Attenuation Estimation Method Research Articles

Depth-resolved attenuation coefficient estimation from optical coherence tomography data in case of incomplete signal attenuation in the imaging depth range

Attenuation coefficient estimation from optical coherent tomography (OCT) data is one of the emerging methods for additional information extraction from the OCT data. With the reasonable assumptions of uniform proportion of the light, scattered backwards, relative to the light, scattered in all directions and the assumption of complete light attenuation within the imaging depth range, the attenuation coefficient can be estimated in every pixel of the OCT data volume, i.e. with the depth resolution. In the present paper the numerically effective method for lifting the second assumption was proposed. With numerical simulations and experiments it was shown, that the proposed method allows attenuation coefficient estimation even if OCT signal was not completely attenuated within the imaging depth range. Since the proposed method lifts one of the requirements for depth-resolved attenuation coefficient estimation, it allows the extension of the depth-resolved attenuation estimation method to the new applications.

Lithium battery attenuation estimation method based on curvature analysis and segmented high-order Gaussian fitting

Lithium battery has been widely used in various areas, and accurate estimation of battery states is vital to efficient and safe application of batteries. Of all the states, life attenuation is essential to batteries. To improve the estimation accuracy of lithium battery life attenuation, a battery attenuation estimation method based on curvature analysis and segmented Gaussian fitting is designed. The designed method firstly utilizes Cardinal spline curve to smooth the battery attenuation curve. Then, a curvature analysis method is used to segment the life attenuation curve into different sections. Then, a least square linear fitting is used to fit the segmented curves. Except the segmented curve with better linear fitting performance, the remaining segmented curves are fitted with high-order Gaussian fitting. Experiments indicates that the designed method can accurately express the characteristics of different battery life stages.

Seismic Attenuation Estimation Using an Enhanced Log Spectral Ratio Method

Seismic attenuation estimation is a significant task for characterizing reservoirs and improving the resolution of seismic data. The logarithmic spectral ratio (LSR) is one of the widely used tools for seismic attenuation estimation. However, how to select a suitable frequency bandwidth for the LSR is a difficult task, especially for field data. Moreover, field data are often contained kinds of noises, which makes seismic attenuation estimation difficult and unstable. We proposed an enhanced LSR (ELSR) workflow to estimate seismic attenuation. First, we built a sparse S-transform (SST) to obtain a sparse time-frequency (TF) spectrum of the analyzed seismic trace. Then, based on the SST spectrum, we introduced an ELSR workflow to estimate seismic attenuation. It should be noticed that we provided an adaptive frequency band selection for the LSR. To demonstrate the effectiveness of the proposed workflow, we apply it on both synthetic and field data. Compared with the results from several traditional attenuation estimation methods, the proposed ELSR provides a more stable and more accurate attenuation estimation result and offers the potentials in improving the resolution of post-stacked seismic data.

Seismic Attenuation Estimation via Unscaled Time–Frequency Representation and Divergence

Time-frequency (TF) representations achieve better TF localization properties compared with Fourier transform (FT) and perform well for Q estimation via methods such as spectral ratio (SR), centroid frequency shift (CFS), and peak frequency shift (PFS). However, these attenuation estimation methods all require a given frequency band or certain source wavelet assumptions, also heavily interfered by noise. In addition, the resolution and accuracy of TF spectrum also determine whether the extracted spectrum can accurately characterize the frequency properties of seismic wavelets, thus affecting the accuracy of seismic estimation results. In this study, we propose an unscaled generalized S-transform (UGST), which achieves better TF localization while avoiding the dominant frequency shift of S-transform (ST). Next, we build a Q estimation method based on the weighted Kullback-Leibler (WKL) divergence and then give an estimation workflow combined with the proposed UGST. Note that the proposed workflow does not need to make specific wavelet assumptions or consider the frequency band selection, which is also proved to be not sensitive to noise. Finally, to demonstrate the effectiveness of the proposed workflow, we apply it to synthetic and field data. Compared with the contrastive methods, our proposed workflow can achieve more accurate estimation results and show better noise immunity, which can benefit delineating seismic hydrocarbon reservoirs.

