An adaptive hybridizable discontinuous Galerkin approach for cardiac electrophysiology

Abstract

Cardiac electrophysiology simulations are numerically challenging because of the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the hybridizable discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular, using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. The HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom, coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle, p-adaptivity reduces the average number of degrees of freedom by 95% compared to the nonadaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing.

Computational model of gastric motility with active‐strain electromechanics

“…From the computational point of view, a deeper investigation of the CV in the circumferential direction using a more realistic gastric geometry should be accomplished, considering also the presence of the fundus, which is electrically quiescent but responsible for other, specific mechanical effects, namely the storage function of the stomach. Also, more efficient numerical schemes and GPU‐based codes are foreseen to speed‐up the wide numerical analyses necessary to fully characterize a complex organ like the stomach.…”

The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling

“…Our structural model can be coupled to a model of electric signal propagation as shown in [51]. However, as the focus in this work is on pericardial boundary conditions, a coupled electro-mechanical model would only introduce unnecessary complexity and variability.…”

“…Rather, all myocardial tissue in our simulations was activated simultaneously. We recently demonstrated the ability to couple our mechanical model to an electrophysiological model [51], which we can include in further studies. However, since the data came from a healthy volunteer, we do no expect relevant variations.…”

A numerical study on the effects of spatial and temporal discretization in cardiac electrophysiology

“…Some researchers have used adaptivity of the discretization in space, 21,22 in time 23 or both 24 . Others have considered p‐adaptivity 13,25 which allows an independent change in the order of the shape functions in the elements. Some authors have resorted to modified element formulations, such as non‐conforming elements 26 or so‐called macro finite elements 27 .…”