Abstract
Tissue engineering constructs and other solid implants with biomedical applications, such as drug delivery devices or bioartificial organs, need oxygen (O(2)) to function properly. To understand better the vascular integration of such devices, we recently developed a novel model sensor containing O(2)-sensitive crystals, consisting of a polymeric capsule limited by a nanoporous filter. The sensor was implanted in mice with hydrogel alone (control) or hydrogel embedded with mouse CD117/c-kit+ bone marrow progenitor cells in order to stimulate peri-implant neovascularization. The sensor provided local partial O(2) pressure (pO(2)) using noninvasive electron paramagnetic resonance signal measurements. A consistently higher level of peri-implant oxygenation was observed in the cell-treatment case than in the control over a 10-week period. To provide a mechanistic explanation of these experimental observations, we present in this article a mathematical model, formulated as a system of coupled partial differential equations, that simulates peri-implant vascularization. In the control case, vascularization is considered to be the result of a foreign body reaction, while in the cell-treatment case, adipogenesis in response to paracrine stimuli produced by the stem cells is assumed to induce neovascularization. The model is validated by fitting numerical predictions of local pO(2) to measurements from the implanted sensor. The model is then used to investigate further the potential for using stem cell treatment to enhance the vascular integration of biomedical implants. We thus demonstrate how mathematical modeling combined with experimentation can be used to infer how vasculature develops around biomedical implants in control and stem cell-treated cases.