Spectral-ratio tomography for seismic attenuation estimation

AbstractWhen measuring surface seismic data, an accurate attenuation estimation method is necessary to compensate for the energy loss and phase distortion of seismic waves, and is also beneficial for further quantitative amplitude analyses and reservoir parameter predictions. For conventional Q-estimation methods (such as the log spectral-ratio (LSR) method and attenuated traveltime tomography), accuracy may be affected by the differences between the overburden ray paths of two selected reflections (we call it the overburden effect). In this study, we design a more accurate Q-tomography method to estimate Q-values (both in the overburden and target layer simultaneously) without overburden assumptions. We address the overburden effect by using an inversion method, which allows us to separate attenuation effects from the overburden through the traveltime differences in the tomography grid cells. We test the method on synthetic data and prove its feasibility and effectiveness by applying it to field data.

Fully automatic liver attenuation estimation combing CNN segmentation and morphological operations.

Manually tracing regions of interest (ROIs) within the liver is the de facto standard method for measuring liver attenuation on computed tomography (CT) in diagnosing nonalcoholic fatty liver disease (NAFLD). However, manual tracing is resource intensive. To address these limitations and to expand the availability of a quantitative CT measure of hepatic steatosis, we propose the automatic liver attenuation ROI-based measurement (ALARM) method for automated liver attenuation estimation. The ALARM method consists of two major stages: (a) deep convolutional neural network (DCNN)-based liver segmentation and (b) automated ROI extraction. First, liver segmentation was achieved using our previously developed SS-Net. Then, a single central ROI (center-ROI) and three circles ROI (periphery-ROI) were computed based on liver segmentation and morphological operations. The ALARM method is available as an open source Docker container (https://github.com/MASILab/ALARM). Two hundred and forty-six subjects with 738 abdomen CT scans from the African American-Diabetes Heart Study (AA-DHS) were used for external validation (testing), independent from the training and validation cohort (100 clinically acquired CT abdominal scans). From the correlation analyses, the proposed ALARM method achieved Pearson correlations=0.94 with manual estimation on liver attenuation estimations. When evaluating the ALARM method for detection of nonalcoholic fatty liver disease (NAFLD) using the traditional cut point of <40HU, the center-ROI achieved substantial agreements (Kappa=0.79) with manual estimation, while the periphery-ROI method achieved "excellent" agreement (Kappa=0.88) with manual estimation. The automated ALARM method had reduced variability compared to manual measurements as indicated by a smaller standard deviation. We propose a fully automated liver attenuation estimation method termed ALARM by combining DCNN and morphological operations, which achieved "excellent" agreement with manual estimation for fatty liver detection. The entire pipeline is implemented as a Docker container which enables users to achieve liver attenuation estimation in five minutes per CT exam.

A Quantitative Evaluation of Joint Activity and Attenuation Reconstruction in TOF PET/MR Brain Imaging.

Time-of-flight (TOF) PET data provide an effective means for attenuation correction (AC) when no (or incomplete or inaccurate) attenuation information is available. Since MR scanners provide little information on photon attenuation of different tissue types, AC in hybrid PET/MR scanners has always been challenging. In this contribution, we aim at validating the activity reconstructions of the maximum-likelihood ordered-subsets activity and attenuation (OSAA) reconstruction algorithm on a patient brain data set. We present a quantitative comparison of joint reconstructions with the current clinical gold standard-ordered-subsets expectation maximization-using CT-based AC in PET/CT, as well as the current state of the art in PET/MR, that is, zero time echo (ZTE)-based AC. Methods: The TOF PET emission data were initially used in a preprocessing stage to estimate crystal maps of efficiencies, timing offsets, and timing resolutions. Applying these additional corrections during reconstructions, OSAA, ZTE-based, and the vendor-provided atlas-based AC techniques were analyzed and compared with CT-based AC. In our initial study, we used the CT-based estimate of the expected scatter and later used the ZTE-based and OSAA attenuation estimates to compute the expected scatter contribution of the data during reconstructions. In all reconstructions, a maximum-likelihood scaling of the single-scatter simulation estimate to the emission data was used for scatter correction. The reconstruction results were analyzed in the 86 segmented regions of interest of the Hammers atlas. Results: Our quantitative analysis showed that, in practice, a tracer activity difference of +0.5% (±2.1%) and +0.1% (±2.3%) could be expected for the state-of-the-art ZTE-based and OSAA AC methods, respectively, in PET/MR compared with the clinical gold standard in PET/CT. Conclusion: Joint activity and attenuation estimation methods can provide an effective solution to the challenging AC problem for brain studies in hybrid TOF PET/MR scanners. With an accurate TOF-based (timing offsets and timing resolutions) calibration, and similar to the results of the state-of-the-art method in PET/MR, regional errors of joint TOF PET reconstructions are within a few percentage points.

