Determination of a constitutive relation for passive myocardium: I. A new functional form.

The specific aim of this study is to determine a constitutive relation for non-contracting myocardium in terms of a pseudostrain-energy function W whose form is guided by both theory and experiment. We assume that the material symmetry of myocardium is initially and locally transversely-isotropic, and seek a W which depends upon only two coordinate invariant measures of the finite deformation. The specific functional form of such a W is inferred directly from experimental protocols in which one invariant is held constant while the other is varied, and vice versa. On the basis of data from families of these "constant invariant" tests on thin slabs of myocardium taken from the mid-walls of six canine left ventricles, we propose a new polynomial form of W containing only five material parameters.