Intervening attenuation affects first-order statistical properties of ultrasound echo signals

Hepatic Steatosis Assessment with Ultrasound Small-Window Entropy Imaging

Nonalcoholic fatty liver disease is a type of hepatic steatosis that is not only associated with critical metabolic risk factors but can also result in advanced liver diseases. Ultrasound parametric imaging, which is based on statistical models, assesses fatty liver changes, using quantitative visualization of hepatic-steatosis-caused variations in the statistical properties of backscattered signals. One constraint with using statistical models in ultrasound imaging is that ultrasound data must conform to the distribution employed. Small-window entropy imaging was recently proposed as a non-model-based parametric imaging technique with physical meanings of backscattered statistics. In this study, we explored the feasibility of using small-window entropy imaging in the assessment of fatty liver disease and evaluated its performance through comparisons with parametric imaging based on the Nakagami distribution model (currently the most frequently used statistical model). Liver donors (n = 53) and patients (n = 142) were recruited to evaluate hepatic fat fractions (HFFs), using magnetic resonance spectroscopy and to evaluate the stages of fatty liver disease (normal, mild, moderate and severe), using liver biopsy with histopathology. Livers were scanned using a 3-MHz ultrasound to construct B-mode, small-window entropy and Nakagami images to correlate with HFF analyses and fatty liver stages. The diagnostic values of the imaging methods were evaluated using receiver operating characteristic curves. The results demonstrated that the entropy value obtained using small-window entropy imaging correlated well with log₁₀(HFF), with a correlation coefficient r = 0.74, which was higher than those obtained for the B-scan and Nakagami images. Moreover, small-window entropy imaging also resulted in the highest area under the receiver operating characteristic curve (0.80 for stages equal to or more severe than mild; 0.90 for equal to or more severe than moderate; 0.89 for severe), which indicated that non-model-based entropy imaging-using the small-window technique-performs more favorably than other techniques in fatty liver assessment.

Effect of ultrasound frequency on the Nakagami statistics of human liver tissues

The analysis of the backscattered statistics using the Nakagami parameter is an emerging ultrasound technique for assessing hepatic steatosis and fibrosis. Previous studies indicated that the echo amplitude distribution of a normal liver follows the Rayleigh distribution (the Nakagami parameter m is close to 1). However, using different frequencies may change the backscattered statistics of normal livers. This study explored the frequency dependence of the backscattered statistics in human livers and then discussed the sources of ultrasound scattering in the liver. A total of 30 healthy participants were enrolled to undergo a standard care ultrasound examination on the liver, which is a natural model containing diffuse and coherent scatterers. The liver of each volunteer was scanned from the right intercostal view to obtain image raw data at different central frequencies ranging from 2 to 3.5 MHz. Phantoms with diffuse scatterers only were also made to perform ultrasound scanning using the same protocol for comparisons with clinical data. The Nakagami parameter-frequency correlation was evaluated using Pearson correlation analysis. The median and interquartile range of the Nakagami parameter obtained from livers was 1.00 (0.98-1.05) for 2 MHz, 0.93 (0.89-0.98) for 2.3 MHz, 0.87 (0.84-0.92) for 2.5 MHz, 0.82 (0.77-0.88) for 3.3 MHz, and 0.81 (0.76-0.88) for 3.5 MHz. The Nakagami parameter decreased with the increasing central frequency (r = -0.67, p < 0.0001). However, the effect of ultrasound frequency on the statistical distribution of the backscattered envelopes was not found in the phantom results (r = -0.147, p = 0.0727). The current results demonstrated that the backscattered statistics of normal livers is frequency-dependent. Moreover, the coherent scatterers may be the primary factor to dominate the frequency dependence of the backscattered statistics in a liver.

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.

Statistical Characterization of the Medical Ultrasound Echo Signals

Medical ultrasound echo signals provide the basic information for obtaining the ultrasonic image in medical ultrasound technology. The statistics of the ultrasound echo signals reveals the systematic structure of the medical ultrasonic image via analyzing the corresponding statistical distributions. A novel statistical distribution, the ascending order K distribution, was proposed here to model the medical ultrasound echo signals. The ascending order K distribution was developed in light of the statistical analysis of the sequential waveforms in the echo signals. Comparison with the previous statistical distributions was made to verify the superiority of the ascending order K distribution. Further discussion showed the determination of the statistical principles for the ultrasound signals can enhance our understanding of the statistical principles of the ultrasound imaging, and thus, facilitate the optimization of the ultrasound image and the tissue identification in the ultrasound diagnosis.