Compensating elastic transmission losses for P‐wave attenuation estimation from sonic logs

ABSTRACTThe decay of seismic amplitude is caused by a variety of physical phenomena that can be divided broadly into elastic transmission losses (including geometrical spreading, interface transmission losses and scattering attenuation) and intrinsic attenuation, where wave energy is converted into heat due to viscous friction. The so‐called statistical averaging method is currently considered as the most advanced sonic wave attenuation estimation method, and there exist various implementations of this method. But the way elastic transmission losses – that mask the true intrinsic attenuation – are compensated for appears to be an issue and in some cases this correction has been overlooked. In this paper, we revisit the statistical averaging method for intrinsic attenuation estimation with particular focus on the role of elastic transmission losses. Through synthetic examples, we demonstrate the importance of compensating for elastic transmission losses even if the variation of velocity and density with depth is not notable. Our implementation of the method uses finite‐difference simulations thereby providing a versatile and accurate way to generate synthetic seismograms. We use a combination of elastic and viscoelastic finite‐difference simulations to demonstrate the significant error without accurate compensation of the elastic transmission losses. We apply our implementation of the method to sonic waveforms acquired in an exploration well from Browse basin, Australia. The resulting intrinsic attenuation estimates are indeed indicative of gas‐saturated zones identified from petrophysical analysis in which viscous friction are thought to be of importance.

Modeling scattering and intrinsic attenuation of crosswell seismic data in the Michigan Basin

Scattering of seismic waves may cause a significant amount of apparent attenuation, particularly in regions having strong heterogeneity. We find that the radiative transfer method can be used to model intrinsic and scattering attenuation of crosswell seismic data. To solve the radiative transfer equation, we assume that the medium can be described by a stationary random field and then we use a particle-based method in which millions of particles are released from a source and scatter through the random medium according to the Born scattering coefficients. Intrinsic attenuation is modeled by assigning probabilities that the particles will die off on the path between scattering events. We apply the seismic particle method to crosswell seismic data acquired on a carbonate reef in the Michigan Basin, and we use a grid search to estimate a set of model parameters that fit the data. Based on well logs, we fixed the velocity heterogeneity strength at 3% and estimated the medium velocity correlation length to be between [Formula: see text] and [Formula: see text]. Our results also indicate that scattering attenuation is one order of magnitude larger than intrinsic attenuation, a result that we interpret as a consequence of the highly heterogeneous nature of the rock comprising the reservoir. Contrary to other attenuation estimation methods, such as the centroid method, in which scattering attenuation is neglected by invoking that the reservoir is homogeneous, our results indicate that accounting for scattering attenuation is of paramount importance in attenuation estimation using crosswell seismic data.

Attenuation estimation from sonic logging waveforms combining seismic interferometry and common-midpoint approach

