Introduction and Numerical Validation of an Open-Source MATLAB Package for Quantitative Ultrasound Tomography via Ray-Born Inversion

TL;DR

The paper presents an open-source MATLAB package for quantitative ultrasound tomography that reconstructs sound-speed maps from transmission data using two-point ray tracing. It combines a fast time-of-flight (ToF) based inversion with a high-resolution ray-Born inversion, where ToF iterates initialize the Born-based updates and Green’s-function–driven ray tracing operates in the frequency domain. The toolbox implements four ray-tracing methods, two interpolation schemes, and ray linking strategies, with a modular pipeline that balances computational efficiency and reconstruction accuracy. Numerical validation against analytic ray trajectories using Maxwell’s fish-eye phantom demonstrates accurate ray paths and consistent acoustic-length calculations, while supplementary experiments on synthetic and public in-vitro/in-vivo datasets support practical applicability. The work delivers a reproducible, extensible toolkit for ultrasound tomography with explicit, well-documented steps suitable for researchers and developers in medical imaging.

Abstract

We present a MATLAB package for reconstructing sound-speed images from transmission ultrasound data. The package is based on two-point ray tracing and implements two complementary inversion strategies for image reconstruction. The first is a time-of-flight (ToF) method that produces low-resolution, low-contrast images with minimal artefacts. The second is a ray-Born inversion method, which integrates high-frequency ray theory with the Born approximation to generate high-resolution sound-speed reconstructions. Early iterations of the ToF reconstruction are used to provide an initial estimate for the more advanced ray-Born approach. The core of this software package consists of four ray-tracing algorithms, whose accuracy is assessed in this study with respect to known analytical trajectories and accumulated acoustic path lengths. Furthermore, both image-reconstruction strategies have been validated numerically with simulated synthetic datasets and experimentally with open-source in-vitro and in-vivo datasets in related parallel studies.

Figures (5)

• Figure 1: Trajectories of rays linking a single emitting transducer to all receiving transducers. The color of each linked ray is scaled by the accumulated time delay referenced to the emitter. Given the positions $\mathbf{x}$ of the linked rays, the red-colored rays represent $\mathbf{x} + 0.01\, \delta \mathbf{x}$, where $\delta \mathbf{x}$ is computed by the paraxial ray tracing.
• Figure 2: (a) Maxwell fish-eye lens. Sampled ray points computed using the second-order Runge--Kutta ray-tracing algorithm: (b) 2D case, (c) 3D case. Distances of sampled points to the centers of the expected circular paths for four different ray tracing algorithms: (d) 2D case, (e) 3D case. The ratio $\Delta s / \Delta x = 1$ is used.
• Figure 3: Mean radius deviation (%) of sampled ray points versus ray-to-grid spacing for four different ray-tracing algorithms.
• Figure 4: Accumulated acoustic length of rays traced using four ray-tracing algorithms as a function of the initial angles $\theta$ and $\varphi$ for 2D and 3D cases, respectively. The ratio $\Delta s / \Delta x = 1$ is used.
• Figure 5: Mean acoustic length deviation (%) of sampled ray points versus ray-to-grid spacing for four ray-tracing algorithms.