Patient-Specific Modeling in Cardiac Electrophysiology: Parameter Estimation and Personalization Pubblico

Abstract

Computational modeling in cardiac electrophysiology (EP) has long played a central role in the study of physio-pathological dynamics of electrical propagation. One of the most significant challenges to face is the translation process of numerical (in silico) investigations to clinical practice. In silico simulations can potentially impact the quality of cardiac arrhythmia therapy, reducing the risk of in vivo testing. However, the clinical use of virtual experiments is hindered by the need of customization of mathematical models to patient-specific data. The personalization process involves the fine tuning of many model parameters, that cannot be measured directly, via accurate and efficient data assimilation techniques. This work is particularly focused on the estimation of cardiac conductivities, crucial parameters of the Bidomain and Monodomain models – currently the most used mathematical descriptions of cardiac electrical behavior. This Thesis addresses the challenge described above yielding four main contributions. (1) We perform an extensive and thorough synthetic and experimental validation of the deterministic variational data assimilation method proposed by Yang and Veneziani in 2015 to retrieve conductivities from potential recordings.

The results demonstrate that the procedure provides accurate space-dependent conductivity estimates that reproduce most of the observed dynamics. (2) The Proper Generalized Decomposition (PGD) reduced-order model technique is investigated for the first time in EP to improve the efficiency of the variational technique. Relying on the off-line/on-line paradigm and without the need of any preliminary knowledge of the high-fidelity solution, we show in 2D and 3D settings that the strategy enables nearly real-time estimation preserving reasonable accuracy. (3) With the goal of assessing the robustness of the results, we propose a statistical formulation of the estimation problem for Monodomain conductivities. Exploiting the computational convenience of the on-line PGD solution, the methodology allows a reliable quantification of the uncertainty of two-dimensional estimates. (4) Using a virtual personalized heart model efficiently reconstructed from high resolution MRI images and ECG data via a physics-based reduced-order model approach, we perform a preliminary study of the induction of ventricular electrical anomalies with respect to different conduction properties in view of optimizing arrhythmia treatments in silico.

Table of Contents

1 Introduction 1

1.1 Contribution and Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Mathematical Models in Cardiac Electrophysiology 8

2.1 Anatomy and Electrophysiology of the Heart . . . . . . . . . . . . . . . . . 8

2.1.1 Macroscopic description . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Electrophysiology of cardiac myocytes . . . . . . . . . . . . . . . . . 11

2.1.3 Electrophysiology of the heart . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Modeling Electrical Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.1 Cell modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.2 Tissue modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 The Inverse Conductivity Problem and its Validation 33

3.1 The Inverse Conductivity Problem . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 The variational formulation of the ICP . . . . . . . . . . . . . . . . . 35

3.1.2 Numerical approximation . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 Synthetic Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.1 Sensitivity analysis in 2D . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2.2 Sensitivity analysis in 3D . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.3 Surrogating the BICP with the MICP . . . . . . . . . . . . . . . . . 59

3.2.4 Moving towards real validation . . . . . . . . . . . . . . . . . . . . . 65

3.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.3.1 Experimental and numerical settings . . . . . . . . . . . . . . . . . . 72

3.3.2 Validation at slow pacing rates . . . . . . . . . . . . . . . . . . . . . 74

3.3.3 The role of CL on the estimation . . . . . . . . . . . . . . . . . . . . 77

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4 Solution of the MICP Based on PGD-Model Reduction 87

4.1 PGD in a Nutshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.2 PGD Model Reduction of the Monodomain Problem . . . . . . . . . . . . . 93

4.2.1 Formulation of the reduced model . . . . . . . . . . . . . . . . . . . 94

4.2.2 Implementation details . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.2.3 Numerical results for the reduction of the forward problem . . . . . 99

4.3 Solving the PGD-MICP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.4 PGD for MICP in a Bayesian Framework . . . . . . . . . . . . . . . . . . . 115

4.4.1 Bayesian estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.4.2 Exploration by sampling . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.4.3 Practical implementation of the MH algorithm . . . . . . . . . . . . 121

4.4.4 Solution of the reduced bayesian MICP . . . . . . . . . . . . . . . . 125

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5 Ventricular Tachycardia Induction in Personalized Heart 131

5.1 Patient-Specific Computational Model of the Heart . . . . . . . . . . . . . . 133

5.1.1 Cardiac anatomical model . . . . . . . . . . . . . . . . . . . . . . . . 134

5.1.2 Electrophysiology personalization . . . . . . . . . . . . . . . . . . . . 136

5.2 VT Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.2.1 Numerical setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.2.2 Detecting VT with ECG signals . . . . . . . . . . . . . . . . . . . . 144

5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6 Conclusion and Outlook 150

Bibliography 154

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School	Laney Graduate School
Department	Mathematics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Mathematics
Parola chiave	Variational Data Assimilation Virtual Heart Model-order Reduction Cardiac Electrophysiology Validation
Committee Chair / Thesis Advisor	Alessandro Veneziani, Emory University
Committee Members	Lars Ruthotto, Emory University James Nagy, Emory University Flavio Fenton, Georgia Institute of Technology

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