Effects of Size Polydispersity and Dense Media on Quantitative Ultrasound Estimates.

Quantitative ultrasound (QUS) techniques based on the backscatter coefficient (BSC) aim to characterize the scattering properties of biological tissues. A scattering model is fit to the measured BSC, and the fitted QUS parameters can provide local tissue microstructure, namely, scatterer size and acoustic concentration. However, these techniques may fail to provide a correct description of tissue microstructure when the medium is polydisperse and/or dense. The objective of this study is to investigate the effects of scatterer size polydispersity in sparse or dense media on the QUS estimates. Four scattering models (i.e., the monodisperse and polydisperse sparse models, and the monodisperse and polydisperse concentrated models based on the structure factor) are compared to assess their accuracy and reliability in quantifying the QUS estimates. Simulations are conducted with different scatterer size distributions for sparse, moderately dense, and dense media (volume fractions of 1%, 20%, and 73%, respectively). The QUS parameters are estimated by using model-based inverse methods at different center frequencies between 8 and 50 MHz. Experimental data are also analyzed using colon adenocarcinoma HT29 cell pellet biophantoms to further validate the results obtained from simulations at the volume fraction of 73%. Our findings reveal that the choice of scattering model has a significant impact on the accuracy of QUS estimates. For sufficiently high frequencies and dense media, the polydisperse concentrated model outperforms the other models and enables more accurate quantification. Furthermore, our results contribute to advancing our understanding of the complexities associated with scatterer size polydispersity and dense media in spectral-based QUS techniques.

Quantitative ultrasound techniques for assessing thermal ablation: Measurement of the backscatter coefficient from ex vivo human liver.

BACKGROUND: Understanding the changes occurring in biological tissue during thermal ablation is at the heart of many current challenges in both therapy and medical imaging research. PURPOSE: The objective of this work is to quantitatively interpret the scattering response of human liver samples, before and after thermal ablation. We report acoustic measurements performed involving n = 21 human liver samples. Thermal ablation is achieved at temperatures between 45 and 80°C and quantification of the irreversible changes in acoustic attenuation and Backscattering Coefficient (BSC) is reported, with a particular attention to the latter. METHODS: Both attenuation coefficient and BSCs were measured in the frequency range from 10 to 52 MHz. Scans were performed before heating and after cooling down. Attenuation coefficients were calculated using spectral difference method and BSC estimated using the reference phantom method. RESULTS: Strong increases of attenuation coefficients and BSCs with heating temperature were observed. Quantitative ultrasonic parameters obtained with the polydisperse structure factor model (poly-SFM)are compared to histological observations and seen to be close to hepatocyte mean diameter (HMD). CONCLUSIONS: The results presented in this study provide a description of the impact of thermal ablation in human liver tissue on acoustic attenuation and the BSC. For the first time, quantitative agreement between the Effective Scatterer Diameter (ESD) estimated from BSC and HMD was shown, highlighting the important role of cellular network in the scattering response of the medium. This core result is an important step toward the determination of the nature of scattering sources in biological tissues.

Influence of storage and buffer composition on the mechanical behavior of flowing red blood cells.

On-chip study of blood flow has emerged as a powerful tool to assess the contribution of each component of blood to its overall function. Blood has indeed many functions, from gas and nutrient transport to immune response and thermal regulation. Red blood cells play a central role therein, in particular through their specific mechanical properties, which directly influence pressure regulation, oxygen perfusion, or platelet and white cell segregation toward endothelial walls. As the bloom of in-vitro studies has led to the apparition of various storage and sample preparation protocols, we address the question of the robustness of the results involving cell mechanical behavior against this diversity. The effects of three conservation media (EDTA, citrate, and glucose-albumin-sodium-phosphate) and storage time on the red blood cell mechanical behavior are assessed under different flow conditions: cell deformability by ektacytometry, shape recovery of cells flowing out of a microfluidic constriction, and cell-flipping dynamics under shear flow. The impact of buffer solutions (phosphate-buffered saline and density-matched suspension using iodixanol/Optiprep) are also studied by investigating individual cell-flipping dynamics, relative viscosity of cell suspensions, and cell structuration under Poiseuille flow. Our results reveal that storing blood samples up to 7 days after withdrawal and suspending them in adequate density-matched buffer solutions has, in most experiments, a moderate effect on the overall mechanical response, with a possible rapid evolution in the first 3 days after sample collection.

