Statistics of envelope of high-frequency ultrasonic backscatter from human skin in vivo

Review of Envelope Statistics Models for Quantitative Ultrasound Imaging and Tissue Characterization

The homodyned K-distribution and the K-distribution, viewed as a special case, as well as the Rayleigh and the Rice distributions, viewed as limit cases, are discussed in the context of quantitative ultrasound (QUS) imaging. The Nakagami distribution is presented as an approximation of the homodyned K-distribution. The main assumptions made are (1) the absence of log-compression or application of nonlinear filtering on the echo envelope of the radiofrequency signal and (2) the randomness and independence of the diffuse scatterers. We explain why other available models are less amenable to a physical interpretation of their parameters. We also present the main methods for the estimation of the statistical parameters of these distributions. We explain why we advocate the methods based on the X-statistics for the Rice and the Nakagami distributions and the K-distribution. The limitations of the proposed models are presented. Several new results are included in the discussion sections, with proofs in the appendix.

A novel algorithm for multiplicative speckle noise reduction in ex vivo human brain OCT images

Optical coherence tomography (OCT) images of ex vivo human brain tissue are corrupted by multiplicative speckle noise that degrades the contrast to noise ratio (CNR) of microstructural compartments. This work proposes a novel algorithm to reduce noise corruption in OCT images that minimizes the penalized negative log likelihood of gamma distributed speckle noise. The proposed method is formulated as a majorize-minimize problem that reduces to solving an iterative regularized least squares optimization. We demonstrate the usefulness of the proposed method by removing speckle in simulated data, phantom data and real OCT images of human brain tissue. We compare the proposed method with state of the art filtering and non-local means based denoising methods. We demonstrate that our approach removes speckle accurately, improves CNR between different tissue types and better preserves small features and edges in human brain tissue.

In Vivo Quantitative Ultrasound on Dermis and Hypodermis for Classifying Lymphedema Severity in Humans

This study investigated the ability of in vivo quantitative ultrasound (QUS) assessment to evaluate lymphedema severity compared with the gold standard method, the International Society of Lymphology (ISL) stage. Ultrasonic measurements were made around the middle thigh (n = 150). Radiofrequency data were acquired using a clinical scanner and 8-MHz linear probe. Envelope statistical analysis was performed using constant false alarm rate processing and homodyned K (HK) distribution. The attenuation coefficient was calculated using the spectral log-difference technique. The backscatter coefficient (BSC) was obtained by the reference phantom method with attenuation compensation according to the attenuation coefficients in the dermis and hypodermis, and then effective scatterer diameter (ESD) and effective acoustic concentration (EAC) were estimated with a Gaussian model. Receiver operating characteristic curves of QUS parameters were obtained using a linear regression model. A single QUS parameter with high area under the curve (AUC) differed between the dermis (ESD and EAC) and hypodermis (HK) parameters. The combinations with ESD and EAC in the dermis, HK parameters in the hypodermis and typical features (dermal thickness and echogenic regions in the hypodermis) improved classification performance between ISL stages 0 and ≥I (AUC = 0.90 with sensitivity of 75% and specificity of 91%) in comparison with ESD and EAC in the dermis (AUC = 0.82) and HK parameters in the hypodermis (AUC = 0.82). In vivo QUS assessment by BSC and envelope statistical analyses can be valuable for non-invasively classifying an extremely early stage of lymphedema, such as ISL stage I, and following its progression.

Corneal Optical Coherence Tomography Speckle in Crosslinked and Untreated Rabbit Eyes in Response to Elevated Intraocular Pressure

Purpose

To ascertain the influence of intraocular pressure (IOP) on corneal optical coherence tomography (OCT) speckle in untreated and ultraviolet A–riboflavin induced corneal collagen crosslinked rabbit eyes.

Methods

Left corneas of eight rabbits were de-epithelialized and crosslinked by applying riboflavin and 30-minute ultraviolet A light exposure. After enucleation (6 months after treatment), each eyeball (treated and untreated) was mounted in a measurement setup, in which IOP was increased from 15 to 45 mm Hg in steps of 5 mm Hg. At each IOP value, single B-scans of the central cornea were acquired three times with the spectral-domain OCT Copernicus-HR. Then, three regions of interest, including the anterior, posterior, and entire corneal stroma, were automatically extracted. Five different probability distributions were used as a model for the corneal speckle and the one with the best goodness of fit was chosen for further analysis.

Results

The generalized gamma distribution achieved the best goodness of fit and its scale (a) and shape (v) parameters statistically significantly changed with increasing IOP in the three regions of analysis (two-way repeated measures analysis of variance, all P < 0.05). The statistically significant difference between untreated and crosslinked eyes was observed for the shape parameters of the posterior and entire corneal stroma.

Conclusions

Corneal OCT speckle is influenced by IOP and shows to be significantly different in untreated and crosslinked eyes. Corneal OCT speckle analysis has the potential to be indirectly used for assessing changes in corneal stroma in ex vivo and in vivo studies.

Translational Relevance

Investigation of corneal OCT speckle statistics can offer additional diagnostic biomarkers related to changes in the corneal stroma after ocular surgeries.

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).

Association Between Muscle Strength and Modeling Estimates of Muscle Tissue Heterogeneity in Young and Old Adults

OBJECTIVES

Assessing aging muscle through estimates of muscle heterogeneity may overcome some of the limitations of grayscale analyses. The objectives of this study included determining statistical model parameters that characterize muscle echogenicity and are associated with strength in younger and older participants.

METHODS

Thirty-three community-dwelling participants were assigned to younger and older groups. Quantitative B-mode ultrasound scanning of the rectus femoris and isometric grip strength testing were completed. Shape or dispersion parameters from negative binomial distribution, Nakagami, gamma, and gamma mixture models were fitted to the grayscale histograms.

RESULTS

The mean ages ± SDs of the younger and older groups were 24.0 ± 2.3 and 65.1 ± 6.5 years, respectively. Statistical model shape and dispersion parameters for the grayscale histograms significantly differed between the younger and older participants (P = .002-.006). Among all of the statistical models considered, the gamma mixture model showed the best fit with the grayscale histograms (χ² goodness of fit = 62), whereas the Nakagami distribution displayed the poorest fit (χ² goodness of fit = 2595). Grayscale values were significantly associated with peak grip strength force in younger adult participants (R²  = 0.36; P < .008). However, the negative binomial dispersion parameter k (adjusted R²  = 0.70; P < .001) and gamma shape parameter α (adjusted R²  = 0.68; P < .01) showed the highest associations with peak grip strength force in older adult participants.

