;
each node having a set of biophysical equations associated with it for
computing a transmembrane current between the intracellular and
extracellular spaces;
b) defining a lattice including each of said nodes;
each node associated with a physical location in heart tissue;
each node connected with at least five adjacent nodes;
each node exhibiting an anisotropic coupling with neighboring nodes
reflecting the anatomic relationship between such nodes;
said coupling modeled as a coupling resistance
c) solving said set of biophysical equations to determine said node
currents associated with extracellular and intracellular currents;
d) summing said node current to compute the voltage present at each
node resulting from the depolarization of each node and the propagation of a
depolarization wave front through each node;
e) displaying a representation of said computed voltage.


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5. A model of a biological organ system comprising:
a plurality of nodes;
each node having associated therewith a set of state defining equations
which take their variables biophysical data, which are substantially local to
the node itself;
each node having at least one state variable which takes as its argument
parameters communicated solely from near neighbors;
a network containing all such nodes;
said network including coupling relationships defined between each
node and its near neighbor node wherein said coupling relationships reflect
the anatomical structure of the biological organ, and are expressed as set of
state defining equations;
whereby said state defining variables can be solved interatively and
state variable values communicated to the network model, whereby said
network equations can be computed for each node.
6. A method of defining a model comprising the steps of:
applying nuclear magnetic resonance imaging to a biological organ to
generate a data file defining tensors associated with the distribution of
water
molecules within the physiologic organ;
applying said tensor dataset to a network to determine the magnitude of
coupling conductances between nodes of the network such that the tensor
information is reflected by the internodal conduction values of the network,
thus embedding the anatomic characteristics of the organ in the model.
7. A method for using a multiple processor computer to solve for the
temporal evolution of state variables defining biophysical and biochemical
properties of nodes within a network model of a biological system
comprising:


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partitioning the lattice of nodes making up the network into N number
of lattice subsets, such that each node within the network is included in at
least one of said subsets;
associating state equations and state variables describing the
biophysical and biochemical properties of each node in said subsets with
particular processing units in the said parallel computer such that each
subset
of nodes is associated with a distinct processing unit, and that all
processing
units are associated with at least one subset of nodes;
computing the temporal evolution of all state variables within each of
the node subsets associated with distinct processing units concurrently across
each of the processing units;
concurrently storing said state variables in computer memory;
displaying a sequence of said state variables.
8. A method of modeling a cardiac disease states in a model of the heart as
set forth in claim 3 comprising the additional steps of:
a) adjusting the lattice defining the anatomic structure of the heart
such that anatomical structural changes known to occur in the heart during
said disease state;
b) using said adjusted tensor dataset to determine the magnitude of
coupling conductances between nodes of the network such that the altered
structure of the heart in the disease state, as represented by the adjusted
tensor
dataset, is embedded in the network model;
c) adjusting parameters of the set of state defining equations,
specifying properties of biochemical cellular processes defined at each node
of the lattice, to reproduce changes in these parameters known to occur in
said
disease state;
d) adjusting initial values of state variables, the temporal evolution of
which is determined by the set of equations specifying properties of
biochemical cellular processes defined at each node of the lattice, in such a


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way as to reproduce changes in these state variables known to occur in said
disease state;
e) solving for the temporal evolution of state variables, defined at
each node of the lattice;
f) storing said state variables in a computer memory for graphical
display and analysis.
9. A computational model of the heart comprising:
a set of n nodes arranged in a cubic lattice with each node having at
least five neighbors;
each node having a set of state variable equations associated with it;
said equations describing biophysical and biochemical reactions at
each node which may be solved to find the currents present at each node;
the lattice having a set of coupling equations associated therewith
defining the coupling between each node which may be solved to determine
the total voltage present at each node in the lattice.
10. A finite-difference computations model of a heart comprising:
a) a set of N nodes arranged in a cubic lattice with each node having at
least five neighbors;
b) a subroutine procedure which uses experimentally measured data on
fiber orientation within the heart (obtained in a number of ways, including
direct anatomical measurements or use of magnetic resonance imaging
methods) for computing the connection currents between lattice nodes;
c) a multi-dimensional data array S(NI,N2,N3,S1,S2,S3, ... SNeq) in
which indices N1, N2, and N3 specify position of a node within the cubic
lattice, and variables S1.... SNeq are values of state variables defined at
node
(NI,NZ,N3) at time t;
d) a multi-dimensional data array F(N1,N2,N3,S1- S2-S3- .. SNeq-) in
which the variable Sx~ denotes the time rate of change, dSx(t)/dt, of state
variable x at time t;


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e) a subroutine procedure which specifies an algorithm for computing
elements of the multi-dimensional data array F(), with this subroutine
procedure itself being composed of a number of subroutine procedures
selected from a library of procedures corresponding to biophysical processes
modeled at the sub-cellular level;
f) a subroutine procedure specifying a numerical integration algorithm
for the computation of values of the array So at time t+At given values of So
and Fo at time t.
11. A computational model of a heart comprising:
a) a set of n nodes arranged in a cubic lattice with each node having at
least five neighbors;
b) each node having a set of state variable equations associated with
it;
c) said equations describing biophysical and biochemical reactions at
each node which may be solved to find the currents present at each node
based upon local parameters, and the voltages present at each node based
upon local and near neighbor parameters;
d) the lattice having a set of coupling equations associated therewith
defining the coupling between each node, which may be solved to determine
the total node voltage present at each node in the lattice.
12. A method of computing the model of claim 8 comprising the steps of:
i) partitioning the lattice into m nodes and assigning state variable
computations to one of (p) processing units;
ii) concurrently computing state variables with the p processing
units;
iii) computing the temporal evolution of all state variables and
storing or displaying the results.


