An effective medium model for ultrasound blood characterization
Résumé
Ultrasonic backscattered echoes from blood contain frequency-dependent information that can be used to obtain quantitative parameters reflecting the aggregation state of red blood cells (RBCs). A Structure Factor Model (SFM) adapted to dense media such as blood has been proposed by Savery and Cloutier (J. Acoust. Soc. Am. 2001). However, the SFM can hardly be implemented to estimate the structural aggregate parameters in the framework of an inverse problem formulation. That is why Yu and Cloutier (J. Acoust. Soc. Am. 2007) recently developed the Structure Factor Size Estimator (SFSE) that uses a second-order Taylor expansion of the structure factor. But the SFSE parameterizes the frequency dependent backscatter coefficient (BSC) by two correlated physical parameters. The goal of this paper is to further develop this strategy by proposing a new scattering model that approximates the SFM. A scattering model called the Effective Medium Theory combined with the SFM (EMTSFM) is proposed. The EMTSFM assumes that aggregates of RBCs can be treated as individual homogeneous scatterers, which have effective properties determined by the acoustical characteristics and concentration of RBCs within aggregates. Based on this new theory, the RBC aggregation can be acoustically characterized by three parameters: the aggregate radius, the internal hematocrit (i.e., the volume concentration of RBCs within aggregates) and the volume concentration of RBCs in blood. The accuracy of the EMTSFM was assessed in the frequency range of 4 - 100 MHz by comparing BSC computed with the EMTSFM and with the SFM. The EMTSFM provided accurate quantitative estimates of the BSC for a product of the wavenumber times the aggregate radius krag<1.36. The study also provided insights into the influence of the aggregate size and internal hematocrit on BSC. The internal hematocrit that has not been studied so far as well as the aggregate size can greatly influence the BSC amplitude. The new EMTSFM theory parameterized the BSC by three physical indices relevant to study the pathophysiological impact of abnormal RBC aggregation. The EMTSFM fitted well BSC computed with the SFM for given ranges of parameterized indices in the frequency bandwidth between 4 MHz and maximum BSC. The EMTSFM provides thus a nice framework for the inversion problem.