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.
Tissue characterization using ultrasound (US) scattering allows extraction of relevant cellular biophysical information noninvasively. Characterization of the level of red blood cell (RBC) aggregation is one of the proposed application. In the current paper, it is hypothesized that the microstructure of the RBCs is a main determinant of the US backscattered power. A simulation model was developed to study the effect of various RBC configurations on the backscattered power. It is an iterative dynamical model that considers the effect of the adhesive and repulsive forces between RBCs, and the effect of the flow. The method is shown to be efficient to model polydispersity in size, shape, and orientation of the aggregates due to the flow, and to relate these variations to the US backscattering properties. Three levels of aggregability at shear rates varying between 0.05 and 10 s(-1) were modeled at 40% hematocrit. The simulated backscattered power increased with a decrease in the shear rate or an increase in the RBC aggregability. Angular dependence of the backscattered power was observed. It is the first attempt to model the US power backscattered by RBC aggregates polydisperse in size and shape due to the shearing of the flow.
The frequency dependence of the ultrasound signal backscattered by blood in shear flow was studied using a simulation model. The ultrasound backscattered signal was computed with a linear model that considers the characteristics of the ultrasound system and tissue acoustic properties. The tissue scattering properties were related to the position and shape of the red blood cells (RBCs). A 2D microrheological model simulated the RBC dynamics in a Couette shear flow system. This iterative model, described earlier [Biophys. J. 82, 1696-1710 (2002)], integrates the hydrodynamic effect of the flow, as well as adhesive and repulsive forces between RBCs. RBC aggregation was simulated at 40% hematocrit and shear rates of 0.05-2 s(-1). The RBC aggregate sizes ranged, on average, from 3.3 RBCs at 2 s(-1) to 33.5 cells at 0.05 s(-1). The ultrasound backscattered power was studied at frequencies between 5-120 MHz and insonification angles between 0-180 degrees. At frequencies below approximately 30 MHz, the ultrasound backscattered power increased as the shear rate was decreased and the size of the aggregates was raised. A totally different scattering behavior was noted above 30 MHz. Typical spectral slopes of the backscattered power (log-log scale) between 5-25 MHz equaled 3.8, whereas slopes down to 0.6 were measured at 0.05 s(-1), between 40-60 MHz. The ultrasound backscattered power was shown to be angle dependent at low frequencies (5-25 MHz). The anisotropy persisted at high frequencies (>25 MHz) for small aggregates (at 2 s(-1)). In conclusion, this study sheds some light on the blood backscattering behavior with an emphasis on the non-Rayleigh regime. Additional experimental studies may be necessary to validate the simulation results, and to fully understand the relation between the ultrasound backscattered power, level of RBC aggregation, shear rate, frequency, and insonification angle.
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