CONCLUSIONS

The negative binomial dispersion parameter k and the gamma shape parameter α have clinical relevance for the assessment of age-related muscle changes. Statistical models of muscle heterogeneity may characterize the association between muscle tissue composition estimates and strength better than grayscale measures in samples of community-dwelling older adults.

Linear and nonlinear characterization of microbubbles and tissue using the Nakagami statistical model

The goal of this work is to exploit the statistical signatures for discrimination between biological tissues and contrast microbubbles in order to develop new strategies for contrast imaging and tissue characterization. For this purpose, the efficiency of the Nakagami statistical model, for describing the ultrasonic echoes of both contrast microbubbles and tissues, was investigated. Experimental measurements have been performed using a linear array probe connected to an open research platform. A commercially available in vitro phantom was used to mimic biological tissue in which SonoVue contrast microbubbles were flowing. Experimental ultrasound echoes have been filtered around the transmitted frequency (fundamental at 2.5MHz) and around twice the transmitted frequency (at 5MHz) for 2nd harmonic analysis, and a logarithmic compression was applied. The signals have been analyzed in order to evaluate the Nakagami parameter m, the scaling parameter Ω and the probability density function at both frequencies. Parametric images based on the Nakagami parameters map (Nakagami-mode images) were reconstructed and compared to B-mode images. Contrary to the B-mode image which is influenced by the system settings and user operations, the Nakagami parametric image is only based on the backscattered statistics of the ultrasonic signals in a local phantom. Such an imaging principle allows the Nakagami image to quantify the local scatterer concentrations in the phantom and to extract the backscattering information from the regions of the weakest echoes that may be lost in the conventional B-mode image. Results show that the tissue and microbubbles characterization is more sensitive in the 2nd harmonic mode when a logarithmic transform is used. These results would be useful for improving the ultrasound image quality and contrast detection in nonlinear mode.

Quantitative Assessment of First Annular Pulley and Adjacent Tissues Using High-Frequency Ultrasound

Due to a lack of appropriate image resolution, most ultrasound scanners are unable to sensitively discern the pulley tissues. To extensively investigate the properties of the A1 pulley system and the surrounding tissues for assessing trigger finger, a 30 MHz ultrasound system was implemented to perform in vitro experiments using the hypodermis, A1 pulley, and superficial digital flexor tendon (SDFT) dissected from cadavers. Ultrasound signals were acquired from both the transverse and sagittal planes of each tissue sample. The quantitative ultrasonic parameters, including sound speed, attenuation coefficient, integrated backscatter (IB) and Nakagami parameter (m), were subsequently estimated to characterize the tissue properties. The results demonstrated that the acquired ultrasound images have high resolution and are able to sufficiently differentiate the variations of tissue textures. Moreover, the attenuation slope of the hypodermis is larger than those of the A1 pulley and SDFT. The IB of A1 pulley is about the same as that of the hypodermis, and is very different from SDFT. The m parameter of the A1 pulley is also very different from those of hypodermis and SDFT. This study demonstrated that high-frequency ultrasound images in conjunction with ultrasonic parameters are capable of characterizing the A1 pulley system and surrounding tissues.

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.

A Sparse Reconstruction Framework for Fourier-Based Plane-Wave Imaging

Ultrafast imaging based on plane-wave (PW) insonification is an active area of research due to its capability of reaching high frame rates. Among PW imaging methods, Fourier-based approaches have demonstrated to be competitive compared with traditional delay and sum methods. Motivated by the success of compressed sensing techniques in other Fourier imaging modalities, like magnetic resonance imaging, we propose a new sparse regularization framework to reconstruct highquality ultrasound (US) images. The framework takes advantage of both the ability to formulate the imaging inverse problem in the Fourier domain and the sparsity of US images in a sparsifying domain. We show, by means of simulations, in vitro and in vivo data, that the proposed framework significantly reduces image artifacts, i.e., measurement noise and sidelobes, compared with classical methods, leading to an increase of the image quality.

Heterogeneous Tissue Characterization Using Ultrasound: A Comparison of Fractal Analysis Backscatter Models on Liver Tumors

Assessment of tumor tissue heterogeneity via ultrasound has recently been suggested as a method for predicting early response to treatment. The ultrasound backscattering characteristics can assist in better understanding the tumor texture by highlighting the local concentration and spatial arrangement of tissue scatterers. However, it is challenging to quantify the various tissue heterogeneities ranging from fine to coarse of the echo envelope peaks in tumor texture. Local parametric fractal features extracted via maximum likelihood estimation from five well-known statistical model families are evaluated for the purpose of ultrasound tissue characterization. The fractal dimension (self-similarity measure) was used to characterize the spatial distribution of scatterers, whereas the lacunarity (sparsity measure) was applied to determine scatterer number density. Performance was assessed based on 608 cross-sectional clinical ultrasound radiofrequency images of liver tumors (230 and 378 representing respondent and non-respondent cases, respectively). Cross-validation via leave-one-tumor-out and with different k-fold methodologies using a Bayesian classifier was employed for validation. The fractal properties of the backscattered echoes based on the Nakagami model (Nkg) and its extend four-parameter Nakagami-generalized inverse Gaussian (NIG) distribution achieved best results-with nearly similar performance-in characterizing liver tumor tissue. The accuracy, sensitivity and specificity of Nkg/NIG were 85.6%/86.3%, 94.0%/96.0% and 73.0%/71.0%, respectively. Other statistical models, such as the Rician, Rayleigh and K-distribution, were found to not be as effective in characterizing subtle changes in tissue texture as an indication of response to treatment. Employing the most relevant and practical statistical model could have potential consequences for the design of an early and effective clinical therapy.

Automatic Cataract Hardness Classification Ex Vivo by Ultrasound Techniques

To demonstrate the feasibility of a new methodology for cataract hardness characterization and automatic classification using ultrasound techniques, different cataract degrees were induced in 210 porcine lenses. A 25-MHz ultrasound transducer was used to obtain acoustical parameters (velocity and attenuation) and backscattering signals. B-Scan and parametric Nakagami images were constructed. Ninety-seven parameters were extracted and subjected to a Principal Component Analysis. Bayes, K-Nearest-Neighbours, Fisher Linear Discriminant and Support Vector Machine (SVM) classifiers were used to automatically classify the different cataract severities. Statistically significant increases with cataract formation were found for velocity, attenuation, mean brightness intensity of the B-Scan images and mean Nakagami m parameter (p < 0.01). The four classifiers showed a good performance for healthy versus cataractous lenses (F-measure ≥ 92.68%), while for initial versus severe cataracts the SVM classifier showed the higher performance (90.62%). The results showed that ultrasound techniques can be used for non-invasive cataract hardness characterization and automatic classification.

