Publication
On some numerical aspects of an active strain model in cardiac mechanics
Abstract
We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, with an orthotropic constitutive law for incompressible tissue at the macroscopic level. The main differences with the active stress model are addressed in detail, and a finite element discretization using Taylor-Hood and MINI elements is proposed and illustrated with numerical examples.
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Related concepts (32)
Orthotropic material
In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational symmetry. These directional differences in strength can be quantified with Hankinson's equation. They are a subset of anisotropic materials, because their properties change when measured from different directions. A familiar example of an orthotropic material is wood.
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
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