Numerical investigations of anisotropic structures of red blood cell aggregates on ultrasonic backscattering.

Although quantitative ultrasound techniques based on the parameterization of the backscatter coefficient (BSC) have been successfully applied to blood characterization, theoretical scattering models assume blood as an isotropic scattering medium. However, the red blood cell (RBC) aggregates form anisotropic structures such as rouleaux. The present study proposes an anisotropic formulation of the effective medium theory combined with the local monodisperse approximation (EMTLMA) that considers perfectly aligned prolate-shaped aggregates. Theoretical BSC predictions were first compared with computer simulations of BSCs in a forward problem framework. Computer simulations were conducted for perfectly aligned prolate-shaped aggregates and more complex configurations with partially aligned prolate-shaped aggregates for which the size and orientation of RBC aggregates were obtained from blood optical observations. The isotropic and anisotropic EMTLMA models were then compared in an inverse problem framework to estimate blindly the structural parameters of RBC aggregates from the simulated BSCs. When considering the isotropic EMTLMA, the use of averaged BSCs over different insonification directions significantly improves the estimation of aggregate structural parameters. Overall, the anisotropic EMTLMA was found to be superior to the isotropic EMTLMA in estimating the scatterer volume distribution. These results contribute to a better interpretation of scatterer size estimates for blood characterization.

Quantifying scattering from dense media using two-dimensional impedance maps.

A better understanding of ultrasound scattering in a three-dimensional (3D) medium can provide more accurate methods for ultrasound tissue characterization. The possibility of using two-dimensional impedance maps (2DZMs) based on correlation coefficients has shown promise in the case of isotropic and sparse medium [Luchies and Oelze, J. Acoust. Soc. Am. 139, 1557-1564 (2016)]. The present study investigates the use of 2DZMs in order to quantify 3D scatterer properties of dense media from two-dimensional (2D) histological slices. Two 2DZM approaches were studied: one based on the correlation coefficient and the other based on the 2D Fourier transform of 2DZMs. Both 2DZM approaches consist in estimating the backscatter coefficient (BSC) from several 2DZMs, and then the resulting BSC was fit to the theoretical polydisperse structure factor model to yield 3D scatterer properties. Simulation studies were performed to evaluate the ability of both 2DZM approaches to quantify scattering of a 3D medium containing randomly distributed polydisperse spheres or monodisperse ellipsoids. Experimental studies were also performed using the histology photomicrographs obtained from HT29 cell pellet phantoms. Results demonstrate that the 2DZM Fourier transform-based approach was more suitable than the correlation coefficient-based approach for estimating scatterer properties when using a small number of 2DZMs.

Ultrasonic backscattering and microstructure in sheared concentrated suspensions.

Quantitative ultrasound techniques based on the parametrization of the backscatter coefficient (BSC) are used to characterize concentrated particle suspensions. Specifically, a scattering model is fit to the measured BSC and the fit parameters can provide local suspension properties. The scattering models generally assume an isotropic microstructure (i.e., spatial organization) of the scatterers, whereas the sheared concentrated suspensions can develop an anisotropic microstructure. This paper studied the influence of the shear-induced anisotropic microstructure of concentrated suspensions on the ultrasonic backscattering. Experiments were conducted on suspensions of polymethylmetacrylate spheres (5.8 µm in radius) sheared in a Couette flow device to obtain anisotropic microstructure and then mixed by hand to obtain isotropic microstructure. Experimental structure factors that are related to the spatial distribution of sphere positions were obtained by comparing the BSCs of one concentrated and one diluted suspension. Finally, Stokesian dynamics numerical simulations of sheared concentrated suspensions are used to determine the pair correlation function, which is linked to the Fourier transform of the structure factor. The experimental structure factors are found to be in good agreement with numerical simulations. The numerical simulation demonstrates that the angular-dependent BSCs and structure factors are caused by the shear-induced anisotropic microstructure within the suspension.

