King's College London

Research portal

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

Research output: Contribution to journalArticle

Original languageEnglish
Article numberN/A
Pages (from-to)557-570
Number of pages14
JournalMedical and Biological Engineering and Computing
Volume51
Issue number5
DOIs
Publication statusPublished - May 2013

King's Authors

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.

View graph of relations

© 2018 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454