Quantitative Liver Imaging

Pulse-echo ultrasound-based liver fat fraction assessment based on quantitative sound speed estimation and aberration correction

Early Liver Sound Speed Estimation Based on Layered Abdomen Model

Early Layered Medium Model for Sound Speed Estimation. During my PhD, I developed one of the first quantitative methods to estimate sound speed directly from pulse-echo data. The key idea is to use the beamforming sound speed to measure the average sound speed in the tissue. In layered media, the profile of the average sound speed that best focuses the signal at each depth can be inverted to recover the local depth-wise profile (Ali et al., 2021). This layered-medium approach has also been tried with plane waves (Ali et al., 2020) and with common midpoint gathers (Ali et al., 2020; Brevett et al., 2022). This model was very useful for quantifying sound speed inside the liver to help diagnose fatty liver disease.

Early work focused on estimating liver sound speed from pulse-echo ultrasound using a layered model of the abdomen (Ali et al., 2021; Ali et al., 2020; Ali et al., 2020; Brevett et al., 2022). The beamforming sound speed that produced the best focus at a given depth was related to the average sound speed of the tissue above that depth, allowing the measured depth-dependent values to be inverted to estimate a local sound-speed profile. This approach was demonstrated in obese Zucker rats with different grades of hepatic steatosis (Ali et al., 2021; Telichko et al., 2022). The estimated liver sound speeds agreed closely with measurements from the corresponding excised liver samples, demonstrating the potential of pulse-echo ultrasound for quantitative assessment of liver tissue.

Example of Liver Imaging in Rats with Average and Local Sound Speed Estimates (Ali et al., 2021). (Top) First rat shown is a female obese Zucker rat with a steatosis grade of 1. The local sound speed in the liver was measured to be 1562.8 m/s. The sound speed measured in the excised liver sample was 1557 m/s. (Bottom) Second rat is a female obese Zucker rat with a steatosis grade of 3. The local sound speed in the liver was measured to be 1522.4 m/s. The sound speed measured in the excised liver sample was 1511 m/s. See the complete study on liver steatosis in obese Zucker rats (Telichko et al., 2022).

Quantitative Full-Wave Estimation of Liver Sound Speed

Subsurface-Offset WEMVA for Sound Speed Estimation and Aberration Correction in Simulations of the Abdominal Wall (Ali et al., 2026).

The layered-medium model provides a useful estimate of liver sound speed, but it cannot adequately describe the lateral sound-speed variations encountered in the abdomen. These variations produce both travel-time errors and diffractive effects that degrade the image when conventional beamforming assumes a constant sound speed. To address this limitation, I developed wave-equation migration velocity analysis (WEMVA) for sound-speed estimation and aberration correction in pulse-echo ultrasound. WEMVA uses reverse-time migration (RTM) to reconstruct the image by cross-correlating the transmitted and backpropagated received wavefields. Because the RTM image is differentiable with respect to the sound-speed distribution, the image-domain error can be used to iteratively update the sound speed estimate.

My most recent form of WEMVA uses extended RTM images with a subsurface offset between the transmit and receive wavefields. The correct sound speed profile should focus the extended image at zero subsurface offset; sound speed errors produce residual energy at nonzero subsurface offsets. Driving this energy toward zero subsurface offset provides an image-domain criterion for estimating the sound speed profile (Ali et al., 2026).

Subsurface-Offset WEMVA in the Abdomen of Obese Zucker Rats and a Healthy Human Subject (Ali et al., 2026).

Future Extension of WEMVA to Curvilinear Human-Abdominal Imaging

The initial WEMVA formulation was developed for linear arrays, whereas clinical abdominal ultrasound commonly uses curvilinear probes. Extending WEMVA to these probes requires the wave-propagation model to account for the curved transducer geometry rather than treating the aperture as planar. I have previously extended the angular spectrum method used in RTM to a polar coordinate system for curvilinear arrays (Ali & Dahl, 2022). The formulation propagates the transmitted and received wavefields in the polar geometry of the curved probe, while retaining the Fourier-domain efficiency of the angular spectrum method. This provides the wave-propagation engine needed to apply RTM and WEMVA directly to curvilinear abdominal acquisitions. The underlying curvilinear angular-spectrum formulation was validated against Field II simulations and demonstrated using in-vivo abdominal channel data. Combining this propagation model with WEMVA would enable sound speed estimation and aberration correction using conventional curvilinear abdominal imaging probes.