Quantitative assessment of media concentration using the Homodyned K distribution.

The Homodyned K distribution has been used successfully as a tool in the ultrasound characterization of sparse media, where the scatterer clustering parameter α accurately discriminates between media with different numbers of scatterers per resolution cell. However, as the number of scatterers increases and the corresponding amplitude statistics become Rician, the reliability of the α estimates decreases rapidly. In the present study, we assess the usefulness of α for the characterization of both sparse and concentrated media, using simulated independent and identically distributed (i.i.d.) samples from Homodyned K distributions, ultrasound images of media with up to 68 scatterers per resolution cell and ultrasound signals acquired from particle phantoms with up to 101 scatterers per resolution cell. All parameter estimates are obtained using the XU estimator (Destrempes et al., 2013). Results suggest that the parameter α can be used to distinguish between media with up to 40 scatterers per resolution cell at 22 MHz, provided that parameter estimation can be performed on very large sample sizes (i.e., >10,000 i.i.d. samples).

Probing the Cellular Size Distribution in Cell Samples Undergoing Cell Death.

A polydisperse scattering model adapted for concentrated medium, namely the polydisperse structure factor model, was examined to explain the backscatter coefficients (BSCs) measured from packed cell samples undergoing cell death. Cell samples were scanned using high-frequency ultrasound in the 10-42 MHz bandwidth. A parameter estimation procedure was proposed to estimate the volume fraction and the relative impedance contrast that could explain the changes in BSC pattern by considering the actual change in cellular size distribution. Quantitative ultrasound parameters were estimated and related to the percentage of dead cells determined by flow cytometry. The standard deviation of scatterer size distribution extracted from the polydisperse structure factor model and the spectral intercept were found to be strongly correlated to the percentage of dead cells (r2 = 0.79 and r2 = 0.72, respectively). This study contributes to the understanding of ultrasonic scattering from cells undergoing cell death toward the monitoring of cancer therapy.

Quantitative Ultrasound in Ex Vivo Fibrotic Rabbit Livers.

Liver fibrosis is the common result of chronic liver disease. Diagnosis and grading liver fibrosis for patient management is mainly based on blood tests and hepatic puncture-biopsy, which is particularly invasive. Quantitative ultrasound (QUS) techniques provide insight into tissue microstructure and are based on the frequency-based analysis of the signals from biologic tissues. This study aims to quantify how spectral-based QUS parameters change with fibrosis grade. The changes in QUS parameters of healthy and fibrotic rabbit liver samples were investigated and were compared with the changes in liver stiffness, using shear wave elastography. Overall, the acoustic concentration was found to decrease with increasing fibrosis grade, and the effective scatterer size was found to be higher in fibrotic livers when compared with normal liver. The result of this study indicates that the combination of three QUS parameters (stiffness, effective scatterer size and acoustic concentration) provides the best classification performance, especially for classifying healthy and fibrotic livers.

Nonlinear ultrasound parameter to monitor cell death in cancer cell samples.

A scaling subtraction method was proposed to analyze the radio frequency data from cancer cell samples exposed to an anti-cancer drug and to estimate a nonlinear parameter. The nonlinear parameter was found to be well correlated (R2 = 0.62) to the percentage of dead cells in apoptosis and necrosis. The origin of the nonlinearity may be related to a change in contacts between cells, since the nonlinear parameter was well correlated to the average total coordination number of binary packings (R2 ≥ 0.77). These results suggest that the scaling subtraction method may be used to early quantify chemotherapeutic treatment efficiency.

