Tissue characterization based on scatterer number density estimation

Local Burr distribution estimator for speckle statistics

Speckle statistics in ultrasound and optical coherence tomography have been studied using various distributions, including the Rayleigh, the K, and the more recently proposed Burr distribution. In this paper, we expand on the utility of the Burr distribution by first validating its theoretical framework with numerical simulations and then introducing a new local estimator to characterize sample tissues of liver, brain, and skin using optical coherence tomography. The spatially local estimates of the Burr distribution's power-law or exponent parameter enable a new type of parametric image. The simulation and experimental results confirm the potential for various applications of the Burr distribution in both basic science and clinical realms.

A robust time delay estimation method for ultrasonic echo signals and elastography

Modern medicine cannot ignore the significance of elastography in diagnosis and treatment plans. Despite improvements in accuracy and spatial resolution of elastograms, robustness against noise remains a neglected attribute. A method that can perform in a satisfactory manner under noisy conditions may prove useful for various elastography methods. Here, we propose a method based on eigenvalue decomposition (EVD). In this method, the estimated time delay is defined as the index of the maximum element in the eigenvector that corresponds to the minimum eigenvalue in the covariance matrix of the received signal. Moreover, the implementation of the least-squares (LS) solution and the lower-upper (LU) decomposition contributes to improving the speed of computation and the accuracy of the estimation under low signal-to-noise ratio (SNR) conditions. To assess the performance of the proposed algorithm, it is evaluated along with generalized cross-correlation (GCC) and EVD. The simulation results clearly confirm that the jitter variance achieved in the proposed algorithm outperforms GCC and EVD in the proximity of the Cramer-Rau lower band. Moreover, our algorithm provides satisfactory performance in terms of variance and bias against sub-sample delay at low SNRS. According to the experimental results, the calculated values of the elastographic signal-to-noise ratio (SNRe) and the elastographic contrast-to-noise ratio (CNRe) of the proposed algorithm were 16.7 and 20.09, respectively, clearly better than the values of the other two methods. Furthermore, the proposed algorithm offers less execution time (about 30% of GCC), with a computational complexity equal to GCC and better than EVD.

Burr, Lomax, Pareto, and Logistic Distributions from Ultrasound Speckle

After 100 years of theoretical treatment of speckle patterns from coherent illumination, there remain some open questions about the nature of ultrasound speckle from soft vascularized tissues. A recent hypothesis is that the fractal branching vasculature is responsible for the dominant echo pattern from organs such as the liver. In that case, an analysis of cylindrical scattering structures arranged across a power law distribution of sizes is warranted. Using a simple model of echo strength and basic transformation rules from probability, we derive the first order statistics of speckle considering the amplitude, the intensity, and the natural log of amplitude. The results are given by long tailed distributions that have been studied in the statistics literature for other fields. Examples are given from simulations and animal studies, and the theoretical fit to these preliminary data support the overall framework as a plausible model for characterizing ultrasound speckle statistics.

Speckle from branching vasculature: dependence on number density

Purpose: Recent theories examine the role of the fractal branching vasculature as a primary site of Born scattering from soft normal tissues. These derivations postulate that the first-order statistics of speckle from soft tissue, such as the liver, thyroid, and prostate, will follow a Burr distribution with a power law parameter that can be related back to the underlying power law, which governs the branching network. However, the issue of scatterer spacing, or the number of cylindrical vessels per sample volume of the interrogating pulse, has not been directly addressed. Approach: Speckle statistics are examined with a 3D simulation that varies the number density and the governing power law parameter of an ensemble of different sized cylinders. Several in vivo liver scans are also analyzed for confirmation across different conditions. Results: The Burr distribution is found to be an appropriate model for the histogram of amplitudes from speckle regions, where the parameters track the underlying power law and scatterer density conditions. These results are also tested in a more general model of rat liver scans in normal versus abnormal conditions, and the resulting Burr parameters are also found to be appropriate and sensitive to underlying scatterer distributions. Conclusions: These preliminary results suggest that the classical Burr distribution may be useful in the quantification of scattering of ultrasound from soft vascularized tissues and as a tool in tissue characterization.