Feature-based fuzzy connectedness segmentation of ultrasound images with an object completion step

Medical ultrasound (US) image segmentation and quantification can be challenging due to signal dropouts, missing boundaries, and presence of speckle, which gives images of similar objects quite different appearance. Typically, purely intensity-based methods do not lead to a good segmentation of the structures of interest. Prior work has shown that local phase and feature asymmetry, derived from the monogenic signal, extract structural information from US images. This paper proposes a new US segmentation approach based on the fuzzy connectedness framework. The approach uses local phase and feature asymmetry to define a novel affinity function, which drives the segmentation algorithm, incorporates a shape-based object completion step, and regularises the result by mean curvature flow. To appreciate the accuracy and robustness of the methodology across clinical data of varying appearance and quality, a novel entropy-based quantitative image quality assessment of the different regions of interest is introduced. The new method is applied to 81 US images of the fetal arm acquired at multiple gestational ages, as a means to define a new automated image-based biomarker of fetal nutrition. Quantitative and qualitative evaluation shows that the segmentation method is comparable to manual delineations and robust across image qualities that are typical of clinical practice.

Effects of fatty infiltration in human livers on the backscattered statistics of ultrasound imaging

Ultrasound imaging has been widely applied to screen fatty liver disease. Fatty liver disease is a condition where large vacuoles of triglyceride fat accumulate in liver cells, thereby altering the arrangement of scatterers and the corresponding backscattered statistics. In this study, we used ultrasound Nakagami imaging to explore the effects of fatty infiltration in human livers on the statistical distribution of backscattered signals. A total of 107 patients volunteered to participate in the experiments. The livers were scanned using a clinical ultrasound scanner to obtain the raw backscattered signals for ultrasound B-mode and Nakagami imaging. Clinical scores of fatty liver disease for each patient were determined according to a well-accepted sonographic scoring system. The results showed that the Nakagami image can visualize the local backscattering properties of liver tissues. The Nakagami parameter increased from 0.62 ± 0.11 to 1.02 ± 0.07 as the fatty liver disease stage increased from normal to severe, indicating that the backscattered statistics vary from pre-Rayleigh to Rayleigh distributions. A significant positive correlation (correlation coefficient ρ = 0.84; probability value (p value) < 0.0001) exists between the degree of fatty infiltration and the Nakagami parameter, suggesting that ultrasound Nakagami imaging has potentials in future applications in fatty liver disease diagnosis.

Quantitative sonography of basal cell carcinoma

A 30-MHz ultrasonic scanner was used to collect B-scan images together with appropriate radiofrequency echoes from diseased and healthy skin regions of patients with diagnosed basal cell carcinoma and pre-cancerous lesions (actinic keratosis). Radiofrequency data were processed to obtain the attenuation coefficient and statistics of the backscattered echo signal determination (K-distribution and effective density of scatterers [EDS]). The attenuation coefficient was significantly higher for patients with basal cell carcinoma than for healthy patients. Also, the pre-cancerous skin lesions had increased attenuation. The averaged EDS values for cancer lesions were significantly lower than those for pre-cancerous lesions and healthy skin. The successful differentiation between the tissue groups examined suggests the potential value of the attenuation coefficient and EDS for carcinoma characterization.

Changes in backscattered ultrasonic envelope statistics as a function of thrombus age: an in vitro study

It is necessary to determine the age of thrombi in planning clinical treatment for thrombolysis. Ultrasound imaging can potentially be used to evaluate thrombus age in real time. The backscattered signals from thrombi may contain useful information regarding their age. On the basis of the randomness of ultrasound backscattering, this study explored changes in backscattered US statistics as a function of thrombus age. Porcine blood samples were used for the in vitro induction of fresh thrombi (day 0) with hematocrits ranging from 0%-40% and aged thrombi (days 0-8) with a hematocrit of 40%. Each thrombus was imaged using a pulse-echo ultrasound scanner equipped with a 7.5-MHz linear array transducer to acquire raw backscattered signals for B-mode and Nakagami imaging, by which the backscattered statistics were visualized. Hematoxylin and eosin staining and scanning electron microscopy were used to observe the histology of fresh and aged thrombi. The results indicated that a decrease in the number of red blood cells in the thrombus caused by the aging effect was observed in the in vitro model, indicating that the proposed model could simulate the structural changes in the thrombus during aging. Compared with fresh thrombi with various hematocrits, the aged thrombi exhibited a trend toward more substantial decreases in the Nakagami parameter with increasing thrombus age (the Nakagami parameter decreased from 1.1 to 0.6 as thrombus age increased from day 0 to day 8), indicating that thrombus aging causes the backscattered statistics to follow a pre-Rayleigh distribution to a high degree. This finding may be applied to the determination of thrombus age using conventional ultrasound imaging in the future.

Artifact reduction of ultrasound Nakagami imaging by combining multifocus image reconstruction and the noise-assisted correlation algorithm

Several studies have investigated Nakagami imaging to complement the B-scan in tissue characterization. The noise-induced artifact and the parameter ambiguity effect can affect performance of Nakagami imaging in the detection of variations in scatterer concentration. This study combined multifocus image reconstruction and the noise-assisted correlation algorithm (NCA) into the algorithm of Nakagami imaging to suppress the artifacts. A single-element imaging system equipped with a 5 MHz transducer was used to perform the brightness/depth (B/D) scanning of agar phantoms with scatterer concentrations ranging from 2 to 32 scatterers/mm(3). Experiments were also carried out on a mass with some strong point reflectors in a breast phantom using a commercial scanner with a 7.5 MHz linear array transducer operated at multifocus mode. The multifocus radiofrequency (RF) signals after the NCA process were used for Nakagami imaging. In the experiments on agar phantoms, an increasing scatterer concentration from 2 to 32 scatterers/mm(3) led to backscattered statistics ranging from pre-Rayleigh to Rayleigh distributions, corresponding to the increase in the Nakagami parameter measured in the focal zone from 0.1 to 0.8. However, the artifacts in the far field resulted in the Nakagami parameters of various scatterer concentrations to be close to 1 (Rayleigh distribution), making Nakagami imaging difficult to characterize scatterers. In the same scatterer concentration range, multifocus Nakagami imaging with the NCA simultaneously suppressed two types of artifacts, making the Nakagami parameter increase from 0.1 to 0.8 in the focal zone and from 0.18 to 0.7 in the far field, respectively. In the breast phantom experiments, the backscattered statistics of the mass corresponded to a high degree of pre-Rayleigh distribution. The Nakagami parameter of the mass before and after artifact reduction was 0.7 and 0.37, respectively. The results demonstrated that the proposed method for artifact reduction allows a sensitive and effective scatterer characterization by Nakagami imaging.