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

Quantitative ultrasound techniques based on the backscatter coefficient (BSC) have been commonly used to characterize red blood cell (RBC) aggregation. Specifically, a scattering model is fitted to measured BSC and estimated parameters can provide a meaningful description of the RBC aggregates' structure (i.e., aggregate size and compactness). In most cases, scattering models assumed monodisperse RBC aggregates. This study proposes the Effective Medium Theory combined with the polydisperse Structure Factor Model (EMTSFM) to incorporate the polydispersity of aggregate size. From the measured BSC, this model allows estimating three structural parameters: the mean radius of the aggregate size distribution, the width of the distribution, and the compactness of the aggregates. Two successive experiments were conducted: a first experiment on blood sheared in a Couette flow device coupled with an ultrasonic probe, and a second experiment, on the same blood sample, sheared in a plane-plane rheometer coupled to a light microscope. Results demonstrated that the polydisperse EMTSFM provided the best fit to the BSC data when compared to the classical monodisperse models for the higher levels of aggregation at hematocrits between 10% and 40%. Fitting the polydisperse model yielded aggregate size distributions that were consistent with direct light microscope observations at low hematocrits.

Coherent and incoherent ultrasound backscatter from cell aggregates.

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 krag around 2.

High-Frequency Quantitative Ultrasound Spectroscopy of Excised Canine Livers and Mouse Tumors Using the Structure Factor Model.

Three scattering models were examined for characterizing ex vivo canine livers and HT29 mouse tumors in the 10-38- and the 15-42-MHz frequency bandwidth, respectively. The spherical Gaussian model (SGM) and the fluid sphere model (FSM) that were examined are suitable for dealing with sparse media, whereas the structure factor model (SFM) is adapted for characterizing concentrated media. For the canine livers, the scatterer radius and the acoustic concentration estimated with the three models were similar and matched well the nuclear structures obtained from histological analysis (with relative errors less than 7%). These results show that the livers could be considered as a diluted medium and that the nuclei in liver could be a dominant source of scattering. For the homogeneous mouse tumors, containing mostly viable HT29 cells, scatterer radius and volume fraction estimated with the SFM showed good agreement with the whole cell structures obtained from histological analysis (with relative errors less than 15%), whereas the sparse models (the SGM and the FSM) gave no consistent quantitative ultrasound parameters. This suggests that the viable HT29 cell areas have densely packed cellular content and that the whole HT29 cell could be responsible for scattering. For the heterogeneous tumors, the hyperechogenic zones observed in the B-mode images were linked to the presence of small necrotic areas surrounded by viable HT29 cells. Comparison between sparse and concentrated models shows that these hyperechogenic zones could be considered as a concentrated medium.

Quantitative Characterization of Tissue Microstructure in Concentrated Cell Pellet Biophantoms Based on the Structure Factor Model.

Quantitative ultrasound (QUS) methods based on the backscatter coefficient (BSC) are typically model-based. The BSC is estimated from experiments and is fit to a model. The fit parameters are often termed QUS estimates and are used to characterize the scattering properties of the tissue under investigation. Nevertheless, for physical interpretation of QUS estimates to be accurate, the scattering model chosen must also be accurate. The goal of this work was to investigate the use of the structure factor model (SFM) to take into account coherent scattering from high volume fractions of scatterers. The study focuses on comparing the performance of two sparse models (fluid-filled sphere and Gaussian) and one concentrated model (SFM) to estimate QUS parameters from simulations and cell pellet biophantoms with a range of scatterer volume fractions. Results demonstrated the superiority of the SFM for all investigated volume fractions (i.e., from 0.006 to 0.30). In particular, the sparse models underestimated scatterer size and overestimated acoustic concentration when the volume fraction was greater than 0.12. In addition, the SFM has the ability to provide the volume fraction and the relative impedance contrast (instead of only the acoustic concentration provided by the sparse models), which could have a great benefit for tissue characterization. This study demonstrates that the SFM could prove to be an invaluable tool for QUS and could help to more accurately characterize tissue from ultrasound measurements.

