Vector Flow Imaging in Layered Models With a High Speed of Sound Contrast Using Pulse-Echo Ultrasound and Photoacoustics

TL;DR

The paper presents a refraction-corrected delay-and-sum (RC-DAS) approach combined with a multi-angle vector flow algorithm to quantify particle flow in layered media with strong speed-of-sound contrasts, using simultaneous photoacoustic and ultrasonographic data. By explicitly accounting for layer interfaces via Snell's law and Kirchhoff migration, RC-DAS improves image geometry and expands the region where flow can be quantified, yielding more accurate flow speeds and directions than conventional DAS. The method is validated on benchtop PMMA-layered phantoms with flowing carbon suspensions, showing MAE reductions of about 0.41–0.63 mm/s and substantial reductions in angular error, while highlighting modality-specific limitations and trade-offs between PA and US. The work underscores the importance of refraction correction for reliable VFI in layered media and suggests dual-modality VFI as a promising avenue for biomedical and nondestructive testing applications.

Abstract

In this study, we develop vector flow imaging techniques for multi-layered models with a high wavespeed contrast using photoacoustic and ultrasonic imaging. We use refraction-corrected delay-and-sum image reconstruction (RC-DAS), which enforces Snell's law to accurately calculate time delays within each layer. We compare RC-DAS against conventional delay-and-sum for vector flow imaging in benchtop phantoms made of transparent polymethyl methacrylate (PMMA) in a water bath. We study the flow beneath a PMMA layer using two phantoms, where the PMMA layer has different shapes and thicknesses. We image a slow-moving suspension of carbon microspheres (~4 mm/s) using interleaved photoacoustic and multi-angle plane wave ultrasound acquisitions measured with a 7.6 MHz linear ultrasound array. Photoacoustic waves are generated by a 1064 nm wavelength nanosecond-pulsed laser at 50 Hz, and multi-angle plane wave ultrasound data are acquired at 100 Hz for eleven steering angles between $\pm$10$^\circ$. RC-DAS improves the flow speed accuracy, reducing the mean absolute error by 0.41-0.63 mm/s compared to the expected flow profile. The error in direction estimates improves when we use RC-DAS, with the interdecile range reducing by up to 17$^\circ$. This work emphasises the importance of refraction correction for accurate flow measurements in layered media with photoacoustics and ultrasonic imaging. While both imaging modalities can quantify flow in these multi-layered models, the modality best suited for a specific application will depend on the imaging target and flow dynamics. These techniques show promise for biomedical applications such as intraosseous and transcranial blood flow quantification, and in nondestructive testing to monitor fluid motion.

Figures (11)

• Figure 1: Refraction of acoustic rays to and from an US scatterer (indicated as the "pixel of interest"). For the plane wave transmission, the steering angle in the lens ($\theta_l$) is chosen by the operator, while the transmit angle at the pixel $\theta$ is calculated and used in \ref{['matrix_vf_US']}. The receive angle at a pixel $\phi$ is changed using multiple receive subapertures (labelled "Rx") to obtain the desired $\phi$ angles during reconstruction.
• Figure 2: (a) Experimental setup for interleaved PA and US acquisitions of the multi-layered models. The carbon particle suspension is pumped through the channel via a syringe pump. The US transducer is suspended at the surface of the water bath, and the laser light is directed to the phantoms via an optical fibre bundle, which has two linear outputs on either side of the US probe. Cross-sections of the PMMA phantoms studied in these experiments are shown in (b-c). The blue lines show the walls of the optically-transparent PVC tubing, which transfers the carbon suspension from the syringe pump through the channel. (d) Timing sequence for interleaved acquisition of PA and US frames. Each frame recorded by each modality is indexed by “i”. Red boxes correspond to the acquisition of a PA frame from a single laser pulse, while each blue box contains one US frame composed of eleven steered plane wave transmissions. The width of the boxes is not to scale. "wait #1" ensures the US FR is 100 Hz, while "wait #2" is the time until the next PA acquisition so that the PA FR is 50 Hz.
• Figure 3: Data processing pipeline for USVF imaging using RC-DAS. The dimensions are: N$_\text{T}$ - the number of fast time samples, N$_\text{Elem.}$ - the number of transducer elements, N$_\text{x/z}$ - the size of the images in the $x/z$ direction, N$_\text{Tx}$ - the number of steered plane waves, and N$_\text{Rx}$ - the number of receive angles. For PAVF, the dimension N$_\text{Tx}$ is removed.
• Figure 4: Process to calculate the expected flow speed profile for PAVF and USVF imaging. We estimate the FWHM distance for PA and US in the elevation direction via Field II simulations. In the two left panels, the colourmap indicates the flow speed at the different locations in the channel cross-section, with yellow indicating faster flow speeds than black.
• Figure 5: The resolution within images acquired with beam steering ($\beta\neq0^\circ$, blue oval) is related to the axial and lateral resolution of the unsteered images (red oval). The largest axial resolution (AR) in the images contributing to a vector flow image corresponds to the largest $\beta$ in the image PSF due to beam steering ($\phi$ and $\theta$).