Implicit Neural Representations for Speed-of-Sound Estimation in Ultrasound

TL;DR

This work introduces implicit neural representations (INRs) for speed-of-sound (SoS) estimation in ultrasound by modeling a per-case continuous SoS field $c(\bar{x})$ with a SIREN-based INR, integrated into a differentiable beamforming framework. The SoS field is expressed as $c(\bar{x}) = \Delta c(\bar{x}) + c_0(\bar{x})$, with $\Delta c$ captured by an INR using $\bar{x} \in [0,1]^2$ and a sine activation $\rho(z)=\sin(\omega z)$ ($\omega=30$). Training optimizes a physics-informed loss $\mathcal{L}(\bar{c}) = \mathcal{L}_{pe}(\bar{c}) + \alpha \mathcal{L}_{tv}(\bar{c})$ ($\alpha=0.01$), allowing per-case adaptation to tissue variability and imaging protocols. In phantom experiments, the INR method achieved RMSE improvements over differentiable beamforming-based automatic methods in most inclusions and yielded more physically plausible, though still challenging, SoS maps; results indicate that INRs can enhance quantitative ultrasound by incorporating complex physics directly into the estimation process. Overall, this approach demonstrates that per-case INR optimization can effectively estimate QUS parameters with potential for 3D extension and broader QUS parameter estimation.

Abstract

Accurate estimation of the speed-of-sound (SoS) is important for ultrasound (US) image reconstruction techniques and tissue characterization. Various approaches have been proposed to calculate SoS, ranging from tomography-inspired algorithms like CUTE to convolutional networks, and more recently, physics-informed optimization frameworks based on differentiable beamforming. In this work, we utilize implicit neural representations (INRs) for SoS estimation in US. INRs are a type of neural network architecture that encodes continuous functions, such as images or physical quantities, through the weights of a network. Implicit networks may overcome the current limitations of SoS estimation techniques, which mainly arise from the use of non-adaptable and oversimplified physical models of tissue. Moreover, convolutional networks for SoS estimation, usually trained using simulated data, often fail when applied to real tissues due to out-of-distribution and data-shift issues. In contrast, implicit networks do not require extensive training datasets since each implicit network is optimized for an individual data case. This adaptability makes them suitable for processing US data collected from varied tissues and across different imaging protocols. We evaluated the proposed SoS estimation method based on INRs using data collected from a tissue-mimicking phantom containing four cylindrical inclusions, with SoS values ranging from 1480 m/s to 1600 m/s. The inclusions were immersed in a material with an SoS value of 1540 m/s. In experiments, the proposed method achieved strong performance, clearly demonstrating the usefulness of implicit networks for quantitative US applications.

Figures (3)

• Figure 1: A schematic of the proposed framework for speed-of-sound estimation in ultrasound. An implicit network is trained to produce speed-of-sound estimates, which are then used for image reconstruction through a differentiable delay-and-sum beamformer. The phase shift error is computed from the reconstructed data and backpropagated to the implicit network, updating its weights accordingly.
• Figure 2: Qualitative results obtained for the proposed method based on implicit networks. Reconstructed B-mode images and the speed-of-sound parametric maps were determined for a tissue-mimicking phantom containing inclusions with varying speed-of-sound values.
• Figure 3: The lateral and longitudinal cross-sections of the speed-of-sound parametric maps were analyzed with respect to the centers of the phantom inclusions.