Comparison of three scattering models for ultrasound blood characterization

Ultrasound simulation of blood with different red blood cell aggregations and concentrations

BACKGROUND

Considerable progress of ultrasound simulation on blood has enhanced the characterizing of red blood cell (RBC) aggregation.

OBJECTIVE

A novel simulation method aims at modeling the blood with different RBC aggregations and concentrations is proposed.

METHODS

The modeling process is as follows: (i) A three-dimensional scatterer model is first built by a mapping with a Hilbert space-filling curve from the one-dimensional scatterer distribution. (ii) To illustrate the relationship between the model parameters and the RBC aggregation level, a variety of blood samples are prepared and scanned to acquire their radiofrequency signals in-vitro. (iii) The model parameters are determined by matching the Nakagami-distribution characteristics of envelope signals simulated from the model with those measured from the blood samples.

RESULTS

Nakagami metrics m estimated from 15 kinds of blood samples (hematocrits of 20%, 40%, 60% and plasma concentrations of 15%, 30%, 45%, 60%, 75%) are compared with metrics estimated by their corresponding models (each with different eligible parameters). Results show that for the three hematocrit levels, the mean and standard deviation of the root-mean-squared deviations of m are 0.27 ± 0.0026, 0.16 ± 0.0021, 0.12 ± 0.0018 respectively.

CONCLUSION

The proposed simulation model provides a viable data source to evaluate the performance of the ultrasound-based methods for quantifying RBC aggregation.

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.

Mean Scatterer Spacing Estimation Using Cepstrum-Based Continuous Wavelet Transform

The goal of this study was to develop an ultrasound (US) scatterer spacing estimation method using an enhanced cepstral analysis based on continuous wavelet transforms (CWTs). Simulations of backscattering media containing periodic and quasi-periodic scatterers were carried out to test the developed algorithm. Experimental data from HT-29 pellets and in vivo PC3 tumors were then used to estimate the mean scatterer spacing. For simulated media containing quasi-periodic scatterers at 1-mm and 100- [Formula: see text] spacing with 5% positional variation, the developed algorithm yielded a spacing estimation error of ~1% for 25- and 55-MHz US pulses. The mean scatterer spacing of HT-29 cell pellets (31.97 [Formula: see text]) was within 3% of the spacing obtained from histology and agreed with the predicted spacing from simulations based on the same pellets for both frequencies. The agreement extended to in vivo PC3 tumors estimation of the spacing with a variance of 1.68% between the spacing derived from the tumor histology and the application of the CWT to the experimental results. The developed technique outperformed the traditional cepstral methods as it can detect nonprominent peaks from quasi-random scatterer configurations. This work can be potentially used to detect morphological tissue changes during normal development or disease treatment.

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 Measurement of Erythrocyte Aggregation as a Systemic Inflammatory Marker by Ultrasound Imaging: A Systematic Review

This systematic review is aimed at answering two questions: (i) Is erythrocyte aggregation a useful biomarker in assessing systemic inflammation? (ii) Does quantitative ultrasound imaging provide the non-invasive option to measure erythrocyte aggregation in real time? The search was executed through bibliographic electronic databases CINAHL, EMB Review, EMBASE, MEDLINE, PubMed and the grey literature. The majority of studies correlated elevated erythrocyte aggregation with inflammatory blood markers for several pathologic states. Some studies used "erythrocyte aggregation" as an established marker of systemic inflammation. There were limited but promising articles regarding the use of quantitative ultrasound spectroscopy to monitor erythrocyte aggregation. Similarly, there were limited studies that used other ultrasound techniques to measure systemic inflammation. The quantitative measurement of erythrocyte aggregation has the potential to be a routine clinical marker of inflammation as it can reflect the cumulative inflammatory dynamics in vivo, is relatively simple to measure, is cost-effective and has a rapid turnaround time. Technologies like quantitative ultrasound spectroscopy that can measure erythrocyte aggregation non-invasively and in real time may offer the advantage of continuous monitoring of the inflammation state and, thus, may help in rapid decision making in a critical care setup.

A Method for Stereological Determination of the Structure Function From Histological Sections of Isotropic Scattering Media

The frequency-dependent ultrasonic backscatter coefficient (BSC) from tissues, a fundamental parameter estimated by quantitative ultrasound (QUS) techniques, contains microstructure information useful for tissue characterization. To extract the microstructure information from the BSC, the tissue under investigation is often modeled as a collection of discrete scatterers embedded in a homogeneous background. From a discrete scatterer point of view, the BSC is dependent on not only the properties of individual scatterers relative to the background but also the scatterer spatial arrangement [described by the structure function (SF)]. Recently, the 2-D SF was computed from histological tissue sections, and was shown to be related to the volumetric SF extracted from QUS measurements. In this paper, a stereological method is proposed to extract the volumetric (3-D) SF from 2-D histological tissue sections. Simulations and experimental cell pellet biophantom studies were conducted to evaluate the proposed method. Simulation results verified the proposed method. Experimental results showed that the volumetric SF extracted using the proposed method had a significantly better agreement with the QUS-extracted SF than did the 2-D SF extracted in the previous study. The proposed stereological approach provides a useful tool for predicting the SF from histology.

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.

