Multiparametric and Elastic FWI

Extending the wave physics model and FWI to reconstruct multiple tissue mechanical properties

Acoustic FWI with Transmission and Reflection Ultrasound

Full-waveform inversion provides a framework for reconstructing quantitative tissue properties by matching measured and simulated ultrasound waveforms. Much of my earlier work focused on reconstructing the sound-speed distribution, which primarily controls the phase and arrival time of transmitted ultrasound. However, the acoustic wave equation contains additional parameters that influence the measured signals, including attenuation and density.

These parameters do not affect the data in the same way. Sound speed primarily changes the timing and shape of the transmitted wavefield, while attenuation reduces its amplitude. Density has a comparatively small effect on the transmitted waveform, making it difficult to recover reliably from transmission measurements alone.

The situation is different for reflected ultrasound. Backscattered signals arise from spatial variations in acoustic impedance Z = ρc, where ρ is density and c is sound speed. Consequently, density can have a much stronger influence on the reflected signal than on the transmitted wavefield. This suggests that combining transmission and reflection measurements could provide information about tissue density that is difficult to obtain from transmission tomography alone.

Transmission vs Reflection in UST/USCT. (Left) The transmission of ultrasound through the breast is primarily impacted by sound speed and attenuation. Sound speed primarily affects the shape of the transmitted wavefront by advancing and delaying the wave. Attenuation affect the amplitude of the transmitted wave. (Right) Ultrasound backscatter reflected by the tissue is the result of spatial changes in the impedance Z=ρc (a product of sound speed c and density ρ). Although density has a small impact on the waveform transmitted through tissue, it plays a much more significant role on the backscattered reflections, so we theorize that modeling the reflected ultrasound signals should enable imaging of the mass density in the breast.

Sound Speed and Attenuation Based on Transmission Tomography

FWI Reconstruction of Sound Speed and Attenuation in UST/USCT Simulations (Ali et al., 2024).

As a first step toward multiparametric reconstruction, I extended FWI for transmission ultrasound computed tomography to simultaneously estimate sound speed and attenuation by modeling each set of parameters as the real and imaginary parts, respectively, of the complex slowness (Ali et al., 2024). This ultimately treats attenuation as a frequency-dependent loss of acoustic energy alongside sound speed. The simulations above demonstrate simultaneous reconstruction of these two properties in breast models. The recovered sound-speed distributions capture the large-scale acoustic structure of the breast, while the attenuation reconstructions provide an additional quantitative property of the tissue. This multiparametric formulation was also evaluated using experimental phantom data below. The reconstructions demonstrate that the additional degrees of freedom can be recovered from the measured waveforms when the forward model accounts for their distinct effects on the data.

FWI Reconstruction of Sound Speed and Attenuation in Phantoms (Ali et al., 2024).

Quantitative Reconstruction in the Breast

The ability to reconstruct multiple acoustic properties is particularly relevant to breast imaging. Conventional B-mode ultrasound primarily depicts spatial variations in scattering, while transmission ultrasound provides quantitative information about the acoustic properties along propagation paths. In the breast, multiparametric FWI can recover both sound speed and attenuation while preserving the spatial localization of lesions and other structures. The key limitation, however, is that an acoustic model still treats the tissue as a fluid and therefore does not model shear-wave propagation or the full mechanical response of tissue.

FWI Reconstruction of Sound Speed and Attenuation in the Breast (Ali et al., 2024). (Top) Benign Cyst. (Bottom) Malignancy.

The examples above show in-vivo breast reconstructions differentiating between a benign cyst and and a diagnosed malignancy, demonstrating the potential of FWI to provide diagnostically relevant tissue characterization in addition to anatomical imaging (Ali et al., 2024). For example, although the fluid-filled cyst has a higher sound speed than the fat background of the breast, the attenuation is through the same region is low, and the globular morphology of the cyst is indicative of a fluid filled pocket of tissue. However, the malignancy is a spiculated mass with branching tissue indicative of tissue scarring that has both high sound speed and attenuation. This ultimately differentiates the malignancy from the fluid-filled cyst.

From the Acoustic to the Fully Elastic Wave Equation

To recover a more complete description of tissue mechanics, the forward model can be extended from the acoustic wave equation to the fully elastic wave equation. Elastic propagation introduces additional mechanical parameters and supports both compressional and shear waves. This provides a path toward reconstructing properties that cannot be represented by an acoustic model alone. In principle, a fully elastic FWI framework could recover multiple tissue mechanical properties from the way both compressional and shear components propagate, reflect, and interact within the breast. In fact, beyond breast imaging, several diagnostic applications involving bone, particularly transcranial imaging, ultimately require full-wave elastic modeling at the bone tissue interface (Marty et al., 2024). Therefore, the transition from acoustic to elastic FWI therefore represents a broader shift in this work: from estimating individual acoustic parameters to using increasingly complete wave physics to quantitatively characterize tissue.

