A System-Based Approach to Modeling the Ultrasound Signal Backscattered by Red Blood Cells

Abstract

A system-based model is proposed to describe and simulate the ultrasound signal backscattered by red blood cells (RBCs). The model is that of a space-invariant linear system that takes into consideration important biological tissue stochastic scattering properties as well as the characteristics of the ultrasound system. The formation of the ultrasound signal is described by a convolution integral involving a transducer transfer function, a scatterer prototype function, and a function representing the spatial arrangement of the scatterers. The RBCs are modeled as nonaggregating spherical scatterers, and the spatial distribution of the RBCs is determined using the Percus-Yevick packing factor. Computer simulations of the model are used to study the power backscattered by RBCs as a function of the hematocrit, the volume of the scatterers, and the frequency of the incident wave (2-500 MHz). Good agreement is obtained between the simulations and theoretical and experimental data for both Rayleigh and non-Rayleigh scattering conditions. In addition to these results, the renewal process theory is proposed to model the spatial arrangement of the scatterers. The study demonstrates that the system-based model is capable of accurately predicting important characteristics of the ultrasound signal backscattered by blood. The model is simple and flexible, and it appears to be superior to previous one- and two-dimensional simulation studies.

Assessment of accuracy of the structure-factor-size-estimator method in determining red blood cell aggregate size from ultrasound spectral backscatter coefficient

“…They arrived at that mathematical form by using a second order Taylor series expansion of the structure factor and thus obtained two physically relevant parameters of aggregation: The mean diameter of aggregates D and the packing factor W. The packing factor is related to the volume ratio of RBCs known as the hematocrit (H), and is sensitive to the spatial arrangement of scatterers. 12,13 The parameter D estimates how many cells are attached as an aggregate. They used the parametric form of the BSC to analyze experimental data in vitro and obtained sound rheological results.…”

An Inverse Scattering Algorithm for the Segmentation of the Luminal Border on Intravascular Ultrasound Data

“…1(a)), where λ = c f is the wavelength, f is the transducer frequency and D is the transducer diameter. Assuming Born approximation scattering, we use the principle of superposition to represent the total scattered wave as a sum of reflections from individual point scatterers [13]. Then, using this model, the ultrasound reflected signal for each transducer's angular position Θ k at time t for a finite set of N scatterers with coordinates (r i , θ i ) where…”

Ultrasound Detection of Scatterer Concentration by Weighted Entropy

“…In the past, several simulation models for ultrasound echoes generation have been developed [35][36][37]. To reduce the computational complexity of performing the simulations, a simplified model based on the convolution of the incident wave with the set of delta functions is an alternative approach [38], which was demonstrated to provide a realistic description of the backscattered signals [38][39][40][41].…”