Craig Bates Thesis Advisor: Dr. George S. Dulikravich, Aerospace Engineering

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


Relative Error Distribution, 23 dipoles


Forward Problem Results

3 dipoles,sphericalouterboundary


3 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)



Inverse Problem Results





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)


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)

Craig Bates Thesis Advisor: Dr. George S. Dulikravich, Aerospace Engineering

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