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 tissue-engineering angiogenesis. Mathematical Biosciences .
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.
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Oxford Centre for Industrial and Applied Mathematics|
|Deposited By:||Ruth Preston|
|Deposited On:||25 Mar 2010 14:54|
|Last Modified:||29 May 2015 18:35|
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