Solution to the Unknown Boundary Tractions in Myocardial Material Parameter Estimations

Passive material parameter estimation can facilitate the in vivo assessment of myocardial stiffness, an important biomarker for heart failure stratification and screening. Parameter estimation strategies employing biomechanical models of various degrees of complexity have been proposed, usually involving a significant number of cardiac mechanics simulations. The clinical translation of these strategies however is limited by the associated computational cost and the model simplifications. A simpler and arguably more robust alternative is the use of data-based approaches, which do not involve mechanical simulations and can be based for example on the formulation of the energy balance in the myocardium from imaging and pressure data. This approach however requires the estimation of the mechanical work at the myocardial boundaries and the strain energy stored, tasks that are challenging when external loads are unknown - especially at the base which deforms extensively within the cardiac cycle. In this work we employ the principle of virtual work in a strictly data-based approach to uniquely identify myocardial material parameters by eliminating the effect of the unknown boundary tractions at the base. The feasibility of the method is demonstrated on a synthetic data set using a popular transversely isotropic material model followed by a sensitivity analysis to modelling assumptions and data noise.