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
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)
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
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
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
Improved early diagnosis of arrythmias Non-invasive treatment of paroxysmal
supraventricular tachycardia (PSVT), a class of deadly arrythmias
Remote monitoring of personnel in high-risk environments
Pre-surgery inverse ECGs would shorten operations and minimize patient risks
Applications of Inverse Electrocardiography (continued)
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
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]
Problem is difficult because it is unsteady both electrically and geometrically
Modeling the Electrical System of the Heart (continued)
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
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
Problem is governed by Poisson’s Equation:
The following simple models were used to test the solution technique:– Concentric spheres with single dipole– Outer spherical boundary with various dipole
configurations inside
0
Problem Formulation (continued)
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
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)
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
Boundary Element Method (BEM) Advantages:
– Decreases dimensionality by one– Non-iterative for linear problems– Short computational time
Disadvantage:– More difficulty with varying material
properties
Computational Technique (continued)
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
3 dipoles,sphericalouterboundary
23 dipoles,sphericalouterboundary
3 dipoles,realistictorso
23 dipoles,realistictorso
2.85% 2.62% 51.50% 109.67%
RMS Errors for Forward Solution (772 panels for sphere, 752 panels for torso)
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
3 dipoles,sphericalouterboundary
23 dipoles,sphericalouterboundary
3 dipoles,realistictorso
23 dipoles,realistictorso
1.33% /0.70%
43.64% /0.56%
10.96% /11.60%
54.79% /21.36%
Normalized Dipole Component Standard Deviations and RMS Potential Errors for Inverse
Solution (772 panels for sphere, 752 panels for torso)
Inverse Problem Results (continued)
PSU BEMModel(386 nodes)
Throne et al.FEM Model(342 nodes)
Pilkington etal. BEM Model(unspecified #of nodes)
0.77% 0.32% 1.60%
RMS Errors for Inverse Solution with Concentric Spheres Compared to Other Researchers
Summary of findings
Forward Problem– Excellent RMS error with spherical boundaries– RMS error with torso poor due to limitations of solution
technique 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
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)
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
Improvements in BEM technique– 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
Professor George S. Dulikravich Mr. Thomas J. Martin Professor Akhlesh Lakhtakia Professor David B. Geselowitz Professor Peter Johnston (University of
Tasmania)