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Ultrasound (US) elastography is a technique that enables non-invasive quantification of material properties, such as stiffness, from ultrasound images of deforming tissue. The displacement field is measured from the US images using image matching algorithms, and then a parameter, often the elastic modulus, is inferred or subsequently measured to identify potential tissue pathologies, such as cancerous tissues. Several traditional inverse problem approaches, loosely grouped as either direct or iterative, have been explored to estimate the elastic modulus. Nevertheless, the iterative techniques are typically slow and computationally intensive, while the direct techniques, although more computationally efficient, are very sensitive to measurement noise and require the full displacement field data (i.e., both vector components). In this work, we propose a deep learning approach to solve the inverse problem and recover the spatial distribution of the elastic modulus from one component of the US measured displacement field. The neural network used here is trained using only simulated data obtained via a forward finite element (FE) model with known variations in the modulus field, thus avoiding the reliance on large measurement data sets that may be challenging to acquire. A U-net based neural network is then used to predict the modulus distribution (i.e., solve the inverse problem) using the simulated forward data as input. We quantitatively evaluated our trained model with a simulated test dataset and observed a 0.0018 mean squared error (MSE) and a 1.14% mean absolute percent error (MAPE) between the reconstructed and ground truth elastic modulus. Moreover, we also qualitatively compared the output of our U-net model to experimentally measured displacement data acquired using a US elastography tissue-mimicking calibration phantom.
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