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 (Bi‑GRU) 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, and in vivo mouse 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.