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

Evaluation of Scatterer Parameters From Ultrasound Scattering Models Taking Into Account Scattering From Nuclei and Cells of Cell-Pellet Biophantoms and Ex Vivo Tumors

The Quantitative Ultrasound backscatter coefficient provides the capability to evaluate tissue microstructure parameters. Tissue-based scatterer parameters are extracted using ultrasound scattering models. It is challenging to correlate ultrasound scatterer parameters of tissue structures from optical-measured histology, possibly because of inappropriate scattering models or the presence of multiple scatterers. The objective of this study is to pursue the quantification of pertinent scatterer parameters with scattering models that consider ultrasound scattering from nuclei and cells. The concentric sphere model (CSM) and the structure factor model adapted for two types of scatterers (SFM2) are evaluated for cell-pellet biophantoms and ex vivo tumors of four cell lines: 4T1, JC, LMTK, and MAT. The structure factor model (SFM) was used for comparison. CSM and SFM2 provided scatterer parameters closer to histology (lower relative errors) for nucleus and cell radii and volume fractions than SFM but were not always accompanied by lower dispersion of the scatterer distribution (lower coefficient of variation). CSM and SFM2 quantified cell and nucleus radius and volume fraction parameters with lower relative error compared to SFM. For tumors, CSM provided better results than SFM2.

A magnetic phantom technique for investigating structural effects on quantitative ultrasound parameters

Media that contain ultrasound scatterers arranged in a regular spatial distribution can be considered as structured. Structural effects affect quantitative ultrasound parameters that reflect the microstructure properties. Prior studies examined structural effects using simulations or phantoms with fixed microarchitecture, focusing on a limited set of ultrasound parameters, with limited attention given to their underlying physical significance. This study aims to investigate the concordance of the physical interpretations of multiple quantitative ultrasound parameters experimentally by introducing a phantom type with an adjustable microarchitecture. The phantom consists of an aqueous solution containing superparamagnetic microspheres, acting as scatterers. The spatial arrangement of the magnetic particles is modified by applying an external magnetic field, therefore changing the degree of structure of the phantom. Quantitative ultrasound parameters are estimated in three different configurations: the magnetic field intensity is varied over time, strength, and orientation. In each experiment, the backscatter coefficient and the envelope quantitative ultrasound parameters are successfully extracted (R2 ≈ 0.94). Their physical interpretations are supported by microphotographs and geometrical considerations through concordant hypotheses. This study paves the way for the use of magnetic phantoms. This methodology could be followed to validate theoretical scattering models and the physical meanings of quantitative ultrasound parameters.

Ultrasound Matrix Imaging-Part II: The Distortion Matrix for Aberration Correction Over Multiple Isoplanatic Patches

This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by spatial variations in the medium speed-of-sound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentally-recorded matrix of reflected acoustic signals to synthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wave-fronts consist of two components: (i) An ideal geometric wave-front linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speed-of-sound variations. These distortions are stored in a so-called distortion matrix, the singular value decomposition of which gives access to an optimized focusing law at any point. We show that, by decoupling the aberrations undergone by the outgoing and incoming waves and applying an iterative strategy, compensation for even high-order and spatially-distributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the in-vivo imaging of a gallbladder. A map of isoplanatic modes is retrieved and is shown to be strongly correlated with the arrangement of tissues constituting the medium. The corresponding focusing laws yield an ultrasound image with drastically improved contrast and transverse resolution. UMI thus provides a flexible and powerful route towards computational ultrasound.

Evaluation of ultrasonic scattering in agar-based phantoms using 3D printed scattering molds

PURPOSE

Acoustic characterization of tissue mimicking materials in terms of attenuation, absorption, scattering and propagation velocity is essential for their utilisation in experiments, thus sparing the need for living tissues or cadavers. Although there is a vast literature regarding the acoustic characterization of such materials in terms of attenuation or propagation velocity, there is limited data regarding the quantification of the scattering coefficient. Herein stimulated the utilisation of four agar-based phantoms featuring different sizes of scattering agar-structures on one of their surfaces so as to provide experimental evaluation of the magnitude of scattering.

