Insights into the passive mechanical behavior of left ventricular myocardium using a robust constitutive model based on full 3D kinematics

The impact of myocardial compressibility on organ-level simulations of the normal and infarcted heart

“…Experimentation with passive myocardium under biaxial testing has demonstrated the pronounced nonlinearity, viscoelasticity, and anisotropy of the tissue 61 , and these features have been consistently reported at the tissue level 55 , 56 , 62 , 63 . More recent studies using full 3D kinematics have demonstrated unique mechanical coupling behaviors not previously observed 14 . These myocardial behaviors are largely results of the limitations in considering myocardium with a continuum approach.…”

“…Direct coupling of electrophysiology with mechanics using ionic models poses many difficulties, particularly in the specification of the constants governing biophysical phenomena, as well as their initial and boundary conditions 68 . Furthermore, significant stresses develop in the cross-fiber direction as a manifestation of the contractile process itself 16 consistent with lateral force generation in other striated muscles and cross-bridge models 14 , 69 , yet these effects remain understudied in the heart. To make our heart-specific model tractable, we utilized measured MAP data to provide a first estimate of spatiotemporally varying contraction kinetics.…”

Graph Neural Network Emulation of Cardiac Mechanics

“…This is a challenging emulation problem, as each LV has a highly non-Euclidean geometry and is also non-isotropic due to the existence of muscle fibres in the myocardium. The convoluted geometry of these fibres around the LV perimeter as well as in different tissue layers, means the amount of strain and tensile forces within the generated meshes are highly variable in different locations and directions [11]. In Section 3 below, we outline how we created training and test data sets on which the two GNN emulators could be trained and evaluated, before the two architectures are explained in Section 4.…”

Integrity basis of polyconvex invariants for modeling hyperelastic orthotropic materials — Application to the mechanical response of passive ventricular myocardium

“…Palit et al [6] have implemented the Holzapfel-Ogden constitutive law in the MSCMarc finite element software in order to inversely estimate the constitutive parameters of the model. Very recently, Li et al [7] have extended the Holzapfel-Ogden model by accounting for the mixed-invariants in the fiber-normal and sheet-normal directions.…”

“…The present paper proposes a new SEF for modeling incompressible orthotropic hyperelastic materials with a specific application to the mechanical response of passive ventricular myocardium. In order to build our SEF, we have followed a strategy based on exponential functions, as proposed by Holzapfel et al [2], but we have selected polyconvex invariants instead of the standard ones generally used in the literature [2][3][4][5][6][7]. Working with the set of polyconvex invariants exhibited in [10] allows to replace the classical mixed invariant 8 , which is non polyconvex (the proof is in Section 4), by the polyconvex invariant 4 defined by Eq.…”