A mathematical model for concentration of blood affecting erythrocyte sedimentation

The rate at which red blood cells fall in vitro is used as a common clinical test for a number of pathological conditions. But this test becomes unreliable when one finds flaws in the model under consideration and these doubts raise the issue of aggregation of the red blood cells in concentration whose mathematical analysis is relatively unknown. However Huang et al. (Biorheology 8, 157-163, 1971) made some efforts and their model resembles certain moving boundary problems. In the present work the modifications to this model have been suggested so far as the concentration of the blood is concerned, it being one of the important factors to decide ESR (Erythrocyte Sedimentation Rate). In the equation for nutrient concentration, to be more realistic, we have taken account of transfer of nutrient to the tissue from the blood. The exact solution has been obtained using Laplace transform. A finite element technique has been suggested which provides results closer to that of the exact solution. Our results for the blood concentration may be useful for conducting the ESR tests. A special case for an emergent patient when nutrient concentration falls down considerably and glucose is provided to improve the condition, has been shown graphically.