METHODS

The agar-based phantoms were developed with 6% w/v agar and 4% w/v silica and featured scatterers of sizes of 0-1 mm. The acoustic properties of propagation speed, impedance, insertion loss and attenuation were evaluated utilising the pulse-echo and through-transmission techniques. Scattering was deduced from the data.

RESULTS

The propagation speed measured at 2.7 MHz was in the range of 1531.23-1542.97 m/s. Respectively the attenuation as measured at 1.1 MHz was in the range of 1.216-1.546 dB/cm increasing with increased scatterer size. Respectively the scattering coefficient was in the range of 0.078-0.324 dB/cm. Moreover, the scattering coefficient was linearly dependent on frequency in the range of 0.8-2.1 MHz indicating a 6-23% effect of the total attenuation.

CONCLUSIONS

The experimental results demonstrate the utilisation of the procedure for quantification of the scattering coefficient of tissue mimicking materials thus improving the diagnostic and therapeutic uses of ultrasound.

Ultrasound Scattering From Cell-Pellet Biophantoms and Ex Vivo Tumors Provides Insight Into the Cellular Structure Involved in Scattering

The histologically identifiable cellular structure(s) involved in ultrasonic scattering is(are) yet to be uniquely identified. The study quantifies six possible cellular scattering parameters, namely, cell and nucleus radii and their respective cell and nucleus volume fractions as well as a combination of cell and nucleus radii and their volume fraction. The six cellular parameters are each derived from four cell lines (4T1, JC, LMTK, and MAT) and two tissue types (cell-pellet biophantom and ex vivo tumor). Optical histology and quantitative ultrasound (QUS), both independent approaches, are used to yield these cellular parameters. QUS scatterer parameters are experimentally determined using two ultrasonic scattering models: the spherical Gaussian model (GM) and the structure factor model (SFM) to yield insight about scattering from nuclei only and cells only. GM is a classical ultrasonic scattering model to evaluate QUS parameters and is well adapted for diluted media. SFM is adapted for dense media to estimate reasonably well scatterer parameters of cellular structures from ex vivo tissue. Nucleus and cell radii and volume fractions are measured optically from histology. They were used as inputs to calculate BSC for scattering from cells, nuclei, and both cells and nuclei. The QUS-derived scatterers (radii and volume fractions) distributions were then compared to the optical histology scatterer parameters derived from these calculated BSCs. The results suggest scattering from cells only (LMTK and MAT) or both cells and nuclei (4T1 and JC) for cell-pellet biophantoms and scattering from nuclei only for tumors.

A study on understanding the physical mechanism of change in ultrasonic envelope statistical property during temperature elevation

PURPOSE

Our previous studies demonstrate that the variation in ultrasonic envelope statistics is correlated with the temperature change inside scattering media. This variation is identified as the change in the scatterer structure during thermal expansion or contraction. However, no specific evidence has been verified to date. This study numerically reproduces the change in the scatterer distribution during thermal expansion or contraction using finite element simulations and also investigates how the situation is altered by different material properties.

METHODS

The material properties of a linear elastic solid depend on the thermal expansion coefficient, thermal conductivity, specific heat, and initial scatterer number density. Three-dimensional displacements, calculated in the simulation, were sequentially used to update the positions of the randomly distributed scatterers. Ultrasound signals from the scatterer distribution were generated by simulating a 7.5-MHz linear array transducer whose specifications were the same as those in the experimental measurements of several phantoms and excised porcine livers. To represent the change in the envelope statistical feature, the absolute value of the ratio change in the logarithmic Nakagami (NA) parameter, Δ m , at each time was calculated as a value normalized with the initial NA parameter.

RESULTS

The change in the scatterer number density relates to the volume change during temperature elevation. The magnitude of the Δ m shift against the temperature change increases depending on the higher thermal expansion coefficient. In contrast, the relationship between Δ m and the scatterer number density is similar with any material property. Additionally, the changes in Δ m obtained by several experimental phantoms with low to high scatterer number densities are comparable with the numerical simulation results.

