Download Inverse Determination of Locations and Strengths of Electrical

Forward and Inverse
Electrocardiographic Calculations On a
Multi-Dipole Model of Human Cardiac
Electrophysiology
Craig Bates
Thesis Advisor: Dr. George S. Dulikravich,
Aerospace Engineering
July 18, 1997
Background
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The leading killer of adults in the U.S. is
cardiovascular diseases with 925,079 deaths
in 1992 (42.5% of total adult deaths)
The key to preventing the onset of
cardiovascular disease is early diagnosis
and prevention
The trend in medicine is away from
expensive and potentially dangerous
invasive procedures
Background (continued)
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Cardiovascular diseases cost Americans
$178 billion annually in medical bills and
lost work
The U.S. population is aging, so
cardiovascular diseases are becoming a
bigger issue
Older patients have more difficulty
surviving invasive procedures
Introduction to Cardiac
Electrophysiology
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A series of polarization and depolarization
cycles make up each heartbeat
Impulses originate in the sinus pacemaker and
end after the ventricles depolarize
Electrocardiograms (ECGs) represent
electrical activity in the heart as a sum of
multiple electrode leads
Presence of conduction blockages or extra
pathways can cause deadly arrythmias
Inverse Electrocardiography
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Inverse electrocardiography uses multiple
measurements taken on the chest surface to
calculate the electrical activity throughout
the heart
This would allow physicians to accurately
detect the origin of electrical anomalies
Accurate location of anomalies allows the
use of non-invasive treatment techniques
Applications of Inverse
Electrocardiography
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Improved early diagnosis of arrythmias
Non-invasive treatment of paroxysmal
supraventricular tachycardia (PSVT), a
class of deadly arrythmias
Remote monitoring of personnel in highrisk environments
Pre-surgery inverse ECGs would shorten
operations and minimize patient risks
Applications of Inverse
Electrocardiography (continued)
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Inverse ECGs would make it easier for
researchers to study the heart and
understand the underlying
electrophysiological processes
Inverse ECGs would allow physicians to do
in-depth examinations of the heart at lower
cost and risk to patient
Modeling the Electrical System
of the Heart
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In order to accurately represent the heart with
a computer simulation a model that defines the
origin of electrical impulses is required
Two major types of models
– Equivalent cardiac generator model
[Geselowitz 1963]
– Epicardial potential model [Martin et al. 1972]
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Problem is difficult because it is unsteady both
electrically and geometrically
Modeling the Electrical System
of the Heart (continued)
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A model based on the equivalent cardiac
generator concept was used
This model was created by Miller and
Geselowitz [Miller and Geselowitz 1979]
The model employs 23 dipoles that remain
stationary throughout the cycle but change
in magnitude and direction with time
The model assumes a homogeneous
conducting medium to simplify calculations
Modeling the Human Torso
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An accurate model of the body surface is
necessary
A torso model from the University of
Tasmania [Johnston 1996] was used
The torso was generated from successive
MRI scans of a 58 year old female patient
The torso consists of 754 boundary nodes
and 752 quadrilateral surface panels
Human Torso Model
Problem Formulation
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Problem is governed by Poisson’s Equation:
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  
  0 were used to
The following
simplemodels
test the solution technique:
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– Concentric spheres with single dipole
– Outer spherical boundary with various dipole
configurations inside
Problem Formulation (continued)
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The torso model was substituted for the
outer spheres for the major calculations
The problems were solved two ways:
– Forward (dipole components or inner surface
potentials specified --> potential solved for on
outer surface)
– Inverse (potentials and fluxes specified on
outer surface --> inner surface potentials or
dipole components solved for)
Methodology
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The spherical geometry was chosen because
it is commonly used in published work and
it provides a benchmark that predicts how
well a solution technique will perform
The torso geometry that was chosen has
been successfully applied to inverse
electrocardiographic calculations in the past
[Johnston 1996]
Methodology (continued)
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All results were compared to the analytic
solutions
In addition to being compared to the
analytic solution, concentric sphere results
were compared to results in the literature
[Throne et al. 1994, Pilkington et al. 1987]
Computational Technique
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Boundary Element Method (BEM)
Advantages:
– Decreases dimensionality by one
– Non-iterative for linear problems
– Short computational time
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Disadvantage:
– More difficulty with varying material
properties
Computational Technique
(continued)
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BEM code already successfully applied to
inverse heat conduction and elasticity
problems
Problem is treated as quasi-static and
solved for at a particular instant in time
[Plonsey and Heppner 1967]
Forward Problem Results
(continued)
Analytic Potential
Distribution, 23 dipoles
Computed Potential
Distribution, 23 dipoles
Forward Problem Results
(continued)
Analytic Potential
Distribution, 3 dipoles
Computed Potential
Distribution, 3 dipoles
Forward Problem Results
(continued)
Analytic Potential
Distribution, 23 dipoles
Computed Potential
Distribution, 23 dipoles
Forward Problem Results
(continued)
Relative Error
Distribution, 23 dipoles
Relative Error
Distribution, 23 dipoles
Forward Problem Results
RMS Errors for Forward Solution
(772 panels for sphere, 752 panels for torso)
3 dipoles,
spherical
outer
boundary
2.85%
23 dipoles,
spherical
outer
boundary
2.62%
3 dipoles,
realistic
torso
23 dipoles,
realistic
torso
51.50%
109.67%
Inverse Problem Results
(continued)
Analytic Potential
Distribution, 3 dipoles
Computed Potential
Distribution, 3 dipoles
Inverse Problem Results
(continued)
Analytic Potential
Distribution, 23 dipoles
Computed Potential
Distribution, 23 dipoles
Inverse Problem Results
(continued)
Relative Error
Distribution, 23 dipoles
Relative Error
Distribution, 23 dipoles
Inverse Problem Results
Normalized Dipole Component Standard
Deviations and RMS Potential Errors for Inverse
Solution
(772 panels for sphere, 752 panels for torso)
3 dipoles,
spherical
outer
boundary
1.33% /
0.70%
23 dipoles,
spherical
outer
boundary
43.64% /
0.56%
3 dipoles,
realistic
torso
23 dipoles,
realistic
torso
10.96% /
11.60%
54.79% /
21.36%
Inverse Problem Results
(continued)
RMS Errors for Inverse Solution with Concentric
Spheres Compared to Other Researchers
PSU BEM
Model
(386 nodes)
Throne et al.
FEM Model
(342 nodes)
0.77%
0.32%
Pilkington et
al. BEM Model
(unspecified #
of nodes)
1.60%
Summary of findings
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Forward Problem
– Excellent RMS error with spherical boundaries
– RMS error with torso poor due to limitations of
solution technique
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Inverse Problem
– Dipole component determination good for
smaller numbers of dipoles
– Error high for both sphere and torso due to
limitations of solution technique coupled with
superposition effects
Significance of Research
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Most previous work has approached the
problem by developing a heart model and
building a solution technique around it
This work began with a solution technique
that has been applied successfully to other
inverse problems and applied it to a heart
model
Significance of Research
(continued)
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Inverse problem errors with realistic torso
confirm other researcher’s work with
equivalent cardiac generator models
Results with smaller numbers of dipoles
were very encouraging
Possible Future Work
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Improvements in BEM technique
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–
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Implementation of discontinuous elements
Use isoparametric quadratic elements
Use triangular elements
Improved singular matrix solution technique
Experiments with determination of
epicardial potentials
Improved torso geometry
Acknowledgments
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Professor George S. Dulikravich
Mr. Thomas J. Martin
Professor Akhlesh Lakhtakia
Professor David B. Geselowitz
Professor Peter Johnston (University of
Tasmania)