Investigation of an elevation-focused transducer model for three-dimensional full-waveform inversion in ultrasound computed tomography

Abstract

Ultrasound computed tomography (USCT) is an emerging medical imaging modality that holds great promise for improving human health. Full-waveform inversion (FWI)-based image reconstruction methods account for the relevant wave physics to produce high spatial resolution images of the acoustic properties of the breast tissues. A practical USCT design employs a circular ring-array comprised of elevation-focused ultrasonic transducers, and volumentric imaging is achieved by translating the ring-array orthogonally to the imaging plane. In commonly deployed slice-by-slice (SBS) reconstruction approaches, the three-dimensional (3D) volume is reconstructed by stacking together two-dimensional (2D) images reconstructed for each position of the ring-array. A limitation of the SBS reconstruction approach is that it does not account for 3D wave propagation physics and the focusing properties of the transducers, which can result in significant image artifacts and inaccuracies. To perform 3D image reconstruction when elevation-focused transducers are employed, a numerical description of the focusing properties of the transducers should be included in the forward model. To address this, a 3D computational model of an elevation-focused transducer is developed to enable 3D FWI-based reconstruction methods to be deployed in ring-array-based USCT. The focusing is achieved by applying a spatially varying temporal delay to the ultrasound pulse (emitter mode) and recorded signal (receiver mode). The proposed numerical transducer model is quantitatively validated and employed in computer-simulation studies that demonstrate its use in image reconstruction for ringarray USCT.

Impact of starting model on waveform inversion in ultrasound tomography

“…Future work should investigate methodologies that eliminate the need for ray tomography by overcoming cycle skipping effects altogether [21][22][23] as well as reduce the impact of out-of-plane artifacts by using a 3D reconstruction model. 24,25 [3] Schreiman, J., Gisvold, J., Greenleaf, J. F., and Bahn, R., "Ultrasound transmission computed tomography of the breast.," Radiology 150(2), 523-530 (1984).…”

A new strategy to overcome cycle skipping: frequency-difference waveform inversion

“…This objective function ( 21) is identical to the original FWI objective function (5), except that ∆ω replaces ω and pobs,i (∆ω) replaces p obs,i (ω). In other words, a single Helmholtz equation at frequency ∆ω is used to simulate p i (∆ω, s); however, rather than compare p i (∆ω, s) to actual content p obs,i (∆ω, s) at frequency ∆ω (which may not be present with sufficient SNR in the recorded signal), we instead compare p i (∆ω, s) to pobs,i (∆ω) resulting from equation (20).…”

“…Low frequencies lengthen this half-cycle window, allowing FWI to overcome errors in a starting model. 5 Unfortunately, the lack of low-frequency signal content on most ultrasound transducers currently designed for B-mode imaging prevents FWI from becoming more broadly applicable.…”

3D full-waveform inversion in ultrasound computed tomography employing a ring-array

“…The employed source pulse and the implementations of the transducer model are described elsewhere. 14,15 The measurements acquired from the five vertical locations are denoted as rings -2, -1, 0, +1, +2. The corresponding imaging planes are at vertical locations of -2.4 mm, -1.2 mm, 0 mm, 1.2 mm, and 2.4 mm, respectively.…”

“…The reconstruction method is a time-domain FWI method in which the forward model is based on the 3D acoustic wave equation and also accounts for the focusing properties of elevation-focused transducers. 14,15 Moreover, a distributed multi-GPU implementation was developed to improve computing efficiency. In this study, a 3D virtual imaging study of ring-array-based USCT that employs a realistic 3D acoustic numerical breast phantom 16 was performed.…”