Mechanical contribution of endocardium during finite extension and torsion experiments on papillary muscles

Finite extension and torsion tests on cardiac papillary muscles are presently the best way to directly measure the response to shear along myocardial fibers. Quantifying this response is necessary for determining the complete three-dimensional constitutive behavior of myocardium as a transversely isotropic material. Analysis of such tests is complicated, however, since papillary muscles are materially inhomogeneous, consisting of a myocardial core surrounded by an endocardial sheath that is rich in collagen. In this article, we show that the papillary muscle response to extension and torsion additively decouples into the response of the bare myocardial core plus the response of an endocardial sheath filled with fluid (assuming the muscle is a radially inhomogeneous and incompressible continuum with cylindrical symmetry). This result allows the endocardial response to be subtracted from the intact papillary muscle response to obtain the response of the bare myocardial core. An initial estimate suggests that the endocardial sheath affects the axial moment significantly (50% of torque for all twists at low stretch) but affects the axial force only slightly (<10% at moderate twists).