Assessment of corneal properties based on statistical modeling of OCT speckle

A new approach to assess the properties of the corneal micro-structure in vivo based on the statistical modeling of speckle obtained from Optical Coherence Tomography (OCT) is presented. A number of statistical models were proposed to fit the corneal speckle data obtained from OCT raw image. Short-term changes in corneal properties were studied by inducing corneal swelling whereas age-related changes were observed analyzing data of sixty-five subjects aged between twenty-four and seventy-three years. Generalized Gamma distribution has shown to be the best model, in terms of the Akaike's Information Criterion, to fit the OCT corneal speckle. Its parameters have shown statistically significant differences (Kruskal-Wallis, p < 0.001) for short and age-related corneal changes. In addition, it was observed that age-related changes influence the corneal biomechanical behaviour when corneal swelling is induced. This study shows that Generalized Gamma distribution can be utilized to modeling corneal speckle in OCT in vivo providing complementary quantified information where micro-structure of corneal tissue is of essence.

Structure Function Estimated From Histological Tissue Sections

Ultrasonic scattering is determined by not only the properties of individual scatterers but also the correlation among scatterer positions. The role of scatterer spatial correlation is significant for dense medium, but has not been fully understood. The effect of scatterer spatial correlation may be modeled by the structure function as a frequency-dependent factor in the backscatter coefficient (BSC) expression. The structure function has been previously estimated from the BSC data. The aim of this study is to estimate the structure function from histology to test if the acoustically estimated structure function is indeed caused by the scatterer spatial distribution. Hematoxylin and eosin stained histological sections from dense cell pellet biophantoms were digitized. The scatterer positions were determined manually from the histological images. The structure function was calculated from the extracted scatterer positions. The structure function obtained from histology showed reasonable agreement in the shape but not in the amplitude, compared with the structure function previously estimated from the backscattered data. Fitting a polydisperse structure function model to the histologically estimated structure function yielded relatively accurate cell radius estimates ([Formula: see text]). Furthermore, two types of mouse tumors that have similar cell size and shape but distinct cell spatial distributions were studied, where the backscattered data were shown to be related to the cell spatial distribution through the structure function estimated from histology. In conclusion, the agreement between acoustically estimated and histologically estimated structure functions suggests that the acoustically estimated structure function is related to the scatterer spatial distribution.

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.

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.

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 kr_ag around 2.

Review of Quantitative Ultrasound: Envelope Statistics and Backscatter Coefficient Imaging and Contributions to Diagnostic Ultrasound

Conventional medical imaging technologies, including ultrasound, have continued to improve over the years. For example, in oncology, medical imaging is characterized by high sensitivity, i.e., the ability to detect anomalous tissue features, but the ability to classify these tissue features from images often lacks specificity. As a result, a large number of biopsies of tissues with suspicious image findings are performed each year with a vast majority of these biopsies resulting in a negative finding. To improve specificity of cancer imaging, quantitative imaging techniques can play an important role. Conventional ultrasound B-mode imaging is mainly qualitative in nature. However, quantitative ultrasound (QUS) imaging can provide specific numbers related to tissue features that can increase the specificity of image findings leading to improvements in diagnostic ultrasound. QUS imaging can encompass a wide variety of techniques including spectral-based parameterization, elastography, shear wave imaging, flow estimation, and envelope statistics. Currently, spectral-based parameterization and envelope statistics are not available on most conventional clinical ultrasound machines. However, in recent years, QUS techniques involving spectral-based parameterization and envelope statistics have demonstrated success in many applications, providing additional diagnostic capabilities. Spectral-based techniques include the estimation of the backscatter coefficient (BSC), estimation of attenuation, and estimation of scatterer properties such as the correlation length associated with an effective scatterer diameter (ESD) and the effective acoustic concentration (EAC) of scatterers. Envelope statistics include the estimation of the number density of scatterers and quantification of coherent to incoherent signals produced from the tissue. Challenges for clinical application include correctly accounting for attenuation effects and transmission losses and implementation of QUS on clinical devices. Successful clinical and preclinical applications demonstrating the ability of QUS to improve medical diagnostics include characterization of the myocardium during the cardiac cycle, cancer detection, classification of solid tumors and lymph nodes, detection and quantification of fatty liver disease, and monitoring and assessment of therapy.

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 function for high-concentration biophantoms of polydisperse scatterer sizes

Ultrasonic backscattering coefficient (BSC) has been used extensively to characterize tissue. In most cases, sparse scatterer concentrations are assumed. However, many types of tissues have dense scattering media. This study addresses the problem of dense media scattering by taking into account the correlation among scatterers using the structure functions. The effect of scatterer polydispersity on the structure functions is investigated. Structure function models based on polydisperse scatterers are theoretically developed and experimentally evaluated against the structure functions obtained from cell pellet biophantoms. The biophantoms were constructed by placing live cells of known concentration in coagulation media to form a clot. The BSCs of the biophantoms were estimated using single-element transducers over the frequency range from 11 to 105 MHz. Experimental structure functions were obtained by comparing the BSCs of two cell concentrations. The structure functions predicted by the models agreed with the experimental structure functions. Fitting the models yielded cell radius estimates that were consistent with direct light microscope measures. The results demonstrate the role of scatterer position correlation on dense media scattering, and the significance of scatterer polydispersity on structure functions. This work may lead to more accurate modeling of ultrasonic scattering in dense medium for improved tissue characterization.