Although attenuation estimation methods using sonic logging waveforms provide the highest resolution among seismic methods and enable us to characterize in great detail the attenuation properties of subsurface rocks, such attenuation estimation methods are not used routinely, indicating that there is still room for improvement. To further improve the performance of an existing modified median frequency shift (MMFS) method, we have developed a new algorithm by combining seismic interferometry (SI) and the common-midpoint (CMP) approach. Redatuming a transmitter position by applying SI can shorten the transmitter-receiver distance, leading not only to higher depth resolution but also to a lower signal-to-noise ratio (S/N) of the attenuation profiles. To compensate for the decrease in the S/N, we used the redundancy of overlapping receivers at each receiver level in a sonic logging measurement using the multireceiver tool; we improved the S/N by stacking the redatumed sonic logging waveforms. Then, based on the CMP approach, we constructed the workflow to estimate attenuation using redatumed sonic logging waveforms. We applied our method to numerical and real sonic logging waveforms to investigate its applicability in comparison with that of the existing MMFS method in terms of depth resolution and S/N. The results of numerical experiments on noisy data and velocity heterogeneity models demonstrate a trade-off relationship between the depth resolution and stability, which can be controlled by selecting transmitter-receiver pairs. Finally, the application of our method to real sonic logging data demonstrates the advantages in terms of resolution and the disadvantages in stability in comparison with the existing MMFS method. Similar to the numerical results, we found a trade-off relationship between such advantages and disadvantages, which can be controlled by selecting transmitter-receiver pairs.

Monitoring Microwave Ablation of Ex Vivo Bovine Liver Using Ultrasonic Attenuation Imaging

Thermal ablation of soft tissue changes the tissue microstructure and, consequently, induces changes in its acoustic properties. Although B-mode ultrasound provides high-resolution and high-frame-rate images of ablative therapeutic procedures, it is not particularly effective at delineating boundaries of ablated regions because of poor contrast in echogenicity between ablated and surrounding normal tissue. Quantitative ultrasound techniques can provide quantitative estimates of acoustic properties, such as backscatter and attenuation coefficients, and differentiate ablated and unablated regions more effectively, with the potential for monitoring minimally invasive thermal therapies. In this study, a previously introduced attenuation estimation method was used to create quantitative attenuation coefficient maps for 11 microwave ablation procedures performed on refrigerated ex vivo bovine liver. The attenuation images correlate well with the pathologic images of the ablated region. The mean attenuation coefficient for regions of interest drawn inside and outside the ablated zones were 0.9 (±0.2) and 0.45 (±0.15) dB/cm/MHz, respectively. These estimates agree with reported values in the literature and establish the usefulness of non-invasive attenuation imaging for monitoring therapeutic procedures in the liver.

The estimation of spectra from time-frequency transforms for use in attenuation studies

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal-dependent time–frequency distribution, as well as the short-time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal-dependent time–frequency distribution, and fixed- and variable-window transforms are used to estimate spectra from a zero-offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well-log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal-dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed- and variable-window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre-stack attenuation estimation method (the pre-stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal-dependent time-frequency distribution produced spectra more consistent with the constant-Q model of attenuation assumed in the pre-stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant-Q expectation for the signal-dependent time-frequency distribution, short-time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal-dependent time-frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.

Signal to noise ratio comparisons for ultrasound attenuation slope estimation algorithms

Attenuation imaging has a promising role in the detection of tissue abnormalities. The authors have previously compared three different frequency domain ultrasound attenuation estimation methods, for accuracy and bias. The mean estimated attenuation value in a region of interest has been the determining factor of how well a method performs; however, the noise level has not been quantified for attenuation estimated using different methods. The authors compare three different frequency domain ultrasound attenuation estimation methods [the reference phantom method (RPM), the centroid downshift method (CEN), and the hybrid method (HYB)] using the signal to noise ratio (SNR) metric. Both simulated and experimental tissue-mimicking phantoms are used in the performance comparison study, evaluating the impact of the variation in acoustical properties. For attenuation estimation in a tissue-mimicking phantom with a known attenuation coefficient of 0.5 dB/cm/MHz, all the three methods estimated the attenuation coefficient to be ≈ 0.49 dB/cm/MHz for a transmit center frequency of 6 MHz, however, the signal to noise ratio obtained was found to be 8.5, 5.7, and 2.2 for the HYB, RPM, and CEN methods, respectively. These results demonstrate the need for the SNR metric in the comparison of different algorithms and to evaluate the impact of varying different ultrasound system and tissue parameters. In this paper, the authors demonstrate that although the estimated mean attenuation value with a region of interest may be closely estimated using different methods, the signal to noise ratio obtained of the estimates can vary significantly. The centroid downshift method presented with the lowest signal-to-noise ratio of the methods compared. The hybrid method was the least susceptible to changes in the acoustical properties and provided unbiased attenuation coefficient estimates with the highest signal-to-noise ratios.

