Multiscale modelling of cardiac perfusion

To elucidate the mechanisms governing coronary blood flow in health and disease requires an understanding of the structure-function relationship of the coronary system, which exhibits distinct characteristics over multiple scales. Given the complexities arising from the multiscale and distributed nature of the coronary system and myocardial mechanical coupling, computational modelling provides an indispensable tool for advancing our understanding. In this work, we describe our strategy for an integrative whole-organ perfusion model, and illustrate a series of examples which apply the framework within both basic science and clinical translation settings. In particular, the one-dimensional reduced approach common in vascular modelling is combined with a new poromechanical formulation of the myocardium that is capable of reproducing the full contractile cycle, to enable simulation of the dynamic coronary and myocardial blood flow. In addition, a methodology for estimating continuum porous medium parameters from discrete network geometry is presented. The benefit of this framework is first demonstrated via an application to coronary wave intensity analysis, a technique developed to study time-dependent aspects of pulse waves invasively measured in the vessels. It is shown that, given experimentally-acquired boundary conditions the 1D model is capable of reproducing a wave behaviour broadly consistent with that observed in vivo, however, its utility is limited to a phenomenological level. The integrated 1D-poromechanical model on the other hand enables a mechanistic investigation of wave generation thus allowing the influence of contractile function and distal hemodynamic states on coronary flow to be described. In addition, when coupled with the advection-diffusion-reaction equation, the integrated model can be used to study the transport of tracers through the vascular network, thus allowing the dependence of noninvasive imaging signal intensities on the diffusive properties of the contrast agent to be quantified. A systematic investigation of the commonly used clinical indices and whole-organ modelling results are illustrated. Taken together, the proposed model provides a comprehensive framework with which to apply quantitative analysis in whole organ coronary artery disease diagnosis using noninvasive perfusion imaging modalities. The added value of the model in clinical practice lies in its ability to combine comprehensive patient-specific information into therapy. In this regard, we close the chapter with a discussion on potential model-aided strategies of disease management.