David Savery

Simulation of ultrasound backscattering by red cell aggregates: effect of shear rate and anisotropy.

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.

A point process approach to assess the frequency dependence of ultrasound backscattering by aggregating red blood cells

To study the shear-thinning rheological behavior of blood, an acoustical measurement of the erythrocyte aggregation level can be obtained by analyzing the frequency dependence of ultrasonic backscattering from blood. However, the relation that exists among the variables describing the aggregation level and the backscattering coefficient needs to be better clarified. To achieve this purpose, a three-dimensional random model, the Neyman-Scott point process, is proposed to simulate red cell clustering in aggregative conditions at a low hematocrit (H<5%). The frequency dependence of the backscattering coefficient of blood, in non-Rayleigh conditions, is analytically derived from the model, as a function of the size distribution of the aggregates and of their mass fractal dimension. Quantitative predictions of the backscatter increase due to red cell aggregation are given. The parametric model of backscatter enables two descriptive indices of red cell aggregation to be extracted from experimental data, the packing factor W and the size factor delta. Previously published backscatter measurements from porcine whole blood at 4.5% hematocrit, in the frequency range of 3.5 MHz-12.5 MHz, are used to study the shear-rate dependence of these two indices.

Non-Gaussian statistics and temporal variations of the ultrasound signal backscattered by blood at frequencies between 10 and 58 MHz

Very little is known about the blood backscattering behavior and signal statistics following flow stoppage at frequencies higher than 10 MHz. Measurements of the radio frequency (rf) signals backscattered by normal human blood (hematocrit = 40%, temperature = 37 degrees C) were performed in a tube flow model at mean frequencies varying between 10 and 58 MHz. The range of increase of the backscattered power during red blood cell (RBC) rouleau formation was close to 15 dB at 10 and 36 MHz, and dropped, for the same blood samples, below 8 dB at 58 MHz. Increasing the frequency from 10 to 58 MHz raised the slope of the power changes at the beginning of the kinetics of aggregation, and could emphasize the non-Gaussian behavior of the rf signals interpreted in terms of the K and Nakagami statistical models. At 36 and 58 MHz, significant increases of the kurtosis coefficient, and significant reductions of the Nakagami parameter were noted during the first 30 s of flow stoppage. In conclusion, increasing the transducer frequency reduced the magnitude of the backscattered power changes attributed to the phenomenon of RBC aggregation, but improved the detection of rapid growth in aggregate sizes and non-Gaussian statistical behavior.

Effect of red cell clustering and anisotropy on ultrasound blood backscatter: a Monte Carlo study

When flowing at a low shear rate, blood appears hyperechogenic on ultrasound B-scans. The formation of red blood cell (RBC) aggregates that also alters blood viscosity is the microscopic mechanism explaining this acoustical phenomenon. In this study, Monte Carlo simulations were performed to predict how RBC clustering increases ultrasound scattering by blood. A bidimensional Gibbs-Markov random point process parameterized by the adhesion energy epsi and an anisotropy index nu was used to describe RBC positions for a hematocrit H=40%. The frequency dependence of the backscattering coefficient chi(f) was computed using Born approximation. The backscattering coefficient chi0 at 5 MHz and the spectral slopes and nx and ny (chipropf(nx) or f(ny)) measured, respectively, when the insonification is parallel and perpendicular with the RBC cluster axis were then extracted. Under isotropic conditions, chi0 increased up to 7 dB with epsi and nx=n y decreased from 4.2 to 3.4. Under anisotropic conditions, the backscattering was stronger perpendicularly to aggregate axis, resulting in nx<ny. The anisotropy in scattering appeared more pronounced when epsi or nu increased. These two dimensional results generally predict that low-frequency blood backscatter is related to cluster dimension, and higher-frequency properties are affected by finer morphological features as anisotropy. This numerically establishes that ultrasound backscatter spectroscopy on a large frequency range is pertinent to characterize in situ hemorheology

Characterization of digital waveforms using thermodynamic analogs: applications to detection of materials defects

We describe characterization of digital signals using analogs of thermodynamic quantities: the topological entropy, Shannon entropy, thermodynamic energy, partition function, specific heat at constant volume, and an idealized version of Shannon entropy in the limit of digitizing with infinite dynamic range and sampling rate. We show that analysis based on these quantities is capable of detecting differences between digital signals that are undetectable by conventional methods of characterization based on peak-to-peak amplitude or signal energy. We report the results of applying thermodynamic quantities to a problem from nondestructive materials evaluation: detection of foreign objects (FO) embedded near the surface of thin graphite/epoxy laminates using backscattered waveforms obtained by C-scanning the laminate. The characterization problem was to distinguish waveforms acquired from the region containing the FO from those acquired outside. In all cases the thermodynamic analogs exhibit significant increases (up to 20-fold) in contrast and for certain types of FO materials permit detection when energy or amplitude methods fail altogether.

