A biomechanics-based parametrized cardiac end-diastolic pressure–volume relationship for accurate patient-specific calibration and estimation

Biomechanical model

We consider the simplified cardiac model proposed in⁷, itself based on the 3D model proposed and analysed in⁸ and derived by approximating the left ventricular geometry as a hollow sphere, and assuming that fiber directions are isotropically distributed across the thickness in order to have complete spherical symmetry. The constitutive behavior, by contrast, is preserved in its full complexity as in⁸, and since we are concerned here with the EDPVR we focus on the static—or quasi-static—passive part, modeled based on a hyperelastic potential inspired from⁹ and in the…