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13. A method of computing the temporal evolution of state variables in the
model of claim 3 on multiprocessor computers consisting of a set of P
processors each with local memory of size M, a communications network
supporting data exchange between processors, and a global shared memory,
with the method comprising the steps of:

a) partitioning the lattice into Q sets of nodes, referred to as node sets,
in such a way that all state variable values at time t, parameters, and
required
temporary storage locations (work space) for any node set fits into the local
memory available to any processing unit;

b) assignment of each node set to a specific processing unit and it's
local memory;

c) inter-processor communication of any data required to compute new
values of state variables for nodes positioned at the borders between
different
node sets;

d) concurrent execution on all P processors of the computations to
compute new values of local state variables at time t+Dt in each of the node
sets that have been assigned to processing units;

e) iteration of steps b) and d) until computation of state variable
values at time t+Dt, where Dt is small, for all Q node sets are completed;

f) storage of the computed set of state variables on external storage
devices for subsequent graphical display;

g) iteration of steps b) - f) until t+Dt equals some end time T.

14. The system of claim 4 with the inclusion of chemical or compound data:
a) a means for modifying one or more of said state variables as a
result of imposing one of said chemical or compound data;

chemical or compound data includes mechanism of action data; kinetic data;
biochemical, mechanical;

b) a means for solving and updating the complete set of integral
network algorithms and chemical/composition data in time sets;


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c) a means to determine the currents present at each node based on
changes in the local and near neighbor state variable parameters as a result
of
chemical/compound data;
d) a means to determine the action potential each node in the lattice;
e) a means for modifying state variables as a result of
chemical/compound data;
f) a means to use parallel computers to solve for the temporal
evolution of state variables and chemical/compound data defined at each node
of the lattice;
g) a means to graphically display the changes at each node in the
lattice as a result of said modification of the system of Claim 4 with
chemical/compound data;
h) a means to store said state variables in computer memory and or
external data storage devices for graphical display and analysis.
15. The system of claim 4 with electrical input data comprising:
a) a means for modifying one or more of said state variables as a
result of imposing one of said electrical input data;
electrical input data includes electric waveform stimulation protocols, etc.
b) a means for solving and updating the complete set of integral
network algorithms and electrical input data in time sets;
c) a means to determine the currents present at each node based on
changes in the local and near neighbor state variable parameters as a result
of
electrical input data;
d) a means to localize the origin the origin of the electrical stimulus;
e) a means to determine the ecg at each node in the lattice;
f) a means for modifying state variables as a result of electrical input
data;
g) a means to use parallel computers to solve for the temporal
evolution of state variables and electrical input data defined at each node of
the lattice;


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h) a means to graphically display the changes at each node in the
lattice as a result of said modification of the system of Claim 4 with
electrical
input data;
i) a means to store said state variables in computer memory and or
external data storage devices for graphical display and analysis.
16. The model of claim 4 further comprising:
a) a means for modifying one or more of said state variables as a
result of imposing chemical compound data in said state equations, wherein
said chemical compound data includes mechanism of action data; kinetic data;
biochemical, or mechanical data;
b) a means for solving and updating the complete set of integral
network algorithms and chemical/composition data in time sets;
c) a means to determine the currents present at each node based on
changes in the local and near neighbor state variable parameters as a result
of
chemical/compound data;
d) a means to determine the ecg at each node in the lattice;
e) a means for modifying state variables as a result of
chemical/compound data;
f) a means to use parallel computers to solve for the temporal
evolution of state variables and chemical/compound data defined at each node
in the lattice;
g) a means to graphically display the changes at each node in the
lattice as a result of said modification of the system with chemical compound
data;
h) a means to store said state variables in computer memory and or
external data storage devices for graphical display and analysis.


1. A computational model of the heart comprising:
a space defining lattice having a set of nodes;
each of said nodes positioned in said lattice such that each node is adjacent
to
neighboring nodes;
whereby said lattice and node together define a three dimensional
representation of at least a portion of the heart;
each node of said set of nodes representing a biophysical subunit of the
myocardium;
each node having associated with it a set of state defining node equations for
computing an action potential at the location of said node based upon a
biophysical model that explicitly relies on the computation of individual
ionic
current that collectively give rise to said action potential, and for
computing a
node potential at the node from the action potentials within the biophysical
subunit derived directly from the computed action potentials;
each node having associated with it a set of coupling relationships related to
the anatomic structure of the heart for computing the contribution to said
node
potential contributed by the voltages and currents exchanged with the
neighboring nodes;
whereby the total set of voltages at each of said nodes represents the global
depolarization state of the heart.
2. A computational model of the heart comprising:
a cubic lattice having a set N nodes;
each of said nodes positioned at a vertex of said lattice;
each node representing a biophysical computational unit of the heart;