Time domain attenuation estimation method from ultrasonic backscattered signals.

Ultrasonic attenuation is important not only as a parameter for characterizing tissue but also for compensating other parameters that are used to classify tissues. Several techniques have been explored for estimating ultrasonic attenuation from backscattered signals. In the present study, a technique is developed to estimate the local ultrasonic attenuation coefficient by analyzing the time domain backscattered signal. The proposed method incorporates an objective function that combines the diffraction pattern of the source/receiver with the attenuation slope in an integral equation. The technique was assessed through simulations and validated through experiments with a tissue mimicking phantom and fresh rabbit liver samples. The attenuation values estimated using the proposed technique were compared with the attenuation estimated using insertion loss measurements. For a data block size of 15 pulse lengths axially and 15 beamwidths laterally, the mean attenuation estimates from the tissue mimicking phantoms were within 10% of the estimates using insertion loss measurements. With a data block size of 20 pulse lengths axially and 20 beamwidths laterally, the error in the attenuation values estimated from the liver samples were within 10% of the attenuation values estimated from the insertion loss measurements.

Tissue Attenuation Estimation from Backscattered Ultrasound Using Spatial Compounding Technique - Preliminary Results

The pathological states of biological tissue are often resulted in attenuation changes. Thus, information about attenuating properties of tissue is valuable for the physician and could be useful in ultrasonic diagnosis. We are currently developing a technique for parametric imaging of attenuation and we intend to apply it for in vivo characterization of tissue. The attenuation estimation method based on the echoes mean frequency changes due to tissue attenuation dispersion, is presented. The Doppler IQ technique was adopted to estimate the mean frequency directly from the raw RF data. The Singular Spectrum Analysis technique was used for the extraction of mean frequency trends. These trends were converted into attenuation distribution and finally the parametric images were computed. In order to reduce variation of attenuation estimates the spatial compounding method was applied. Operation and accuracy of attenuation extracting procedure was verified by calculating the attenuation coefficient distribution using the data from the tissue phantom (DFS, Denmark) with uniform echogenicity while attenuation coefficient underwent variation.

Hybrid Spectral Domain Method for Attenuation Slope Estimation

Attenuation estimation methods for medical ultrasound are important because attenuation properties of soft tissue can be used to distinguish between benign and malignant tumors and to detect diffuse disease. The classical spectral shift method and the spectral difference method are the most commonly used methods for the estimation of the attenuation; however, they both have specific limitations. Classical spectral shift approaches for estimating ultrasonic attenuation are more sensitive to local spectral noise artifacts and have difficulty in compensating for diffraction effects because of beam focusing. Spectral difference approaches, on the other hand, fail to accurately estimate attenuation coefficient values at tissue boundaries that also possess variations in the backscatter. In this paper, we propose a hybrid attenuation estimation method that combines the advantages of the spectral difference and spectral shift methods to overcome their specific limitations. The proposed hybrid method initially uses the spectral difference approach to reduce the impact of system-dependent parameters including diffraction effects. The normalized power spectrum that includes variations because of backscatter changes is then filtered using a Gaussian filter centered at the transmit center frequency of the system. A spectral shift method, namely the spectral cross-correlation algorithm is then used to compute spectral shifts from these filtered power spectra to estimate the attenuation coefficient. Ultrasound simulation results demonstrate that the estimation accuracy of the hybrid method is better than the centroid downshift method (spectral shift method), in uniformly attenuating regions. In addition, this method is also stable at boundaries with variations in the backscatter when compared with the reference phantom method (spectral difference method). Experimental results using tissue-mimicking phantom also illustrate that the hybrid method is more robust and provides accurate attenuation estimates in both uniformly attenuating regions and across boundaries with backscatter variations. The proposed hybrid method preserves the advantages of both the spectral shift and spectral difference approaches while eliminating the disadvantages associated with each of these methods, thereby improving the accuracy and robustness of the attenuation estimation. (E-mail: hyungsukkim@wisc.edu)