The first order statistics of backscatter from the fractal branching vasculature

The issue of speckle statistics from ultrasound images of soft tissues such as the liver has a long and rich history. A number of theoretical distributions, some related to random scatterers or fades in optics and radar, have been formulated for pulse-echo interference patterns. This work proposes an alternative framework in which the dominant echoes are presumed to result from Born scattering from fluid-filled vessels that permeate the tissue parenchyma. These are modeled as a branching, fractal, self-similar, multiscale collection of cylindrical scatterers governed by a power law distribution relating to the number of branches at each radius. A deterministic accounting of the echo envelopes across the scales from small to large is undertaken, leading to a closed form theoretical formula for the histogram of the envelope of the echoes. The normalized histogram is found to be related to the classical Burr distribution, with the key power law parameter directly related to that of the number density of vessels vs diameter, frequently reported in the range of 2 to 4. Examples are given from liver scans to demonstrate the applicability of the theory.

Anisotropic diffusion filter with memory based on speckle statistics for ultrasound images

Ultrasound (US) imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle, which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods. With the aim of alleviating the effect of speckle, many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection. Most of the state-of-the-art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature. However, the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes. This loss of information is even magnified due to the iterative process of some speckle filters, e.g., diffusion filters, which tend to produce over-filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process. In this paper, we propose an anisotropic diffusion filter with a probabilistic-driven memory mechanism to overcome the over-filtering problem by following a tissue selective philosophy. In particular, we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues, by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved. Results both in synthetic and real US images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures, which are removed by the state-of-the-art filters.

Ex vivo study of quantitative ultrasound parameters in fatty rabbit livers

Nonalcoholic fatty liver disease (NAFLD) affects more than 30% of Americans, and with increasing problems of obesity in the United States, NAFLD is poised to become an even more serious medical concern. At present, accurate classification of steatosis (fatty liver) represents a significant challenge. In this study, the use of high-frequency (8 to 25 MHz) quantitative ultrasound (QUS) imaging to quantify fatty liver was explored. QUS is an imaging technique that can be used to quantify properties of tissue giving rise to scattered ultrasound. The changes in the ultrasound properties of livers in rabbits undergoing atherogenic diets of varying durations were investigated using QUS. Rabbits were placed on a special fatty diet for 0, 3, or 6 weeks. The fattiness of the livers was quantified by estimating the total lipid content of the livers. Ultrasonic properties, such as speed of sound, attenuation, and backscatter coefficients, were estimated in ex vivo rabbit liver samples from animals that had been on the diet for varying periods. Two QUS parameters were estimated based on the backscatter coefficient: effective scatterer diameter (ESD) and effective acoustic concentration (EAC), using a spherical Gaussian scattering model. Two parameters were estimated based on the backscattered envelope statistics (the k parameter and the μ parameter) according to the homodyned K distribution. The speed of sound decreased from 1574 to 1565 m/s and the attenuation coefficient increased from 0.71 to 1.27 dB/cm/MHz, respectively, with increasing fat content in the liver. The ESD decreased from 31 to 17 μm and the EAC increased from 38 to 63 dB/cm(3) with increasing fat content in the liver. A significant increase in the μ parameter from 0.18 to 0.93 scatterers/mm(3) was observed with increasing fat content in the liver samples. The results of this study indicate that QUS parameters are sensitive to fat content in the liver.

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.

Application of a real-time, calculable limiting form of the Renyi entropy for molecular imaging of tumors

Previously, we reported new methods for ultrasound signal characterization using entropy, H(f); a generalized entropy, the Renyi entropy, I(f)(r); and a limiting form of Renyi entropy suitable for real-time calculation, I(f),(infinity). All of these quantities demonstrated significantly more sensitivity to subtle changes in scattering architecture than energy-based methods in certain settings. In this study, the real-time calculable limit of the Renyi entropy, I(f),(infinity), is applied for the imaging of angiogenic murine neovasculature in a breast cancer xenograft using a targeted contrast agent. It is shown that this approach may be used to reliably detect the accumulation of targeted nanoparticles at five minutes post-injection in this in vivo model.

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.