Computational modeling of photoacoustic signals from mixtures of melanoma and red blood cells

A theoretical approach to model photoacoustic (PA) signals from mixtures of melanoma cells (MCs) and red blood cells (RBCs) is discussed. The PA signal from a cell approximated as a fluid sphere was evaluated using a frequency domain method. The tiny signals from individual cells were summed up obtaining the resultant PA signal. The local signal to noise ratio for a MC was about 5.32 and 5.40 for 639 and 822 nm illuminations, respectively. The PA amplitude exhibited a monotonic rise with increasing number of MCs for each incident radiation. The power spectral lines also demonstrated similar variations over a large frequency range (5-200 MHz). For instance, spectral intensity was observed to be 5.5 and 4.0 dB greater at 7.5 MHz for a diseased sample containing 1 MC and 22,952 RBCs than a normal sample composed of 22,958 RBCs at those irradiations, respectively. The envelope histograms generated from PA signals for mixtures of small numbers of MCs and large numbers of RBCs seemed to obey pre-Rayleigh statistics. The generalized gamma distribution found to facilitate better fits to the histograms than the Rayleigh and Nakagami distributions. The model provides a means to study PAs from mixtures of different populations of absorbers.

Correlation of quantitative texture analysis of cranial ultrasound with later neurobehavior in preterm infants

The purpose of the study was to evaluate the association between a quantitative texture analysis of early neonatal brain ultrasound images and later neurobehavior in preterm infants. A prospective cohort study including 120 preterm (<33 wk of gestational age) infants was performed. Cranial ultrasound images taken early after birth were analyzed in six regions of interest using software based on texture analysis. The resulting texture scores were correlated with the Neonatal Behavioural Assessment Scale (NBAS) at term-equivalent age. The ability of texture scores, in combination with clinical data and standard ultrasound findings, to predict the NBAS results was evaluated. Texture scores were significantly associated with all but one NBAS domain and better predicted NBAS results than clinical data and standard ultrasound findings. The best predictive value was obtained by combining texture scores with clinical information and ultrasound standard findings (area under the curve = 0.94). We conclude that texture analysis of neonatal cranial ultrasound-extracted quantitative features that correlate with later neurobehavior has a higher predictive value than the combination of clinical data with abnormalities in conventional cranial ultrasound.

Modeling the envelope statistics of three-dimensional high-frequency ultrasound echo signals from dissected human lymph nodes

This work investigates the statistics of the envelope of three-dimensional (3D) high-frequency ultrasound (HFU) data acquired from dissected human lymph nodes (LNs). Nine distributions were employed, and their parameters were estimated using the method of moments. The Kolmogorov Smirnov (KS) metric was used to quantitatively compare the fit of each candidate distribution to the experimental envelope distribution. The study indicates that the generalized gamma distribution best models the statistics of the envelope data of the three media encountered: LN parenchyma, fat and phosphate-buffered saline (PBS). Furthermore, the envelope statistics of the LN parenchyma satisfy the pre-Rayleigh condition. In terms of high fitting accuracy and computationally efficient parameter estimation, the gamma distribution is the best choice to model the envelope statistics of LN parenchyma, while, the Weibull distribution is the best choice to model the envelope statistics of fat and PBS. These results will contribute to the development of more-accurate and automatic 3D segmentation of LNs for ultrasonic detection of clinically significant LN metastases.

Statistical analysis of high frequency ultrasonic backscattered signals from basal cell carcinomas

A statistical approach was implemented in the study of histologic characteristics from ex vivo basal cell carcinomas, based on the properties of backscattered acoustic waves, for the purpose of evaluating the method as a diagnostic tool. The study was developed using an ultrasound biomicroscope working at a frequency of 45 MHz. The parameters examined were signal-to-noise ratio (SNR), and shape parameters from the Weibull (b(W)) and generalized gamma (c(GG) and υ(GG)) probability density functions. Twenty-seven carcinomatous skin samples were obtained from volunteer patients and classified into two groups (BCC1 and BCC2) based on the distribution patterns of their tumor nests; also, seven non-tumoral samples were used for comparative purposes. Significant differences between groups were obtained for all studied parameters. The successful differentiation between some tissue groups suggests its potential use for carcinoma characterization.

A new multiplicative denoising variational model based on mth root transformation

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are contaminated by multiplicative noise. Due to the edge-preserving feature of the total variation (TV), variational models with TV regularization have attracted much interest in removing multiplicative noise. However, the fidelity term of the variational model, based on maximum a posteriori estimation, is not convex, and so, it is usually difficult to find a global solution. Hence, the logarithmic function is used to transform the nonconvex variational model to the convex one. In this paper, instead of using the log, we exploit the m th root function to relax the nonconvexity of the variational model. An algorithm based on the augmented Lagrangian function, which has been applied to solve the log transformed convex variational model, can be applied to solve our proposed model. However, this algorithm requires solving a subproblem, which does not have a closed-form solution, at each iteration. Hence, we propose to adapt the linearized proximal alternating minimization algorithm, which does not require inner iterations for solving the subproblems. In addition, the proposed method is very simple and highly parallelizable; thus, it is efficient to remove multiplicative noise in huge SAR images. The proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation.

Using ultrasound Nakagami imaging to assess liver fibrosis in rats

This study explored the feasibility of using the ultrasound Nakagami image to assess the degree of liver fibrosis in rats. The rat has been widely used as a model in investigations of liver fibrosis. Ultrasound grayscale imaging makes it possible to observe fibrotic rat livers in real time. Statistical analysis of the envelopes of signals backscattered from rat livers may provide useful clues about the degree of liver fibrosis. The Nakagami-model-based image has been shown to be useful for characterizing scatterers in tissues by reflecting the echo statistics, and hence the Nakagami image may serve as a functional imaging tool for quantifying rat liver fibrosis. To validate this idea, fibrosis was induced in each rat liver (n=21) by an intraperitoneal injection of 0.5% dimethylnitrosamine. Livers were excised from rats for in vitro ultrasound scanning using a single-element transducer. The backscattered-signal envelopes of the acquired raw ultrasound signals were used for Nakagami imaging. The Metavir score determined by a pathologist was used to histologically quantify the degree of liver fibrosis. It was found that the Nakagami image could be used to distinguish different degrees of liver fibrosis in rats, since the average Nakagami parameter increased from 0.55 to 0.83 as the fibrosis score increased from 0 (i.e., normal) to 4. This correlation may be due to liver fibrosis in rats involving an increase in the concentration of local scatterers and the appearance of the periodic structures or clustering of scatterers that would change the backscattering statistics. The current findings indicate that the ultrasound Nakagami image has great potential as a functional imaging tool to complement the use of the conventional B-scan in animal studies of liver fibrosis.

