title: Cell proliferation and oxygen diffusion in a vascularising scaffold.
abstract: The supply of oxygen to proliferating cells within a scaffold is a key factor for the successful building of new tissue in soft tissue engineering applications. A recent in vivo model, where an arteriovenous loop is placed in a scaffold, allows a vascularising network to form within a scaffold, establishing an oxygen source within, rather than external, to the scaffold. A one-dimensional model of oxygen concentration, cell proliferation and cell migration inside such a vascularising scaffold is developed and investigated. In addition, a vascularisation model is presented, which supports a vascularisation front which moves at a constant speed. The effects of vascular growth, homogenous and heterogenous seeding, diffusion of cells and critical hypoxic oxygen concentration are considered. For homogenous seeding, a relationship between the speed of the vascular front and a parameter defining the rate of oxygen diffusion relative to the rate of oxygen consumption determines whether a hypoxic region exists at some time. In particular, an estimate of the length of time that a fixed point in the scaffold will remain under hypoxic conditions is determined. For heterogenous seeding, a Fisher-like travelling wave of cells is established behind the vascular front. These findings provide a fundamental understanding of the important interplay between the parameters and allows for a theoretical assessment of a seeding strategy in a vascularising scaffold.
authors.affiliation: Department of Mathematics and Statistics, University of Melbourne, Victoria, 3010, Australia. k.landman@ms.unimelb.edu.au
authors.forename: Kerry A
authors.initials: KA
authors.lastname: Landman
authors.forename: Anna Q
authors.initials: AQ
authors.lastname: Cai
mesh_terms: D000465:Algorithms; D043925:Angiogenesis Inducing Agents / Q000378:metabolism; D000818:Animals; D002452:Cell Count; D015687:Cell Hypoxia; D002465:Cell Movement / Q000502:physiology; D049109:Cell Proliferation; D004058:Diffusion; D006801:Humans; D000860:Hypoxia; D008954:Models, Biological; D018919:Neovascularization, Physiologic / Q000502:physiology*; D010100:Oxygen / Q000737:chemistry / Q000378:metabolism*; D046509:Tissue Culture Techniques / Q000379:methods; D023822:Tissue Engineering / Q000379:methods; D054457:Tissue Scaffolds
chemical_list: D043925:Angiogenesis Inducing Agents; D010100:Oxygen