Scalable Computational Framework for Cardiac Radiofrequency Ablation: Multiphysics Modeling and Domain Decomposition Open Access

Abstract

Radiofrequency ablation (RFA) is the cornerstone treatment for various cardiac arrhythmias; however, its long-term efficacy is often hampered by limited understanding of the biophysical mechanisms governing lesion formation. Traditional computational models primarily rely on secondary structural indicators, such as thermal thresholds or damage integrals, for procedural assessment. These metrics fundamentally fail to account for the distinction between reversible tissue stunning and the permanent functional block, required for clinical success.

This dissertation addresses these shortcomings by introducing a high-fidelity computational framework that integrates cardiac electrophysiology (EP) directly into the assessment of RFA outcomes. By shifting the evaluative paradigm toward functional conduction block, this work establishes a new foundation for predictive ablation modeling.

The framework consists of two core computational pillars implemented within the MFEM finite element library. The Multiphysics RFA Solver couples electrostatics, bioheat transfer, cellular death, and fluid dynamics across heterogeneous domains. To handle disparate time scales and high-gradient regions near the electrode, we utilize non-overlapping domain decomposition methods to solve interface problems efficiently.

The Integrated EP Solver addresses the Monodomain problem through an operator-splitting scheme. To handle the stiff nonlinearities of membrane kinetics, we implement an automated ODE code-generation pipeline via gotranx, streamlining the integration of biophysically detailed ionic models into the MFEM API, with minimal manual effort. The primary novelty lies in the coupling between solvers, where thermal and damage-induced feedback mechanisms dynamically modulate tissue excitability.

Ultimately, this research highlights the potential of advanced numerical methods and DOE-supported software libraries to solve complex, multiscale problems in predictive medicine. Through numerical verification and targeted test cases, we demonstrate that this high-fidelity approach provides a path toward the in silico optimization of ablation strategies, paving the way for personalized treatment planning and improved patient outcomes.

Table of Contents

List of Figures

List of Tables

List of Abbreviations

Copyright and Permissions Notice

1 Introduction

1.1 Clinical Background

1.1.1 Heart Anatomy & Tissue Organization

1.1.2 Electrical Activity of the Heart

1.1.3 Arrhythmias & Ablation Therapies

1.2 State of the Art in RFA Modeling

1.3 Research Objectives and Contributions

1.4 Thesis Outline

2 Multiphysics Mathematical Model

I RADIOFREQUENCY MODEL

2.1 Preliminaries

2.1.1 Geometry

2.1.2 Fiber Distribution

2.2 Energy Source: Radiofrequency (RF)

2.3 Continuum Modeling of Thermal Transport

2.3.1 Electrode Domain

2.3.2 Blood Domain

2.3.3 Cardiac Tissue Domain

2.3.4 Summary

2.3.5 Perspectives: Beyond Pennes Bioheat Model

2.4 Damage Assessment in Thermal Modeling

2.4.1 Some Models of Thermal Damage Assessment

2.4.2 The Three-State Model

2.5 Blood Flow Modeling

2.5.1 General Governing Equations for Fluid Motion

2.5.2 The Incompressible Navier-Stokes Equations

2.6 Material Properties for RFA Model

II CARDIAC ELECTROPHYSIOLOGY

2.7 Cell-scale: Ionic Models

2.7.1 Preliminaries

2.7.2 Biophysically Detailed (Mechanistic) Ionic Models

2.7.3 Reduced (Phenomenological) Ionic Models

2.8 Tissue-scale: Bidomain and Monodomain Models

2.8.1 Bidomain Model

2.8.2 Monodomain Model

2.9 Thermo-electric Coupling and Influence of Damage

2.9.1 Role of Temperature

2.9.2 Role of Damage

2.9.3 Thermo-Electrical-Damage (TED) Monodomain Model

3 Numerical Discretization through High-Order Methods

3.1 General Discretization Framework

3.1.1 Spatial Discretization

3.1.2 Time Discretization

3.2 Discretization of the RF Problem

3.3 Discretization of the Heat Transfer Problem

3.4 Discretization of the Fluid Dynamics Problem

3.5 Discretization of the Cellular Death Problem

3.6 Discretization of the Electrophysiology Problem

3.6.1 Operator Splitting for Cardiac Electrophysiology

3.6.2 Space-time Discretization of the Monodomain Model

3.6.3 Adaptive Mesh Refinement

4 Domain Decomposition & Multiphysics Coupling

4.1 Motivation and Computational Challenges

4.2 Domain Decomposition and Interface Formulations

4.2.1 Non-Overlapping Domain Decomposition Methods

4.2.2 Interface Reduction and Steklov–Poincaré Operators

4.3 Multiphysics Segregation

4.3.1 Coupling of the Multiphysics RFA Model

4.3.2 Coupling of RFA and Electrophysiology

4.4 Non-overlapping Domain Decomposition

4.4.1 Dirichlet–Neumann Interface Formulation

4.4.2 Robin–Robin Interface Formulation

4.4.3 Convergence Analysis of the DN and RR Couplings

5 Parallel Implementation & Software Framework

5.1 Software Framework

5.1.1 The MFEM Finite Element Library

5.1.2 Meshing and Other Software

5.2 Implementation Details of Multiphysics Solvers

5.2.1 General Solver Structure

5.2.2 Physics-Specific Implementation

5.3 InterfaceTransfer Class

5.4 Automatic ODE Code Generation

5.4.1 The GotranxODEModel Class

5.4.2 HOWTO: Generate and Integrate a New Ionic Model

5.4.3 HOWTO: Add Thermal and Damage Dependence to an Ionic Model

6 Numerical Results

6.1 Computational Resources

6.2 Convergence Studies and Verification

6.3 Physics-Specific Benchmarks

6.4 Impact of Anisotropy

6.5 Effect of Blood Perfusion Models

6.6 Power Control Algorithm

6.7 Performance of Domain Decomposition Framework

6.7.1 Optimization of the RF Coupling via Robin–Robin Conditions

6.8 Coupled RFA Simulations

6.9 Electrophysiology and Arrhythmia Assessment

6.9.1 Ionic Models and Basic Stimuli

6.9.2 Niederer Benchmark

6.9.3 Spiral Waves Generation

6.9.4 Effect of Temperature

6.9.5 Coupled Effect of Temperature and Damage

7 Conclusions

Appendix

A Stability Analysis of the Cellular-Death Model

B Derivation of the Navier-Stokes Equations

C Material Properties

D Variable-coefficient BDF Parameters

Bibliography

About this Dissertation

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School	Laney Graduate School
Department	Mathematics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Applied Mathematics Biophysics, Biomechanics Engineering, Biomedical
Keyword	Computational Modeling Domain Decomposition Radiofrequency Ablation Finite Element Method (FEM)
Committee Chair / Thesis Advisor	Alessandro Veneziani, Emory University
Committee Members	Talea Mayo, Emory University Flavio Fenton, Georgia Institute of Technology Elizabeth Cherry, Georgia Institute of Technology Yuanzhe Xi, Emory University

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