Nakagami-m Parametric Imaging for Atherosclerotic Plaque Characterization Using the Coarse-to-Fine Method

The Nakagami model was used to analyze the statistical differences in ultrasound backscattered signals between different plaque types. To improve image resolution, Nakagami-m parametric imaging using the coarse-to-fine method based on the maximum likelihood estimation (CTF-BOW) was proposed for atherosclerotic plaque characterization. Simulation results confirmed that the CTF-BOW method significantly outperforms the sliding window method in precision, smoothness and resolution. Preliminary in vivo results (n = 45) indicated that the ranges of the m parameters for calcified, mixed and echolucent plaques are, respectively, 0.2852-0.5225, 0.6532-0.8784 and 0.8908-1.4011, with no overlap. Results revealed that the CTF-BOW method significantly improves image resolution without sacrificing accuracy and can distinguish between calcified, mixed and echolucent plaques. Moreover, it was found that the parameter m is related to the composition of the plaque, indicating that Nakagami-m parametric imaging has the potential to characterize plaques.

Detecting changes in ultrasound backscattered statistics by using Nakagami parameters: Comparisons of moment-based and maximum likelihood estimators

The Nakagami distribution is an approximation useful to the statistics of ultrasound backscattered signals for tissue characterization. Various estimators may affect the Nakagami parameter in the detection of changes in backscattered statistics. In particular, the moment-based estimator (MBE) and maximum likelihood estimator (MLE) are two primary methods used to estimate the Nakagami parameters of ultrasound signals. This study explored the effects of the MBE and different MLE approximations on Nakagami parameter estimations. Ultrasound backscattered signals of different scatterer number densities were generated using a simulation model, and phantom experiments and measurements of human liver tissues were also conducted to acquire real backscattered echoes. Envelope signals were employed to estimate the Nakagami parameters by using the MBE, first- and second-order approximations of MLE (MLE₁ and MLE₂, respectively), and Greenwood approximation (MLE_gw) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE₁, the MLE₂ and MLE_gw enabled more stable parameter estimations with small sample sizes. Notably, the required data length of the envelope signal was 3.6 times the pulse length. The phantom and tissue measurement results also showed that the Nakagami parameters estimated using the MLE₂ and MLE_gw could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE₂ and MLE_gw are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization.

Window-modulated compounding Nakagami imaging for ultrasound tissue characterization

Ultrasound Nakagami parametric imaging is a useful tool for tissue characterization. Previous literature has suggested using a square with side lengths corresponding to 3 times the transducer pulse length as the minimum window for constructing the Nakagami image. This criterion does not produce sufficiently smooth images for the Nakagami image to characterize homogeneous tissues. To improve image smoothness, we proposed window-modulated compounding (WMC) Nakagami imaging based on summing and averaging the Nakagami images formed using sliding windows with varying window side lengths from 1 to N times the transducer pulse length in 1 pulse length step. Simulations (the number densities of scatterers: 2-16 scatterers/mm(2)) and experiments on fully developed speckle phantoms (the scatterer diameters: 20-106 μm) were conducted to suggest an appropriate number of frames N and to evaluate the image smoothness and resolution by analyzing the full width at half maximum (FWHM) of the parameter distribution and the widths of the image autocorrelation function (ACF), respectively. In vivo ultrasound measurements on rat livers without and with cirrhosis were performed to validate the practical performance of the WMC Nakagami image in tissue characterization. The simulation results showed that using a range of N from 7 to 10 as the number of frames for image compounding reduces the estimation error to less than 5%. Based on this criterion, the Nakagami parameter obtained from the WMC Nakagami image increased from 0.45 to 0.95 after increasing the number densities of scatterers from 2 to 16 scatterers/mm(2). The FWHM of the parameter distribution (bins=40) was 13.5±1.4 for the Nakagami image and 9.1±1.43 for the WMC Nakagami image, respectively (p-value<.05). The widths of the ACF for the Nakagami and WMC Nakagami images were 454±5.36 and 458±4.33, respectively (p-value>.05). In the phantom experiments, we also found that the FWHM of the parameter distribution for the WMC Nakagami image was smaller than that of the conventional Nakagami image (p-value<.05), and there was no significant difference of the ACF width between the Nakagami and WMC Nakagami images (p-value>.05). In the animal experiments, the Nakagami parameters obtained from the WMC Nakagami image for normal and cirrhotic rat livers were 0.62±0.08 and 0.92±0.07, respectively (p-value<.05). The results demonstrated that the WMC technique significantly improved the image smoothness of Nakagami imaging without resolution degradation, giving Nakagami model-based imaging the ability to visualize scatterer properties with enhanced image quality.