CONCLUSIONS

The change in Δ m is indirectly related to the change in the scatterer number density owing to the volume change during thermal expansion or contraction.

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.

Ultrasonic particle volume fraction profiling: an evaluation of empirical approaches

ABSTRACT

We discuss empirical techniques to extract quantitative particle volume fraction profiles in particle-laden flows using an ultrasound transducer. A key step involves probing several uniform suspensions with varying bulk volume fractions from which two key volume fraction dependent calibration parameters are identified: the peak backscatter amplitude (acoustic energy backscattered by the initial layer of the suspension) and the amplitude attenuation rate (rate at which the acoustic energy decays with depth owing to scattering losses). These properties can then be used to reconstruct spatially varying particle volume fraction profiles. Such an empirical approach allows circumventing detailed theoretical models which characterize the interaction between ultrasound and suspensions, which are not universally applicable. We assess the reconstruction techniques via synthetic volume fraction profiles and a known particle-laden suspension immobilized in a gel. While qualitative trends can be easily picked up, the following factors compromise the quantitative accuracy: (1) initial reconstruction errors made in the near-wall regions can propagate and grow along the reconstruction direction, (2) multiple scattering can create artefacts which may affect the reconstruction, and (3) the accuracy of the reconstruction is very sensitive to the goodness of the calibration. Despite these issues, application of the technique to particle-laden pipe flows shows the presence of a core with reduced particle volume fractions in laminar flows, whose prominence reduces as the flow becomes turbulent. This observation is associated with inertia-induced radial migration of particles away from the pipe axis and is observed in flows with bulk volume fractions as high as 0.08. Even transitional flows with low levels of intermittency are not devoid of this depleted core. In conclusion, ultrasonic particle volume fraction profiling can play a key complementary role to ultrasound-based velocimetry in studying the internal features of particle-laden flows.

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).

Ultrasound assessment of translation of microbubbles driven by acoustic radiation force in a channel filled with stationary fluid

In this report, a method is proposed to quantify the translation of ultrasound contrast agent (UCA) microbubbles driven by acoustic radiation for the detection of channels filled with stationary fluid. The authors subjected UCA microbubbles in a channel with diameters of 0.1 and 0.5 mm to ultrasound pulses with a center frequency of 14.4 MHz. The translational velocity of the UCA microbubbles increased with the sound pressure and pulse repetition frequency (PRF) of the transmitted ultrasound. The mean translational velocity reached 0.75 mm/s at a negative peak sound pressure of 2.76 MPa and a PRF of 2 kHz. This trend agreed with the theoretical prediction, which indicated that the translational velocity was proportional to the square of the sound pressure and the PRF. Furthermore, an experiment was carried out with a phantom that mimics tissue and found that the proposed method aided in detection of the channel, even in the case of a low contrast-echo to tissue-echo ratio. The authors expect to develop the proposed method into a technique for detecting lymph vessels.

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.

Comprehensive backscattering characteristics analysis for quantitative ultrasound with an annular array: a basic study on homogeneous scattering phantom

High-frequency ultrasound (HFU, >20 MHz) and quantitative ultrasound (QUS) methods permit a means to understand the relationship between anatomical and acoustic characteristics. In our previous research, we showed that analyzing the acoustic scattering with HFU was an effective method for noninvasive diagnosis. However, the depth of field (DOF) of HFU transducers was limited, which constrains the range of QUS analysis. In this study, we seek to improve the accuracy of HFU, QUS-based parameters on the envelope statistics and frequency-based analysis by using an annular array that allows for an extended DOF. A 20-MHz annular-array transducer with five elements was employed to obtain signals which were beamformed in post-processing. Two kinds of low concentration scattering phantoms were scanned with 30-μm step size. Two QUS analysis techniques were employed: the Nakagami distribution and the reflector method. The results demonstrated that the annular array provides a stable analysis over an extended axial range.

