The Multi-Scale Modelling of Coronary Blood Flow

Abstract

Coronary flow is governed by a number of determinants including network anatomy, systemic afterload and the mechanical interaction with the myocardium throughout the cardiac cycle. The range of spatial scales and multi-physics nature of coronary perfusion highlights a need for a multiscale framework that captures the relevant details at each level of the network. The goal of this review is to provide a compact and accessible introduction to the methodology and current state of the art application of the modelling frameworks that have been used to study the coronary circulation. We begin with a brief description of the seminal experimental observations that have motivated the development of mechanistic frameworks for understanding how myocardial mechanics influences coronary flow. These concepts are then linked to an overview of the lumped parameter models employed to test these hypotheses. We then outline the full and reduced-order (3D and 1D) continuum mechanics models based on the Navier–Stokes equations and highlight, with examples, their application regimes. At the smaller spatial scales the case for the importance of addressing the microcirculation is presented, with an emphasis on the poroelastic approach that is well-suited to bridge an existing gap in the development of an integrated whole heart model. Finally, the recent accomplishments of the wave intensity analysis and related approaches are presented and the clinical outlook for coronary flow modelling discussed.

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

“…Validation of such models requires direct comparison of simulated and experimental waveform shapes, including any high-frequency flow transients. However, although this has been performed for systemic large arteries (53), very little validation of 1D/multiscale coronary arterial models has been presented, a void that has been recognized in recent reviews (34,73).Moreover, to our knowledge no models (multiscale or otherwise) of the newborn coronary circulation have been described or validated. Indeed, aside from a few published Doppler velocity recordings (47, 48), relatively little information about phasic coronary hemodynamics in the newborn is available.…”

“…Validation of such models requires direct comparison of simulated and experimental waveform shapes, including any high-frequency flow transients. However, although this has been performed for systemic large arteries (53), very little validation of 1D/multiscale coronary arterial models has been presented, a void that has been recognized in recent reviews (34,73).…”

3D Blood Vessels Reconstruction Based on Segmented CT Data for Further Simulations of Hemodynamic in Human Artery Branches

“…Computational Fluid Dynamic (CFD) technique in solving problems related to blood flow in cardiac system is widely described in the literature [10,19]. CFD technique is most often performed with the use of the medical data from CTAngio, MRI or X-Ray [1].…”

Validation of a multi-scale model of the coronary circulation in adult sheep and newborn lambs

“…Recently, interest in the study of waves in conduit coronary arteries has been increasing [3]- [5], although the importance of wave propagation effects on flow waveforms is disputed [6], [7] and is hypothesized to vary during development due to changes in body size [8].…”

“…Multi-scale modelling is a promising avenue for studying both wave propagation effects and other phenomena crucial to coronary haemodynamics [7], however very little in-vivo validation of such models has been performed. Accordingly, in this study we propose a convenient and physiologicallyrelevant multi-scale modelling approach in which a onedimensional (1D) representation of conduit coronary arteries is combined with a lumped parameter (0D) model of the coronary microvasculature.…”