Transcranial ultrasound imaging assumes a growing significance in the detection and monitoring of intracranial lesions and cerebral blood flow. Accurate solution of partial differential equation (PDE) is one of the prerequisites for obtaining transcranial ultrasound wavefields. Grid-based numerical solvers such as finite difference (FD) and finite element methods have limitations including high computational costs and discretization errors. Purely data-driven methods have relatively high demands on training datasets. The fact that physics-informed neural network can only target the same model limits its application. In addition, compared to time-domain approaches, frequency-domain solutions offer advantages of reducing computational complexity and enabling stable and accurate inversions. Therefore, we introduce a framework called FD-embedded UNet (FEUNet) for solving frequency-domain transcranial ultrasound wavefields. The PDE error is calculated using the optimal 9-point FD operator, and it is integrated with the data-driven error to jointly guide the network iterations. We showcase the effectiveness of this approach through experiments involving idealized skull and brain models. FEUNet demonstrates versatility in handling various input scenarios and excels in enhancing prediction accuracy, especially with limited datasets and noisy information. Finally, we provide an overview of the advantages, limitations, and potential avenues for future research in this study.

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.

Transcranial ultrasound imaging has been playing an increasingly important role in the non-invasive treatment of brain disorders. However, the conventional mesh-based numerical wave solvers, which are an integral part of imaging algorithms, suffer from limitations such as high computational cost and discretization error in predicting the wavefield passing through the skull. In this paper, we explore the use of physics-informed neural networks (PINNs) for predicting the transcranial ultrasound wave propagation. The wave equation, two sets of time snapshots data and a boundary condition (BC) are embedded as physical constraints in the loss function during training. The proposed approach has been validated by solving the two-dimensional (2D) acoustic wave equation under three increasingly complex spatially varying velocity models. Our cases demonstrate that due to the meshless nature of PINNs, they can be flexibly applied to different wave equations and types of BCs. By adding physics constraints to the loss function, PINNs can predict wavefields far outside the training data, providing ideas for improving the generalization capability of existing deep learning methods. The proposed approach offers exciting perspectives because of the powerful framework and simple implementation. We conclude with a summary of the strengths, limitations and further research directions of this work.

Plane Wave Imaging (PWI) plays a crucial role in the field of medical ultrasound imaging; however, its application scenarios are constrained by the predominant use of rigid probes. This study presents a design and fabrication process of a type of flexible ultrasound transducer suitable for PWI. The process involves attaching specifically shaped PZT-5H thin films to copper electrodes adhered to PDMS material. The linear array comprises 32 individual elements, each with dimensions of 10mm × 1mm × 0.4mm. The average resonance frequency, capacitance, and loss tangent are 7.58 MHz, 1082.2 pF, and 0.018, respectively. Experimental results illustrate the transducer’s flexibility by adhering it to curved surfaces (convex and limb surfaces). Moreover, both single plane-wave and multi-angle plane-wave imaging experiments were conducted using the flexible transducers, demonstrating the feasibility for PWI. With its compact size, flexibility, and portability, the transducers hold potential for long-term non-invasive monitoring applications in the future.

This paper proposes a modeling method for scattered acoustic fields under complex structures based on Physics-informed Neural Networks (PINNs), with particular attention to the acquisition of training sets and the embedding of physical governing equations. First, using acoustic simulation softwares to obtain the scattered acoustic field under various models, and select the scattered acoustic field data at several moments as the training sets. Then, according to the characteristics of the simulated model, the corresponding physical equations have been embedded in the loss function of the network. We tested the method by predicting the propagation of ultrasonic waves and the scattering of acoustic fields with various simple scatterers. Furthermore, we also use PINN to simulate the scattered acoustic field of the real complex damaged structure. The results show that the mean square error (MSE) between prediction and ground truth is in the order of 10-4, which illustrate PINN can effectively simulate the propagation and reflection of ultrasonic waves, and can also simulate the scattered acoustic field of complex structures accurately. The meshless and accurate characteristics of PINN provide a reliable alternative for the theoretical prediction of complex and continuous scattered acoustic fields.