Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

Abstract

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Influence of passive mechanical properties in healthy and infarcted rat myocardium on the cardiac cycle

“…In particular, by setting f ib = 0, the intact cardiac tissue is modelled. In the present work, the active contraction for the intact myocardium is modelled following the approach from our previous work [1], which is based on [2]. It is as well scaled by the amount of fibrosis and the second Piola Kirchhoff tensor (PK2) reads as…”

“…The model is applied on the generic ellipsoidal rat LV displayed in Figure 1, right. Firstly, different passive material parameter sets from [3], [1] and [6] are used for the healthy LV (f ib = 0). These parameters are obtained via fitting the model to the experimental data for different animal species.…”

“…Based on our previous experimental and modelling works [1,6], we model the healthy and infarcted cardiac tissue as a mixture of the intact myocardium and fibrotic scar structure. Corresponding to the infarct size, the amount of fibrosis f ib, serves as a scaling factor.…”

“…where F Φ is the non-linear current for the electrical excitation and Q = D • ∇Φ is the flux with the anisotropic conductivity tensor D. For more detail, we refer to [1,2]. In addition to the last works [1,2], a pressure boundary condition on the endocardium, represented via the three-element Windkessel model, is included. Here, the parameters are adjusted such that the end-systolic pressure in the left ventricle (LV) reaches a physiological value for rats (12 kPa) [5].…”