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each node having associated with it a set of state defining equations
expressing state variables sufficient to compute node response at time
t+deltat
given node response at time t, said equations including at least one equation
selected from biophysical processes selected from the set:
(i) equations for time-varying, voltage-dependent transmembrane
conductance permeable to sodium (Na), potassium (K), calcium (Ca),
and/or chloride (CI) ions, the temporal evolution of which are molded
using ordinary differential equations;
(ii) equations for time-varying transmembrane ionic pump and exchanger
currents, properties of which are modeled using algebraic equations;
(iii) equations for time-varying Ca uptake, sequestration, and release
currents modeling the regulation of intracellular Ca levels by cellular
organelles, the properties of which are modeled using coupled systems
of ordinary differential equations;
(iv) equations for total transmembrane flux of each ionic species to which
the cell membrane is permeable;
each node connection to neighboring nodes represented by a coupling
conductance, the value of which is defined by the anatomic relationship of the
two nodes;
each node having a coupling current associated with it determined by
the total current entering the node through all said coupling conductance
defined at that node;
whereby said coupling currents and node state equations may be
solved for the temporal evolution of all state variables at all nodes.
3. A process for computing a model of a heart comprising the steps of:
(a) defining a set of lattice nodes;


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each lattice node representing a biophysical subunit of the heart;
each node having a set of biophysical equations for computing a total
node current associated with Na, Ca and K ion transport across cellular
membranes in said biophysical subunit;
each node associated with at least five adjacent nodes;
each node coupled to neighboring nodes;
said node coupling modeled as a resistance between adjacent nodes;
(b) solving said set of biophysical equations to determine said node currents;
(c) summing said node current to determine the voltage present at each node
resulting from the depolarization of each node in conjunction with each
neighboring node;
(d) displaying a representation of said computed voltage to show the time
course
of changes in voltages at nodes.
4. A method for modeling a heart with a computer comprising:
(a) defining a set of nodes;
each node representing a biophysical subunit of the heart;
each node having a membrane, defining an intracellular and an extracellular
space;
each node having a set of biophysical equations associated with it for
computing a coupling current associated with ion transport in said
intracellular
space;
each node having a set of biophysical equations associated with it for
computing a coupling current associated with ion transport in said
extracellular
space;
(b) defining a lattice including each of said nodes;


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each node associated with a physical location in heart tissue;
each node connected with at least five adjacent nodes;
each node exhibiting an anisotropic coupling with neighboring nodes
reflecting the anatomic relationship between such nodes;
said coupling modeled as a coupling resistance
(c) solving said set of biophysical equations to determine said node currents
associated with extracellular and intracellular currents;
(d) summing said node current to compute the voltage present at each node
resulting from the depolarization of each node and the propagation of a
depolarization wave front through each node;
(e) displaying a representation of said computed voltage.
5. A model of a biological organ system comprising:
A plurality of nodes;
each node having associated therewith a set of state defining equations which
take their variables biophysical data, which are substantially local to the
node itself,
and which include explicit computations for ionic flux across cellular
membranes for
giving rise to action potentials at the node;
each node having at least one state variable which takes as its argument
parameters communicated solely from near neighbors which is either current,
voltage;
a network containing all such nodes;
said network including coupling relationships defined between each node where
each coupling relationship is modeled as a conductance which permits voltage
and
current summations at each node, and its near neighbor node wherein said
coupling


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relationships reflect the anatomical structure of the biological organ, and
are
expressed as set of state defining equations;
whereby said state defining variables can be solved interactively and state
variable values communicated to the network model, whereby said network
equations can be computed for each node.
6. A method of defining a model comprising the steps of:
applying nuclear magnetic resonance imaging to a biological organ to
generate a data file defining tensors associated with the distribution of
water
molecules within the physiologic organ;
applying said tensor dataset to a network to determine the magnitude of
coupling conductance between nodes of the network such that the tensor
information is reflected by the internodal conduction values between the nodes
of the network, thus embedding the anatomic characteristics of the organ in
the
model by representing the coupling relationships as conductanes between
neighboring nodes.
7. A method for using a multiple processor computer to solve for the temporal
evolution of state variables defining biophysical and biochemical properties
of
nodes within a network model of a biological system comprising:
partitioning the lattice of nodes making up the network into N number of
lattice subsets, such that each node within the network is included in at
least on of
said subsets;
associating state equations and state variables describing the biophysical and
biochemical properties of each node in said subsets with particular processing
units
in the said parallel computer such that each subset of nodes is associated
with a


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distinct processing unit, and that all processing units are associated with at
least one
subset of nodes;
computing the temporal evolution of all state variables within each of the
node subsets associated with distinct processing units concurrently across
each of
the processing units;
concurrently storing said variables in computer memory;
displaying a sequence of said state variables.
8. A method of modeling a cardiac disease states in a model of the heart as
set forth
in claim 3 comprising the additional steps of:
(a) adjusting the lattice defining the anatomic structure of the heart such
that
anatomical structural changes known to occur in the heart during said disease
state;
(b) using said adjusted tensor dataset to determine the magnitude of coupling
conductance between nodes of the network such that the altered structure of
the heart in the disease state, as represented by the adjusted tensor dataset,
is
embedded in the network model;
(c) adjusting parameters of the set of state defining equations, specifying
properties of biochemical cellular processes defined at each node of the
lattice, to reproduce changes in these parameters known to occur in said
disease state;
(d) adjusting initial values of state variables, the temporal evolution of
which is
determined by the set of equations specifying properties of biochemical
cellular ionic current exchange processes defined at each node of the lattice,
in
such a way as to reproduce changes in these state variables known to occur in
said disease state;


