Oxygen transport and release of adenosine triphosphate in micro-channels and arterioles in the human microcirculation
The governing nonlinear equations for oxygen transport and ATP concentration in a microfluidic channel and tube are solved with the aid of Maple and COMSOL Multiphysics simulation software. Considering a cell-rich and cell free region with RBCs and blood plasma, we obtain results showing clearly that there is a significant decrease in oxygen tension in the vicinity of an oxygen permeable membrane placed midway on the upper channel/tube wall and to the right side of it in the downstream field. The purpose of the membrane is to cause a rapid change in oxygen saturation as RBC’s flow through channel/tube. To the right of the membrane downstream the greatest amount of ATP is released. Finally the corresponding time-dependent oxygen transport problem for plug flow in a channel, which has not been simulated in previous models in the literature, is analyzed and different starting times are shown for ATP release at different points in the channel. The FE modelling is very accurate: The time evolution problem is modelled and solved in it`s entirety with exact parameters used in the literature for blood flow and oxygen transport in the microcirculation. A comparison is made between the steady state and time dependent solutions in order to validate the results. The implications of the time dependent model for biological systems such as the human microcirculation requires exact information on release of energy as ATP is released from blood cells and the present work is important in providing this information.