Estimation of red cell flow microvessels: consequences of the Baker-Wayland spatial averaging model

The dual sensor cross-correlation method of H. Wayland and P.C. Johnson [1967), J. Appl. Physiol. 22, 333-337) has become a standard technique for determining the velocity of red blood cells (RBCs) in glass tubes and blood vessels. M. Baker and H. Wayland [1974), Microvasc. Res. 7, 131-143) found that under a variety of conditions the ratio of dual sensor velocity at the centerline of a glass tube to the blood velocity averaged over the lumen was close to 1.6. They provided an explanation of this factor based on spatial averaging of RBC velocity vertically through the tube as well as laterally across the face of the sensor. Their spatial averaging model could also account for the apparent blunting of RBC velocity profiles determined with the dual sensor technique. We used Baker and Wayland's spatial averaging model to calculate how the above velocity ratio depends on sensor size. A nonlinear relation between the velocity ratio and sensor size was found such that the velocity ratio varied from 1.6 to 1.33 as the ratio of sensor width to vessel or tube diameter was varied from 0 to 1. These results also hold for vessels or tubes of elliptic cross section. Some investigators have found that the velocity of red cells near the walls of blood vessels can be a substantial fraction of centerline velocity which suggests that RBC velocity distributions can be blunter than a Poiseuille distribution. We repeated the above calculation for blunted parabolic profiles and we found that the velocity ratio ranged from 1 for plug flow to 1.6 for Poiseuille flow. These calculations show that reliable estimates of RBC flow from dual sensor centerline velocity measurements require one to take into account the relative size of the sensor and blood vessel diameter as well as the bluntness of the RBC velocity distribution.