In the age of big data availability, data-driven techniques have been proposed recently to compute the time evolution of spatio-temporal dynamics. Depending on the required a priori knowledge about the underlying processes, a spectrum of black-box end-to-end learning approaches, physics-informed neural networks, and data-informed discrepancy modeling approaches can be identified. In this work, we propose a purely data-driven approach that uses fully convolutional neural networks to learn spatio-temporal dynamics directly from parameterized datasets of linear spatio-temporal processes. The parameterization allows for data fusion of field quantities, domain shapes, and boundary conditions in the proposed U$$^p$$ p -Net architecture. Multi-domain U$$^p$$ p -Net models, therefore, can generalize to different scenes, initial conditions, domain shapes, and domain sizes without requiring re-training or physical priors. Numerical experiments conducted on a universal and two-dimensional wave equation and the transient heat equation for validation purposes show that the proposed U$$^p$$ p -Net outperforms classical U-Net and conventional encoder–decoder architectures of the same complexity. Owing to the scene parameterization, the U$$^p$$ p -Net models learn to predict refraction and reflections arising from domain inhomogeneities and boundaries. Generalization properties of the model outside the physical training parameter distributions and for unseen domain shapes are analyzed. The deep learning flow map models are employed for long-term predictions in a recursive time-stepping scheme, indicating the potential for data-driven forecasting tasks. This work is accompanied by an open-sourced code.
Shear Wave Elasticity Imaging (SWEI) has become a popular medical imaging technique [1] in which soft tissue is excited by the acoustic radiation forces of a focused ultrasonic beam. Tissue stiffness can then be derived from measurements of shear wave propagation speeds [2]. The main objective of this work is a comparison of a finite element (FEM) and a finite difference method (FDM) in terms of their computational efficiency when modeling shear wave propagation in tissue phantoms. Moreover, the propagation of shear waves is examined in experiments with ballistic gelatin to assess the simulation results. In comparison to the FEM the investigated FDM proves to be significantly more performant for this computing task.
Elasticity of soft tissue is a valuable information to physicians in treatment and diagnosis of diseases. The elastic properties of tissue can be estimated with ultrasound (US) shear wave imaging (SWEI). In US-SWEI, a force push is applied inside the tissue and the resulting shear wave is detected by high-frequency imaging. The properties of the wave such as the shear wave velocity can be mapped to tissue elasticity. Commonly, wave features are extracted by tracking the peak of the shear wave, estimating the phase velocity or with machine learning methods. To tune and test these methods, often simulation data is employed since material properties and excitation can be accurately controlled. Subsequent validation on real US-SWEI data is in many cases performed on tissue phantoms such as gelatine. Clearly, validation performance of these procedures is dependent on the accuracy of the simulated tissue phantom and a thorough comparison of simulation and experimental data is needed. In this work, we estimate wave parameters from 400 US-SWEI data sets acquired in various homogeneous gelatine phantoms. We tune a linear material model to these parameters. We report an absolute percentage error for the shear wave velocity between simulation and phantom experiment of <2.5%. We validate our material model on unknown gelatine concentrations and estimate the shear wave velocity with an error <3.4% for in-range concentrations indicating that our material model is in good agreement with US-SWEI measurements.
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