Abstract
Biological tissue can be viewed as porous, permeable and deformable media infiltrated by fluids, such as blood and interstitial fluid. A finite element model has been developed based on the multiple-network poroelastic theory to investigate transport phenomenon in such biological systems. The governing equations and boundary conditions are adapted for the cerebral environment as an example. The numerical model is verified against analytical solutions of classical consolidation problems and validated using experimental data of infusion tests. It is then applied to three-dimensional subject-specific modelling of brain, including anatomically realistic geometry, personalised permeability map and arterial blood supply to the brain. Numerical results of smoking and non-smoking subjects show hypoperfusion in the brains of smoking subjects, which also demonstrate that the numerical model is capable of capturing spatio-temporal fluid transport in biological systems across different scales.
Highlights
Poroelastic theory is widely used in civil, petroleum and biomedical engineering
The objective of this paper is to present a newly developed finite element model of the multiple-network poroelastic theory for biological systems and application to three-dimensional subject-specific modelling of cerebral fluid transport that features anatomically realistic geometry and personalised parameters and boundary conditions
A finite element model for biological systems has been developed based on the multiple-network poroelastic theory
Summary
Poroelastic theory is widely used in civil, petroleum and biomedical engineering. Two directions are commonly acknowledged for the development of the poroelastic theory (Coussy, Dormieux & Detournay, 1998; de Boer, 1992): one is based on mixture theory while the other one is founded on macroscale theories, mainly represented by the work of Biot. Mixture theory owes much of its current structure to the early works of Truesdell (1957a, 1957b, 1962). Extensive reviews of the literature on mixture theory can be found in the papers by Atkin and Craine (1976a), Bowen (1976) and Bedford and Drumheller (1983), and the books by Samohyl (1987) and Rajagopal and Tao (1995), Truesdell (1984). Mixture theory assumes that the domain of a mixture can be viewed as a superposition of several single interpenetrating continua, each representing a different constituent and following its own motion; at any time, each position in the mixture domain is occupied simultaneously by one particle from each constituent, in a homogenised sense (Atkin & Craine, 1976a). The governing equations for poroelasticity are derived through averaging procedures, generally using a Eulerian description
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