A point process approach to assess the frequency dependence of ultrasound backscattering by aggregating red blood...

To study the shear-thinning rheological behavior of blood, an acoustical measurement of the erythrocyte aggregation level can be obtained by analyzing the frequency dependence of ultrasonic backscattering from blood. However, the relation that exists among the variables describing the aggregation level and the backscattering coefficient needs to be better clarified. To achieve this purpose, a three-dimensional random model, the Neyman-Scott point process, is proposed to simulate red cell clustering in aggregative conditions at a low hematocrit (H<5%). The frequency dependence of the backscattering coefficient of blood, in non-Rayleigh conditions, is analytically derived from the model, as a function of the size distribution of the aggregates and of their mass fractal dimension. Quantitative predictions of the backscatter increase due to red cell aggregation are given. The parametric model of backscatter enables two descriptive indices of red cell aggregation to be extracted from experimental data, the packing factor W and the size factor delta. Previously published backscatter measurements from porcine whole blood at 4.5% hematocrit, in the frequency range of 3.5 MHz-12.5 MHz, are used to study the shear-rate dependence of these two indices.