P.M. Shankar

Advantages of Subharmonic Over Second Harmonic Backscatter for Contrast-To-Tissue Echo Enhancement

It is shown experimentally that backscatter from two ultrasonic contrast agents suspended in water or saline contains subharmonics of the incident frequency that are stronger than those backscattered at the same incident pressure from chicken breast. It is also shown that the ratio of subharmonic backscattered from contrast to that backscattered from tissue, is stronger than the ratio of backscattered second harmonic. In consequence, blood that contains contrast should be more easily detectable with respect to tissue if the subharmonic, rather than the second harmonic, is used for imaging.

Classification of ultrasonic B-mode images of breast masses using Nakagami distribution

The Nakagami distribution was proposed recently for modeling the echo from tissue. In vivo breast data collected from patients with lesions were studied using this Nakagami model. Chi-square tests showed that the Nakagami distribution is a better fit to the envelope than the Rayleigh distribution. Two parameters, m (effective number) and /spl alpha/ (effective cross section), associated with the Nakagami distribution were used for the classification of breast masses. Data from 52 patients with breast masses/lesions were used in the studies. Receiver operating characteristics were calculated for the classification methods based on these two parameters. The results indicate that these parameters of the Nakagami distribution may be useful in classification of the breast abnormalities. The Nakagami distribution may be a reasonable means to characterize the backscattered echo from breast tissues toward a goal of an automated scheme for separating benign and malignant breast masses.

Ultrasonic tissue characterization using a generalized Nakagami model

The statistics of the backscattered ultrasonic echo from tissue have been described using Rayleigh, K, and Nakagami distributions. The Nakagami and K distributions, each with two parameters, can model the envelope reasonably well. However, a three-parameter distribution is likely to match the envelope of the backscattered echo much better than these two-parameter distributions. Starting with the Nakagami distribution and including an additional parameter to account for the tails of the density function, a generalized Nakagami distribution has been derived. Computer simulation of A-scans and analysis of data collected from tissue-mimicking phantoms show that the generalized Nakagami distribution fits the statistics of the echo of the envelope better than the Nakagami distribution. The parameters of the generalized Nakagami distribution appear to be far more sensitive to the scattering conditions than the parameters of the Nakagami distribution.

Non-Rayleigh statistics of ultrasonic backscattered signals

The statistics of the envelope of the backscattered signal from tissues have been known to vary from the well-known Rayleigh model. The K-distribution is used to model this non-Rayleigh behavior, since the generalized K-distribution encompasses a wide range of distributions like Rayleigh, Lognormal, and Rician. Computer simulations were conducted using a simple one-dimensional discrete scattering model to investigate the properties of the echo envelope. Significant departures from Rayleigh statistics were seen as the scattering cross sections of the scatterers became random. The validity of this model was also tested using data from tissue mimicking phantoms. Results indicate that the density function of the envelope can be modeled by the K-distribution and the parameters of the K-distribution can provide information on the nature of the scattering region in terms of the number as well as the scattering cross sections of the scatterers.<<ETX>>

A compound scattering pdf for the ultrasonic echo envelope and its relationship to K and Nakagami distributions

A compound probability density function (pdf) is presented to describe the envelope of the backscattered echo from tissue. This pdf allows local and global variation in scattering cross sections in tissue. The ultrasonic backscattering cross sections are assumed to be gamma distributed. The gamma distribution also is used to model the randomness in the average cross sections. This gamma-gamma model results in the compound scattering pdf for the envelope. The relationship of this compound pdf to the Rayleigh, K, and Nakagami distributions is explored through an analysis of the signal-to-noise ratio of the envelopes and random number simulations. The three parameter compound pdf appears to be flexible enough to represent envelope statistics giving rise to Rayleigh, K, and Nakagami distributions.

Comparisons of the Rayleigh and K-distribution models using in vivo breast and liver tissue

There is a strong interest in finding out which statistical model is the most appropriate for describing the envelope of the backscattered ultrasonic echoes from different types of tissues. The Rayleigh model is commonly employed, but this requires conditions, such as the presence of large number of randomly located scatterers with fairly uniform cross-sections, that are not always met. However, our research indicates that a model based on the K-distribution may provide a better fit to empirical data over a range of scattering conditions than the standard Rayleigh model. In this study, we looked at the K-distribution as a descriptor of the backscattered envelope of the breast and liver tissues (in vivo). By examining data from various tissue regions, a goodness-of-fit test (a least squares error method) was used to determine whether a Rayleigh or K-distribution model is more appropriate. From a large group of patients and volunteer scans (a total of 72 subjects), the fit between the K-distribution and the data is shown to have a much smaller error than the Rayleigh model.

Use of the K-distribution for classification of breast masses

The K-distribution had been introduced as a valid model to represent the statistics of the envelope of the backscattered echo from phantom and tissue. This paper investigates the efficacy of the parameters of this statistical model; namely, the effective number and the effective cross-section, to characterize breast lesions as benign or malignant. Based on the normalized values of the effective number and the effective scattering cross-section, images containing benign and malignant masses were classified for a data set from 52 patients having breast masses/lesions. The receiver operating characteristic (ROC) curves were then obtained to test the classification based on these two parameters. The results indicate that the parameters of the K-distribution may be useful in classification of the breast lesions as benign and malignant.

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 /spl chi//sup 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.

Application of the compound probability density function for characterization of breast masses in ultrasound B scans

The compound probability density function (pdf) is investigated for the ability of its parameters to classify masses in ultrasonic B scan breast images. Results of 198 images (29 malignant and 70 benign cases and two images per case) are reported and compared to the classification performance reported by us earlier in this journal. A new parameter, the speckle factor, calculated from the parameters of the compound pdf was explored to separate benign and malignant masses. The receiver operating characteristic curve for the parameter resulted in an A(z) value of 0.852. This parameter was combined with one of the parameters from our previous work, namely the ratio of the K distribution parameter at the site and away from the site. This combined parameter resulted in an A(z) value of 0.955. In conclusion, the parameters of the K distribution and the compound pdf may be useful in the classification of breast masses. These parameters can be calculated in an automated fashion. It should be possible to combine the results of the ultrasonic image analysis with those of traditional mammography, thereby increasing the accuracy of breast cancer diagnosis.

Classification of ultrasonic B mode images of the breast using frequency diversity and Nakagami statistics

The parameters of the Nakagami distribution have been utilized in the past to classify lesions in breast tissue as benign or malignant. To avoid the effect of operator-gain settings on the parameters of the Nakagami distribution, normalized parameters were utilized for the classification. The normalized parameter was defined as the ratio of the parameter at the site of the lesion to its average value over several regions away from the site. This technique, however, was very time consuming. In this paper, the application of frequency diversity and compounding is explored to achieve this normalization. Lesions are classified using these normalized parameters at the site. A receiver operating characteristic (ROC) analysis of the parameters of the Nakagami distribution has been conducted before and after compounding on a data set of 60 benign and 65 malignant lesions. The ROC results indicate that this technique can reasonably classify lesions in breast tissue as benign or malignant.