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(e) solving for the temporal evolution of state variables, defined at each
node of
the lattice;
(f) storing said state variables in a computer memory for graphical display
and
analysis.
9. A computational model of the heart comprising:
a set of N nodes arranged in a cubic lattice with each node having at least
five
neighbors;
each node having a set of state variables equations associated with it;
said equations describing biophysical and biochemical reactions at each node
which may be solved to find the currents present at each node based upon
computed
ionic currents across cellular membranes;
the lattice having a set of coupling equations associated therewith defining
the coupling conductance between each node which may be solved to determine
the
total voltage present at each node in the lattice derived from voltages
generated
within the node and communicated to the node from near neighbors.
10. A finite-difference computations model of the heart comprising:
(a) a set of N nodes arranged in a cubic lattice with each node having at
least five
neighbors;
(b) a subroutine procedure which uses experimentally measured data on fiber
orientation within the heart (obtained in a number of ways, including direct
anatomical measurements or use of magnetic resonance imaging methods) for
computing the connection currents between lattice nodes;
(c) a multi-dimensional data array S(N1,N2,N3,S1,S2,S3, ... Sneq) in which
indices N1, N2, and N3 specify position of a node within the cubic lattice,
and


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variables S1 .... Sneq are values of state variables defined at node
(N1,N2,N3)
at time t;
(d) a multi-dimensional data array F(N1,N2,N3,S1-S2-S3-.Sneq-) in which the
variable Sx' denotes the time rate of change, dSx(t)/dt, of state variable x
at
time t;
(e) a subroutine procedure which specifies an algorithm for computing elements
of the multi-dimensional data array F~, with the subroutine procedure itself
being composed of a number of subroutine procedures selected from a library
of procedures corresponding to biophysical processes modeled at the sub-
cellular level;
(f) a subroutine procedure specifying a numerical integration algorithm for
the
computation of values of the array So at time t+At given values of So and Fo
at time t.
11. A computational model of a heart comprising:
(a) a set of n nodes arranged in a cubic lattice with each node having at
least five
neighbors;
(b) each node having a set of state variable equations associated with it;
(c) said equations describing biophysical and biochemical reactions at each
node
which may be solved to find the currents present at each node based upon
local parameters, and the voltages present at each node based upon local and
near neighbor parameters;
(d) the lattice having a set of coupling equations associated therewith
defining
the coupling between each node, which may be Solved to determine the total
node voltage present at each node in the lattice.


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12. A method of computing the model of claim 8 comprising the steps of:
(i) partitioning the lattice into m nodes and assigning state variable
computations to one of (p) processing units;
(ii) concurrently computing state variables with the p processing units;
(iii) computing the temporal evolution of all state variables and storing or
displaying the results.
13. A method of computing the temporal evolution of state variables in the
model of
claim 3 on multiprocessor computers consisting of a set of P processors each
with
local memory of size M, a communications network supporting data exchange
between processors, and a global shared memory, with the method comprising
the steps of:
(a) partitioning the lattice into Q sets of nodes, referred to as node sets,
in such a
way that all state variable values at time t, parameters, and required
temporary storage locations (work space) for any node set fits into the local
memory available to any processing unit;
(b) assignment of each node set to a specific processing unit and it's local
memory;
(c) inter-processor communication of any data required to compute new values
of state variables for nodes positioned at the borders between different node
sets;
(d) concurrent execution on all P processors of the computations to compute
new
values of local state variables at time t+Dt in each of the node sets that
have
been assigned to processing units;
(e) iteration of steps b) and d) until computation of state variable values at
time
t+Dt, where Dt is small, for all Q node sets are completed;


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(f) storage of the computed set of state variables on external storage devices
for
subsequent graphical display;
(g) iteration of steps b) - f) until t-Dt equals some end time T.
14. The system of claim 4 with the inclusion of chemical or compound data
which
has an impact on the ionic currents computed for a node:
(a) a means for modifying one or more or said state variables as a result of
imposing one of said chemical or compound data;
chemical or compound data includes mechanism of action data; kinetic data;
biochemical, mechanical;
(b) a means for solving and updating the complete set of integral network
algorithms and chemical/composition data in time sets;
(c) a means to determine the currents present at each node based on changes in
the local and near neighbor state variable parameters as a result of
chemical/compound data;
(d) a means to determine the action potential each node in the lattice;
(e) a means for modifying state variables as a results of chemical/compound
data;
(f) a means to use parallel computers to solve for the temporal evolution of
state
variables and chemical/compound data defined at each node of the lattice;
(g) a means to graphically display the changes at each node in the lattice as
a
result of said modification of the system of Claim 4 with chemical/compound
data;
(h) a means to store said state variables in computer memory and or external
data
storage devices for graphical display and analysis.


