Ultrasonic Backscatter Coefficient Research Articles

Efficient grain size evaluation based on single direction measurement of ultrasonic backscattering coefficient

<sec>GH4742 nickel-based superalloy exhibits excellent mechanical properties, and grain size is a key factor affecting its performance. A physical model-based ultrasonic backscattering method makes grain size measurement accurate and efficient. Nevertheless, it is constrained by complex models or multiple measurements taken from various beam angles. As a result, a backscattering coefficient method that requires only a single measurement for grain size evaluation is proposed. In contrast to the existing methods, the proposed method solely focuses on the backscattering coefficient component of the backscattering signal. It effectively eliminates the influence of unrelated factors, such as the measurement system and the acoustic field, through the utilization of reference signals.</sec><sec>The independent scattering model is employed to derive the backscattering coefficient, which solely pertains to the material itself. The relationship between grain size and backscattering coefficient is described by using a spatial correlation function. To consider the irrelevant factors, an experimental measurement method is developed by using the reference signals. Through numerical calculation and analysis, it has been observed that the backscattering coefficient is closely related to the frequency. When the product of the wavenumber and the grain size is significantly greater than 1 (<inline-formula><tex-math id="M1">\begin{document}$ ka\gg 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.png"/></alternatives></inline-formula>), a Stochastic scattering limit is reached. Conversely, when <inline-formula><tex-math id="M2">\begin{document}$ ka\ll 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.png"/></alternatives></inline-formula>, a Rayleigh scattering limit is observed. Furthermore, the backscattering coefficient is directly proportional to the grain size. As a general trend, larger grain sizes result in higher backscattering coefficient.</sec><sec>Three sets of GH4742 specimens with different grain sizes are prepared for phased array ultrasound experiments. It can be observed that the experimental backscattering coefficients, root mean square (RMS) values, and the amplitude trend of time domain signal are consistent. To perform grain size inversion, the backscattering coefficients in the effective bandwidth range of the probe are selected. By utilizing the least-square method, the theoretical backscattering coefficient is employed to fit the curves of the experimental backscattering coefficients. The evaluation results are compared with those obtained by metallographic analysis. The results show that the grain sizes obtained by the proposed method have a maximum relative error of –22.7% and a minimum relative error of –3.7%.</sec>

Simultaneous imaging of ultrasonic relative backscatter and attenuation coefficients for quantitative liver steatosis assessment

Prevalence of liver disease is continuously increasing and nonalcoholic fatty liver disease (NAFLD) is the most common etiology. We present an approach to detect the progression of liver steatosis based on quantitative ultrasound (QUS) imaging. This study was performed on a group of 55 rats that were subjected to a control or methionine and choline deficient (MCD) diet known to induce NAFLD. Ultrasound (US) measurements were performed at 2 and 6 weeks. Thereafter, animals were humanely euthanized and livers excised for histological analysis. Relative backscatter and attenuation coefficients were simultaneously estimated from the US data and envelope signal-to-noise ratio was calculated to train a regression model for: (1) fat fraction percentage estimation and (2) performing classification according to Brunt’s criteria in grades (0 <5%; 1, 5–33%; 2, >33–66%; 3, >66%) of liver steatosis. The trained regression model achieved an R^2 of 0.97 (p-value < 0.01) and a RMSE of 3.64. Moreover, the classification task reached an accuracy of 94.55%. Our results suggest that in vivo QUS is a promising noninvasive imaging modality for the early assessment of NAFLD.

Extracting Quantitative Ultrasonic Parameters from the Backscatter Coefficient.

The ultrasonic backscatter coefficient (BSC) is a fundamental quantitative ultrasound (QUS) parameter that contains rich information about the underlying tissue. Deriving parameters from the BSC is essential for fully utilizing the information contained in BSC for tissue characterization. In this chapter, we review two primary approaches for extracting parameters from the BSC versus frequency curve: the model-based approach and the model-free approach, focusing on the model-based approach, where a scattering model is fit to the observed BSC to yield model parameters. For this approach, we will attempt to unite commonly used models under a coherent theoretical framework. We will focus on the underlying assumptions and conditions for various BSC models. Computer code is provided to facilitate the use of some of the models. The strengths and weaknesses of various models are also discussed.