Ultrasound window-modulated compounding Nakagami imaging: Resolution improvement and computational acceleration for liver characterization

Ultrasound Nakagami imaging is an attractive method for visualizing changes in envelope statistics. Window-modulated compounding (WMC) Nakagami imaging was reported to improve image smoothness. The sliding window technique is typically used for constructing ultrasound parametric and Nakagami images. Using a large window overlap ratio may improve the WMC Nakagami image resolution but reduces computational efficiency. Therefore, the objectives of this study include: (i) exploring the effects of the window overlap ratio on the resolution and smoothness of WMC Nakagami images; (ii) proposing a fast algorithm that is based on the convolution operator (FACO) to accelerate WMC Nakagami imaging. Computer simulations and preliminary clinical tests on liver fibrosis samples (n=48) were performed to validate the FACO-based WMC Nakagami imaging. The results demonstrated that the width of the autocorrelation function and the parameter distribution of the WMC Nakagami image reduce with the increase in the window overlap ratio. One-pixel shifting (i.e., sliding the window on the image data in steps of one pixel for parametric imaging) as the maximum overlap ratio significantly improves the WMC Nakagami image quality. Concurrently, the proposed FACO method combined with a computational platform that optimizes the matrix computation can accelerate WMC Nakagami imaging, allowing the detection of liver fibrosis-induced changes in envelope statistics. FACO-accelerated WMC Nakagami imaging is a new-generation Nakagami imaging technique with an improved image quality and fast computation.

Evaluation of thrombolysis by using ultrasonic imaging: an in vitro study

The hematocrit of a thrombus is a key factor associated with the susceptibility to thrombolysis. Ultrasonic imaging is currently the first-line screening tool for thrombus examinations. Different hematocrits result in different acoustical structures of thrombi, which alter the behavior of ultrasonic backscattering. This study explored the relationships among thrombolytic efficiencies, hematocrits, and ultrasonic parameters (the echo intensity and backscattered statistics). Porcine thrombi with different hematocrits, ranging from 0% to 50%, were induced in vitro. An ultrasonic scanner was used to scan thrombi and acquire raw image data for B-mode (echo intensity measurements) and Nakagami imaging (backscattered statistics analysis). Experiments on thrombolysis were performed using urokinase to explore the effect of the hematocrit on thrombolytic efficiency. Results showed that the weight loss ratio of thrombi exponentially decreased as the hematocrit increased from 0% to 50%. Compared with the echo intensity obtained from the conventional B-scan, the Nakagami parameter predicts the weight loss ratio, increasing from 0.6 to 1.2 as the weight loss ratio decreased from 0.67 to 0.26. The current findings suggest that using Nakagami imaging characterizing thrombi provides information of backscattered statistics, which may be associated with the thrombolytic efficiency.

Effects of fatty infiltration in human livers on the backscattered statistics of ultrasound imaging

Ultrasound imaging has been widely applied to screen fatty liver disease. Fatty liver disease is a condition where large vacuoles of triglyceride fat accumulate in liver cells, thereby altering the arrangement of scatterers and the corresponding backscattered statistics. In this study, we used ultrasound Nakagami imaging to explore the effects of fatty infiltration in human livers on the statistical distribution of backscattered signals. A total of 107 patients volunteered to participate in the experiments. The livers were scanned using a clinical ultrasound scanner to obtain the raw backscattered signals for ultrasound B-mode and Nakagami imaging. Clinical scores of fatty liver disease for each patient were determined according to a well-accepted sonographic scoring system. The results showed that the Nakagami image can visualize the local backscattering properties of liver tissues. The Nakagami parameter increased from 0.62 ± 0.11 to 1.02 ± 0.07 as the fatty liver disease stage increased from normal to severe, indicating that the backscattered statistics vary from pre-Rayleigh to Rayleigh distributions. A significant positive correlation (correlation coefficient ρ = 0.84; probability value (p value) < 0.0001) exists between the degree of fatty infiltration and the Nakagami parameter, suggesting that ultrasound Nakagami imaging has potentials in future applications in fatty liver disease diagnosis.

