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 (μ 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 to 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 two 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 (μ=5 and k=1), the bias and variance were reduced 67% and 16%, respectively, for the μ 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 μ 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 two 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.

Conventional B-mode imaging in ultrasound consists of displaying the log-compressed envelope of the backscattered signal. While clinical ultrasonic B-mode images have good spatial resolution, i.e., better than a millimeter, the contrast resolution of ultrasonic B-mode images is typically low. However, additional information is contained in the ultrasonic backscattered signal, which can be used to create images related to tissue microstructure. Because diagnosis of disease is typically based on histological examination of tissue microstructure, the ability to quantify and describe tissue microstructure through ultrasound may result in improved diagnostic capabilities of ultrasound. Tissue-mimicking phantoms and animal models of breast cancer were used to assess the ability of novel ultrasonic imaging techniques to quantify microstructure. Four parameters were extracted from the ultrasonic backscattered signal and related to the microstructure. The effective scatterer diameter (ESD) and the effective acoustic concentration (EAC) parameters were based on modeling the frequency dependence of the backscatter. The k parameter (which quantifies the periodicity of scatterer locations) and the mu parameter (which estimates the number of scatterers per resolution cell) were based on modeling the statistics of the backscattered envelope. Images constructed with these parameters resulted in an increase in contrast between diseased tissue and normal tissues but at the expense of spatial resolution. Specifically, in simulation, quantitative ultrasound (QUS) increased the contrast-to-noise ratio (CNR) between targets and background by more than 10 times in some cases. Statistically significant differences were observed between three kinds of tumors using the ESD, EAC, and k parameters. QUS imaging was also improved with the addition of coded excitation. A novel coded excitation technique was used that improved the variance of estimates over conventional pulsing methods, e.g- , the variance of ESD estimates were reduced by a factor of up to 10.

We study a nonlinear evolutionary partial differential equation that can be viewed as a generalization of the heat equation where the temperature gradient is a priori bounded but the heat flux provides merely $$L^1$$ L 1 -coercivity. Applying higher differentiability techniques in space and time, choosing a special weighted norm (equivalent to the Euclidean norm in $$\mathbb {R}^d$$ R d ), incorporating finer properties of integrable functions and flux truncation techniques, we prove long-time and large-data existence and uniqueness of weak solution, with an $$L^1$$ L 1 -integrable flux, to an initial spatially-periodic problem for all values of a positive model parameter. If this parameter is smaller than $$2/(d+1)$$ 2 / ( d + 1 ) , where d denotes the spatial dimension, we obtain higher integrability of the flux. As the developed approach is not restricted to a scalar equation, we also present an analogous result for nonlinear parabolic systems in which the nonlinearity, being the gradient of a strictly convex function, gives an a-priori $$L^\infty $$ L ∞ -bound on the gradient of the unknown solution.

No abstract

Envelope statistics from ultrasound backscatter based on the homodyned K distribution were used to characterize organizational patterns of tissue microstructure in three rodent models of breast cancer: a mouse mammary carcinoma, a mouse mammary sarcoma, and a rat fibroadenoma. The homodyned K distribution was used to model the amplitude of the envelope of backscattered ultrasound yielding two parameters to characterize tissues: one related to the effective scatterer density and the other related to periodicity of scatterer locations. Ten tumors of each of the three kinds of tumors were scanned. Envelope statistics model parameters were estimated for regions of interest measuring 1 × 1 mm in each of the tumor images. These estimates were then averaged together for each tumor. A linear combination of the two estimated parameters was derived for each tumor in order to obtain a lumped parameter for discriminating between the different kinds of tumors. This linear combination yielded the following (mean±SD): carcinomas 9.58±1.17, sarcomas 12.01±0.78, and fibroadenomas 11.66±1.15. These estimates were statistically significant in distinguishing carcinomas from sarcomas (p<0.05) and carcinomas from fibroadenomas (p<0.05), but a statistically significant difference was not observed between the sarcomas and fibroadenomas (p=0.44). [Work supported by NIH CA111289.]