SSI-Net: a hybrid physics-constrained deep learning framework for quantitative ultrasound speed-of-sound reconstruction

Objective.Quantitative ultrasound tomography faces challenges in reconstructing speed-of-sound (SoS) distributions due to the ill-posed nature of the inverse problem and the computational complexity of full-waveform inversion. This study aims to develop an efficient and physically consistent deep learning framework for accurate SoS mapping from ultrasound signals.Approach. We propose speed of sound inversion network (SSI-Net), a dual data-physics-driven framework that integrates a bidirectional gated recurrent unit encoder for temporal feature extraction, a U-Net decoder for high-resolution spatial mapping, and a physics-constraint module based on an exact, differentiable finite-difference time-domain solver of the nonlinear Westervelt equation. The network model is trained through a joint optimization strategy that minimizes both data-fidelity loss and physics-informed residual loss, with a two-phase training schedule to ensure stable convergence.Main results.SSI-Net was validated across simulated, tissue-mimicking phantom, andin vivomouse datasets. It achieved superior reconstruction accuracy, with peak signal-to-noise ratio improvements of 7.4%-18.9% over state-of-the-art methods, while reducing the physics-based residual by 25.6%-57.5%. The framework demonstrated strong generalization to different transducer geometries (ring and linear arrays) and maintained stable performance across a ten-fold frequency range. Inference was completed within 109.4 ms per sample.Significance.By embedding an exact wave solver into a trainable architecture, SSI-Net combines the representational capacity of deep learning with strict physical consistency. It provides a robust, efficient, and clinically translatable solution for quantitative SoS imaging, offering a promising tool for tissue characterization in diagnostic ultrasound.