Coherent and incoherent ultrasound backscatter from cell aggregates

Abstract

The effective medium theory (EMT) was recently developed to model the ultrasound backscatter from aggregating red blood cells [Franceschini, Metzger, and Cloutier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2668-2679 (2011)]. The EMT assumes that aggregates can be treated as homogeneous effective scatterers, which have effective properties determined by the aggregate compactness and the acoustical characteristics of the cells and the surrounding medium. In this study, the EMT is further developed to decompose the differential backscattering cross section of a single cell aggregate into coherent and incoherent components. The coherent component corresponds to the squared norm of the average scattering amplitude from the effective scatterer, and the incoherent component considers the variance of the scattering amplitude (i.e., the mean squared norm of the fluctuation of the scattering amplitude around its mean) within the effective scatterer. A theoretical expression for the incoherent component based on the structure factor is proposed and compared with another formulation based on the Gaussian direct correlation function. This theoretical improvement is assessed using computer simulations of ultrasound backscatter from aggregating cells. The consideration of the incoherent component based on the structure factor allows us to approximate the simulations satisfactorily for a product of the wavenumber times the aggregate radius kr around 2.

Estimation of polydispersity in aggregating red blood cells by quantitative ultrasound backscatter analysis

“…7 in Ref. 13) demonstrated that the magnitude and frequency dependency of the form factor corresponding to randomly oriented ellipsoidal scatterers are in good agreement with those obtained from spherical ones of same volume within the range kr ag < 1.5. The major discrepancy in backscatter responses between randomly oriented ellipsoids and spheres of equivalent volume remains the magnitude of dips (see Fig.…”

“…5 in Ref. 13). The relative errors between simulated and theoretical r ag were shown to be less than 15% for a product of the wavenumber times the mean aggregate radius kr ag 2.…”

“…7 in Ref. 13). Moreover, the polydisperse EMTSFM assumed polydispersity in aggregate size, but not polydispersity in aggregate compactness or shape.…”

“…The EMT detailed in Ref. 13 for modeling one aggregate of RBCs is briefly recalled as follows. The EMT model assumes that an aggregate of cells can be treated as an effective homogeneous spherical scatterer of radius r ag .…”

“…In the proposed study, the term BSC coh was computed using the structure function (denoted SF) of the effective particle defined as the ratio between the total BSC and the incoherent BSC inc , 10,20 BSC coh ðkÞ ¼ BSC inc ðkÞðSFðkÞ À 1Þ; (13) where the expression of the structure function SF is given in Appendix B of Ref.…”