On a fractal packing approach for understanding ultrasonic backscattering from blood

A new theoretical model is proposed to explain the change in the backscattered Doppler power with flow conditions. It defines a fractional packing dimension to represent the manner in which red blood cells are packed and this in turn is related to the variance of the scatterer number density. An explicit expression for the packing factor in terms of the integral of the pair correlation function is presented. Comparison of published experimental results for the backscattered power versus hematocrit with the theoretical model suggests that turbulence reduces the packing dimension. This reduction reflects a modification of the pair correlation function caused by changes in the flow field.