Fast linear least-squares method for ultrasound attenuation and backscatter estimation

The ultrasonic attenuation and backscatter coefficients of tissues are relevant acoustic parameters due to their wide range of clinical applications. In this paper, a linear least-squares method for the estimation of these coefficients in a homogeneous region of interest based on pulse-echo measurements is proposed. The method efficiently fits an ultrasound backscattered signal model to the measurements in both the frequency and depth dimension simultaneously at a low computational cost. It is demonstrated that the inclusion of depth information has a positive effect particularly on the accuracy of the estimated attenuation. The sensitivity of the attenuation and backscatter coefficients’ estimates to several predefined parameters such as the window length, window overlap and usable bandwidth of the spectrum is also studied. Comparison of the proposed method with a benchmark approach based on dynamic programming highlights better performance of our method in estimating these coefficients, both in terms of accuracy and computation time. Further analysis of the computation time as a function of the predefined parameters indicates our method’s potential to be used in real-time clinical settings.

High-frequency ultrasonic backscatter coefficient analysis considering microscopic acoustic and histopathological properties of lymphedema dermis

We studied the effect of acoustic and histopathological features on the ultrasound backscatter properties of lymphedema (LE) dermis. Experimental effective scatterer diameter (ESD) and effective acoustic concentration (EAC) were calculated from a backscatter coefficient using the reflector method for backscattered signals. Predicted parameters were also analyzed using two-dimensional Fourier transforms of the acoustic impedance and histopathological distributions. Backscattered signals were obtained from ex vivo human tissues negative (n = 5) and positive (n = 5) for LE using a laboratory-made scanner with a 14 MHz transducer. Acoustic impedance was analyzed using scanning acoustic microscopy with a 68 MHz transducer, and histopathological features, such as fiber number density and thickness, were assessed with digital histopathology. Both experimental and predicted EACs showed differences (in the range 25.7%–102%) between negative and positive LE. Although the mean and standard deviation of the acoustic impedance were related to the difference in EACs, the ESD and histopathological features were the same regardless of the presence of LE.

Effects of acoustic nonlinearities on the ultrasonic backscatter coefficient estimation.

The backscatter coefficient (BSC) is a fundamental property of tissues and can be used to classify tissues. Two BSC calibration methods are the planar reflector method and the reference phantom method. In both methods, linear acoustic propagation is assumed. In this study, the calibration methods were evaluated when acoustic nonlinear distortion was present. Radio frequency data were acquired from two physical phantoms using a 5 MHz single-element transducer and low power (one excitation level) and high power (six increasing excitation levels) excitation signals. BSCs estimated from the high power settings were compared to the BSCs estimated using the low power by calculating the root mean square error (RMSE). The BSCs were parameterized by fitting the BSC curve to a power law and estimating the power law exponent and by estimating the effective scatterer diameter (ESD). When using the planar reflector method, estimates of the exponent were observed to monotonically increase in value versus increasing excitation level and the ESD decreased with increasing excitation level. The RMSE increased monotonically versus excitation level using the planar reflector method but did not increase using the reference phantom method. The results suggest that the effects of nonlinear distortion are minimized using the reference phantom method.

Correlations of the frequency dependence of the ultrasonic backscatter coefficient with the bone volume fraction and the trabecular thickness in bovine trabecular bone: Application of the binary mixture model.

The ultrasonic backscatter coefficient and the exponent n (frequency dependence of the backscatter coefficient) were measured in 24 bovine femoral trabecular bone samples. The binary mixture model for ultrasonic scattering from trabecular bone was applied to predict the variations of the ultrasound parameters with the bone volume fraction (BV/TV) and the trabecular thickness (Tb.Th) in trabecular bone. The backscatter coefficient exhibited significant, positive correlations with the BV/TV (R = 0.82) and the Tb.Th (R = 0.79). In contrast, the exponent n was found to be significantly, negatively correlated with the BV/TV (R = -0.77) and the Tb.Th, (R = -0.71).

Comparison of two ultrasonic backscatter coefficient methods under nonlinear distortion

The backscatter coefficient (BSC) is a fundamental property of tissues and can be parameterized for tissue characterization. The BSC requires a reference signal, which is estimated through either the planar reflector method (PRM) or the reference phantom method (RPM). In both methods, linear acoustic propagation is assumed. In this work, the BSC estimation methods are evaluated when nonlinear distortion is present. RF data were acquired from two physical phantoms, labeled A and B, with a 5 MHz single-element transducer using low power (1 excitation level) and high power (6 increasing excitation levels) excitation signals. Phantom A contained glass beads with diameters ranging from 75 to 90 μm and phantom B had glass beads with diameters ranging from 9 to 43 μm. The BSCs estimated using the low power setting and high power settings were compared for the both the PRM and RPM through a root mean square error (RMSE). Estimates of the effective scatterer diameter (ESD) were obtained using each method for each high power setting and compared to the low power setting. The RMSE increased as the power setting increased with much higher RMSEs using the PRM compared to RPM, i.e., a maximum of 7.3 times larger for phantom A and 8.6 times larger for phantom B. Estimates of ESD matched the ranges of glass beads sizes for both phantoms except when using the PRM at higher power settings. These findings suggest that the RPM is more robust to nonlinear distortion effects compare to the PRM.