Curvilinear Extension of the Angular Spectrum Method in Reverse-Time Migration and its Application to Liver + Kidney Imaging (Ali & Dahl, 2022).

References

2026

Wave-Equation Migration Velocity Analysis for Multistatic Synthetic Aperture Ultrasound

Rehman Ali, Trevor M Mitcham, Marvin M Doyley, and 2 more authors

2026

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Sound speed heterogeneities can create aberrations in B-mode ultrasound images by inducing tissue-dependent delays and diffractive effects that conventional beamforming does not incorporate. By using the Fourier split-step method to simulate pressure fields in heterogenous sound speed media, reverse-time migration (RTM) can reconstruct the B-mode image by cross-correlating transmitted and received pressure fields. As a result, RTM is differentiable with respect to sound speed. This enables the reconstruction of the sound speed profile that minimizes the aberration in the B-mode image. In seismic imaging, this form of diffraction tomography, known as wave-equation migration velocity analysis, can roughly be understood as a type of full-waveform inversion (FWI) that acts in the image domain rather than errors in the received channel data. This is the first work applying WEMVA to medical pulse-echo ultrasound imaging. Phantom experiments show dramatic improvements in image quality with measured improvements in point target resolution from 1.22±1.01 to 0.32±0.07 mm and lesion contrast from 3.05 to 4.39 dB.
@misc{Ali2026WEMVA, title = {Wave-Equation Migration Velocity Analysis for Multistatic Synthetic Aperture Ultrasound}, author = {Ali, Rehman and Mitcham, Trevor M and Doyley, Marvin M and Duric, Nebojsa and Dahl, Jeremy J}, year = {2026}, archiveprefix = {arXiv}, primaryclass = {physics.med-ph}, doi = {10.48550/arXiv.2604.27428}, url = {https://arxiv.org/abs/2604.27428}, }

2022

Speed of Sound Estimation at Multiple Angles from Common Midpoint Gathers of Non-Beamformed Data

Thurston Brevett, Sergio J Sanabria, Rehman Ali, and 1 more author

In 2022 IEEE International Ultrasonics Symposium (IUS), 2022

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Sound speed estimation is a promising quantitative parameter in ultrasound for both for it’s potential as a biomarker, where sound speed is known to be correlated with biological changes, and for aberration correction, where knowledge of the sound speed allows for correction of distortions in the image. Previous methods for sound speed estimation rely on the use of an a-priori sound speed for beamforming, from which sound-speed estimates are then calculated. However, this assumption introduces a bias in the estimation technique, because errors in the a-priori sound speed lead to distortions in the image. Here we present a method for sound speed estimation that avoids this bias by estimating the sound speed without beamforming.
@inproceedings{Brevett2022CMP, title = {Speed of Sound Estimation at Multiple Angles from Common Midpoint Gathers of Non-Beamformed Data}, author = {Brevett, Thurston and Sanabria, Sergio J and Ali, Rehman and Dahl, Jeremy}, booktitle = {2022 IEEE International Ultrasonics Symposium (IUS)}, pages = {1--4}, year = {2022}, organization = {IEEE}, doi = {10.1109/IUS54386.2022.9958779}, url = {https://ieeexplore.ieee.org/abstract/document/9958779} }
Noninvasive estimation of local speed of sound by pulse-echo ultrasound in a rat model of nonalcoholic fatty liver