Changes in backscattered ultrasonic envelope statistics as a function of thrombus age: an in vitro study

It is necessary to determine the age of thrombi in planning clinical treatment for thrombolysis. Ultrasound imaging can potentially be used to evaluate thrombus age in real time. The backscattered signals from thrombi may contain useful information regarding their age. On the basis of the randomness of ultrasound backscattering, this study explored changes in backscattered US statistics as a function of thrombus age. Porcine blood samples were used for the in vitro induction of fresh thrombi (day 0) with hematocrits ranging from 0%-40% and aged thrombi (days 0-8) with a hematocrit of 40%. Each thrombus was imaged using a pulse-echo ultrasound scanner equipped with a 7.5-MHz linear array transducer to acquire raw backscattered signals for B-mode and Nakagami imaging, by which the backscattered statistics were visualized. Hematoxylin and eosin staining and scanning electron microscopy were used to observe the histology of fresh and aged thrombi. The results indicated that a decrease in the number of red blood cells in the thrombus caused by the aging effect was observed in the in vitro model, indicating that the proposed model could simulate the structural changes in the thrombus during aging. Compared with fresh thrombi with various hematocrits, the aged thrombi exhibited a trend toward more substantial decreases in the Nakagami parameter with increasing thrombus age (the Nakagami parameter decreased from 1.1 to 0.6 as thrombus age increased from day 0 to day 8), indicating that thrombus aging causes the backscattered statistics to follow a pre-Rayleigh distribution to a high degree. This finding may be applied to the determination of thrombus age using conventional ultrasound imaging in the future.

Artifact reduction of ultrasound Nakagami imaging by combining multifocus image reconstruction and the noise-assisted correlation algorithm

Several studies have investigated Nakagami imaging to complement the B-scan in tissue characterization. The noise-induced artifact and the parameter ambiguity effect can affect performance of Nakagami imaging in the detection of variations in scatterer concentration. This study combined multifocus image reconstruction and the noise-assisted correlation algorithm (NCA) into the algorithm of Nakagami imaging to suppress the artifacts. A single-element imaging system equipped with a 5 MHz transducer was used to perform the brightness/depth (B/D) scanning of agar phantoms with scatterer concentrations ranging from 2 to 32 scatterers/mm(3). Experiments were also carried out on a mass with some strong point reflectors in a breast phantom using a commercial scanner with a 7.5 MHz linear array transducer operated at multifocus mode. The multifocus radiofrequency (RF) signals after the NCA process were used for Nakagami imaging. In the experiments on agar phantoms, an increasing scatterer concentration from 2 to 32 scatterers/mm(3) led to backscattered statistics ranging from pre-Rayleigh to Rayleigh distributions, corresponding to the increase in the Nakagami parameter measured in the focal zone from 0.1 to 0.8. However, the artifacts in the far field resulted in the Nakagami parameters of various scatterer concentrations to be close to 1 (Rayleigh distribution), making Nakagami imaging difficult to characterize scatterers. In the same scatterer concentration range, multifocus Nakagami imaging with the NCA simultaneously suppressed two types of artifacts, making the Nakagami parameter increase from 0.1 to 0.8 in the focal zone and from 0.18 to 0.7 in the far field, respectively. In the breast phantom experiments, the backscattered statistics of the mass corresponded to a high degree of pre-Rayleigh distribution. The Nakagami parameter of the mass before and after artifact reduction was 0.7 and 0.37, respectively. The results demonstrated that the proposed method for artifact reduction allows a sensitive and effective scatterer characterization by Nakagami imaging.

Ultrasonic measurement of scleral cross-sectional strains during elevations of intraocular pressure: method validation and initial results in posterior porcine sclera

BACKGROUND

Scleral biomechanical properties may be important in the pathogenesis and progression of glaucoma. The goal of this study is to develop and validate an ultrasound method for measuring cross-sectional distributive strains in the sclera during elevations of intraocular pressure (IOP).

METHOD OF APPROACH

Porcine globes (n = 5) were tested within 24 hs postmortem. The posterior scleral shells were dissected and mounted onto a custom-built pressurization chamber. A high-frequency (55-MHz) ultrasound system (Vevo660, VisualSonics Inc., Toronto) was employed to acquire the radio frequency data during scans of the posterior pole along both circumferential and meridian directions. The IOP was gradually increased from 5 to 45 mmHg. The displacement fields were obtained from correlation-based ultrasound speckle tracking. A least-square strain estimator was used to calculate the strains in both axial and lateral directions. Experimental validation was performed by comparing tissue displacements calculated from ultrasound speckle tracking with those induced by an actuator. Theoretical analysis and simulation experiments were performed to optimize the ultrasound speckle tracking method and evaluate the accuracy and signal-to-noise ratio (SNR) in strain estimation.