Ultrasound motion estimation using a hierarchical feature weighting algorithm

The quality of ultrasonic images is usually influenced by speckle noises and the temporal decorrelation of the speckle patterns. Most traditional motion estimation algorithms are not suitable for speckle tracking in medical ultrasonic images which usually have a low signal-to-noise ratio (SNR). This paper proposes a new motion estimation algorithm that is designed for assessing the dense velocity fields of soft tissue motion in a sequence of ultrasonic B-mode images. We design a hierarchical maximum a posteriori estimator together with an adaptive feature weighted mechanism to estimate the motion field from an ultrasonic image sequence. The proposed method was compared with several existing motion estimation methods via a series of experiments with synthetic speckle image sequences. Performance was also tested on in vivo ultrasonic images. The experimental results show that motion can be assessed with better accuracy than other methods for synthetic speckle images and a good correspondence with clinicians' observations has also been achieved for clinical ultrasonic images.

A parametric imaging approach for the segmentation of ultrasound data

When an ultrasonic examination is performed, a segmentation tool would often be very useful, either for the detection of pathologies, the early diagnosis of cancer or the follow-up of the lesions. Such a tool must be both reliable and accurate. However, because of the relatively reduced quality of ultrasound images due to the speckled texture, the segmentation of ultrasound data is a difficult task. We have previously proposed to tackle the problem using a multiresolution Bayesian region-based algorithm. For computation time purposes, a multiresolution version has been implemented. In order to improve the quality of the segmentation, we propose to perform the segmentation not only from the envelope image but to combine more information about the properties of the tissues in the segmentation process. Several acoustical parameters have thus been computed, either directly from the images or from the radio-frequency (RF) signal. In a previous study, two parametric images were involved in the segmentation process. The parameter represented the integrated backscatter (IBS) and the mean central frequency (MCF), which is a measurement related to the attenuation of ultrasound waves in the media. In this study, parameters representative of the scattering conditions in the tissue are evaluated in the multiparametric segmentation process. They are extracted from the K-distribution (alpha,b) and the Nakagami distribution (m,Omega) and are related to the local density of scatterers (alpha,m), the size of the scatterers (b) and the backscattering properties of the medium (Omega). The acoustical features are calculated locally on a sliding window. This procedure allows to built parametric mapping representing the particular characteristics of the medium. To test the influence of the acoustical parameters in the segmentation process, a set of numerical phantoms has been computed using the Field software developed by J.A. Jensen. Each phantom consists in two regions with two different acoustical properties: the density of scatterers and the scattering amplitude. From both the simulated RF signals and envelope images, the parameters have been computed; their relevance to represent a particular characteristic of the medium is evaluated. The segmentation has been processed for each phantom. The ability of each parameter to improve the segmentation results is validated. A agar-gel phantom has also been created, in order to test the accuracy of the parameters in conditions closer to the in vivo ultrasound imaging. This phantom contains four inclusions with different concentrations of silica. A B&K ultrasound device provides the RF data. The quantification of the segmentation quality is based on the rate of correctly classified pixels and it has been computed for all the parameters either from the field images or the phantom images. The large improvement in the segmentation results obtained reveals that the multiparametric segmentation scheme proposed in this study can be a reliable tool for the processing of noisy ultrasound data.

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

The statistics of envelope of high-frequency ultrasonic backscatter signals from in vivo normal human dermis and subcutaneous fat were studied. The capability of six probability distributions (Rayleigh, Rician, K, Nakagami, Weibull, and Generalized Gamma) to model empirical envelope data was studied using the Kolmogorov-Smirnov (KS) goodness of fit statistic. The parameters of all the distributions were obtained using the maximum likelihood method. It was found that the Generalized Gamma distribution with two shape parameters provided the best fit among all the distributions in terms of the KS goodness of fit. The K and Weibull distributions also modeled the envelope statistics well. The Rayleigh and Rician distributions provided poorer fits. The parameters of the Generalized Gamma distribution, however, showed a larger variability than those of the other distributions. The intersubject variability in the estimated parameters of all the distributions was found to be comparable to the intrasubject variability. Fat was seen to exhibit significantly more pre-Rayleigh behavior compared to the dermis. The parameters of the Generalized Gamma distribution also showed significant differences between the dermis at the forearm and fingertip regions.

