Regulating the development of accurate data-driven physics-informed deformation models

Abstract

The challenge posed by the inverse problem associated with ultrasonic elasticity imaging is well matched to the capabilities of data-driven solutions. This report describes how data properties and the time sequence by which the data are introduced during training influence deformation-model accuracy and training times. Our goal is to image the elastic modulus of soft linear-elastic media as accurately as possible within a limited volume. To monitor progress during training, we introduce metrics describing convergence rate and stress entropy to guide data acquisition and other timing features. For example, a regularization term in the loss function may be introduced and later removed to speed and stabilize developing deformation models as well as establishing stopping rules for neural-network convergence. Images of a 14.4 cm³ volume within 3D software phantom visually indicate the quality of modulus images resulting over a range of training variables. The results show that a data-driven method constrained by the physics of a deformed solid will lead to quantitively accurate 3D elastic modulus images with minimum artifacts.