RESULTS

Porcine sclera exhibited significantly larger axial strains (e.g., -5.1 ± 1.5% at 45 mmHg, meridian direction) than lateral strains (e.g., 2.2 ± 0.7% at 45 mmHg, meridian direction) during IOP elevations (P's < 0.01). The strain magnitudes increased nonlinearly with pressure increase. The strain maps displayed heterogeneity through the thickness. The lateral strains were significantly smaller in the circumferential direction than the meridian direction at 45 mmHg (P < 0.05). Experimental validation showed that the ultrasound speckle tracking method was capable of tracking displacements at the accuracy of sub-micron to micron. Theoretical analysis predicted the dependence of the strain estimation SNR on the strain level, as well as signal processing parameters such as kernel size. Simulation results showed that ultrasound speckle tracking had a high accuracy for estimating strains of 1-5% and a high SNR for strains of 0.5-5%.

CONCLUSIONS

A new experimental method based on ultrasound speckle tracking has been developed for obtaining cross-sectional strain maps of the posterior sclera. This method provides a useful tool to examine distributive strains through the thickness of the sclera during elevations of IOP.

Characterization of lamina propria and vocal muscle in human vocal fold tissue by ultrasound Nakagami imaging

PURPOSE

A number of ultrasound techniques have been applied to identify the biomechanical properties of the vocal folds. These conventional ultrasound methods, however, are not capable of visually mapping the concentration of collagen and elastic fibers in the vocal folds in the form of a parametric image. This study proposes to use a statistical parameter, the Nakagami factor estimated from the statistical distribution of the ultrasonic signals backscattered from tissues, as a means for parametric imaging of the biomechanical properties of the vocal folds.

METHODS

The ultrasonic backscattered signals were acquired from four larynges (eight vocal folds) obtained from individuals without vocal fold pathology for constructing the Nakagami images. The textures of the Nakagami image in the lamina propria (LP) and the vocal muscle (VM) were observed and compared. The average and standard deviation of the Nakagami parameter for the LP and the VM were also calculated.

RESULTS

The results showed that the Nakagami parameter of the LP is larger than that of the VM. Moreover, the LP and the VM have different shading features in the Nakagami images. It was found that the Nakagami parameter may depend on the concentration of collagen and elastic fibers, demonstrating that the Nakagami imaging may allow visual differentiation between the LP and the VM in the vocal folds.

CONCLUSIONS

Current preliminary results suggested that the high-frequency Nakagami imaging may allow real-time visual characterization of the vocal fold tissues in clinical routine examinations.

Effect of adaptive threshold filtering on ultrasonic nakagami parameter to detect variation in scatterer concentration

The Nakagami parameter is associated with the Nakagami distribution estimated from ultrasonic backscattered signals and closely reflects the scatterer concentrations in tissues. There is an interest in exploring the possibility of enhancing the ability of the Nakagami parameter to characterize tissues. In this paper, we explore the effect of adaptive thresholdfiltering based on the noise-assisted empirical mode decomposition of the ultrasonic backscattered signals on the Nakagami parameter as a function of scatterer concentration for improving the Nakagami parameter performance. We carried out phantom experiments using 5 MHz focused and nonfocused transducers. Before filtering, the dynamic ranges of the Nakagami parameter, estimated using focused and nonfocused transducers between the scatterer concentrations of 2 and 32 scatterers/mm3, were 0.44 and 0.1, respectively. After filtering, the dynamic ranges of the Nakagami parameter, using the focused and nonfocused transducers, were 0.71 and 0.79, respectively. The experimental results showed that the adaptive threshold filter makes the Nakagami parameter measured by a focused transducer more sensitive to the variation in the scatterer concentration. The proposed method also endows the Nakagami parameter measured by a nonfocused transducer with the ability to differentiate various scatterer concentrations. However, the Nakagami parameters estimated by focused and nonfocused transducers after adaptive threshold filtering have different physical meanings: the former represents the statistics of signals backscattered from unresolvable scatterers while the latter is associated with stronger resolvable scatterers or local inhomogeneity due to scatterer aggregation.