On modeling biomedical ultrasound RF echoes using a power-law shot-noise model

We propose a new model for the RF ultrasound echo, namely the power-law shot-noise process. Based on this model, the in-phase and quadrature components of the echo are shown to exhibit 1/f beta-type spectral behavior, in a sense that is defined in the paper. The envelope also exhibits this type of spectral behavior, but with a different exponent. This result explains the experimental observations by other researchers of the power-law trend of the RF echo spectrum. Although the shot-noise model has been used in the past for modeling the RF echo, this is the first time that a power-law impulse response filter is used and that the resulting 1/f beta-type spectral behavior of the RF echo has been investigated. The model parameters are linked to tissue characteristics, such as scatterer density and attenuation; thus, they have the potential to be used as tissue characterization features. The validity of the proposed model is tested based on a database of 100 clinical ultrasound images of the breast.

Detection of lines and boundaries in speckle images--application to medical ultrasound

This paper describes an approach to boundary detection in ultrasound speckle based on an image enhancement technique. The enhancement algorithm works by filtering the image with "sticks," short line segments which are varied in orientation to achieve the maximum projected value at each point. The statistical properties of this approach have been described in an earlier paper; in this work we present three significant extensions to improve the performance of the basic method. First, we investigate the effect of varying the size and shape of the sticks. We show that these variations affect the performance of the algorithm in very fundamental ways, for example by making it more or less sensitive to thinner or more tightly curving boundaries. Second, we present a means of improving the performance of this technique by estimating the distribution function of the orientation of the line passing through each point. Finally, we show that images can be "stained" for easier visual interpretation by applying to each pixel a false color whose hue is related to the orientation of the most prominent line segment at that point. Examples are given to illustrate the performance of the different settings on a single image.

Combined ultrasound and near infrared diffused light imaging in a test object

We have investigated the use of combining near infrared (NIR) diffuse light and ultrasound imaging methods to increase the detection sensitivity and to reduce the false alarm rate in small target detection. A line-of-sight optical projection through a test object is identified from an amplitude null and a sharp phase transition produced by diffusive waves originating from two in-phase (initial phase 0 degrees ) and out-of-phase (initial phase 180 degrees ) light emitting diode sources. This line-of-sight is scanned across a scattering phantom. A complete ultrasound B-scan image is recorded at each projected line in the optical scan. Each acoustic image plane is bisected by the optical beam path and lies in the optical scan plane. The scattering phantom simulates acoustic and optical properties of homogeneous tissue. A single small cylinder-like object simulating some acoustic and optical breast tumor properties is inserted at various places in the scattering phantom. With this single object, the optical scanning identifies the line-of-sight passing through the simulated tumor quite well. Most of these simulated tumors were at or below the threshold for acoustic detection and were not seen consistently with unguided ultrasound. For tests in which a target was apparently detected optically, the selected line-of-sight was indicated in each of three adjacent ultrasound images. Two radiologist observers were statistically more accurate (83%) in identifying the target location on the optically-selected ultrasound images than in the unmarked images (52%). That is, in these single-targets of homogeneous scattering background, the optical technique usually provided the correct line-of-sight, and ultrasound generally showed the location along that line.

Tissue-characterization of the prostate using radio frequency ultrasonic signals

In this paper, we will present a complete method and system for the detection of prostatic carcinoma, providing color-coded images of the estimated probability of malignancy by processing radio-frequency ultrasonic echo signals. For this, a hardware setup based on a conventional diagnostic sonograph was realized. The image-processing software works on ultrasound images automatically segmented into regions of about 3x3.5 mm. System-dependent effects, as well as tissue attenuation, were measured and compensated for. Tissue-characterisation parameters, which have been used successfully by other authors, were calculated for each segment. To demonstrate the methods of selection of relevant parameters and comparison of different classifiers, a first clinical study using data of 33 patients with local prostatic carcinoma was performed. For these patients, location and extent of the carcinoma were known from histological findings after radical prostatectomy. Classifiers investigated during the study were: the linear and quadratic Bayes classifier, a nearest neighbor classifier, and several classifiers based on Kohonen-maps. The best classifier was used to calculate color-coded result images. Applying a threshold of 50% to the estimated probability of malignancy, produced the encouraging results of 82 and 88% for sensitivity and specificity, respectively.

