A computationally efficient framework for the simulation of cardiac perfusion using a multi-compartment Darcy porous-media flow model

• Published in: International journal for numerical methods in biomedical engineering Vol. 29; no. 2; pp. 217 - 232
• Main Authors: Michler, C., Cookson, A. N., Chabiniok, R., Hyde, E., Lee, J., Sinclair, M., Sochi, T., Goyal, A., Vigueras, G., Nordsletten, D. A., Smith, N. P
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.02.2013; Wiley Subscription Services, Inc; John Wiley and Sons
• Subjects: Algorithms; cardiac perfusion; Computer Simulation; Darcy flow; Finite Element Analysis; finite-element modelling; Heart - physiology; Humans; Mathematics; Models, Theoretical; multi-compartment modelling; Numerical Analysis; Porosity; porous-media flow; Pressure; multi-compartment modelling; cardiac perfusion; porous-media flow; Darcy flow; finite-element modelling
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.2520

SUMMARY We present a method to efficiently simulate coronary perfusion in subject‐specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous‐media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi‐compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi‐compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N‐compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting ‘reduced’ Darcy formulation leads to a dramatic reduction in algebraic‐system size and is therefore computationally cheaper to solve than the full multi‐compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject‐specific model of the left ventricle. Copyright © 2012 John Wiley & Sons, Ltd. We present a method to efficiently simulate coronary perfusion within clinically relevant time frames and demonstrate this on a subject‐specific model of the left ventricle with geometry, inflow rates and source locations derived from experimental data. Perfusion is modeled as a multicompartment Darcy porous‐media flow, where each compartment encapsulates the spatial scales of the vascular network in a certain range. Reducing the N‐compartment system of Darcy equations to N pressure equations and N subsequent projection problems to recover the Darcy velocity significantly enhances computational efficiency.