Modeling ultrasound echoes in skin tissues using symmetric α-stable processes

Starting from the widely accepted point-scattering model, this paper establishes, through analytical developments, that ultrasound signals backscattered from skin tissues converge to a complex Levy flight random process with non- Gaussian α-stable statistics. The envelope signal follows a generalized (heavy-tailed) Rayleigh distribution. It is shown that these signal statistics imply that scatterers have heavy-tailed power-law cross sections. This model generalizes the Gaussian framework and provides a formal representation for a new case of non-Gaussian statistics, in which both the number of scatterers and the variance of their cross sections tend to infinity. In addition, analytical expressions are derived to relate the α-stable parameters to scatterer properties. Simulations show that these expressions can be used as rigorous interpretation tools for tissue characterization. Several experimental results supported by excellent goodness-of-fit tests confirm the proposed analytical model. Finally, these fundamental results set the basis for new echography processing methods and quantitative ultrasound characterization tools.

Effects of cell spatial organization and size distribution on ultrasound backscattering

In ultrasound tissue characterization dealing with cellular aggregates (such as tumors), it can be hypothesized that cell microstructure and spatial distribution dominate the backscatter signal. Effects of spatial organization and size distribution of nuclei in cell aggregates on ultrasound backscatter are examined in this work using 2-D computer simulations. The nuclei embedded in cytoplasm were assumed to be weak scatterers of incident ultrasound waves, and therefore multiple scattering could be neglected. The fluid sphere model was employed to obtain the scattering amplitude for each nucleus and the backscatter echo was generated by summing scattered signals originating from many nuclei. A Monte Carlo algorithm was implemented to generate realizations of cell aggregates. It was found that the integrated backscattering coefficient (IBSC) computed between 10 and 30 MHz increased by about 27 dB for a spatially random distribution of mono-disperse nuclei (radius = 4.5 μm) compared with that of a sample of periodically positioned mono-disperse nuclei. The IBSC also increased by nearly 7 dB (between 10 and 30 MHz) for a spatially random distribution of poly-disperse nuclei (mean radius ± SD = 4.5 ± 1.54 μm) compared with that of a spatially random distribution of mono-disperse nuclei. Two different Gaussian pulses with center frequencies 5 and 25 MHz were employed to study the backscatter envelope statistics. An 80% bandwidth was chosen for each case with approximately 0.32 mm as the full-width at half-maximum (FWHM) for the first pulse and 0.06 mm for the second. The incident beam was approximated as a Gaussian beam (FWHM = 2.11 and 1.05 mm for those pulses, respectively). The backscatter signal envelope histograms generally followed the Rayleigh distribution for mono-disperse and poly-disperse samples. However, for samples with partially ordered nuclei, if the irradiating pulse contained a frequency for which ultrasound wavelength and scatter periodicity became comparable (d ~ λ/2), then the histograms were better fitted by the Nakagami distribution. This study suggests that the shape of an envelope histogram depends upon the periodicity in the spatial organization of scatterers and bandwidth of the ultrasound pulse.

Three-dimensional high-frequency backscatter and envelope quantification of cancerous human lymph nodes

Quantitative imaging methods using high-frequency ultrasound (HFU) offer a means of characterizing biological tissue at the microscopic level. Previously, high-frequency, 3-D quantitative ultrasound (QUS) methods were developed to characterize 46 freshly-dissected lymph nodes of colorectal-cancer patients. 3-D ultrasound radiofrequency data were acquired using a 25.6 MHz center-frequency transducer and each node was inked before tissue fixation to recover orientation after sectioning for 3-D histological evaluation. Backscattered echo signals were processed using 3-D cylindrical regions-of-interest (ROIs) to yield four QUS estimates associated with tissue microstructure (i.e., effective scatterer size, acoustic concentration, intercept and slope). These QUS estimates, obtained by parameterizing the backscatter spectrum, showed great potential for cancer detection. In the present study, these QUS methods were applied to 112 lymph nodes from 77 colorectal and gastric cancer patients. Novel QUS methods parameterizing the envelope statistics of the ROIs using Nakagami and homodyned-K distributions were also developed; they yielded four additional QUS estimates. The ability of these eight QUS estimates to classify lymph nodes and detect cancer was evaluated using receiver operating characteristics (ROC) curves. An area under the ROC curve of 0.996 with specificity and sensitivity of 95% were obtained by combining effective scatterer size and one envelope parameter based on the homodyned-K distribution. Therefore, these advanced 3-D QUS methods potentially can be valuable for detecting small metastatic foci in dissected lymph nodes.

Influence of cell packing by centrifugation on 40-MHz ultrasound backscatter

High-frequency ultrasound (HFUS) signals backscattered from RBL-2H3 cell pellets prepared under different centrifugal forces were analyzed to investigate the packing effect of cell aggregates. The measurements were performed in a pulse-echo setup with a 40-MHz transducer. The changes of ultrasound signals from cell pellet in backscattered power, statistical parameter, and pellet thickness were monitored after centrifugation at between 100g and 1600g. Experimental results showed that the HFUS backscattered power from cell pellets was inversely proportional to centrifugal force and increased to a plateau within 1-2h after centrifugation. The initial thickness of cell pellets decreased with higher centrifugal force, but the changes in thickness and time that took to reach a plateau increased at higher centrifugal force. The envelope statistics of backscattered signals with Nakagami distribution indicates that the centrifugal force and elapsed time after centrifugation affected the backscattering characteristics. The present study suggests that centrifugal force and data acquisition time after cell pellet formation should be considered in in vitro cell packing method with centrifugation to emulate the tissue in vivo.

Quantitative assessments of burn degree by high-frequency ultrasonic backscattering and statistical model

An accurate and quantitative modality to assess the burn degree is crucial for determining further treatments to be properly applied to burn injury patients. Ultrasounds with frequencies higher than 20 MHz have been applied to dermatological diagnosis due to its high resolution and noninvasive capability. Yet, it is still lacking a substantial means to sensitively correlate the burn degree and ultrasonic measurements quantitatively. Thus, a 50 MHz ultrasound system was developed and implemented to measure ultrasonic signals backscattered from the burned skin tissues. Various burn degrees were achieved by placing a 100 °C brass plate onto the dorsal skins of anesthetized rats for various durations ranged from 5 to 20 s. The burn degrees were correlated with ultrasonic parameters, including integrated backscatter (IB) and Nakagami parameter (m) calculated from ultrasonic signals acquired from the burned tissues of a 5 × 1.4 mm (width × depth) area. Results demonstrated that both IB and m decreased exponentially with the increase of burn degree. Specifically, an IB of -79.0 ± 2.4 (mean ± standard deviation) dB for normal skin tissues tended to decrease to -94.0 ± 1.3 dB for those burned for 20 s, while the corresponding Nakagami parameters tended to decrease from 0.76 ± 0.08 to 0.45 ± 0.04. The variation of both IB and m was partially associated with the change of properties of collagen fibers from the burned tissues verified by samples of tissue histological sections. Particularly, the m parameter may be more sensitive to differentiate burned skin due to the fact that it has a greater rate of change with respect to different burn durations. These ultrasonic parameters in conjunction with high-frequency B-mode and Nakagami images could have the potential to assess the burn degree quantitatively.

