Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

Abstract

Non-linear electrical waves propagate through the heart and control cardiac contraction. Abnormal wave propagation causes various forms of the heart disease and can be lethal. One of the main causes of abnormality is a condition of cardiac fibrosis, which, from mathematical point of view, is the presence of multiple non-conducting obstacles for wave propagation. The fibrosis can have different texture which varies from diffuse (e.g., small randomly distributed obstacles), patchy (e.g., elongated interstitional stria), and focal (e.g., post-infarct scars) forms. Recently, Nezlobinsky et al. (2020) used 2D biophysical models to quantify the effects of elongation of obstacles (fibrosis texture) and showed that longitudinal and transversal propagation differently depends on the obstacle length resulting in anisotropy for wave propagation. In this paper, we extend these studies to 3D tissue models. We show that 3D consideration brings essential new effects; for the same obstacle length in 3D systems, anisotropy is about two times smaller compared to 2D, however, wave propagation is more stable with percolation threshold of about 60% (compared to 35% in 2D). The percolation threshold increases with the obstacle length for the longitudinal propagation, while it decreases for the transversal propagation. Further, in 3D, the dependency of velocity on the obstacle length for the transversal propagation disappears.

Keywords

• cardiac fibrosis
• excitable media
• wave break
• elongated obstacle