Quantitative ultrasound imaging of cell-laden hydrogels and printed constructs

In the present work we have revisited the application of quantitative ultrasound imaging (QUI) to cellular hydrogels, by using the reference phantom method (RPM) in combination with a local attenuation compensation algorithm. The investigated biological samples consisted of cell-laden collagen hydrogels with PC12 neural cells. These cell-laden hydrogels were used to calibrate the integrated backscattering coefficient (IBC) as a function of cell density, which was then used to generate parametric images of local cell density. The image resolution used for QUI and its impact on the relative IBC error was also investigated. Another important contribution of our work was the monitoring of PC12 cell proliferation. The cell number estimates obtained via the calibrated IBC compared well with data obtained using a conventional quantitative method, the MTS assay. Evaluation of spectral changes as a function of culture time also provided additional information on the cell cluster size, which was found to be in close agreement with that observed by microscopy. Last but not least, we also applied QUI on a 3D printed cellular construct in order to illustrate its capabilities for the evaluation of bioprinted structures. STATEMENT OF SIGNIFICANCE: While there is intensive research in the areas of polymer science, biology, and 3D bio-printing, there exists a gap in available characterisation tools for the non-destructive inspection of biological constructs in the three-dimensional domain, on the macroscopic scale, and with fast data acquisition times. Quantitative ultrasound imaging is a suitable characterization technique for providing essential information on the development of tissue engineered constructs. These results provide a detailed and comprehensive guide on the capabilities and limitations of the technique.

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.

Limitations on estimation of effective scatterer diameters

The influence of spatial diversity in acoustic scattering properties on estimates of the effective scatterer diameter (ESD) applied to soft biological tissues is investigated. This study is based on two-dimensional simulations of scattering media, beginning with random distributions of simple disk structures where all scattering features are known exactly. It concludes with an analysis of histology maps from healthy and fatty rabbit liver. Further, the liver histology is decomposed using an orthonormal basis to separate acoustic scattering at various spatial scales and observe how it influences ESD estimates. Overall, the goal is to quantitatively interpret ESD results for diagnostic assessments despite wide variations in tissue scatterer properties.

High frequency ultrasound imaging and simulations of sea urchin oocytes

High frequency ultrasound backscatter signals from sea urchin oocytes were measured using a 40 MHz transducer and compared to numerical simulations. The Faran scattering model was used to calculate the ultrasound scattered from single oocytes in suspension. The urchin oocytes are non-nucleated with uniform size and biomechanical properties; the backscatter from each cell is similar and easy to simulate, unlike typical nucleated mammalian cells. The time domain signal measured from single oocytes in suspension showed two distinct peaks, and the power spectrum was periodic with minima spaced approximately 10 MHz apart. Good agreement to the Faran scattering model was observed. Measurements from tightly packed oocyte cell pellets showed similar periodic features in the power spectra, which was a result of the uniform size and consistent biomechanical properties of the cells. Numerical simulations that calculated the ultrasound scattered from individual oocytes within a three dimensional volume showed good agreement to the measured signals and B-scan images. A cepstral analysis of the signal was used to calculate the size of the cells, which was 78.7 μm (measured) and 81.4 μm (simulated). This work supports the single scattering approximation, where ultrasound is discretely scattered from single cells within a bulk homogeneous sample, and that multiple scattering has a negligible effect. This technique can be applied towards understanding the complex scattering behaviour from heterogeneous tissues.

Taking advantage of acoustic inhomogeneities in photoacoustic measurements

This paper proposes a method for improving the localization and the quantification of the optical parameters in photoacoustic (PA) tomography of biological tissues that are intrinsically heterogeneous in both optical and acoustic properties. It is based on the exploitation of both the PA signal, generated by the heterogeneous optical structures, and the secondary acoustic echoes due to the interaction between a primary PA wave generated near the tissue surface and the heterogeneous acoustic structures. These secondary echoes can also be collected through proper measurements of the PA signals. The experimental procedure is presented along with the method to filter the signal and the reconstruction algorithm that includes the account of the acoustic information.

