Effective Medium Theory combined with a polydisperse Structure Factor Model for characterizing red blood cell aggregation

International audienceQuantitative ultrasound techniques for determining red blood cell (RBC) aggregate structures rely on a theoretical scattering model to fit the BackScatter Coefficient (BSC) of blood to an estimated theoretical BSC. The two scattering theories commonly used are the Structure Factor Size Estimator (SFSE) and the Effective Medium Theory combined with the Structure Factor Model (EMTSFM), that assume locally RBC aggregates of identical size. The aim of this work was to further develop the EMTSFM to incorporate the polydispersity in terms of aggregate size, and assess its ability to estimate the aggregate size distribution with \textit{in vitro} experiments.The polydisperse EMTSFM assumes that the aggregate compactness is identical and that the aggregate radius follows a statistical Schulz distribution. This model consists of treating the RBC aggregates as individual homogenous spheres and of calculating the scattering from the polydisperse system of effective spheres using the local monodisperse approximation. The polydisperse EMTSFM allows to estimate three parameters: the compactness of aggregates, the mean radius of aggregates rag/a, where a is the radius of a single RBC, and the width factor z of the aggregate size distribution. Ultrasonic backscatter measurements were conducted at frequencies ranging from 10 to 43 MHz on porcine blood sheared in a Couette flow device. The distribution of aggregate sizes estimated with the polydisperse EMTSFM was compared with those obtained with the SFSE and the monodisperse EMTSFM. Aggregate sizes were also quantified under the same shear rates using a plane-plane rheometer coupled with a light microscope.The aggregate size distributions estimated with the polydisperse EMTSFM agreed well with the optical observations performed on the same blood sheared in the plane-plane rheometer, especially for the smallest shear rates (corresponding to the highest aggregation levels)