Effect of adaptive threshold filtering on ultrasonic nakagami parameter to detect variation in scatterer concentration

The Nakagami parameter is associated with the Nakagami distribution estimated from ultrasonic backscattered signals and closely reflects the scatterer concentrations in tissues. There is an interest in exploring the possibility of enhancing the ability of the Nakagami parameter to characterize tissues. In this paper, we explore the effect of adaptive thresholdfiltering based on the noise-assisted empirical mode decomposition of the ultrasonic backscattered signals on the Nakagami parameter as a function of scatterer concentration for improving the Nakagami parameter performance. We carried out phantom experiments using 5 MHz focused and nonfocused transducers. Before filtering, the dynamic ranges of the Nakagami parameter, estimated using focused and nonfocused transducers between the scatterer concentrations of 2 and 32 scatterers/mm3, were 0.44 and 0.1, respectively. After filtering, the dynamic ranges of the Nakagami parameter, using the focused and nonfocused transducers, were 0.71 and 0.79, respectively. The experimental results showed that the adaptive threshold filter makes the Nakagami parameter measured by a focused transducer more sensitive to the variation in the scatterer concentration. The proposed method also endows the Nakagami parameter measured by a nonfocused transducer with the ability to differentiate various scatterer concentrations. However, the Nakagami parameters estimated by focused and nonfocused transducers after adaptive threshold filtering have different physical meanings: the former represents the statistics of signals backscattered from unresolvable scatterers while the latter is associated with stronger resolvable scatterers or local inhomogeneity due to scatterer aggregation.

A critical review and uniformized representation of statistical distributions modeling the ultrasound echo envelope

In ultrasound imaging, various statistical distributions have been proposed to model the first-order statistics of the amplitude of the echo envelope. We present an overview of these distributions based on their compound representation, which comprises three aspects: the modulated distribution (Rice or Nakagami); the modulating distribution (gamma, inverse Gaussian or even generalized inverse Gaussian); and the modulated parameters (the diffuse signal power with or without the coherent signal component or the coherent signal power). This unifying point of view makes the comparison of the various models conceptually easier. In particular, we discuss the implications of the modulated parameters on the mean intensity and the signal-to-noise ratio of the intensity in the case of a vanishing diffuse signal. We conclude that the homodyned K-distribution is the only model among the literature for which the parameters have a physical meaning that is consistent with the limiting case, although the other distributions may fit real data.

Use of nakagami statistics and empirical mode decomposition for ultrasound tissue characterization by a nonfocused transducer

The Nakagami parameter associated with the Nakagami distribution estimated from ultrasonic backscattered signals reflects the scatterer concentration in a tissue. A nonfocused transducer does not allow tissue characterization based on the Nakagami parameter. This paper proposes a new method called the noise-assisted Nakagami parameter based on empirical mode decomposition of noisy backscattered echoes to allow quantification of the scatterer concentration based on data obtained using a nonfocused transducer. To explore the practical feasibility of the proposed method, the current study performed experiments on phantoms and measurements on rat livers in vitro with and without fibrosis induction. The results show that using a nonfocused transducer makes it possible to use the noise-assisted Nakagami parameter to classify phantoms with different scatterer concentrations and different stages of liver fibrosis in rats more accurately than when using techniques based on the echo intensity and the conventional Nakagami parameter. However, the conventional Nakagami parameter and the noise-assisted Nakagami parameter have different meanings: the former represents the statistics of signals backscattered from unresolvable scatterers, whereas the latter is associated with stronger resolvable scatterers or local inhomogeneity caused by scatterer aggregation.

Improved parameter estimates based on the homodyned K distribution

Quantitative techniques based on ultrasound backscatter are promising tools for ultrasonic tissue characterization. There is a need for fast and accurate processing strategies to obtain consistent estimates. An improved parameter estimation algorithm for the homodyned K distribution was developed based on SNR, skewness, and kurtosis of fractional- order moments. From the homodyned K distribution, estimates of the number of scatterers per resolution cell (micro parameter) and estimates of the ratio of coherent to incoherent backscatter signal energy (k parameter) were obtained. Furthermore, angular compounding was used to reduce estimate variance while maintaining spatial resolution of subsequent parameter images. Estimate bias and variance from Monte Carlo simulations were used to quantify the improvement using the new estimation algorithm compared with existing techniques. Improvements due to angular compounding were quantified by the decrease in estimate variance in both simulations and measurements from tissue-mimicking phantoms and by the increase in target contrast. Finally, the new algorithm was used to derive estimates from 2 kinds of mouse mammary tumors for tissue characterization. The new estimation algorithm yielded estimates with lower bias and variance than existing techniques. For a typical pair of parameters (micro = 5 and k = 1), the bias and variance were reduced 67% and 16%, respectively, for the mu parameter estimates and 79% and 37%, respectively, for the k parameter estimates. The use of angular compounding further reduced the estimate variance, e.g., the variance of estimates for the micro parameter from measurements was reduced by a factor of approximately 90 when using 120 angles of view. Finally, statistically significant differences were observed in parameter estimates from 2 kinds of mouse mammary tumors using the new algorithm. These improvements suggest estimating parameters from the backscattered envelope can enhance the diagnostic capabilities of ultrasonic imaging.

