Theoretical models of microvascular oxygen transport to tissue

To improve understanding of microvascular O(2) transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (i.e., biochemical, structural, and hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O(2) transport to tissue by discrete microvessels. A brief discussion of intravascular O(2) transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O(2) transfer. This is followed by a description of the Krogh tissue cylinder model of O(2) transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multivessel models are discussed that have shown the physiological importance of heterogeneities in vessel spacing, O(2) supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O(2) delivery models is discussed, and new directions in O(2) transport modeling are outlined.