A pole-zero constitutive law for myocardium
This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.
Myocardial tissue consists of layers of interconnected sheets of tissue, separated by cleavage planes. The muscle fibres lie in the plane of a sheet, and adjacent fibres are coupled more strongly in the plane of the sheet than traverse to it. This results in three microstructural axes:
one along the fibre direction called the fibre axis;
one orthogonal to the fibre axis but also in the plane of the sheet called the sheet axis; and
one which is orthogonal to these two, directed across the cleavage planes called the sheet normal.
The most obvious difference in the material behaviour of the myocardial tisue along these three axes is the limiting strain for an elastic response. Another feature of the biaxial tests is that the stress-strain curve along one axis is almost independent of the degree of lateral stretch. To account for these microstructural properties, a strain energy function called the pole-zero law has been proposed (see the figure below). By using a separate pole for each microstructurally defined axis, the different strain limiting behaviour along each axis is accounted for without the need for numerically unstable, large exponents which are needed in exponential or power law expressions.
The original paper reference is cited below:
Computational mechanics of the heart: from tissue structure to ventricular function, M P Nash and P J Hunter, Journal of Elasticity 61(1/3): 113-141, 2000.