Monte Carlo study on ultrasound backscattering by three-dimensional distributions of red blood cells

Abstract

A Monte Carlo study on ultrasound backscattering by red blood cells (RBCs) is presented for three-dimensional (3D) distributions of particles. The cells were treated as classical spherical particles and accordingly, the Boltzmann distribution was considered to describe probability distribution of energy states of a system composed of such particles. The well-known Metropolis algorithm can generate configurations according to that probability distribution and therefore, was employed in this study to simulate some realizations of both nonaggregating and aggregating RBCs. The study of nonaggregating particles was motivated to compare simulations with existing experimental results and consequently, to validate the model. In the case of aggregating RBCs, the interaction potential between cells was modeled with the Morse potential and the frequency-dependent backscattering coefficient (BSC) was investigated at different hematocrits (H, particle volume fractions). The impact of aggregation potential on the spectral slope (SS) was also evaluated. It is shown that BSC increased as the magnitude of aggregating potential was raised and the effect was more pronounced at higher hematocrits. Moreover, spectral slopes at nonaggregating and low aggregating conditions were found to be around 4, which is consistent with the Rayleigh scattering theory. However, it had diminished significantly, particularly at higher hematocrits as the magnitude of the attractive potential energy was raised. For instance, at H=40% SS dropped from 4.04 for nonaggregating particles to 3.62 at the highest aggregating potential considered in this study. Our results suggest that this 3D model is capable of reflecting the effects of RBC aggregation on BSC and SS.