Mathematical modelling of tissue-engineered angiogenesis.
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.
Lemon
Greg
G
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Howard
Daniel
D
Tomlinson
Matthew J
MJ
Buttery
Lee D
LD
Rose
Felicity R A J
FR
Waters
Sarah L
SL
King
John R
JR
D000465:Algorithms; D000818:Animals; D016923:Cell Death / Q000502:physiology; D015687:Cell Hypoxia / Q000502:physiology; D002642:Chick Embryo; D049033:Chorioallantoic Membrane / Q000098:blood supply / Q000166:cytology / Q000254:growth & development / Q000378:metabolism; D003198:Computer Simulation; D042783:Endothelial Cells / Q000166:cytology / Q000378:metabolism; D005109:Extracellular Matrix / Q000378:metabolism; D005347:Fibroblasts / Q000166:cytology / Q000378:metabolism; D008264:Macrophages / Q000166:cytology / Q000378:metabolism; D055806:Microvessels / Q000033:anatomy & histology / Q000254:growth & development; D008954:Models, Biological; D018919:Neovascularization, Physiologic / Q000502:physiology*; D010100:Oxygen / Q000378:metabolism; D020286:Pericytes / Q000166:cytology / Q000378:metabolism; D013997:Time Factors; D023822:Tissue Engineering / Q000379:methods*; D054457:Tissue Scaffolds; D019737:Transplants; D042461:Vascular Endothelial Growth Factor A / Q000378:metabolism
D042461:Vascular Endothelial Growth Factor A; D010100:Oxygen