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15. The system for claim 4 with electrical input data comprising:
(a) a means for modifying one or more of said state variables as a results of
imposing one of said electrical input data;
electrical input data includes electric waveform stimulation protocols, etc.
(b) a means for solving and updating the complete set of integral network
algorithms and electrical input data in time sets;
(c) a means to determine the currents present at each node based on changes in
the local and near neighbor state variable parameters as a result of
electrical
input data;
(d) a means to localize the origin the origin of the electrical stimulus;
(e) a means to determine the ecg at each node in the lattice;
(f) a means for modifying state variables as a result of electrical input
data;
(g) a means to use parallel computers to solve for the temporal evolution of
state
variables and electrical input data defined at each node of the lattice;
(h) a means to graphically display the changes at each node in the lattice as
a
result of said modification of the system of Claim 4 with electrical input
data;
(i) a means to store said state variables in computer memory and or external
data
storage devices for graphical display and analysis.
16. The model of claim 4 further comprising:
(a) a means for modifying one or more of said state variables as a result of
imposing chemical compound data in said state equations, wherein said
chemical compound data includes mechanism of action data; kinetic data;
biochemical, or mechanical data;
(b) a means for solving and updating the complete set of integral network
algorithms and chemical/composition data in time sets;


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(c) a means to determine the currents present at each node based on changes in
the local and near neighbor state variable parameters as a result of
chemical/compound data;
(d) a means to determine the ecg at each node in the lattice;
(e) a means for modifying state variables as a result of chemical/compound
data;
(f) a means to use parallel computer to solve for the temporal evolution of
state
variables and chemical/compound data defined at each node in the lattice;
(g) a means to graphically display the changes at each node in the lattice as
a
result of said modification of the system with chemical compound data;
(h) a means to store said state variables in computer memory and or external
data
storage devices for graphical display and analysis.

