Multiscale Modelling of Cardiac Perfusion

Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models

“…The numerical results in Table show robust behaviour with respect to mesh refinements and variation of the parameters including high contrasts of the hydraulic conductivities. Moreover, in Table , we have confirmed the robustness of the proposed block‐diagonal preconditioners for larger values of the transfer coefficient β , while varying the hydraulic conductivities as considerably higher values than that in the work of Kolesov et al have been reported in the work of Lee et al when modelling cardiac perfusion. With the choice of parameter ranges for K 1 and K 2 , we encompassed interesting test scenarios revealing changes in the convergence properties.…”

Impact of coronary bifurcation morphology on wave propagation

“…The mathematical background of the 1D blood flow formulation has been extensively described in the literature (14, 36, 37, 58, 59). Importantly, the forward and backward wave reflection coefficients at a bifurcation derive from the following system of conservation equations (mass and momentum) in three variables: cross-sectional area, pressure, and velocity ( A , p, v ): $\frac{\partial A}{\partial t}+\frac{\partial \left(Av\right)}{\partial x}=0$ $\frac{\partial v}{\partial t}+\alpha v\frac{\partial v}{\partial x}+\frac{1}{\rho }\frac{\partial p}{\partial x}=-\kappa v.$…”

“…Aside from the physical organization of the vessel segments, pulsatility in flow is also a central feature that is strongly characteristic in the coronary circulation in both large (36, 55) and small vessels (66), in that the magnitude of the pulsatile component is not necessarily dominated by the steady component. Surprisingly, to date, investigations of coronary network scaling laws have been conducted largely independent of the wave phenomena.…”

Measurement and modeling of coronary blood flow

“…The diagnostic potential of cWIA is still largely being explored, and it comes at a time when computational modeling is primed to provide further insight into the mechanistic origins of measured coronary waves. The coupled multiscale, multiphysics model of Lee et al has demonstrated the ability to reproduce all the major waves in the heart cycle in silico (discussed further below). This modeling approach has the potential to allow investigation into mechanistic relationships between forward‐ and backward‐traveling waves and the changing cardiac dynamics associated with various diseased states as represented by model parameters.…”

“…Total coronary resistance was the only parameter iteratively fitted from the measured mean coronary flow, and the model was able to accurately reproduce the effects of systolic flow impediment as well as transient features of the measured flow waveform. More recently a multiscale, multiphysics model simulating the interaction between cardiac contraction and coronary blood flow was proposed by Lee . Lee coupled 1D flow in the major epicardial vessels, a porous continuum distal BC representing the microcirculation, and large deformation mechanics of a porcine LV model, as illustrated in Figure .…”