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We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay.

Original publication

DOI

10.1016/j.mbs.2009.07.003

Type

Journal article

Journal

Math Biosci

Publication Date

10/2009

Volume

221

Pages

101 - 120

Keywords

Algorithms, Animals, Cell Death, Cell Hypoxia, Chick Embryo, Chorioallantoic Membrane, Computer Simulation, Endothelial Cells, Extracellular Matrix, Fibroblasts, Macrophages, Microvessels, Models, Biological, Neovascularization, Physiologic, Oxygen, Pericytes, Time Factors, Tissue Engineering, Tissue Scaffolds, Transplants, Vascular Endothelial Growth Factor A