Elastography using harmonic ultrasonic imaging: a feasibility study

Tissue Harmonic Imaging (THI) is a relatively new modality that has had a significant impact in the ultrasound field. In the recent past, imaging the mechanical properties of tissues using elastography has also gained great interest. In this paper, we investigate the feasibility of combining these two state-of-the-art ultrasound-imaging modalities. The performance of elastograms obtained using harmonic ultrasonic signals is studied with simulations and compared to the performance of conventional elastograms using standard statistical methods. Experiments are used as a proof of the technical feasibility of generating tissue-harmonic elastograms using experimental harmonic signals. The results of our simulation study indicate that all image quality factors considered in this study (elastographic signal-to-noise ratio, elastographic contrast-to-noise ratio and spatial resolution) may be improved when using harmonic ultrasonic signals, provided that the ultrasound system is characterized by high bandwidth, high sampling frequency and large lateral sampling. Preliminary experimental results suggest that it is technically feasible to generate experimental elastograms using harmonic signals, provided that the sonographic signal-to-noise ratio of the pre- and postcompression harmonic frames is sufficiently high to guarantee reliable values of correlation.

Use of nakagami statistics and empirical mode decomposition for ultrasound tissue characterization by a nonfocused transducer

The Nakagami parameter associated with the Nakagami distribution estimated from ultrasonic backscattered signals reflects the scatterer concentration in a tissue. A nonfocused transducer does not allow tissue characterization based on the Nakagami parameter. This paper proposes a new method called the noise-assisted Nakagami parameter based on empirical mode decomposition of noisy backscattered echoes to allow quantification of the scatterer concentration based on data obtained using a nonfocused transducer. To explore the practical feasibility of the proposed method, the current study performed experiments on phantoms and measurements on rat livers in vitro with and without fibrosis induction. The results show that using a nonfocused transducer makes it possible to use the noise-assisted Nakagami parameter to classify phantoms with different scatterer concentrations and different stages of liver fibrosis in rats more accurately than when using techniques based on the echo intensity and the conventional Nakagami parameter. However, the conventional Nakagami parameter and the noise-assisted Nakagami parameter have different meanings: the former represents the statistics of signals backscattered from unresolvable scatterers, whereas the latter is associated with stronger resolvable scatterers or local inhomogeneity caused by scatterer aggregation.

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.

The effect of transducer characteristics on the estimation of Nakagami paramater as a function of scatterer concentration

The effect of transducer characteristics on the sensitivity of the Nakagami parameter to detect the variation of scatterer concentrations was studied. The rationale for this study stems from our pilot results which showed that the Nakagami parameters, estimated using a nonfocused transducer were not as sensitive as those of measurements using a commercial ultrasonic scanner in previous reports. This discrepancy may be attributed to the effects of transducer characteristics relative to the size of the resolution cell as verified by measurements of phantoms and 2-D computer simulations. The Nakagami parameter as a function of scatterer concentration was calculated using backscattered signals acquired from the scattering medium of different scatterer concentrations ranging from 2 to 32 scatterers/mm(3) using both 5 MHz nonfocused and focused transducers. Experimental and simulation results obtained from the nonfocused transducer represent that their respective Nakagami parameters increased from 1.17 to 1.31 and from 0.82 to 1.01 corresponding to the increase of scatterer concentrations. For the results obtained from the focused transducer, their average Nakagami parameters increased from 0.27 to 0.72 and from 0.33 to 0.81. These consistent results demonstrated that Nakagami parameter estimated using a focused transducer tends to be more sensitive than that by a nonfocused transducer to detect the variation of low scatterer concentration. This difference is fully due to the effect of transducer characteristics associated with the effective number of scatterers in the resolution cell.

Computer-aided classification of breast masses in ultrasonic B-scans using a multiparameter approach

Classification of breast masses in ultrasonic B-scan images is undertaken using a multiparameter approach. The parameters are generated on the basis of a non-Rayleigh statistic model of the backscattered envelope from the breast tissue. They can be computed automatically with minimal clinical intervention once the location of the mass is known. A new discriminant is developed that combines these parameters linearly. It is seen that this new discriminant performs classification of masses into benign or malignant better than the classification by any one of the individual parameters. The data set studied consisted of 99 cases (70 patients with benign masses and 29 patients with malignant masses). The areas under the receiver operating characteristic (ROC) curves (Az) and statistical attributes of the areas were studied to establish the enhancement in performance. The Az value after combining all the parameters was found to be 0.8701. Upon combining this parameter with the level of suspicion (LOS) scores of a radiologist, the performance is further enhanced with an area under the (empirical) ROC of 0.94 having an operating point at a sensitivity of 0.965 and specificity of 0.87. It is suggested that this automated approach may hold promise as a means of classifying breast masses.

