An isogeometric analysis framework for ventricular cardiac mechanics

TL;DR

This paper introduces an isogeometric analysis framework for cardiac mechanics that integrates geometry and solution approximation, reducing computational costs while maintaining accuracy, and demonstrating its effectiveness through benchmarking and anatomy variation analysis.

Contribution

The study develops a novel IGA framework for cardiac mechanics that directly uses spline geometry for discretization, improving efficiency and geometric flexibility over traditional FEM methods.

Findings

IGA accurately captures hemodynamic responses with fewer elements.

The framework demonstrates geometric flexibility for anatomy variations.

Benchmarking shows comparable results to high-fidelity FEM models.

Abstract

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical features many elements may be required, possibly leading to unnecessarily large computation costs. Without loss of accuracy, a reduction in computation cost can be achieved by integrating geometry representation and solution approximation into a single framework using the Isogeometric Analysis (IGA) paradigm. In this study, we propose an IGA framework suitable for echocardiogram data of cardiac mechanics, where we show the advantageous properties of smooth splines through the development of a multi-patch anatomical model. A nonlinear cardiac model is discretized following the IGA paradigm, meaning that the spline geometry parametrization is directly used for the discretization of the physical fields. The IGA model is benchmarked with a state-of-the-art biomechanics model based on traditional FEM. For this benchmark, the hemodynamic response predicted by the high-fidelity FEM model is accurately captured by an IGA model with only 320 elements and 4,700 degrees of freedom. The study is concluded by a brief anatomy-variation analysis, which illustrates the geometric flexibility of the framework. The IGA framework can be used as a first step toward an efficient workflow for an improved understanding of, and clinical decision support for, the treatment of cardiac diseases like heart rhythm disorders.