A Galerkin-type finite element solution for simulation of mass diffusion in the application of tissue engineering: Heterogeneous and non-porous media

Abstract

This study is an effort to produce a generic and comprehensive solution to the simulation of mass diffusion through a multiphasic and heterogeneous material model. A Galerkin-type finite element formulation is developed to solve Fick's equation for steady-state and time-dependent analysis. The effect of the interface in modelling of a liquid—solid medium is presented in this work. To show the robustness of the proposed approach, the gas exchange (oxygen and carbon dioxide) process through the capillary network between the alveolar membrane and red blood cells has been analysed and then validated with experimental data. The current work is a significant asset to modelling the diffusion of oxygen between cells and scaffolds in tissue engineering or tissue regeneration/repair studies. It is one step towards the development of high-order elements for application of the simulation of mass transfer through a multiphasic and porous model with varying degrees of interconnectivity and pore size for tissue engineering applications.

Keywords

finite element method oxygen diffusion Galerkin-type FEM mass transfer variational calculus

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