Inter-platform reproducibility of ultrasonic attenuation and backscatter coefficients in assessing NAFLD.

To assess inter-platform reproducibility of ultrasonic attenuation coefficient (AC) and backscatter coefficient (BSC) estimates in adults with known/suspected nonalcoholic fatty liver disease (NAFLD). This HIPAA-compliant prospective study was approved by an institutional review board; informed consent was obtained. Participants with known/suspected NAFLD were recruited and underwent same-day liver examinations with clinical ultrasound scanner platforms from two manufacturers. Each participant was scanned by the same trained sonographer who performed multiple data acquisitions in the right liver lobe using a lateral intercostal approach. Each data acquisition recorded a B-mode image and the underlying radio frequency (RF) data. AC and BSC were calculated using the reference phantom method. Inter-platform reproducibility was evaluated for AC and log-transformed BSC (logBSC = 10log10BSC) by intraclass correlation coefficient (ICC), Pearson's correlation, Bland-Altman analysis with computation of limits of agreement (LOAs), and within-subject coefficient of variation (wCV; applicable to AC). Sixty-four participants were enrolled. Mean AC values measured using the two platforms were 0.90 ± 0.13 and 0.94 ± 0.15dB/cm/MHz while mean logBSC values were - 30.6 ± 5.0 and - 27.9 ± 5.6dB, respectively. Inter-platform ICC was 0.77 for AC and 0.70 for log-transformed BSC in terms of absolute agreement. Pearson's correlation coefficient was 0.81 for AC and 0.80 for logBSC. Ninety-five percent LOAs were - 0.21 to 0.13dB/cm/MHz for AC, and - 9.48 to 3.98dB for logBSC. The wCV was 7% for AC. Hepatic AC and BSC are reproducible across two different ultrasound platforms in adults with known or suspected NAFLD. • Ultrasonic attenuation coefficient and backscatter coefficient are reproducible between two different ultrasound platforms in adults with NAFLD. • This inter-platform reproducibility may qualify quantitative ultrasound biomarkers for generalized clinical application in patients with suspected/known NAFLD.

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.

Inter-sonographer reproducibility of ultrasonic attenuation backscatter coefficient measures in adults with nonalcoholic fatty liver disease

The attenuation coefficient (AC) and backscatter coefficient (BSC) measures in the liver were found repeatable and inter-transducer reproducible in previous studies. This study assesses the inter-sonographer reproducibility of the two parameters. 56 participants (sex: 20M, 36F; age: 51.5±13.5, 24–74 yo; BMI: 32.2±5.2, 23.9–47.4 kg/m2; 43 had MRI-PDFF: 15.6±10.4%, 0.7–41.1%) with known or suspected NAFLD each underwent two same-day ultrasound liver examinations performed by two sonographers (out of six in total) using the Siemens S3000® ultrasound system. Each examination included five RF acquisitions in separate breathholds from the right liver lobe and one from a calibrated phantom using the same settings. The AC and BSC were estimated using the reference phantom technique from each liver RF acquisition. AC and log-transformed BSC (10logBSC) are frequency-averaged within 2.6-3.0 MHz. Intraclass correlation coefficient (ICC) was used to evaluate the inter-sonographer reproducibility. Without averaging mul...

Estimating liver fat fraction from ultrasonic attenuation and backscatter coefficient measures in adults with nonalcoholic fatty liver disease

Between 80 and 100 million people in the United States suffer from nonalcoholic fatty liver disease (NAFLD). It is currently being diagnosed via MRI and biopsies; however, these tend to be expensive and painful. In this study, a Siemens 3000 ultrasound scanner was used to obtain the quantitative ultrasound (QUS) parameters [backscatter coefficient, BSC, and attenuation coefficient, AC] of 84 participants with known or suspected NAFLD (thus few uncompromised liver samples expected). Participant recruitment is continuing. Also obtained was the liver proton density fat fraction (PDFF) via MRI. AC and BSC individually were linearly correlated (~0.6) to PDFF. The data were then divided into two equally sized sets, training and test, in order to calculate PDFF from a function of AC and BSC. Using the training set a polynomial equation was created where AC and BSC were used to estimate PDFF. It was found that a polynomial 1,2 [AC,BSC] yielded an improved correlation (0.76) when evaluated using the test set. Significant improvement is obtained to estimate PDFF using both AC and BSC as opposed to using either of these QUS parameters separately. [Support: NIH R01DK106419 and NIH R37EB002641.]Between 80 and 100 million people in the United States suffer from nonalcoholic fatty liver disease (NAFLD). It is currently being diagnosed via MRI and biopsies; however, these tend to be expensive and painful. In this study, a Siemens 3000 ultrasound scanner was used to obtain the quantitative ultrasound (QUS) parameters [backscatter coefficient, BSC, and attenuation coefficient, AC] of 84 participants with known or suspected NAFLD (thus few uncompromised liver samples expected). Participant recruitment is continuing. Also obtained was the liver proton density fat fraction (PDFF) via MRI. AC and BSC individually were linearly correlated (~0.6) to PDFF. The data were then divided into two equally sized sets, training and test, in order to calculate PDFF from a function of AC and BSC. Using the training set a polynomial equation was created where AC and BSC were used to estimate PDFF. It was found that a po...

