Data-driven medical image formation without a priori models

Elastograms are 3-D images of tissue mechanical properties constructed from a sparse set of force-displacement measurements recorded using ultrasonic imaging. They can be an important medical resource if we can solve a difficult ill-posed inverse problem. The usual solution is to assume a parametric constitutive model of mechanical behavior and constrain the experiment to reduce model dimensionality until it matches the available data. A better approach is to enter the sparse measurements into two finite-element algorithms (FEAs) operating on one meshed volume of the deformed medium. One FEA operates on measured forces and the other on measured displacements, each modeling the deformation patterns based on the data they receive and an initial guess at material properties. We replace the constitutive matrix that FEA depends on for material properties with initialized neural networks that iteratively learn those properties by training with data gathered after each FEA cycle. The FEA models agree once both converge to the true medium properties. This approach relies only on the measurements and the principles of equilibrium and compatibility imposed by the FEAs on the data when training the networks. In this way, training occurs without assuming a constitutive model of material properties, making it ideal for model discovery.



The neural networks learn material properties from sparse ultrasound measurements because every estimate of displacement made within a slowly deformed tissue contains information about the properties and boundary conditions throughout the entire contiguous medium. As an operator probes tissues and numerical model development begins, an entropy-based measure of data diversity indicates to the operator when sufficient information has been collected. Once a numerical model has converged, a constitutive model is applied to it to estimate parametric images for medical diagnosis. Unlike deep learning methods that require training data spanning any object that might be encountered, this method focuses on collecting a comprehensive data set for a given patient. We aim to discover what constitutes the comprehensive data set that informs machine learning for high-quality image formation.