Analysis and classification of tissue with scatterer structure templates

Back-scattered ultrasonic signals provide scatterer structure information. Large-scale structures, such as tissue and tumor boundaries, typically create significant amplitude differences that reveal boundaries in conventional intensity images. Small-scale structures typically result in textures observed over regions of the intensity image. This paper describes the generalized spectrum (GS) for characterizing small-scale scatterer structures and applies it to analyze scatterer structures in a class of malignant and benign breast masses. Methods are presented for scaling and normalizing the GS to reduce effects from system response, overlaying tissue, and variability from noncritical structures. Results from a limited clinical study demonstrate an application of using the GS to discriminate between benign and malignant breast masses that contain internal echoes. Sections of rf A-scans in 41 breast mass regions were taken from 26 patients. A GS analysis was applied to determine critical structural properties between a class of fibroadenoma and carcinoma masses. Classifiers designed using significant structure differences identified by the GS analysis achieved approximately 82% true-positive and 10% false-positive rates.

Assessment of bone density using ultrasonic backscatter

The goal of this project was to investigate the utility of ultrasonic backscatter for the assessment of bone status. Ultrasound offers a low-cost, portable, nonionizing alternative or complement to common X-ray- or radioisotope (gamma ray)-based methods of bone densitometry. Ultrasonic backscatter may provide useful information not revealed by ultrasonic attenuation and sound-speed densitometers. Backscatter is sensitive to microstructural variations in acoustic impedance and should therefore provide information regarding architecture (which is related to fracture risk), as well as density. Ultrasonic backscatter at 2.25 MHz and CT bone densitometric data have been acquired from 10 healthy human volunteers. The degree of correlation between CT and ultrasonic backscatter is high (r = 0.87, p < 0.001). The envelope signal-to-noise ratio was 1.81 +/- 0.08 (mean +/- standard deviation). This suggests that the number of scatterers per resolution cell is large, the radiofrequency signal approximately obeys circular Gaussian statistics, and the envelope obeys Rayleigh statistics. These results indicate promise for ultrasonic backscatter as a substitute for or an adjunct to other ultrasonic measurements (attenuation and sound speed) and X-ray measurements for the assessment of bone status.

Statistical properties of estimates of signal-to-noise ratio and number of scatterers per resolution cell

Elementary theory underlying the relationship between the number of scatterers per resolution cell (N) and echo intensity signal-to-noise ratio (SNR) is reviewed. A relationship between the probability density functions for estimates of N and SNR2 is derived. This relationship is validated using a computer simulation. Phantom and in vitro experiments are described. In one set of experiments on phantoms, empirical distributions of estimates of N and SNR2 are measured and compared to theoretical predictions. The utility of SNR2 for discrimination of phantoms with different values for N is assessed using receiver operating characteristic (ROC) analysis. In another set of experiments, the frequency dependence of the SNR2 estimate is investigated for a two-component phantom and for excised dog kidney. It is shown that the frequency dependence of the SNR can help to identify the presence of two or more scattering components that are spatially mixed. With regard to kidney data, measurements performed both parallel and perpendicular to the predominant nephron orientation are reported. The observed anisotropy is compared to the anisotropy of backscatter coefficient encountered in previous investigations.

Studies on ultrasonic scattering from quasi-periodic structures

This study extends the work done on nonuniform phase statistics by including additional results based on quasi-periodic scattering. Three parameters are used to predict the presence of regular structure within the region of interest. The signal-to-noise ratio of phase and the chi (2) statistic resulting from conducting a goodness of fit test are two parameters used to verify whether the phase signal followed a uniform distribution. A third parameter, the power spectral density (PSD), was studied and its ability to provide information on the level of periodicity present was analyzed. Computer simulations and experiments on tissue mimicking phantoms were carried out, the results of which indicate that the parameters introduced in this paper have good potential in providing a better understanding of scattering from a collection of quasi-periodic scatterers.

