A Transmural Path Model Improves the Definition of the Orthotropic Tissue Structure in Heart Simulations

Abstract

In the past decades, the structure of the heart, human as well as other species, has been explored in a detailed way e.g. via histological studies or diffusion tensor magnetic resonance imaging. Nevertheless, the assignment of the characteristic orthotropic structure of the material in a patient-specific finite element model remains a challenging task. Various types of rule-based models, which define the local fibre and sheet orientation depending on the transmural depth, have been developed. However, the correct assessment of the transmural depth is not trivial. Its accuracy has a substantial influence on the overall mechanical and electrical properties of the model. The main purpose of this study is the developement of a finite-element-based approach to accurately determine the transmural depth. We propose a finite-element-based discontinuous Galerkin approach to determine the transmural path, thickness and depth. Based on the accurate transmural depth, we assign the local material orientation of the orthotropic tissue structure in a usual fashion. We show that this approach leads to a more accurate definition of the transmural depth. Furthermore, for the left ventricle, we propose rules for the transmural fibre and sheet orientation by fitting them to literature based data. The proposed functions show a distinct improvement compared to existing rules.

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

“…Today, most popular models for heart muscle tissue are Holzapfel-type models [32] that use an invariantbased formulation of the free energy function [62] and can naturally incorporate tissue incompressibility and orthotropy in the fiber, sheet, and normal directions [33]. Invariant-based modeling of cardiac tissue has rapidly gained popularity [16, 23, 24, 30, 45, 46, 52] and is now widely used in many common finite element packages [1, 7]. Notably, the initial Holzapfel Ogden model was made up of four exponential quadratic terms in the first invariant I 1 , the fourth invariants I 4f and I 4s , and the eighth invariant I 8fs , with two parameters each; one with the unit of stiffness and the other unit-less [33].…”

Support Pressure Acting on the Epicardial Surface of a Rat Left Ventricle—A Computational Study

“…However, the influence of a direct cardiac compression device on cardiac performance is not straightforward to compute, due to, e.g., the varying mechanical properties of active biological cardiac tissue that is undergoing complex deformations. The complex orthotropic tissue structure of the healthy myocardium, which can be modeled with different approaches ( 11 – 13 ), plays an important role. Furthermore, the amount of fibrosis in the ventricular wall strongly influences cardiac performance.…”