Mathematics Seminar - 10/30/26

Abstract:

Atrial fibrillation (AFib) is an irregular heart rhythm (i.e., an arrhythmia) which currently affects approximately 33 to 59 people worldwide. This is a serious heart rhythm disorder which often causes the heart to beat very rapidly. AFib may lead to blood clots in the heart, as well as an increased risk of stroke and heart failure. It is caused by abnormal electrical signals in the heart. Treatments for AFib focus on resetting and controlling the heartbeat and preventing blood clots and may include medication, electrical cardioversion, catheter ablation, pacemaker implantation, and maze surgery.

In this talk, I will present our image-based, high-order finite element framework for computational simulation of electro-thermal cardiac ablation. High-order calculations are used to accurately predict the electrical energy deposition and resulting transient thermal response which allows one to determine the thermal dose for the ablation procedure. There are two main components of our high-order finite element framework. The first component is the reconstruction of the cardiac myocardium anatomy from segmented MRI voxel data. This involves extraction of a smooth reference surface using the marching cubes method. An initial low-order hexahedral mesh is generated directly on the voxels, and a pillow layer of elements is added to conform the elements to the exterior boundary. The low-order mesh is enriched with midpoints, which are then projected onto the reference surface, followed by smoothing. This straight-sided high-order mesh is then curved, resulting in a highly-accurate representation of the cardiac anatomy.

The second component is a high-order finite element solver used to simulate electrothermal cardiac ablation. The electrical field is governed by quasi-static current conservation, and the resulting Joule heating is coupled to the transient Pennes bioheat equation, which incorporates thermal conduction, blood perfusion, and convective cooling. Temperature-dependent electrical and thermal properties are also considered. The results produced by the PDE solver are in good agreement with those obtained using COMSOL. The proposed framework, therefore, provides an accurate basis for high-fidelity radiofrequency cardiac ablation simulation and may be used in patient-specific treatment planning for individuals diagnosed with atrial fibrillation.

This talk represents joint work with Dr. Sumit Kumar of the University of Kansas.