References

2024

2-D Slicewise Waveform Inversion of Sound Speed and Acoustic Attenuation for Ring Array Ultrasound Tomography Based on a Block LU Solver

Rehman Ali, Trevor M Mitcham, Thurston Brevett, and 5 more authors

IEEE transactions on medical imaging, 2024

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Ultrasound tomography is an emerging imaging modality that uses the transmission of ultrasound through tissue to reconstruct images of its mechanical properties. Initially, ray-based methods were used to reconstruct these images, but their inability to account for diffraction often resulted in poor resolution. Waveform inversion overcame this limitation, providing high-resolution images of the tissue. Most clinical implementations, often directed at breast cancer imaging, currently rely on a frequency-domain waveform inversion to reduce computation time. For ring arrays, ray tomography was long considered a necessary step prior to waveform inversion in order to avoid cycle skipping. However, in this paper, we demonstrate that frequency-domain waveform inversion can reliably reconstruct high-resolution images of sound speed and attenuation without relying on ray tomography to provide an initial model. We provide a detailed description of our frequency-domain waveform inversion algorithm with open-source code and data that we make publicly available.
@article{Ali2024_BlockLU_2DFWI, title = {2-D Slicewise Waveform Inversion of Sound Speed and Acoustic Attenuation for Ring Array Ultrasound Tomography Based on a Block LU Solver}, author = {Ali, Rehman and Mitcham, Trevor M and Brevett, Thurston and Agudo, {\`O}scar Calder{\'o}n and Martinez, Cristina Dur{\'a}n and Li, Cuiping and Doyley, Marvin M and Duric, Nebojsa}, journal = {IEEE transactions on medical imaging}, volume = {43}, number = {8}, pages = {2988--3000}, year = {2024}, doi = {10.1109/TMI.2024.3383816}, publisher = {IEEE}, url = {https://ieeexplore.ieee.org/document/10486959}, }
Towards elastic bone characterization in transcranial ultrasound

Patrick Marty, Trevor Mitcham, Rehman Ali, and 3 more authors

In Medical Imaging 2024: Ultrasonic Imaging and Tomography, 2024

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Constructing a physics-augmented digital twin of the skull is imperative for a wide range of transcranial ultrasound applications including ultrasound computed tomography and focused ultrasound therapy. The high impedance contrast as well as the acoustic-elastic coupling observed between soft tissue and bone increase the complexity of the ultrasound wavefield considerably, thus emphasizing the need for waveform-based inversion approaches. This work applies reverse time migration in conjunction with the spectral-element method to an in vitro human skull to obtain a starting model, which can be used for full-waveform inversion and adjoint-based shape optimization. Two distinct brain phantoms are considered where the cranial cavity of the in vitro human skull was filled with (1) homogeneous water and (2) gelatin with two cylindrical inclusions. A 2D slice through the posterior of the skull was collected using a ring-like aperture consisting of 1024 ultrasound transducers with a bandwidth of approximately 1MHz to 3MHz. Waveform-based reverse time migration was then used to resolve the inner and outer contours of the skull from which a conforming hexahedral finite-element mesh was constructed. The synthetically generated measurements which are obtained by solving the coupled acoustic-viscoelastic wave equation are in good agreement with the observed laboratory measurements. It is demonstrated that using this revised wave speed model for recomputing the reverse time migration reconstructions allows for improved localization of the gelatin inclusions within the cranial cavity.
@inproceedings{Marty2024ElasticBoneCharacterization, title = {Towards elastic bone characterization in transcranial ultrasound}, author = {Marty, Patrick and Mitcham, Trevor and Ali, Rehman and Boehm, Christian and Duric, Neb and Fichtner, Andreas}, booktitle = {Medical Imaging 2024: Ultrasonic Imaging and Tomography}, volume = {12932}, pages = {116--129}, year = {2024}, organization = {SPIE}, doi = {10.1117/12.3006769}, url = {https://www.spiedigitallibrary.org/conference-proceedings-of-spie/12932/3006769/Towards-elastic-bone-characterization-in-transcranial-ultrasound/10.1117/12.3006769.full} }