Parameterisation of multi-scale continuum perfusion models from discrete vascular networks

Abstract

Experimental data and advanced imaging techniques are increasingly enabling the extraction of detailed vascular anatomy from biological tissues. Incorporation of anatomical data within perfusion models is non-trivial, due to heterogeneous vessel density and disparate radii scales. Furthermore, previous idealised networks have assumed a spatially repeating motif or periodic canonical cell, thereby allowing for a flow solution via homogenisation. However, such periodicity is not observed throughout anatomical networks. In this study, we apply various spatial averaging methods to discrete vascular geometries in order to parameterise a continuum model of perfusion. Specifically, a multi-compartment Darcy model was used to provide vascular scale separation for the fluid flow. Permeability tensor fields were derived from both synthetic and anatomically realistic networks using (1) porosity-scaled isotropic, (2) Huyghe and Van Campen, and (3) projected-PCA methods. The Darcy pressure fields were compared via a root-mean-square error metric to an averaged Poiseuille pressure solution over the same domain. The method of Huyghe and Van Campen performed better than the other two methods in all simulations, even for relatively coarse networks. Furthermore, inter-compartment volumetric flux fields, determined using the spatially averaged discrete flux per unit pressure difference, were shown to be accurate across a range of pressure boundary conditions. This work justifies the application of continuum flow models to characterise perfusion resulting from flow in an underlying vascular network.

Transmural Variation and Anisotropy of Microvascular Flow Conductivity in the Rat Myocardium

“…The permeability tensor in itself provides fundamental information about (the inverse of) network flow resistivity. In addition, these permeability results could be used to parameterize tissue-scale models of volume-averaged flow in the myocardium 3; 10; 11; 27 .…”

Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media

“…Recently a multicompartment model of cardiac perfusion was presented in Michler et al (2013), cf. Hyde et al (2013). For two compartments it can be derived using the homogenization of the Darcy flow in porous medium with large contrasts in the permeability (Rohan and Cimrman, 2010;Rohan et al, 2012a).…”

Measurement and modeling of coronary blood flow

“…With regards to homogenizing large multiscale networks, Huyghe and Van Campen (HvC) proposed a method of averaging vessel properties with a moving representative volume element (RVE), but only applied their method to an idealized two‐dimensional (2D) network . Recently Hyde et al proposed a projected principle components analysis (PCA)‐method for multiscale homogenization of both an idealized network and a section of the rat coronary microcirculation . This method was compared with the HvC method and a porosity‐scaled isotropic method, which demonstrated the superiority of the HvC method for accuracy of simulated pressures compared to a discrete network Poiseuille solution.…”

“…141 Recently Hyde et al proposed a projected principle components analysis (PCA)-method for multiscale homogenization of both an idealized network and a section of the rat coronary microcirculation. 154 This method was compared with the HvC method and a porosity-scaled isotropic method, which demonstrated the superiority of the HvC method for accuracy of simulated pressures compared to a discrete network Poiseuille solution. The same homogenization methods applied to whole-heart canine and porcine arterial networks, as illustrated in Figure 4 demonstrated that the porosity-scaled isotropic method performed best due to the presence of small length-large bore vessels which confounded the HvC method.…”