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

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.

Statistical Analysis of Ultrasonic Scattered Echoes Enables the Non-invasive Measurement of Temperature Elevations inside Tumor Tissue during Oncological Hyperthermia

Non-invasive monitoring of temperature elevations inside tumor tissue is imperative for the oncological thermotherapy known as hyperthermia. In the present study, two cancer patients, one with a developing right renal cell carcinoma and the other with pseudomyxoma peritonei, underwent hyperthermia. The two patients were irradiated with radiofrequency current for 40 min during hyperthermia. We report the results of our clinical trial study in which the temperature increases inside the tumor tissues of patients with right renal cell carcinoma and pseudomyxoma peritonei induced by radiofrequency current irradiation for 40 min could be detected by statistical analysis of ultrasonic scattered echoes. The Nakagami shape parameter m varies depending on the temperature of the medium. We calculated the Nakagami shape parameter m by statistical analysis of the ultrasonic echoes scattered from the tumor tissues. The temperature elevations inside the tumor tissues were expressed as increases in brightness on 2-D hot-scale maps of the specific parameter α_mod, indicating the absolute values of the percentage changes in m values. In the α_mod map for each tumor tissue, the brightness clearly increased with treatment time. In quantitative analysis, the mean values of α_mod were calculated. The mean value of α_mod for the right renal cell carcinoma increased to 1.35 dB with increasing treatment time, and the mean value of α_mod for pseudomyxoma peritonei increased to 1.74 with treatment time. The increase in both α_mod brightness and the mean value of α_mod implied temperature elevations inside the tumor tissues induced by the radiofrequency current; thus, the acoustic method is promising for monitoring temperature elevations inside tumor tissues during hyperthermia.

Improved Linear Contrast-Enhanced Ultrasound Imaging via Analysis of First-Order Speckle Statistics

The linear subtraction methods commonly used for preclinical contrast-enhanced imaging are susceptible to registration errors and motion artifacts that lead to reduced contrast-to-tissue ratios. To address this limitation, a new approach to linear contrast-enhanced ultrasound (CEUS) is proposed based on the analysis of the temporal dynamics of the speckle statistics during wash-in of a bolus injection of microbubbles. In the proposed method, the speckle signal is approximated as a mixture of temporally varying random processes, representing the microbubble signal, superimposed onto spatially heterogeneous tissue backscatter in multiple subvolumes within the region of interest. A wash-in curve is constructed by plotting the effective degrees of freedom (EDoFs) of the histogram of the speckle signal as a function of time. The proposed method is, therefore, named the EDoF method. The EDoF parameter is proportional to the shape parameter of the Nakagami distribution. Images acquired at 18 MHz from a murine mammary fat pad breast cancer xenograft model were processed using gold-standard nonlinear amplitude modulation, conventional linear subtraction, and the proposed statistical method. The EDoF method shows promise for improving the robustness of linear CEUS based on reduced frame-to-frame variability compared with the conventional linear subtraction time-intensity curves. Wash-in curve parameters estimated using the EDoF method also demonstrate higher correlation to nonlinear CEUS than the conventional linear method. The conceptual basis of the statistical method implies that EDoF wash-in curves may carry information about vascular complexity that could provide valuable new imaging biomarkers for cancer research.

Echocardiographic speckle reduction comparison

In this paper, a detailed description and comparison of speckle reduction of medical ultrasound, and in particular echocardiography, is presented. Fifteen speckle reduction filters are described in a detailed fashion to facilitate implementation for research and evaluation. The filtering techniques considered include anisotropic diffusion, wavelet denoising, and local statistics. Common nomenclature and notation are adopted, to expedite comparison between approaches. Comparison of the filters is based on their application to simulated images, clinical videos, and a computational requirement analysis. The ultrasound simulation method provides a realistic model of the image acquisition process, and permits the use of a noise-free reference image for comparison. Application of objective quality metrics quantifies the preservation of image edges, overall image distortion, and improvement in image contrast. The computational analysis quantifies the number of operations required for each speckle reduction method. A speed-accuracy analysis of discretization methods for anisotropic diffusion is included. It is concluded that the optimal method is the OSRAD diffusion filter. This method is capable of strong speckle suppression, increasing the average SNRA of the simulated images by a factor of two. This method also shows favorable edge preservation and contrast improvement, and may be efficiently implemented.

Statistical variations of ultrasound signals backscattered from flowing blood

The statistical distributions of ultrasonic signals backscattered from blood have recently been used to characterize hemodynamic properties, such as red blood cell (RBC) aggregation and blood coagulation. However, a thorough understanding of the relationship between blood properties and the statistical behavior of signals backscattered from flowing blood is still lacking. This prompted us to use the statistical parameter to characterize signals backscattered from both whole blood and RBC suspensions at different flow velocities (from 10 to 60 cm/s) and hematocrits (from 20% to 50%) under a steady laminar flow condition. The Nakagami parameter, scaling parameter, backscatter amplitude profile and flow velocity profile across a flow tube were acquired using a 10 MHz focused ultrasonic transducer. The backscattered signal peaked approximately at the centerline of the flow tube due to the effects of RBC aggregation, with the peak value increasing as the flow velocity of whole blood decreased. The Nakagami parameter increased from 0.45 to 0.78 as the flow velocity increased from 10 to 60 cm/s. The probability density function (PDF) of signals backscattered from flowing whole blood conformed with a pre-Rayleigh distribution. The Nakagami parameter was close to 1 for signals backscattered from RBC suspensions at all the flow velocities and hematocrits tested, for which the PDF was Rayleigh distributed. These differences in the statistical distributions of backscattered signals between whole blood and RBC suspensions suggest that variations in the size of dynamic scatterers in the flow affect the shape of the backscattered signal envelope, which should be considered in future statistical models used to characterize blood properties.

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.

Detection of coagulating blood under steady flow by statistical analysis of backscattered signals

The main purpose of this study is to detect blood coagulation under flow condition by analyzing Nakagami statistical model of backscattered signals. The radiofrequency (RF) signals backscattered from flowing blood were measured with a 10-MHz focused transducer. A 30 ml aliquot of blood was circulated in the flow model, and 3 ml of 0.5 M calcium chloride solution was added to induce blood coagulation. The progression in the blood coagulation due to the addition of the calcium chloride solution resulted in the integrated backscatter being increased by 4.2 +/- 0.5 dB, then tended to stabilize as the clot was formed. The Nakagami parameter was approximately 0.75 +/- 0.1 for flowing blood during the initial stage of blood coagulation, and it increased rapidly to its highest level of 2.6 +/- 0.5 during clotting. These experimental results demonstrate the feasibility of using the ultrasonic statistical parameter for detecting blood coagulation from flowing blood and provide a novel method for further monitoring the progress of clotting and thrombosis in vivo.

Comments on ‘The effect of logarithmic compression on the estimation of the Nakagami parameter for ultrasonic tissue characterization’

In a recently published paper (Tsui et al 2005 Phys. Med. Biol. 50 3235-44), the authors demonstrated estimation of the Nakagami parameter of the logcompressed envelopes and the application of such an approach in ultrasonic tissue characterization. The comments in this letter suggest that the authors ignored some important statistical properties of logcompressed data leading to serious errors in their studies and results.