Wigner-Ville distribution and its application in seismic attenuation estimation

The attenuation of seismic signals is often characterized in the frequency domain using statistical measures of the power spectrum. However, the conventional Fourier transform-based power spectrum estimation methods suffer from time-frequency resolution problems. Wigner-Ville distribution, which is a member of Cohen class time-frequency distributions, possesses many appealing properties, such as time-frequency marginal distribution, time-frequency localization, etc. Therefore, Wigner-Ville distribution offers a new way for estimating the attenuation of seismic signals. This paper initially gives a brief introduction to Wigner-Ville distribution and the smoothed Wigner-Ville distribution that is effective in reducing the cross-term effect, and then presents a method for seismic attenuation estimation based on the instantaneous energy spectrum of the Wigner-Ville distribution. A real data example from central Tarim Basin in western China is presented to illustrate the effectiveness of the proposed method. The results show that the Wigner-Ville distribution-based seismic attenuation estimation method can effectively detect the difference between reef, shoal and lagoon facies by their attenuation properties, indicating that the estimated seismic attenuation can be used for reef and shoal carbonate reservoir characterization.

Attenuation estimation using spectral cross-correlation

Estimation of the local attenuation coefficient in soft tissue is important both for clinical diagnosis and for further analysis of ultrasound B-mode images. However, it is difficult to extract spectral properties in a small region of interest from noisy backscattered ultrasound radio frequency (RF) signals. Diffraction effects due to transducer beam focal properties also have to be corrected for accurate estimation of the attenuation coefficient. In this paper, we propose a new attenuation estimation method using spectral cross-correlation between consecutive power spectra obtained from the backscattered RF signals at different depths. Since the spectral cross-correlation method estimates the spectral shift by comparing the entire power spectra, it is more robust and stable to the spectral noise artifacts in the backscattered RF signals. A diffraction compensation technique using a reference phantom with a known attenuation coefficient value is also presented. Local attenuation coefficient estimates obtained using spectral cross-correlation are within 2.3% of the actual value with small estimation variances, as demonstrated in the simulation results.

Application of the ultrasonic characterization methods for highly attenuating plastic materials

In this paper, prediction of the back surface reflection, which is based on attenuation and phase velocity dispersion estimation method, in highly attenuating plastic (polyvinylidene fluoride—PVDF) has been described. Estimation of the attenuation law is based on the inverse transfer function of the object approximation in the frequency domain. The oscillating character of the inverse transfer function of the highly attenuating plastic material gives rise to an ill-posed problem for approximation. It has been solved in two ways: application of the Tikhonov regularization process and iterative adjustment of the approximation parameters. The estimated attenuation coefficient α 0 and power n have been used for calculation of phase velocity dispersion using the Kramers–Kronig relations and having attenuation coefficient measured at single-frequency value. The reconstructed waveforms of the ultrasonic back surface reflections using the estimated attenuation and phase velocity dispersion curves have been presented and compared with the experimental one.

Comparison of high intensity focused ultrasound (HIFU) exposures using empirical and backscatter attenuation estimation methods

Currently, the intensity to be used in our clinical HIFU treatments is calculated from the acoustic path lengths in different tissues measured on diagnostic ultrasound images of the patient in the treatment position, and published values of ultrasound attenuation coefficients. This yields an approximate value for the acoustic power at the transducer required to give a stipulated focal intensity in situ. Estimation methods for the actual acoustic attenuation have been investigated in large parts of the tissue path overlying the target volume from the backscattered ultrasound signal for each patient (backscatter attenuation estimation: BAE). Several methods have been investigated. The backscattered echo information acquired from an Acuson scanner has been used to compute the diffraction-corrected attenuation coefficient at each frequency using two methods: a substitution method and an inverse diffraction filtering process. A homogeneous sponge phantom was used to validate the techniques. The use of BAE to determine the correct HIFU exposure parameters for lesioning has been tested in ex vivo liver. HIFU lesions created with a 1.7-MHz therapy transducer have been studied using a semiautomated image processing technique. The reproducibility of lesion size for given in situ intensities determined using BAE and empirical techniques has been compared.