High-frequency ultrasound backscattering by blood : Analytical and semianalytical models of the erythrocyte cross section

This paper proposes analytical and semianalytical models of the ultrasonic backscattering cross section (BCS) of various geometrical shapes mimicking a red blood cell (RBC) for frequencies varying from 0 to 90 MHz. By assuming the first-order Born approximation and by modeling the shape of a RBC by a realistic biconcave volume, different scattering behaviors were identified for increasing frequencies. For frequencies below 18 MHz, a RBC can be considered a Rayleigh scatterer. For frequencies less than 39 MHz, the general concept of acoustic inertia tensor is introduced to describe the variation of the BCS with the frequency and the incidence direction. For frequencies below 90 MHz, ultrasound backscattering by a RBC is equivalent to backscattering by a cylinder of height 2 microm and diameter 7.8 microm. These results lay the basis of ultrasonic characterization of RBC aggregation by proposing a method that distinguishes the contribution of the individual RBC acoustical characteristics from collective effects, on the global blood backscattering coefficient. A new method of data reduction that models the frequency dependence of the ultrasonic BCS of micron-sized weak scatterers is also proposed. Applications of this method are in tissue characterization as well as in hematology.

Monte Carlo simulation of ultrasound backscattering by aggregating red blood cells

When blood flows at a low shear rate, red cells aggregate and form clusters that affect vascular resistance to flow and blood echogenicity. This study intends to clarify the relation between the red cell aggregation level and the ultrasonic backscatter increase. Red cell positioning in plasma is modeled by a 2D Markov point process at a 40% hematocrit. A square well potential is adopted to take into account the erythrocyte adhesive interaction energy. Monte Carlo simulations of the point process and computations of the mean structure factor enables to assess the frequency dependence of the blood backscatter for different aggregation potentials. The ultrasonic sensitivity to the erythrocyte clustering phenomenon is demonstrated and could be used as a noninvasive measurement method of blood microstructure and rheology.

MODELING OF THE ACOUSTIC SIGNAL BACKSCATTERED BY A BIPHASIC SUSPENSION : APPLICATION TO THE CHARACTERIZATION OF RED BLOOD CELL AGGREGATION

The model explained experimental observations on the power backscattered by flowing blood, namely the increase in power at low frequencies and the decrease of the spectral slope at higher frequencies both due to the growing size of scatterers. The angular dependence of BSC for anisotropic particles could also be reproduced by the simulations. However, some improvements would be necessary to get more insight into the understanding of ultrasound backscattering by blood. Firstly, the model is valid for diluted suspensions but cannot be easily generalized for a dense medium, where the packing of particles plays an important role. Another limitation is the hypothesis that all scatterers are identical and have Gaussian shapes. Polydispersity and variations in orientation are not currently taken into account. It remains yet that blood characterization by the backscattering method has a good potential to provide accurate information about the RBC aggregation level.

Anisotropy of ultrasonic backscatter by blood in shear flow: Monte Carlo simulations

The relation between the heterogeneous microstructure of biological tissues and their measurable scattering properties is still poorly understood. In particular, physical explanation of blood hyperechogenicity when submitted to low shear forces appears incomplete. To quantify the contribution of erythrocyte aggregation to this phenomenon, Monte Carlo 2D simulations of the red cell spatial pattern are performed. The backscattering coefficient of blood at 5 and 40 MHz is estimated for two orthogonal insonification angles, as a function of effective adhesive energy V/sub agg/ and anisotropy index a. Isotropic aggregation resulted in an enhanced backscatter at 5 MHz (+7 dB) but had a minor effect at 40 MHz. Addition of spatial anisotropy essentially diminished the backscatter at 5 MHz, independently on the angle, whereas at 40 MHz, the perpendicular backscatter largely exceeded the parallel backscatter (+6 dB). This showed that anisotropy present in the spatial microscopic pattern can be detected in the high frequency scattering regime, while low frequency backscatter is more affected by larger geometrical features as the aggregate size.