Repeatability and Reproducibility of the Ultrasonic Attenuation Coefficient and Backscatter Coefficient Measured in the Right Lobe of the Liver in Adults With Known or Suspected Nonalcoholic Fatty Liver Disease.

To assess the repeatability and reproducibility of the ultrasonic attenuation coefficient (AC) and backscatter coefficient (BSC) measured in the livers of adults with known or suspected nonalcoholic fatty liver disease (NAFLD). The Institutional Review Board approved this Health Insurance Portability and Accountability Act-compliant prospective study; informed consent was obtained. Forty-one research participants with known or suspected NAFLD were recruited and underwent same-day ultrasound examinations of the right liver lobe with a clinical scanner by a clinical sonographer. Each participant underwent 2 scanning trials, with participant repositioning between trials. Two transducers were used in each trial. For each transducer, machine settings were optimized by the sonographer but then kept constant while 3 data acquisitions were obtained from the liver without participant repositioning and then from an external calibrated phantom. Raw RF echo data were recorded. The AC and BSC were measured within 2.6 to 3.0 MHz from a user-defined hepatic field of interest from each acquisition. The repeatability and reproducibility were analyzed by random-effects models. The mean AC and log-transformed BSC (logBSC) were 0.94 dB/cm-MHz and -27.0 dB, respectively. Intraclass correlation coefficients were 0.88 to 0.94 for the AC and 0.87 to 0.95 for the logBSC acquired without participant repositioning. For between-trial repeated scans with participant repositioning, the intraclass correlation coefficients were 0.80 to 0.84 for the AC and 0.69 to 0.82 for the logBSC after averaging results from 3 within-trial images. The variability introduced by the transducer was less than the repeatability error. Hepatic AC and BSC measures using a reference phantom technique on a clinical scanner are repeatable and reproducible between transducers in adults with known or suspected NAFLD.

Ultrasonic characterization of human colon carcinoma cells in the 5-25 MHz frequency range

Early recognition of cancerous tissue is crucial in receiving a favorable prognosis. Diagnostic tools that allow for an understanding of differences in the ultrasonic characteristics (such as speed of sound (SOS), attenuation, and backscatter coefficients (BSC)) in malignant and benign cells can aid in early diagnostics. Although statistically significant distinctions between benign and cancerous tumor scatterer properties have been demonstrated, there is little knowledge about which cell characteristics create differences in scattering. This study centers on techniques using quantitative ultrasound to quantify the microstructure of HTC (colon cancer) cells in an attempt to establish a greater understanding of scattering mechanisms. To analyze these characteristics HTC cells were cultured, suspended in agar and prepared into samples. Broadband BSC measurements were conducted using focused transducers and narrowband attenuation and SOS measurements were performed using receiving and transmitting transducers. All experiments were made in the 5-25 MHz range at 21°C. A comparison of the obtained results was made with a similar study using a higher concentration of HTC cells to test the ability to accurately estimate the ultrasonic properties. The results introduce relevant data useful for comparative studies and further analysis.

Repeatability and reproducibility of ultrasonic attenuation coefficient and backscatter coefficient measures in adults with non-alcoholic fatty liver disease

The attenuation coefficient (AC) and backscatter coefficient (BSC) are two promising quantitative ultrasound biomarkers, yet their repeatability and reproducibility (RR with and without visible blood vessels) were drawn for each image. AC and BSC were estimated within the FOIs. AC and log-transformed BSC mean values within 2.6-3.0 MHz were used for the R&R analysis based on an unweighted sums of ...

