Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter

The primary objectives of this study were 1) to determine the functional relationship between microvascular blood flow (Q) and arteriolar internal diameter (D) and 2) to determine whether this relationship conformed to a theoretical optimality prediction--that blood flow is proportional to the cube of the diameter (Q = kD3). Paired blood velocity and arteriolar diameter measurements in the cremaster muscle microvasculature of eight normotensive (WKY) and eight hypertensive (SHR) rats were made under control conditions and following maximal dilation of the microvasculature with topically applied adenosine. A total of 160 paired flow-diameter measurements were made in arteriolar vessels with diameters ranging from 6 to 108 micron. Analysis of this data showed that Q and D were functionally linked by Q = kDm with k = 417 and m = 3.01 with D expressed in centimeters. Confidence intervals at the 99.9% level were 331-503 and 2.86-3.14 for k and m, respectively. A theoretical development based on the minimization of the energy cost of blood volume and arteriolar wall volume led to a theoretical estimate for the range of k to be 92-132 and a value for m to be 3. Predicted pressure gradients in single vessels of the cat mesentery and shear rates in the rat cremaster based on Q = kD3 compared well with measured data reported in the literature and that determined in the present study. On the basis of the direct and predictive evidence, it is concluded that the relationship Q = kD3 represents a general average property of the microvasculature.