Trade-offs between the axial resolution and the signal-to-noise ratio in elastography

Elastography involves tracking the ultrasonic A-mode signals before and after mechanical compression of tissue to form a computed image of the local strains undergone by various tissue components. The quality of the strain estimates in elastography is typically quantified using factors such as the elastographic SNR (SNR(e)), contrast-to-noise ratio (CNR(e)), and the spatial resolution. These quality factors depend on the mechanical parameters (such as the applied strain and the boundary conditions), the acoustic parameters (such as the sonographic SNR, the center frequency, and the bandwidth), and the signal-processing parameters (such as the window length and the window separation). Theoretical developments in elastography have established functional relationships between the SNR(e) and CNR(e) and these parameters. Similarly, simulations have established empirical relationships between the axial resolution and the acoustic and signal-processing parameters. We find that a trade-off exists between the achievable SNR(e) (CNR(e)) and the axial resolution in elastography and that the trade-off occurs only with respect to the signal-processing parameters. Theoretical work on the spatial resolution accompanied with simulations and experiments were used to confirm such an observation. The trade-off between the SNR(e) (CNR(e)) and the resolution was found to be nonlinear, with large improvements in the SNR(e) being possible at the expense of small reductions in the axial resolution. All the quality factors improve with the acoustic parameters, which suggests the preferred use of transducers with high absolute bandwidths and center frequencies.

A zero-crossing strain estimator for elastography

A novel zero-crossing tracking strain estimator (ZCT) has been developed for elastography. This technique is based on tracking the zero-crossings between the pre- and postcompression A-lines, and does not require global or adaptive A-line stretching. For multicompression elastography, ZCT can be implemented as a tracking scheme, where a temporal track of the zero-crossings between successive radiofrequency (RF) A-lines is obtained, or as an averaging scheme, where a cumulation of the interframe strains is performed, to yield high elastographic signal-to-noise ratio (SNR). Other advantages of the scheme include fast processing and its potential to be implemented in hardware. The limitations of the technique are the need for small compression steps due to lack of robustness when large compression steps (> 3% applied compression) are used. Simulations and experiments were performed to illustrate its utility as an alternative strain-estimation technique. This technique provides lower SNR but higher contrast-to-noise ratio (CNR) than the conventional strain-estimation techniques in elastography.

The effects of digitization on the elastographic signal-to-noise ratio

In elastography, the tissue under investigation is compressed and the resulting strain is estimated from the gradient of the displacement (time-delay) estimates. The displacements are typically estimated by cross-correlating the radiofrequency (RF) ultrasound signals of the pre- and postcompressed tissue. One of the parameters used to quantify the resulting quality of the elastogram is the elastographic signal-to-noise ratio (SNR(e)). For a uniformly elastic target (a single elastic modulus), the dependence of the SNR(e) on the applied strain has a bandpass characteristic that has been termed the strain filter. Theoretical expressions for the upper bound on the strain filter were developed earlier. Yet, simulated as well as experimental strain filters derived from uniformly elastic phantoms deviate from these upper bounds. The failure to achieve the upper bounds could be partially attributed to the fact that, in both simulations and experiments, the RF signals used to compute the TDEs are sampled and quantized. Using simulated models of uniformly elastic phantoms, a study of the dependence of the strain filter on the quantization and sampling rates was performed. The results indicated that the strain filter improves with both the sampling rate and the quantization, as expected. A theoretical analysis was done to incorporate quantization as a derating factor to the strain filter.

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.

Analysis of an adaptive strain estimation technique in elastography

Elastography is based on the estimation of strain due to tissue compression or expansion. Conventional elastography involves computing strain as the gradient of the displacement (time-delay) estimates between gated pre- and postcompression signals. Uniform temporal stretching of the postcompression signals has been used to reduce the echo-signal decorrelation noise. However, a uniform stretch of the entire postcompression signal is not optimal in the presence of strain contrast in the tissue and could result in loss of contrast in the elastogram. This has prompted the use of local adaptive stretching techniques. Several adaptive strain estimation techniques using wavelets, local stretching and iterative strain estimation have been proposed. Yet, a quantitative analysis of the improvement in quality of the strain estimates overconventional strain estimation techniques has not been reported. We propose a two-stage adaptive strain estimation technique and perform a quantitative comparison with the conventional strain estimation techniques in elastography. In this technique, initial displacement and strain estimates using global stretching are computed, filtered and then used to locally shift and stretch the postcompression signal. This is followed by a correlation of the shifted and stretched postcompression signal with the precompression signal to estimate the local displacements and hence the local strains. As proof of principle, this adaptive stretching technique was tested using simulated and experimental data.