I will describe two problems I have worked on recently in biomedical mathematical modeling. The first concerns tissue engineering within a porous scaffold, focusing particularly on how the scaffold environment (pore shape and nutrient flow characteristics) can affect the outcome in terms of final tissue yield. The second concerns Ischemia-Reperfusion Injury (IRI), the paradoxical damage that can occur to tissue when blood flow is reintroduced to an ischemic organ. Our focus here is on a promising therapy known as ischemic post-conditioning, whereby the extent of IRI may be reduced by restoring the blood flow cyclically, interspersed with periods of further ischemia.