Optimally discriminant moments for speckle detection in real B-scan images

The paper presents and evaluates a speckle detection method for B-scan images. This is a fully automatic method and does not require information about the sensor parameters, which is often missing in retrospective studies. The characterization and posterior detection of speckle noise in ultrasound (US) has been regarded as an important research topic in US imaging, for improving signal-to-noise ratio by removing speckle noise and for exploiting speckle correlation information. Most of the existing methods require either manual intervention, the need to know sensor parameters or are based on statistical models which often do not generalize well to B-scans of different imaging areas. The proposed method aims to overcome those limitations. The main novelty of this work is to show that speckle detection can be improved based on finding optimally discriminant low order speckle statistics. In addition, and in contrast with other approaches the presented method is fully automatic and can be efficiently implemented to B-scan images. The method detects speckle patches using an ellipsoid discriminant function which classifies patches based on features extracted from optimally discriminant low order moments of the uncompressed intensity B-scan information. In addition, if the uncompressed signal is not available, we propose and evaluate a method for the estimation of this factor. The computation of low order moments using an optimality criteria, the decompression factor estimation and other key aspects of the method are quantitatively evaluated using both simulated and real (phantom and in vivo) data. Speckle detection results are obtained using again phantom and in vivo studies which show the validity of our approach. In addition, speckle probability images (SPI) are presented which provide valuable information about the distribution of speckle and non-speckle areas in an image. The presented evaluation and results show the effectiveness of our approach. In particular, the need for using discriminant analysis to determine the optimal discriminant power of the statistical moments and that this optimal value strongly depends on the characteristics and imaged tissues in the B-scan data.

Modeling envelope statistics of blood and myocardium for segmentation of echocardiographic images

The objective of this study was to investigate the use of speckle statistics as a preprocessing step for segmentation of the myocardium in echocardiographic images. Three-dimensional (3D) and biplane image sequences of the left ventricle of two healthy children and one dog (beagle) were acquired. Pixel-based speckle statistics of manually segmented blood and myocardial regions were investigated by fitting various probability density functions (pdf). The statistics of heart muscle and blood could both be optimally modeled by a K-pdf or Gamma-pdf (Kolmogorov-Smirnov goodness-of-fit test). Scale and shape parameters of both distributions could differentiate between blood and myocardium. Local estimation of these parameters was used to obtain parametric images, where window size was related to speckle size (5 x 2 speckles). Moment-based and maximum-likelihood estimators were used. Scale parameters were still able to differentiate blood from myocardium; however, smoothing of edges of anatomical structures occurred. Estimation of the shape parameter required a larger window size, leading to unacceptable blurring. Using these parameters as an input for segmentation resulted in unreliable segmentation. Adaptive mean squares filtering was then introduced using the moment-based scale parameter (sigma(2)/mu) of the Gamma-pdf to automatically steer the two-dimensional (2D) local filtering process. This method adequately preserved sharpness of the edges. In conclusion, a trade-off between preservation of sharpness of edges and goodness-of-fit when estimating local shape and scale parameters is evident for parametric images. For this reason, adaptive filtering outperforms parametric imaging for the segmentation of echocardiographic images.

Performance evaluation of ultrasonic Nakagami image in tissue characterization

Conventional ultrasonic B-mode images qualitatively describe tissue structures but are unsuitable for quantitative analyses of scatterer properties. We have recently developed an ultrasonic parametric imaging technique based on the Nakagami statistical distribution that is able to quantify scatterer concentrations. The aim of the present study is to further explore both the behavior of a Nakagami image in characterizing different scatterer structures at different signal-to-noise ratios (SNRs) and the feasibility of Nakagami imaging using a general commercial ultrasound scanner for tissue examinations. Simulations, experiments on a tissue-mimicking phantom and in vitro measurements on a muscle tissue before and after microwave treatment were carried out. The SNR and contrast-to-noise ratio (CNR) were estimated to quantify image performance. The results demonstrate that a Nakagami image can differentiate different scatterer concentrations for single, hypoechoic and hyperechoic targets. Also, a Nakagami image, when combined with an ultrasound scanner, can complement the B-scan to characterize tissue and to identify the region of interest with a larger CNR. However, the noise effect can degrade the performance of a Nakagami image. When the signal SNR decreased to 15 dB in simulations and to 8 dB in experiments, the CNR of the hyperechoic Nakagami image decreased by 4% and 27%, respectively, and that of the hypoechoic one decreased by 42% and 80%, respectively. These results indicate that a Nakagami image behaves well in identifying regions with high scatterer concentrations but does not perform well when both the scatterer concentration and SNR are low.

In vivo ultrasound biomicroscopy of skin: spectral system characteristics and inverse filtering optimization

High-frequency ultrasound (HFUS) in the 20 MHz to 100 MHz range has to meet the opposite requirements of good spatial resolution and of high penetration depth for in vivo ultrasound biomicroscopy (UBM) of skin. The attenuation of water, which serves as sound propagation medium between utilized single element transducers and the skin, becomes very eminent with increasing frequency. Furthermore, the spectra of acquired radio frequency (rf) echo signals change over depth because of the diffracted sound field characteristics. The reduction of the system's center frequency and bandwidth causes a significant loss of spatial resolution over depth. In this paper, the spectral characteristics of HFUS imaging systems and the potential of inverse echo signal filtering for the optimization of pulse-echo measurements is analyzed and validated. A Gaussian model of the system's transfer function, which takes into account the frequency-dependent attenuation of the water path, was developed. Predictions of system performance are derived from this model and compared with measurement results. The design of a HFUS skin imaging system with a 100 MHz range transducer and a broadband driving electronics is discussed. A time-variant filter for inverse rf echo signal filtering was designed to compensate the system's depth-dependent imaging properties. Results of in vivo measurements are shown and discussed.

Statistical distributions of potential interest in ultrasound speckle analysis

Compound statistical modelling of the uncompressed envelope of the backscattered signal has received much interest recently. In this note, a comprehensive collection of models is derived for the uncompressed envelope of the backscattered signal by compounding the Nakagami distribution with 13 flexible families. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. The sensitivity of the models to their various parameters is examined. It is expected that this work could serve as a useful reference and lead to improved modelling of the uncompressed envelope of the backscattered signal.

Imaging local scatterer concentrations by the Nakagami statistical model

The ultrasonic B-mode image is an important clinical tool used to examine the internal structures of the biological tissue. Due to the fact that the conventional B-scans cannot fully reflect the nature of the tissue, some useful quantitative parameters have been applied to quantify the properties of the tissue. Among various possibilities, the Nakagami parameter was demonstrated to have an outstanding ability to detect the variation of the scatterer concentration. This study is aimed to develop a scatterer concentration image based on the Nakagami parameter map to assist in the B-mode image for tissue characterization. In particular, computer simulations are carried out to generate phantoms of different scatterer concentrations and echogenicity coefficients and their B-mode and Nakagami parametric images are compared to evaluate the performance of the Nakagami image in differentiating the properties of the scatterers. The simulated results show that the B-mode image would be affected by the system settings and user operations, whereas the Nakagami parametric image provides a comparatively consistent image result when different diagnosticians use different dynamic ranges and system gains. This is largely because the Nakagami image formation is only based on the backscattered statistics of the ultrasonic signals in local tissues. Such an imaging principle allows the Nakagami image to quantify the local scatterer concentrations in the tissue and to extract the backscattering information from the regions of the weaker echoes that may be lost in the B-mode image. These findings suggest that the Nakagami image can be combined with the use of the B-mode image simultaneously to visualize the tissue structures and the scatterer properties for a better medical diagnosis.