Unifying Concepts of Statistical and Spectral Quantitative Ultrasound Techniques.

Quantitative ultrasound (QUS) techniques using radiofrequency (RF) backscattered signals have been used for tissue characterization of numerous organ systems. One approach is to use the magnitude and frequency dependence of backscatter echoes to quantify tissue structures. Another approach is to use first-order statistical properties of the echo envelope as a signature of the tissue microstructure. We propose a unification of these QUS concepts. For this purpose, a mixture of homodyned K-distributions is introduced to model the echo envelope, together with an estimation method and a physical interpretation of its parameters based on the echo signal spectrum. In particular, the total, coherent and diffuse signal powers related to the proposed mixture model are expressed explicitly in terms of the structure factor previously studied to describe the backscatter coefficient (BSC). Then, this approach is illustrated in the context of red blood cell (RBC) aggregation. It is experimentally shown that the total, coherent and diffuse signal powers are determined by a structural parameter of the spectral Structure Factor Size and Attenuation Estimator. A two-way repeated measures ANOVA test showed that attenuation (p-value of 0.077) and attenuation compensation (p-value of 0.527) had no significant effect on the diffuse to total power ratio. These results constitute a further step in understanding the physical meaning of first-order statistics of ultrasound images and their relations to QUS techniques. The proposed unifying concepts should be applicable to other biological tissues than blood considering that the structure factor can theoretically model any spatial distribution of scatterers.

Structure factor model for understanding the measured backscatter coefficients from concentrated cell pellet biophantoms.

Ultrasonic backscatter coefficient (BSC) measurements were performed on K562 cell pellet biophantoms with cell concentrations ranging from 0.006 to 0.30 in the 10-42 MHz frequency bandwidth. Three scattering models, namely, the fluid-filled sphere model (FFSM), the particle model (PM), and the structure factor model (SFM), were compared for modeling the scattering from an ensemble of concentrated cells. A parameter estimation procedure was developed in order to estimate the scatterer size and relative impedance contrast that could explain the measured BSCs from all the studied cell concentrations. This procedure was applied to the BSC data from K562 cell pellet biophantoms in the 10-42 MHz frequency bandwidth and to the BSC data from Chinese hamster ovary cell pellet biophantoms in the 26-105 MHz frequency bandwidth given in Han, Abuhabsah, Blue, Sarwate, and O'Brien [J. Acoust. Soc. Am. 130, 4139-4147 (2011)]. The data fitting quality and the scatterer size estimates show that the SFM was more suitable than the PM and the FFSM for modeling the responses from concentrated cell pellet biophantoms.

Comparison of three scattering models for ultrasound blood characterization.

Ultrasonic backscattered signals from blood contain frequency-dependent information that can be used to obtain quantitative parameters reflecting the aggregation level of red blood cells (RBCs). The approach is based on estimating structural aggregate parameters by fitting the spectrum of the backscattered radio-frequency echoes from blood to an estimated spectrum considering a theoretical scattering model. In this study, three scattering models were examined: a new implementation of the Gaussian model (GM), the structure factor size estimator (SFSE), and the new effective medium theory combined with the structure factor model (EMTSFM). The accuracy of the three scattering models in determining mean aggregate size and compactness was compared by 2-D and 3-D computer simulations in which RBC structural parameters were controlled. Two clustering conditions were studied: 1) the aggregate size varied and the aggregate compactness was fixed in both 2-D and 3-D cases, and 2) the aggregate size was fixed and the aggregate compactness varied in the 2-D case. For both clustering conditions, the EMTSFM was found to be more suitable than GM and SFSE for characterizing RBC aggregation.