Bone ultrasound backscatter in the detection of bone nutritional status in term infants

Objective To establish a reference range of cancellous bone ultrasonic backscatter coefficient (BSC) in term neonates, and to determine the significance of BSC in bone nutritional status in term newborns and infants. Methods Six hundred and sixty-five term newborns, who were born in Shanghai First Maternity and Infant Hospital from July 2014 to August 2014, were enrolled. On the third day and the 42nd day after birth, all infants underwent ultrasonic measurement of the calcaneum bone using a broadband–non-focus ultrasonic transducer at three frequencies (2.25, 3.5 and 5 MHz). MATLAB software was used to analyze the backscatter signals. Clinical data of the infants, including gestational age, birth weight and birth age, were recorded at the same time. Statistical analyses of the data included variance analysis, Tukey's test, rank sum test, Dunn test and Pearson or Spearman correlation analysis. Results (1) Of the 665 infants, 335 were male. The mean gestational age at birth was (38.0±1.9) weeks, and the mean birth weight was (3 152±226) g. (2) On the third day, there were significant differences in BSC values acquired at 2.25 and 3.5 MHz among the groups with different gestational ages or birth weights (2.25 MHz: H=9.842 and 17.271; 3.5 MHz: H=6.275 and 21.450, respectively, all P<0.05). At 3.5 and 2.25 MHz, BSC values were positively correlated with gestational age (r=0.047 and 0.035, respectively, both P<0.05) and birth weight (r=0.125 and 0.186, both P<0.05). (3) On the 42nd day, significant differences in BSC were observed at each frequency among the groups with different gestational ages or birth weights (gestational age: H=76.832, 16.498 and 32.756; birth weight: H=70.014, 18.095 and 34.126; all P<0.01). Gestational age and birth weight were positively correlated with BSC value acquired at each frequency (r=0.397, 0.286 and 0.272 for gestational age, 0.451, 0.223 and 0.196 for birth weight; all P<0.01). Conclusions A preliminary BSC reference percentile in term-born infants is established. There are positive correlations between BSC value and newborn gestational age and birth weight at certain frequencies, which can reflect the status of the newborn's cancellous bone. Determination of BSC value should be performed during the follow-up period to assess the nutritional status of neonatal bone. Key words: Bone density; Bone and bones; Ultrasonography; Infant, newborn; Nutritional satus

Structure-factor model for quantifying the ultrasound scattering from concentrated cell pellet biophantoms

Ultrasonic backscatter coefficient (BSC) measurements were performed on K562 cell pellet biophantoms with cell concentrations ranging from 0.6% to 30% using ultrasound in the 10–42 MHz frequency band. The concentrated biophantoms mimic densely packed cells with known concentrations and are thus simplified versions of real tumor. Three scattering models, the fluid-filled-sphere model (FFSM), the Gaussian model (GM), and the structure factor model (SFM), were compared for modeling the scattering of the biophantoms. The GM and FFSM assume sparse, independently, and randomly distributed scatterers and are thus suitable for modeling dilute media; however, the SFM does not contain these assumptions and therefore can model dense media accurately. First, a parameter-estimation procedure was developed to estimate scatterer size and acoustic impedance contrast (assuming that cell concentrations were known a priori) and thereby compare theoretical with measured BSCs for all studied concentrations. The SFM yielded scatterer-radius estimates of 6.4 μm, which were consistent with the cell radius measured by optical microscopy. Second, the ability of the three models to estimate the scatterer size and acoustic concentration was compared. These scatterer properties were predicted well by the SFM, whereas the GM and the FFSM underestimated cell size and overestimated acoustic concentration for the more-concentrated biophantoms.

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.

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.

Nonlinear propagation effects on measurement of backscatter coefficient of tissue-mimicking materials

Measurement of the ultrasonic backscatter coefficient (BSC) holds great promise in providing quantitative diagnostic information on various diseases. Many clinical studies utilize the reference phantom method. In this method, the measured BSC is the ratio of the power spectrum of the scattered sound from the patient to the power spectrum from the reference phantom multiplied by the known BSC of the reference and an attenuation correction factor. In these studies, nonlinear propagation has been ignored. Nonlinear propagation causes changes in the power spectrum as incident energy is converted to harmonics and the acoustic signal undergoes nonlinear attenuation. This study characterized the effects of nonlinear propagation on reference phantom measurements of BSC from four tissue-mimicking samples in the frequency range from 2 to 20 MHz and incident pressure from 1 to 10 MPa (measured in water) using single element focused transducers. Samples consisted of glass microspheres suspended in a mixture of agar and concentrated milk. The resulting BSC varied by up to a factor of 30 depending on the incident pressure. Substantial changes in the overall shape of the BSC vs frequency were also observed. New methods of measurement of BSC that account for nonlinear propagation are explored.