Studies on the use of non-Rayleigh statistics for ultrasonic tissue characterization

The research groups at Drexel University and Thomas Jefferson University had proposed the use of non-Rayleigh statistics for tissue characterization. Previous work based on the hypothesis that the envelope of the backscattered echosignal from abnormal regions of the tissue is more likely to be K-distributed than Rayleigh distributed, used the parameter of the K-distribution, M, to distinguish between regions containing benign or malignant masses and normal ones. In this work the B-scan breast images of 19 patients were studied using this approach. Previous studies have also been extended to exploit the existence of non-uniform phase characteristics of the echosignal from scatterers with some regular spacings, such as those in a periodic or quasi-periodic alignment. Computer simulations were carried out to show that the phase statistics deviate significantly from uniform in the range of (0, 2 pi) if the imaging region contained a number of periodically aligned (regular lattice) scatterers along with a collection of randomly distributed scatterers resulting in a quasi-periodic arrangement. This methodology was then applied to B-scan images of the breasts to distinguish between benign and malignant masses. If benign lesions show some sort of quasi-periodic or regular structures in the tissue, they will present non-uniform phase characteristics while more randomly structured malignant masses will have uniform phase characteristics. It is seen that the K-distribution may be used to identify the abnormal regions in the breast images and information on the phase may be used to further separate the abnormal regions into benign and malignant ones.

A model for ultrasonic scattering from tissues based on the K distribution

A model for the backscattered ultrasound echo from tissues is presented. The model takes into account the fact that the range cell being insonified may contain only a few scatterers and the number may not be large enough to justify the use of a Gaussian model which results in Rayleight statistics for the echo. Furthermore, the model also considers the case where the echogenicity of the scatterers in the range cell may not be uniform, the lack of uniformity resulting from variations in scattering cross-sections produced by the chemical as well as biochemical changes brought on by the presence of disease, growth of benign or malignant tumours, etc. The model is developed from the fundamental principles of scattering using the results available in radar. This new model results in a two-parameter distribution, namely the K distribution for the echo, thereby making it possible to gain information on the number as well as scattering cross-sections of the scatterers in the range cell. The model is extended to include the effects due to the presence of scatterers having some regular or periodic orientation in the range cell, resulting in the so-called generalized K distribution which approximates to Rayleight, Rician, or Gaussian under various limiting cases. Results of computer simulations and experiments on tissue-mimicking phantoms are also provided, which strongly suggest that this new model offers potential for tissue characterization.

Detection of diffuse liver disease by quantitative echography: dependence on a Priori choice of parameters

Quantitative acoustic parameters and image texture parameters were used in a linear discriminant analysis. This analysis was applied to detect retrospectively the classes of diffuse liver disease against a population of normal livers. Three different sets of parameters were employed. The first set was selected by the authors, and the other two were taken from the literature. The area under the Receiver Operating Characteristic (ROC) (or percentage correct classification) obtained with the first set ranged from 88% to 97%, depending on the disease class. It is concluded that the first-order statistical parameters of the image texture (diffuse scattering model) together with the slope of the attenuation coefficient are the most important parameters. As an alternative to the texture parameters, the backscattering parameters (second set of parameters) also yielded a comparably high score. The texture analysis involving structural scattering (third set of parameters) produced a lower percentage of correct classification. The overall conclusion is that the methods devised might be used for prospective diagnosis.

Correlations between acoustic and texture parameters from RF and B-mode liver echograms

Radio frequency (RF) echograms were acquired from human subjects without liver pathology (n = 126), who were in the range of 20 to 84 years of age. After appropriate correction for the equipment settings and performance characteristics, acoustospectrographic parameters were estimated. The data were corrected for the frequency-dependent attenuation and then software demodulated. Image texture parameters were calculated based on the assumption of a particular tissue model, and purely statistical parameters were also estimated. The data thus obtained from each subject were corrected for the age trend that was assessed in an earlier publication by the authors. A total of 18 parameters was considered and the correlations were analyzed. It is concluded that nine parameters could be identified which did not strongly correlate with each other. This conclusion is supported by analysis of correlation data from patients. In a companion paper, a discriminant analysis is reported, based on the selected parameters (nine) and applied to the differentiation between normals and various classes of diffuse liver disease.

Use of non-Rayleigh statistics for the identification of tumors in ultrasonic B-scans of the breast

A model for the scattering of ultrasound from breast tissue is proposed. The model is based on the use of non-Rayleigh statistics, specifically the K distribution to describe the backscattered echo from the tissue. A multiparameter test based on this model has been designed to characterize the tissue. The data from the B-scan images of the breasts of 6 different patients were analyzed using this model. The results indicate that the non-Rayleigh statistics seem to be useful in characterizing and identifying malignant, benign, and normal tissue regions.