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

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. Human Torso Model

12. 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

13. 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)

14. 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]

15. 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]

16. 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

17. 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]

18. Forward Problem Results (continued) Analytic Potential Distribution, 23 dipoles Computed Potential Distribution, 23 dipoles

19. Forward Problem Results (continued) Analytic Potential Distribution, 3 dipoles Computed Potential Distribution, 3 dipoles

20. Forward Problem Results (continued) Analytic Potential Distribution, 23 dipoles Computed Potential Distribution, 23 dipoles

21. Forward Problem Results (continued) Relative Error Distribution, 23 dipoles Relative Error Distribution, 23 dipoles

22. Forward Problem Results RMS Errors for Forward Solution (772 panels for sphere, 752 panels for torso)

23. Inverse Problem Results (continued) Analytic Potential Distribution, 3 dipoles Computed Potential Distribution, 3 dipoles

24. Inverse Problem Results (continued) Analytic Potential Distribution, 23 dipoles Computed Potential Distribution, 23 dipoles

25. Inverse Problem Results (continued) Relative Error Distribution, 23 dipoles Relative Error Distribution, 23 dipoles

26. Inverse Problem Results Normalized Dipole Component Standard Deviations and RMS Potential Errors for Inverse Solution (772 panels for sphere, 752 panels for torso)

27. Inverse Problem Results (continued) RMS Errors for Inverse Solution with Concentric Spheres Compared to Other Researchers

28. 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

29. 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

30. 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

31. 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

32. Acknowledgments • Professor George S. Dulikravich • Mr. Thomas J. Martin • Professor Akhlesh Lakhtakia • Professor David B. Geselowitz • Professor Peter Johnston (University of Tasmania)