Arsenii V Telichko, Rehman Ali, Thurston Brevett, and 5 more authors

Physics in Medicine & Biology, 2022

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Objective. Speed of sound has previously been demonstrated to correlate with fat concentration in the liver. However, estimating speed of sound in the liver noninvasively can be biased by the speed of sound of the tissue layers overlying the liver. Here, we demonstrate a noninvasive local speed of sound estimator, which is based on a layered media assumption, that can accurately capture the speed of sound in the liver. We validate the estimator using an obese Zucker rat model of non-alcoholic fatty liver disease and correlate the local speed of sound with liver steatosis. Approach. We estimated the local and global average speed of sound noninvasively in 4 lean Zucker rats fed a normal diet and 16 obese Zucker rats fed a high fat diet for up to 8 weeks. The ground truth speed of sound and fat concentration were measured from the excised liver using established techniques. Main Results. The noninvasive, local speed of sound estimates of the livers were similar in value to their corresponding ‘ground truth’ measurements, having a slope ± standard error of the regression of 0.82 ± 0.15 (R2 = 0.74 and p < 0.001). Measurement of the noninvasive global average speed of sound did not reliably capture the ‘ground truth’ speed of sound in the liver, having a slope of 0.35 ± 0.07 (R2 = 0.74 and p < 0.001). Decreasing local speed of sound was observed with increasing hepatic fat accumulation (approximately −1.7 m s−1 per 1% increase in hepatic fat) and histopathology steatosis grading (approximately −10 to −13 m s−1 per unit increase in steatosis grade). Local speed of sound estimates were highly correlated with steatosis grade, having Pearson and Spearman correlation coefficients both ranging from −0.87 to −0.78. In addition, a lobe-dependent speed of sound in the liver was observed by the ex vivo measurements, with speed of sound differences of up to 25 m s−1 (p < 0.003) observed between lobes in the liver of the same animal. Significance. The findings of this study suggest that local speed of sound estimation has the potential to be used to predict or assist in the measurement of hepatic fat concentration and that the global average speed of sound should be avoided in hepatic fat estimation due to significant bias in the speed of sound estimate.
@article{Telichko2022RatStudy, title = {Noninvasive estimation of local speed of sound by pulse-echo ultrasound in a rat model of nonalcoholic fatty liver}, author = {Telichko, Arsenii V and Ali, Rehman and Brevett, Thurston and Wang, Huaijun and Vilches-Moure, Jose G and Kumar, Sukumar U and Paulmurugan, Ramasamy and Dahl, Jeremy J}, journal = {Physics in Medicine \& Biology}, volume = {67}, number = {1}, pages = {015007}, year = {2022}, doi = {10.1088/1361-6560/ac4562}, publisher = {IOP Publishing}, url = {https://iopscience.iop.org/article/10.1088/1361-6560/ac4562}, }
Angular spectrum method for curvilinear arrays: Theory and application to Fourier beamforming

Rehman Ali and Jeremy Dahl

JASA Express Letters, 2022

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Fourier beamforming techniques for medical ultrasound imaging have largely been limited to linear transducer arrays. This work extends the angular spectrum method to curvilinear arrays and demonstrates a migration-based Fourier beamforming technique that has implications for sound speed estimation and distributed aberration correction for abdominal imaging applications. When compared to Field II simulations, the proposed angular spectrum method simulates the pressure field from a focused transmission to within 3.7% normalized root mean square error. The resulting Fourier beamforming technique is then compared to virtual source synthetic aperture using in vivo abdominal imaging examples where resolution and imaging quality improvements are observed.
@article{Ali2022CurvilinearAngularSpectrumMethod, title = {Angular spectrum method for curvilinear arrays: Theory and application to Fourier beamforming}, author = {Ali, Rehman and Dahl, Jeremy}, journal = {JASA Express Letters}, volume = {2}, number = {5}, year = {2022}, doi = {10.1121/10.0010536}, publisher = {AIP Publishing}, url = {https://pubs.aip.org/asa/jel/article/2/5/052001/2843365}, }

2021

Local Sound Speed Estimation for Pulse-Echo Ultrasound in Layered Media

Rehman Ali, Arsenii V Telichko, Huaijun Wang, and 4 more authors

IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2021

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Our previous methodology in local sound speed estimation utilized time delays measured by the cross correlation of delayed full-synthetic aperture channel data to estimate the average speed of sound. However, focal distortions in this methodology lead to biased estimates of the average speed of sound, which, in turn, leads to biased estimates of the local speed of sound. Here, we demonstrate the bias in the previous methodology and introduce a coherence-based average sound speed estimator that eliminates this bias and is computationally much cheaper in practice. Because this coherence-based approach estimates the average sound speed in the medium over an equally spaced grid in depth rather than time, we derive a refined model that relates the local and average speeds of sound as a function of depth in layered media. A fast, closed-form inversion of this model yields highly accurate local sound speed estimates. The root-mean-square (rms) error of local sound speed reconstruction in simulations of two-layer media is 4.6 and 2.5 m/s at 4 and 8 MHz, respectively. This work examines the impact of frequency, f -number, aberration, and reverberation on sound speed estimation. Phantom and in vivo experiments in rats further validate the coherence-based sound speed estimator.
@article{Ali2021LayeredMedia, title = {Local Sound Speed Estimation for Pulse-Echo Ultrasound in Layered Media}, author = {Ali, Rehman and Telichko, Arsenii V and Wang, Huaijun and Sukumar, Uday K and Vilches-Moure, Jose G and Paulmurugan, Ramasamy and Dahl, Jeremy J}, journal = {IEEE transactions on ultrasonics, ferroelectrics, and frequency control}, volume = {69}, number = {2}, pages = {500--511}, year = {2021}, doi = {10.1109/TUFFC.2021.3124479}, publisher = {IEEE}, url = {https://ieeexplore.ieee.org/abstract/document/9597614}, }

