Physics-Informed Deep Learning for Elasticity—Forward, Inverse and Mixed Problems

Elastography is an emerging imaging modality to estimate the elasticity of biological tissues by comparing ultrasound signals before and after a light compression. Ultrasound examinations are much more accurate in the axial direction than in the lateral direction. However, current elastography methods generally require both axial and lateral displacement components, making them ineffective for clinical applications. Additionally, the assumption of incompressibility adopted in current elastography methods results in inaccurate Young’s modulus reconstructions. Here, we introduce a new physics-informed deep learning method for elastography. By integrating a displacement network and an elasticity network, the proposed method can reconstruct the Young’s modulus field of a heterogeneous object based on only a measured axial displacement field. Moreover, the proposed method can remove the assumption of incompressibility and reconstruct the Young’s modulus and Poisson’s ratio fields at the same time. We show that the “egg shell” effect where the stiff material prevents the generation of strain in the soft material could be a source of error, and using multiple measurements can help mitigate this potential problem and increase the prediction accuracy. While the proposed method is an iterative approach, we demonstrate that the initial guess has no significant effect on the final prediction. Lastly, we show that activation functions play an important role when using deep neural networks to approximate physical fields. The proposed method opens new venues for efficiently and accurately solving inverse problems in materials characterization, medical imaging, and beyond.