Description

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COMPUTATIONAL SYSTEM AND METHOD
FOR MODELING THE HEART
BACKGROUND OF THE INVENTION
Field of the Invention:
The present invention constitutes a computing system and
software model of a physical organ, and more particularly to processes and
procedures for generating a biophysically detailed, predictive model of the
mammalian heart which accepts anatomic and biophysical data and generates
a representation of the electrophysiologic state of the heart.
Description of the Prior Art:
Physiologic organs consist of various types of cells organized
into tissues. These tissues form an organ, which in turn interacts with the
whole body. The ability to model organ function with a high level of
biophysical, biochemical, and structural detail is of enormous value to
biology and medicine, because such models provide deep insight into the
cause of disease.
Given the immense complexity of even the simplest organ, the
principal task that confronts the model builder is to recognize what
biophysical detail can be successfully disregarded in constructing a
computationally useful model.
The heart for example includes a sino-atrial node and atrio-
ventricular node, as well as the bundle of His and the Purkinje fiber system.
These structures have a profound impact on the electrical activation sequence
of the heart muscle fibers within the atria and ventricles, and thus have an
enormous impact on the heart's mechanical function. It is well known that
organic and anatomic defects in these structures can result in life-
threatening
cardiac arrhythmias. A model that allows a user to interact with an accurate
and predictive model of the heart's cells and tissues would be of great value.
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This objective has spurred the development of computational
models of cardiac cells and tissues. These computational models have sought
to integrate experimental observations and theoretical knowledge into a
formal model expressed in mathematical terms. Various algorithms,
processes and procedures are used to describe the behavior of the cells and
tissues that comprise the organ system. A useful computer-implemented
model should effectively emulate interesting behaviors.
The earliest mathematical models of the heart used formal
mathematical assumptions about cellular physiology; for example Van der Pol
and Mark's description of the heartbeat as a relaxation oscillator in 1928.
Real physiological parameters were not included in models until 1952 when
Hodgkin and Huxley explained their observations on the action potential of
the giant squid axon in their classic work on membrane processes and ion
fluxes. The success of their work can be measured by the many models that
have followed their paradigm to model systems as diverse as neurons, cardiac
cells, pancreatic beta cells, and other excitable cells. One descendent model
was the 1962 Noble model of the cardiac Purkinje fiber which was based on
experimental evidence that two potassium conductances, together with a
sodium conductance, are sufficient to generate action potentials and
pacemaker potentials.
Technical innovations have led to more precise experimental
data which in turn has led to the ongoing refinement of models as new
information has been incorporated. The result has been that the accuracy and
predictability of models have been upgraded with respect to actual
biophysical and physiological parameters; for example, beginning with the
Noble model of the Purkinje fiber, subsequent experiments extended the
description of cardiac electrophysiology to include more refined models of the
Purkinje conducting system, as well as sinus node, atrial, and ventricular
cells. These single cell models have evolved, through successive
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improvements and refinements, into a software package called "OXSOFT
HEART 4.5" presently available to investigators under license from Takhus,
Inc.
Presently the "OXSOFT" model is restricted to the modeling of
cardiac function at the single cell (or "zero-dimensional") level. This model
incorporates mathematical expressions that represent the biochemical,
biophysical, and cellular mechanisms (Hodgkin-Huxley) within single cardiac
cells. These equations collectively define a given cardiac-cell state.
The "OXSOFT" models require the solution of thirty or more
simultaneous non-linear differential equations. Even on the fastest personal
computers it can take several minutes to compute only a few seconds of
activity. Nonetheless zero-dimensional models have proven to be successful
not only in reproducing normal single cell cardiac electrical activity, but
also
in reconstructing some of the cellular mechanisms of arrhythmia, including
ectopic beating and the effects of therapeutic drug administration (e.g.,
cardiac glycosides). These models can exhibit the action potential shortening
during ATP depletion, and the early after-depolarizations characteristic of
potassium blocking compounds and calcium agonists observed in actual
hearts. Initial success has prompted researchers to try to extend the
dimensionally of these models but just how best to do this has remained
elusive.
To date, efforts to extend the single cell models and to develop
large scale higher dimensional models usually have favored simplicity,
flexibility, and computational efficiency. While these characteristics make it
possible to simulate large systems for extended periods, it requires that
biophysical and biochemical mechanisms essential to the explanation of
arrhythmias be extrapolated and rule driven. Extrapolation of the essential
mechanisms governing real systems is done by guesswork and, to some extent
is justified only when basic rules have been tested in simulation. Such
models are not usefully predictive.
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Some limitations of existing 1-D and 2-D models have been
eliminated by development of software packages called "SA" and "VENT",
licensed to (Takus, Inc.). These one-and two-dimensional network models of
the mammalian sino-atrial node, atrium, and ventricles incorporate all of the
biophysical detail described within the "OXSOFT" single cell models, but
also account for cell to cell propagation of electrical activity within simple
cardiac cell networks. When 1-D and 2-D models are iterated by the
computer, the state of the various nodes change, giving rise to data that
expresses the propagation of electric wave fronts in the model. However the
2-D model's electrophysiological wave front characteristics do not accurately
mimic the complex characteristics of actual arrhythmias.
Many laboratories value this work but existing versions of
OXSOFT, HEART, AS, and VENT (1-D and 2-D network models) neither
simulate nor accurately predict the heart's three-dimensional
electrophysiological behavior.
SUMMARY OF THE INVENTION
In contrast to prior models, the present model renders detailed
three-dimensional information about the heart based on cell function. The
present invention is a composite of procedures that, through interaction,
permits three dimensional electrophysiological simulation of the heart,
commonly referred to as the "3-D heart" model.
The model computationally represents cardiac anatomy and a
system of mathematical equations describing the spatio-temporal behavior of
biophysical quantities such as cardiac voltages at various locations. The
computer processes combines these two parts of the model in a simulation
presenting the temporal evolution of the state defining quantities in the
anatomical model.
The preferred finite difference expression of the computerized
anatomical model consists of a set of N nodes that are arrayed in a three-
dimensional network. Each node corresponds to a region of tissue within the
heart. And each node has at least five neighbors. This region of tissue may
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be defined as follows: a) a segment of an individual cardiac cell; b) an
entire
