The mechanical function of cardiac tissue results from the complex interplay of
contracting cardiomyocytes and the passive extracellular matrix. Most computational
models of cardiac mechanics are based on a continuum approach, where the tissue
is viewed as a continuous and homogeneous mix of cells and extracellular material.
This approach has been successfully applied in numerous studies,
and will undoubtedly remain a cornerstone of computational biomechanics.
However, the extensive homogenization limits the models' ability to give detailed
insight into the mechanical forces experienced by individual cardiac cells, and
to delineate the mechanical contributions of myocytes and the extracellular matrix.
More detailed models exist, in the form of continuum mechanics models
of individual myocytes, but these are typically limited to a single myocyte and
do not consider the extracellular matrix.

Computational models of cardiac electrophysiology are typically based on the
same continuous and homogenized concept as the mechanics model, with the
bidomain model being the reference model for several decades. More recently,
models have been developed that explicitly represent the cells, the membrane,
and the domain between the cells. The approach is commonly referred to as the EMI
(Extracellular-Membrane-Intracellular) model, and has been applied in
studies of cardiac and neuronal electrophysiology. Natural extensions of the
EMI framework include detailed models of intra- and extracellular ion concentrations
and electro-diffusion, as well as coupling to models for cell contraction and mechanics.

We present a mechanical analogue of the EMI model, i.e., a continuum based
cardiac mechanics model that explicitly represents a three-dimensional network
of cells embedded in an extracellular matrix. Both the intra- and extracellular domains
are modeled as hyperelastic, with constitutive models based based on
the Holzapfel-Ogden model for passive myocardium. The two domains
have different passive mechanical properties, and the intracellular domain is
actively contracting while the extracellular domain is completely passive.
The active contraction is incorporated through a so-called active strain model,
and in this first version of the model it is assumed to be synchronous and homogeneous
across the entire intracellular domain. The model was parameterized using
publicly available experimental data for stretching and shear experiments,
and was used in preliminary explorations of mechanical interactions between
the intra- and extracellular domains. In particular, we studied how myocyte
stress and strain are affected by the mechanical properties of the two domains,
during passive stretching and active contraction. The results show considerable
spatial variations in both stress and strain, and indicate that the detailed
geometrical representation of the cells may give improved insight into certain
mechanisms of biomechanics and mechano-biology. Further development of
the model should include a more detailed exploration of material parameters,
cell geometry, and the mechanical coupling between the cells and the surrounding
matrix, as well as extending the framework to consider inhomogeneous contraction
and potentially coupling of contraction to cell electrophysiology and calcium diffusion.