The velocity-diffusion equation in the exchange microvessels

Abstract

In human and animal microvascular networks, the exchange microvessels are the capillaries and postcapillary venules where material transport between the circulating blood and tissue takes place. For small-size molecules, this material transport is done by the physical mechanism of diffusion through the endothelium wall and the diffusion rate J in relation to blood volume flow Q is described by the flow-diffusion (Q-J) equation. However, the volume flow is not easy to be measured in vivo. The objective of this work was to transform the classical flow-diffusion equation into a new form with axial velocity V as an independent variable instead of volume flow Q. The new form was called the velocity-diffusion (V-J) equation and has the advantage that V can be measured directly in vivo by optical imaging techniques. The V-J equation could have important applications in the calculation of the mass diffusion rate of various substances in vivo.