Modeling of Transcranial Ultrasound in Frequency Domain Based on Physics-constrained UNet

Modeling of transcranial ultrasound has received increasing attention in the treatment of brain diseases due to its fast, non-invasive and real-time advantages. The commonly used numerical methods suffer from limitations such as discretization error and high computational cost when dealing with high-dimensional or high-frequency problems. In recent years, the ability of neural networks (NNs) has been continuously explored and gradually applied in medical ultrasound imaging. However, NNs are known to relatively rely on training data. For cases outside of the data set, accurate results are not always available. By employing the approach of Physics-informed Neural Networks (PINN), the predicament of excessive dependence of NNs on training data has been largely mitigated. However, each instance of PINN can only target a specific input model. In this paper, we introduce a Physics-constrained UNet (PCUNet) framework for addressing frequency-domain transcranial wavefields. PCUNet utilizes the UNet architecture for data-driven processing while concurrently integrating physical constraints derived from the governing equations to guide the network's iterations. The physical constraints are calculated using the optimal 9-point finite difference method, which is different from PINN in principle. We showcased the effectiveness of this approach using two-dimensional (2D) brain models, indicating its ability to enhance network predictive performance, particularly in scenarios with limited samples and noisy data.