Study of ultrasonic echo envelope based on Nakagami-inverse Gaussian distribution

A new probability density function (pdf) to describe the envelope of the backscattered echoes from tissues is proposed. The combined effect of multiple scattering and randomness arising from local and global variations in scattering cross-section is captured through Nakagami-inverse Gaussian distribution (NIGD). The proposed distribution has the advantage that it has a closed form unlike the realistic Nakagami-lognormal distribution (NLD). The degree of closeness, as measured in terms of Kullback-Leibler (KL) distance between two probability distributions is computed. It is shown that NIGD much more closely approximates NLD compared to Nakagami-gamma distribution (NGD) used to model such problems.

Despeckling of medical ultrasound images

Speckle noise is an inherent property of medical ultrasound imaging, and it generally tends to reduce the image resolution and contrast, thereby reducing the diagnostic value of this imaging modality. As a result, speckle noise reduction is an important prerequisite, whenever ultrasound imaging is used for tissue characterization. Among the many methods that have been proposed to perform this task, there exists a class of approaches that use a multiplicative model of speckled image formation and take advantage of the logarithmical transformation in order to convert multiplicative speckle noise into additive noise. The common assumption made in a dominant number of such studies is that the samples of the additive noise are mutually uncorrelated and obey a Gaussian distribution. The present study shows conceptually and experimentally that this assumption is oversimplified and unnatural. Moreover, it may lead to inadequate performance of the speckle reduction methods. The study introduces a simple preprocessing procedure, which modifies the acquired radio-frequency images (without affecting the anatomical information they contain), so that the noise in the log-transformation domain becomes very close in its behavior to a white Gaussian noise. As a result, the preprocessing allows filtering methods based on assuming the noise to be white and Gaussian, to perform in nearly optimal conditions. The study evaluates performances of three different, nonlinear filters--wavelet denoising, total variation filtering, and anisotropic diffusion--and demonstrates that, in all these cases, the proposed preprocessing significantly improves the quality of resultant images. Our numerical tests include a series of computer-simulated and in vivo experiments.

Monitoring structural changes in cells with high-frequency ultrasound signal statistics

We investigate the use of signal envelope statistics to monitor and quantify structural changes during cell death using an in vitro cell model. Using a f/2.35 transducer (center frequency 20 MHz), ultrasound backscatter data were obtained from pellets of acute myeloid leukemia cells treated with a DNA-intercolating chemotherapy drug, as well as from pellets formed with mixtures of treated and untreated cells. Simulations of signals from pellets of mixtures of cells were generated as a summation of point scatterers. The signal envelope statistics were examined by fitting the Rayleigh and generalized gamma distributions. The fit parameters of the generalized gamma distribution showed sensitivity to structural changes in the cells. The scale parameter showed a 200% increase (p<0.05) between untreated and cells treated for 24 h. The shape parameter showed a 50% increase (p<0.05) over 24 h. Experimental results showed reasonable agreement with simulations. The results indicate that high-frequency ultrasound signal statistics can be used to monitor structural changes within a very low percentage of treated cells in a population, raising the possibility of using this technique in vivo.

The effect of logarithmic compression on estimation of the Nakagami parameter for ultrasonic tissue characterization: a simulation study

Previous studies have demonstrated that the Nakagami parameter estimated using the envelopes of backscattered ultrasound is useful in detecting variations in the concentration of scatterers in tissues. The signal processing in those studies was linear, whereas nonlinear logarithmic compression is routinely employed in existing ultrasonic scanners. We therefore explored the effect of the logarithmic compression on the estimation of the Nakagami parameter in this study. Computer simulations were used to produce backscattered signals of various scatterer concentrations for the estimation of the Nakagami parameters before and after applying the logarithmic compression on the backscattered envelopes. The simulated results showed that the logarithmic compression would move the statistics of the backscattered envelopes towards post-Rayleigh distributions for most scatterer concentrations. Moreover, the Nakagami parameter calculated using compressed backscattered envelopes is more sensitive than that calculated using uncompressed envelopes in differentiating variations in the scatterer concentration, making the former better at quantifying the scatterer concentration in biological tissues.

The effect of transducer characteristics on the estimation of Nakagami paramater as a function of scatterer concentration

The effect of transducer characteristics on the sensitivity of the Nakagami parameter to detect the variation of scatterer concentrations was studied. The rationale for this study stems from our pilot results which showed that the Nakagami parameters, estimated using a nonfocused transducer were not as sensitive as those of measurements using a commercial ultrasonic scanner in previous reports. This discrepancy may be attributed to the effects of transducer characteristics relative to the size of the resolution cell as verified by measurements of phantoms and 2-D computer simulations. The Nakagami parameter as a function of scatterer concentration was calculated using backscattered signals acquired from the scattering medium of different scatterer concentrations ranging from 2 to 32 scatterers/mm(3) using both 5 MHz nonfocused and focused transducers. Experimental and simulation results obtained from the nonfocused transducer represent that their respective Nakagami parameters increased from 1.17 to 1.31 and from 0.82 to 1.01 corresponding to the increase of scatterer concentrations. For the results obtained from the focused transducer, their average Nakagami parameters increased from 0.27 to 0.72 and from 0.33 to 0.81. These consistent results demonstrated that Nakagami parameter estimated using a focused transducer tends to be more sensitive than that by a nonfocused transducer to detect the variation of low scatterer concentration. This difference is fully due to the effect of transducer characteristics associated with the effective number of scatterers in the resolution cell.

Robust deconvolution of high-frequency ultrasound images using higher-order spectral analysis and wavelets

Deconvolution of high-frequency (30-40 MHz) ultrasonic images of human skin was studied in vivo. Separate one-dimensional (1-D) functions for the axial and lateral profiles were first estimated using higher-order spectral methods. Subsequently, deconvolution was implemented us ing a regularized inverse Wiener filtering of the wavelet and scaling coefficients that were obtained after a wavelet decomposition of the RF signals. Deconvolution was first performed in the axial direction, then in the lateral direction. The methods were applied to data obtained from the skin of 16 volunteers using three different transducers. Significant improvements in both the axial and lateral resolutions were obtained in all the cases. Features such as hair follicles in the dermis and fingerprints on the surface of the finger were more clearly displayed in the processed images compared to the original images. The results indicate that the deconvolution method using higher-order spectral methods and wavelet analysis could significantly improve the quality of high-frequency ultrasonic skin images.