Model Studies of Leukocyte-Endothelium-Blood Interactions

Using a large scale model and the concept of dimensional similarity, we have developed a dimensionless correlation which permits the estimation of the drag force of blood flow in an in vivo vessel on a leukocyte adherent to the vessel wall. This relationship is Re · C d = 8.15 − 7.52 ln [ d / D ] 2 where Re is a Reynolds number, C_d is a drag coefficient, and d/D is the leukocyte-to-vessel diameter ratio. This function increases rapidly with increasing d/D when d/D is greater than 0.5. A relationship between the drag force on the leukocyte, F_f, and the commonly used wall shear stress in the absence of the adherent cell, τ w , has also been developed, and is given by F f τ w D 2 = 0.598 + 1.847 ln [ d / D ] 2 This study shows that the discrepancy between the in vivo and in vitro critical wall stresses (above which leukocytes do not adhere to endothelial cell layers) is not due to misrepresentation of the corresponding drag forces on the leukocytes. The discrepancy must be due to real differences in the flow and/or cellular conditions between the in vivo and in vitro experiments.