2020

Sound Speed Estimation in Layered Media Using the Angular Coherence of Plane Waves

Rehman Ali, Sharil Maredia, Arsenii Telichko, and 4 more authors

In Medical Imaging 2020: Ultrasonic Imaging and Tomography, 2020

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We present a refraction-corrected sound speed reconstruction technique for layered media based on the angular coherence of plane waves. Previous work has successfully shown that sound speed estimation and refraction- corrected image reconstruction can be achieved using the coherence of full-synthetic aperture channel data. However, methods for acquiring the full-synthetic aperture dataset require a large number of transmissions, which can confound sound speed estimation due to the scatterer motion between transmit events, especially for in-vivo application. Furthermore, sound speed estimation requires producing full-synthetic aperture coherence images for each trial sound speed, which can make the overall computational cost quite burdensome. The angular coherence beamformer, initially devised as a quicker alternative to the more conventional spatial coherence beamformer, measures coherence between fully-beamformed I/Q channel data for each plane wave as opposed to the receive channel data prior to receive beamforming. As a result, angular coherence beamforming can significantly reduce the computation time needed to reconstruct a coherence image by taking advantage of receive beamforming. Previous work has used the coherence maximization of full-synthetic aperture channel data to perform sound speed estimation. By replacing spatial coherence with angular coherence, we apply a similar methodology to channel data from plane-waves to significantly reduce the computational cost of sound speed estimation. This methodology has been confirmed by both simulated and experimental channel data from plane waves.
@inproceedings{Ali2020PlaneWaveSoS, title = {Sound Speed Estimation in Layered Media Using the Angular Coherence of Plane Waves}, author = {Ali, Rehman and Maredia, Sharil and Telichko, Arsenii and Wang, Huaijun and Paulmurugan, Ramasamy and Vilches-Moure, Jose and Dahl, Jeremy}, booktitle = {Medical Imaging 2020: Ultrasonic Imaging and Tomography}, volume = {11319}, pages = {81--90}, year = {2020}, organization = {SPIE}, doi = {10.1117/12.2548878}, url = {https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11319/2548878/Sound-speed-estimation-in-layered-media-using-the-angular-coherence/10.1117/12.2548878.full} }
Application of Common Midpoint Gathers to Medical Pulse-Echo Ultrasound for Optimal Coherence and Improved Sound Speed Estimation in Layered Media

Rehman Ali, Dongwoon Hyun, and Jeremy J Dahl

In 2020 IEEE International Ultrasonics Symposium (IUS), 2020

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In seismic imaging, common midpoint (CMP) gathers are collections of time-series data organized by source-receiver pairs having a common midpoint. CMP gathers have been used in geophysics to image the subsurface of the Earth and estimate wave velocity as a function of depth. According to the Van Cittert-Zernike (VCZ) theorem, if the signals from a CMP gather are focused using an ideal set of delays based on the true speed of sound in the medium, there should be a perfect correlation between any two signals in the CMP gather in the absence of noise. In ultrasound imaging, Walker et al. have applied this concept to translating transmit and receive apertures. The goal of this work is to apply CMP gathers to pulse-echo ultrasound imaging in order to improve coherence-based sound speed estimation in layered media.
@inproceedings{Ali2020CMP, title = {Application of Common Midpoint Gathers to Medical Pulse-Echo Ultrasound for Optimal Coherence and Improved Sound Speed Estimation in Layered Media}, author = {Ali, Rehman and Hyun, Dongwoon and Dahl, Jeremy J}, booktitle = {2020 IEEE International Ultrasonics Symposium (IUS)}, pages = {1--4}, year = {2020}, organization = {IEEE}, doi = {10.1109/IUS46767.2020.9251370}, url = {https://ieeexplore.ieee.org/abstract/document/9251370} }