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.

Multidimensional spectral analysis of the ultrasonic radiofrequency signal for characterization of media

The importance of the analysis of the radiofrequency signal is by now recognized in the field of tissue characterization via ultrasound. The RF signal contains a wealth of information and structural details that are usually lost in the B-Mode representation. The HyperSPACE (Hyper SPectral Analysis for Characterization in Echography) algorithm presented by the authors in previous papers for clinical applications is based on the radiofrequency ultrasonic signal. The present work describes the method in detail and evaluates its performance in a repeatable and standardized manner, by using two test objects: a commercial test object that simulates the human parenchyma, and a laboratory-made test object consisting of human blood at different dilution values. In particular, the sensitivity and specificity in discriminating different density levels were estimated. In addition, the robustness of the algorithm with respect to the signal-to-noise ratio was also evaluated.

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.

Experimental evaluation of spectral-based quantitative ultrasound imaging using plane wave compounding

Quantitative ultrasound (QUS) based on backscatter coefficient (BSC) estimation has shown potential for tissue characterization. Beamforming using plane wave compounding has advantages for echographic, Doppler, and elastographic imaging; however, to date, plane wave compounding has not been experimentally evaluated for the purpose of BSC estimation. In this study, two BSC-derived parameters (i.e., the BSC midband fit and intercept) were estimated from experimental data obtained using compound plane wave beamforming. For comparison, QUS parameters were also estimated from data obtained using both fixed focus and dynamic receive beamforming. An ultrasound imaging system equipped with a 9-MHz center frequency, 64-element array was used to collect data up to a depth of 45 mm. Two gelatin phantoms with randomly distributed 20-μm inclusions with a homogeneous scatterer concentration and a two-region scatterer concentration were used for assessing the precision and lateral resolution of QUS imaging, respectively. The use of plane wave compounding resulted in accurate QUS estimation (i.e., bias in the BSC parameters of less than 2 dB) and relatively constant lateral resolution (i.e., BSC midband fit 10% to 90% rise distance ranging between 1.0 and 1.5 mm) throughout a 45 mm field of view. Although both fixed focus and dynamic receive beamforming provided the same performance around the focal depth, the reduction in SNR away from the focus resulted in a reduced field of view in the homogeneous phantom (i.e., only 28 mm). The lateral resolution also degraded away from the focus, with up to a 2-fold and 10-fold increase in the rise distance at 20 mm beyond the focal depth for dynamic receive and fixed focus beamforming, respectively. These results suggest that plane wave compounding has the potential to improve the performance of spectral-based quantitative ultrasound over other conventional beamforming strategies.

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.

Estimating cell concentration in three-dimensional engineered tissues using high frequency quantitative ultrasound

Histology and biochemical assays are standard techniques for estimating cell concentration in engineered tissues. However, these techniques are destructive and cannot be used for longitudinal monitoring of engineered tissues during fabrication processes. The goal of this study was to develop high-frequency quantitative ultrasound techniques to nondestructively estimate cell concentration in three-dimensional (3-D) engineered tissue constructs. High-frequency ultrasound backscatter measurements were obtained from cell-embedded, 3-D agarose hydrogels. Two broadband single-element transducers (center frequencies of 30 and 38 MHz) were employed over the frequency range of 13-47 MHz. Agarose gels with cell concentrations ranging from 1 × 10(4) to 1 × 10(6) cells mL(-1) were investigated. The integrated backscatter coefficient (IBC), a quantitative ultrasound spectral parameter, was calculated and used to estimate cell concentration. Accuracy and precision of this technique were analyzed by calculating the percent error and coefficient of variation of cell concentration estimates. The IBC increased linearly with increasing cell concentration. Axial and lateral dimensions of regions of interest that resulted in errors of less than 20% were determined. Images of cell concentration estimates were employed to visualize quantitatively regional differences in cell concentrations. This ultrasound technique provides the capability to rapidly quantify cell concentration within 3-D tissue constructs noninvasively and nondestructively.

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.