Experimental assessment of four ultrasound scattering models for characterizing concentrated tissue-mimicking phantoms.

Tissue-mimicking phantoms with high scatterer concentrations were examined using quantitative ultrasound techniques based on four scattering models: The Gaussian model (GM), the Faran model (FM), the structure factor model (SFM), and the particle model (PM). Experiments were conducted using 10- and 17.5-MHz focused transducers on tissue-mimicking phantoms with scatterer concentrations ranging from 1% to 25%. Theoretical backscatter coefficients (BSCs) were first compared with the experimentally measured BSCs in the forward problem framework. The measured BSC versus scatterer concentration relationship was predicted satisfactorily by the SFM and the PM. The FM and the PM overestimated the BSC magnitude at actual concentrations greater than 2.5% and 10%, respectively. The SFM was the model that better matched the BSC magnitude at all the scatterer concentrations tested. Second, the four scattering models were compared in the inverse problem framework to estimate the scatterer size and concentration from the experimentally measured BSCs. The FM did not predict the concentration accurately at actual concentrations greater than 12.5%. The SFM and PM need to be associated with another quantitative parameter to differentiate between low and high concentrations. In that case, the SFM predicted the concentration satisfactorily with relative errors below 38% at actual concentrations ranging from 10% to 25%.

Conformal ultrasound imaging system for anatomical breast inspection.

Ultrasound tomography has considerable potential as a means of breast cancer detection because it reduces the operator-dependency observed in echography. A half-ring transducer array was designed based on breast anatomy, to obtain reflectivity images of the ductolobular structures using tomographic reconstruction procedures. The 3-MHz transducer array comprises 1024 elements set in a 190-degree circular arc with a radius of 100 mm. The front-end electronics incorporate 32 independent parallel transmit/receive channels and a 32-to-1024 multiplexer unit. The transmit and receive circuitries have a variable sampling frequency of up to 80 MHz and 12-bit precision. Arbitrary waveforms are synthesized to improve the signal-to-noise ratio and to increase the spatial resolution when working with low-contrast objects. The setup was calibrated with academic objects and a needle hydrophone to develop the data correction tools and specify the properties of the system. The backscattering field was recorded using a restricted aperture, and tomographic acquisitions were performed with a pair of 0.08-mm-diameter steel wires, a low-contrast 2-D breast phantom, and a breast-shaped phantom containing inclusions. Data were processed with dedicated correction tools and a pulse compression technique. Objects were reconstructed using the elliptical back-projection algorithm.

A restoration framework for ultrasonic tissue characterization.

Ultrasonic tissue characterization has become an area of intensive research. This procedure generally relies on the analysis of the unprocessed echo signal. Because the ultrasound echo is degraded by the non-ideal system point spread function, a deconvolution step could be employed to provide an estimate of the tissue response that could then be exploited for a more accurate characterization. In medical ultrasound, deconvolution is commonly used to increase diagnostic reliability of ultrasound images by improving their contrast and resolution. Most successful algorithms address deconvolution in a maximum a posteriori estimation framework; this typically leads to the solution of l(2)-norm or (1)-norm constrained optimization problems, depending on the choice of the prior distribution. Although these techniques are sufficient to obtain relevant image visual quality improvements, the obtained reflectivity estimates are, however, not appropriate for classification purposes. In this context, we introduce in this paper a maximum a posteriori deconvolution framework expressly derived to improve tissue characterization. The algorithm overcomes limitations associated with standard techniques by using a nonstandard prior model for the tissue response. We present an evaluation of the algorithm performance using both computer simulations and tissue-mimicking phantoms. These studies reveal increased accuracy in the characterization of media with different properties. A comparison with state-of-the-art Wiener and l(1)-norm deconvolution techniques attests to the superiority of the proposed algorithm.