cardiac cell; c) a small region of cardiac tissue consisting of more than one
cell.
Regardless of how a node is defined, each node communicates
with its neighbors. This communication reflects electrical coupling between
adjacent parts of cells, cells, or groups of cells within the heart. In an
actual
heart the coupling strength depends on local anatomy. Thus the network level
description the coupling strength between nodes allows one to encode or
model the heart's anisotropic anatomic detail.
Thus the anatomical and biophysical portions of the model are
constructed and then they are passed to a solution procedure, along with a
file
that specifies the initial state of the heart.
The model's organization and structure facilitates computation
on multiprocessor computers because the nodes engage only in near-neighbor
interactions. Therefore the updating process for a large number of locally
coupled nodes can be easily segmented and assigned to a single processor.
This specific approach enables reasonable processing times for large numbers
of nodes, and so resolves the fundamental problem of prior art large-scale
biophysically detailed models which are computationally intractable.
BRIEF DESCRIPTION OF THE DRAWINGS
Throughout the several figures identical reference numerals
indicate identical structure, wherein:
FIG. 1 is representation of the model depicting the organization
of the software processes;
FIG. 2 is a representation of the ventricles of the heart
represented in the form of a finite difference network;
FIG. 3 is a representation of the model depicting the
organization of nodes and coupling relationships;
FIG. 4 is a representation of the action potentials which result
from the set of equations associated with each node;
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FIG. 5 is a representation of the model depicting the
relationship between the organization of an illustrative computer system with
the model;
FIG. 6a is a table setting forth preferred set of node equations;
FIG. 6b is a table setting forth preferred set of node equations;
FIG. 6c is a table setting forth preferred set of node equations;
FIG. 7 is a representation of a computed action potential along
with corresponding membrane currents.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
1. Overview
The composite model includes both "nodes" and a
complimentary "network". The network reflects and represents the
anatomical structure of the heart; the nodes reflect the spatio-temporal
evolution of the nodes' biophysical quantities.
Therefore at each node of the model, various biophysical
quantities and their related equations are defined. This biophysical model
along with the anatomical network is used by the solution program to compute
the evolution of the biophysical quantities defined at the nodes. In this
manner the electrophysiology of the whole heart can be modeled.
2. Description of the Computerized Anatomical Portion of the Model
FIG. 1 represents the composite model and illustrates procedures
for modeling the heart.
At process 10 of the heart's anatomical detail is extracted from
the heart and communicated to the geometry generator 12. Two ways to
acquire anatomic data sets are these: published data sets that have been
created by careful dissection of hearts and data derived from magnetic
resonance imaging of the heart. However anatomic data sets can come from
any of several sources.
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Geometry generator 12 creates a computerized anatomical model
of the heart represented by object 14. The exact form that anatomic model
object 14 assumes depends upon the type of generation process. The finite
difference modeling technique is shown in the specification and drawings but
finite element and multigrid models are contemplated within the scope of this
disclosure.
In the preferred development, process 12 is used to construct a
finite difference anatomic representation of the heart which is best
illustrated
in FIG. 2, which shows a finite difference heart model 40 comprised of a
lattice 41 of nodes typified by node 46.
The node locations and interconnections are specified by object
16. The conductivity between nodes is modeled by object 18. These
conductivity relationships between cells of the mammalian heart are specified
by coupling relationships between the nodes of the model. In object 20,
I S nodes representing specific tissues types and how they are coupled to the
rest
of the heart are specified. For example, a set of nodes and their coupling
relationships could be modified to represent Purkinje fiber cells, thus
representing the physical extent and direction of Purkinje fibers within the
myocardium. Object 20 is used in this fashion to capture tissues like these in
the model. Object 14 corresponds to the finite difference heart model 40
shown in FIG. 2. This portion of the model is combined with the biophysical
model in the simulation program 28.
FIG. 2 depicts a finite difference network of the ventricles of a
heart 40 with a portion 42 of the heart cleaved away to show the endocardial
surfaces and the chamber geometry. It should be recognized that the set of
nodes forms a lattice 41. The figure also shows that the nodes typified by
node 44 lie on or in the myocardium and that no nodes are present in the
chamber proper.
This figure illustrates a direct relationship between each node
and its corresponding spatial location in the heart depicted in the completed
lattice 41. One should observe that when a finite difference geometry
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generator process 12 is used, the nodes form a cubic lattice structure with
each node having at least five (and more commonly six) near neighbors.
Fig. 3 shows a subject node 46 extracted from the finite
difference model of the myocardium and presented with its near neighbors.
The lattice 41 reveals three global orthogonal axes. The X-axis 48 and Y-axis
50 and Z-axis 52, pass through an origin which is occupied by the subject
reference node 46. The coupling relationship between node 46 and its
companions is shown as a block typified by block 60 connecting node 46 with
node 58. The anisotropy of the heart as taken from the anatomic data set 10 is
used to defined each of the many relationships illustrated by coupling
relationship depicted by block 60. In general the tensor of the anatomic data
will be resolved into the three orthogonal axes shown on the figure. This
figure is intended to show the computational coupling relationship between
nodes such as node 58 and node 46. In general the coupling relationship
between nodes depends on both cell type and cell orientation.
For example, in the heart, conductivity between adjacent cells is
strongest in the direction of the long axis of each cell (cardiac cells are
typically long and thin). This direction is known as the fiber orientation.
Fiber orientation changes throughout the myocardium, thus varying from node
to node in the model. In the 3-D heart model, coupling strength between each
node is varied according to these spatial changes of fiber orientation. Thus,
the lattice parameters (coupling strength), which control the communication
of data between cellular nodes is used to encode the detailed anatomical
structure of the heart model. This coupling relationship is a part of the
object
14 and is represented by object 18.
Computation of the, spatial dependency of voltage depends on
determining the electrical current flow between adjacent nodes of the lattice,
because a triggered depolarization results when current flows into a node from
an adjacent node. This current flow is simulated in simulation program 28 by
using Ohm's Law. Defining VA and VB as the transmembrane voltages at
node 58 and 46 (Fig. 3), and G as the coupling conductance (i.e., inverse of
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resistance) between these two nodes, then the coupling current flowing from
node 46 to node 58 is given by
I=G * (VA - VB).
Thus, in order to compute the coupling current I between any
