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

Abstract

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.

Experimental assessment of four ultrasound scattering models for characterizing concentrated tissue-mimicking phantoms

“…The SFM has generally been applied to an ensemble of fluid spheres to model red blood cells in blood. 15,16,19 Herein, the SFM was slightly adapted to the case of an ensemble of solid spheres which are homogeneously distributed in space. In comparison with the Faran model described in Eq.…”

“…aggregating red blood cell distributions) by introducing the frequency dependent structure factor, and called the Structure Factor model (SFM). 15,16 The SFM sums the contributions from individual cells and models the cellular interaction by a statistical mechanics structure factor, which is defined as the Fourier transform of the spatial distribution of the cells. 15,16 Note that the low frequency limit of the structure factor is by definition the packing factor used under Rayleigh conditions.…”

“…15,16 The SFM sums the contributions from individual cells and models the cellular interaction by a statistical mechanics structure factor, which is defined as the Fourier transform of the spatial distribution of the cells. 15,16 Note that the low frequency limit of the structure factor is by definition the packing factor used under Rayleigh conditions. 13 Until quite recently, the PM and SFM were only used for blood characterization purposes, but…”

A Fractal Multi-Dimensional Ultrasound Scatterer Distribution Model

“…The Neyman-Scott point process model has been used for studying the effect of blood cell aggregation on ultrasonic signals [1]. The model creates random cluster centers and spawns daughter points surrounding them.…”

“…In order to validate image processing applications or study image properties across different tissue types, it is useful to be able to generate random lists of point scatterers with varying density and spatial organisation, ranging from highly clustered to random to nearly regular. There is currently a lack of models displaying such flexibility along with computational efficiency and simple parameterisation.The Neyman-Scott point process model has been used for studying the effect of blood cell aggregation on ultrasonic signals [1]. The model creates random cluster centers and spawns daughter points surrounding them.…”