A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics

Abstract

The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.

Ultrasound Shear Wave Elasticity Imaging Quantifies Coronary Perfusion Pressure Effect on Cardiac Compliance

“…This phenomenon has been termed the “erectile,” “turgor,” “garden hose,” and “Salisbury” effect in the literature [25], [30]. Furthermore, this effect has been verified by mechanical modeling of cardiac vasculature and tissue using a porous model [31]. …”

In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

“…2010; Cookson et al. 2012) have applied large deformation poroelasticity Biot (1972); Coussy 1995, 2004); Boer 2005). It should be mentioned also that although the theory deals exclusively with macroscopic quantities, the micro–macro averaging technique (Whitaker 1986) has retrospectively provided theoretical rigour to the fundamental governing laws and remains an indispensable tool for characterising the macroscopic properties of a specific physical medium with known microstructure.…”

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

“…In this regard we first list some of the straightforward extensions to the model compartments we have been already studied in previous contributions [185,216,219]. Some specific aspects of modelling cardiac function that have not been covered include the fast conduction system (Purkinje network [264] and Purkinje-muscle junctions), cardiac perfusion [46] and its coupling with coronary flow [66,169], autoregulation aspects of heart rate [139], myocardial tissue damage and remodelling [101], the modelling of the atria [47,64,252], the heart-torso coupling that is needed for the simulation of an ECG [33,55,75], fluid dynamics in idealized ventricles [194,248,249], and many others. As discussed in Sect.…”