Volume flow estimation in the precapillary mesenteric microvasculature in vivo and the principle of constant pressure gradient

Volume flow was estimated from axial erythrocyte velocity measurements in 30 mesenteric microvessels of 6 rabbits and was compared to Murray's law predictions. The diameters of capillaries and precapillary arterioles ranged between 5.6 and 12 microm. The significant pulsating flow component existing in these microvessels was taken into account by measuring instantaneous axial blood velocity throughout the course of a cardiac cycle and then averaging over the period. In addition, the effect of the velocity profile variation with diameter was taken into account, for the first time, by using a profile factor function. According to Murray's law, the relation between blood volume flow and diameter is governed by a 'cube' law. Curve fitting to volume flow and diameter data pairs for rabbits, showed a dependence of volume flow on diameter raised to the 4th power (with a correlation coefficient equal to 0.97). The above result supports the hypothesis that, in the precapillary part of microvasculature, the principle of constant longitudinal pressure gradient rather than the principle of minimum work may be valid.