Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

Abstract

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes

“…Where W is the strain energy function and E ij are components of the Green-Lagrange strain tensor E in a fibre-based coordinate system [35]. We use parameters C 2 = 8, C 3 = 3, C 4 = 4 based on Nasopoulou et al [48] and C 1 = 1 kPa to match end-diastolic volume.…”

“…Figure 7C shows the resulting finite element meshes. To simulate biventricular cardiac function, we use our multi-scale cardiac mechanics framework [34,38], which has recently been verified [35].…”

Influence of atrial contraction dynamics on cardiac function

“…In simulations of ventricular mechanics in isolation, boundary conditions are typically applied to the base of the ventricles, using Dirichlet or Robin boundary conditions [23]. However, in four chamber simulations, the situation is more complex.…”

“…Models of cardiac ventricular mechanics are increasingly used to study the physiology of the heart with a range of mature software packages having been developed [23]. At the same time, atrial models of electrophysiology are moving towards clinical applications, particularly in the study of atrial ablation sites [43].…”

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

“…We proved there that the activation model considered herein is capable of reproducing the desired wall thickening in a natural way under several loading conditions. A purely mechanical benchmark, under more physiological conditions, has also been recently published in [152] where the performances of different codes and discretization methods where thoroughly tested. Here, our aim is to evaluate the effects of considering the term JF …”