pair of nodes typified by node 46 and node 58, it is sufficient that the nodes
communicate only with their transmembrane voltages to each other.
Communication in the model is therefore local. G may be a constant linear
conductance, or it could be given by a biophysically accurate mode of
properties of cardiac gap junction channels. The transmembrane voltages are
discussed in the following section.
3. Description of the Biophysical Portion of the Model
Fig. 4 is similar to Fig. 3 in that it shows a representative node
46 of the heart 40. In this representation the node 46 is associated with
chart
68 which depicts a computed action potential at the node. The action
potential is the biologic term used to denominate the time course or evolution
of cellular voltage. All cells have a potential difference between the
interior
of the cell and the exterior of the cell. This so called transmembrane
potential
results from the accumulation of negatively charged ions within the cell. In
the case of physical excitable cells, ion channels in the membrane open and
close sequentially which allows the ions to migrate across the membrane
results in the depolarization portion of the wave form shown as intrinsic
deflection 70. In this phase the rapid sodium (Na) channels open. This sharp
change in voltage is communicated to the near neighbor cells, triggering a
depolarization in the adjacent cells. Metabolic processes then commence to
repolarize the cell. The return to the resting potential is shown in the
action
potential table 68 by curve 72.
Again referring to Fig. l, once the object 14 has been defined
and created, the biophysical model 22 must be specified. First, a choice is
made of what biophysical quantities are of interest. Next, a mathematical
model that describes their spatio-temporal behavior is developed in process
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26. Usually these processes can be described in the form of partial
differential equations. These equations describe the cellular and subcelluar
processes that determine the values of the biophysical quantities from one
moment in time to the next. Then this mathematical model must be translated
S into a computational form by process 26 so that the solution program of
process 28 can use the process 26 as a subroutine. The structure of this
simulation program 28 will depend upon what type of anatomical mode was
constructed-i.e., a finite difference anatomical model demands a finite
difference representation of the biophysical model.
The biophysical model 22 (Fig. 1 ) includes in a set of N x Neq
coupled (through voltage) nonlinear ordinary differential equations (ODES),
with coupling as defined by the anatomical model. Given initial values 34 for
the state variables defined by each of these equations (referred to as an
initial
condition), and given boundary conditions on electrical current flow at the
bounding surfaces of the model, these ODEs may be evolved in time to
predict electrical activity within the heart. The ability to relate this
predicted
electrical activity to cellular electrophysiology is the single most useful
characteristic of this model.
Representative equations for defining the state of the node are
set forth in tables in Fig. 6a; Fig. 6b and in Fig. 6c. They include: voltage
dependent transmembrane currents for (Na), (K), and Ca) ionic species,
transmembrane ion pump currents for (Na), (K), and (Ca) ionic species; total
transmembrane flux of (Na), (K), and (Ca) ionic species; total transmembrane
ion flux in cellular organelles; each node having a total transmembrane flux
due to lipid bilayer membrane capacitance.
In the preferred and illustrative finite difference development,
the partial differential equations reduce to a set of ordinary differential
equations defined at each node. These equations define the biophysical
processes giving rise to the unique properties of cardiac tissue. In general,
this system includes: a) equations defining properties of nonlinear, voltage-
gated transmembrane currents; b) equations describing properties of ion
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pumps and exchangers in the cell membrane; c) equations describing the
buffering, uptake, storage, transfer. and release of calcium ions by
intracellular organelles; and d) equations describing time-varying changes of
intracellular ion concentration.
Fig. 6a sets forth exemplary equations while the tables of Fig.
6b and Fig. 6c identify a grouping of biophysical processes that are suitable
for use in the preferred model. These tables may be related to the action
potential of Fig. 7. The corresponding ionic current flows are associated with
the time course of Fig. 7.
With respect to Fig. 1, the simulation program 28 interactively
computes the action potential defining equations from the biophysical model
22 for all the nodes and additionally computes the contribution that near
neighbors have on the voltage at the nodes. This process is represented in the
figure by integration process 30. The initial conditions are presented to the
simulation process 28 by the object 34 which is typically a data file. In a
similar fashion the run parameters are presented by a data file shown as
object
32. The output 36 of the simulation program 28 can be expressed in any one
of a number of ways. One very useful output format is a 3D animation of the
time course of voltage over several heartbeats. Normally the animation is
created by a graphics terminal dedicated to animating large data files. Single
node results are also available and may be presented in the form of computed
action potentials.
Fig. 5 among other things illustrates a parallel processor
computer system 86. The operating system software can select a set of nodes
81 and have the state equations run on a single process 90. A separate set of
nodes 82 can be concurrently computed on processor 92. In this fashion the
state defining equations at the nodes can be calculated simultaneously. The
fact that the state of each node is essentially local renders this approach
practical. Once the action potentials of all nodes is completed the
appropriate
state data can be accumulated in the shared memory 94. With this data
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available the individual processors can next compute the coupling
relationships giving rise to the output 36 (Fig. 1).
Various graphical display techniques can be used to present this
data to the user including 3D animation 38, single node action potential
results 39 or simulated surface presentations 37.
Figure 7 shows a computed-action potential for a single node.
By convention, the action potential is broken into several phases: the resting
potential corresponds to Phase 4; the rapid depolarization of the cell across
the membrane is represented by Phase 0; Phases 1 and 2 correspond to a
depolarization plateau; and Phase 3 corresponds to the return of the node to
the quiescent state.
The action potential of cardiac cells has been the subject of
intense study, and it should be appreciated that the time course of the
potential shown in Figure 7 is the result of various ionic transfers shown in
Figure 7. The initial in-rush of calcium and sodium gives rise to the loss of
potential difference between the extra-cellular and intra-cellular space. This
process induces voltage-gated ionic current, which gives rise to Phase 3 of
the
figure. Thus, the time course of the voltage is taken as the sum of the Phase
0
through Phase 4 currents. Although the currents depicted in Figure 6(a), 6(b),
and 6(c) are preferred, the precise formulation of the currents are subject to
further refinement as additional experimental evidence becomes available.
Further detail related to these specific currents can be found in Oxsoft
documentation.
The above specification, examples and data provide an
illustrative description of the invention. Since many embodiments of the
invention can be made without departing from the spirit and scope of the
invention, the invention resides in the following claims.
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