Lemon, Greg and Howard, Daniel and Tomlinson, Matthew J and Buttery, Lee D and Rose, Felicity R A J and Waters, Sarah L and King, John R (2009) Mathematical modelling of tissueengineering angiogenesis. Mathematical Biosciences .

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Abstract
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 nonlinear 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.
Item Type:  Article 

Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  906 
Deposited By:  Ruth Preston 
Deposited On:  25 Mar 2010 14:54 
Last Modified:  29 May 2015 18:35 
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