Abstract
The Autoprogressive Method (AutoP) is a fundamentally different approach to solving the inverse problem in quasi-static ultrasonic elastography (QUSE). By exploiting the nonlinear adaptability of artificial neural networks and physical constraints imposed through finite element analysis, AutoP is able to build patient specific soft-computational material models from a relatively sparse set of force-displacement measurement data. Physics-guided, data-driven models offer a new path to the discovery of mechanical properties most effective for diagnostic imaging. AutoP was originally applied to modeling mechanical properties of materials in geotechnical and civil engineering applications. The method was later adapted to reconstructing maps of linear-elastic material properties for cancer imaging applications. Previous articles describing AutoP focused on high-level concepts to explain the mechanisms driving the training process. In this review, we focus on AutoP as applied to QUSE to present a more thorough explanation of the ways in which the method fundamentally differs from classic model-based and other machine learning approaches. We build intuition for the method through analogy to conventional optimization methods and explore how maps of stresses and strains are extracted from force-displacement measurements in a model-free way. In addition, we discuss a physics-based regularization term unique to AutoP that illuminates the comparison to typical optimization procedures. The insights gained from our hybrid inverse method will hopefully inspire others to explore combinations of rigorous mathematical techniques and conservation principles with the power of machine learning to solve difficult inverse problems.
Highlights
Soft tissues are complex structures that exhibit non-linear, time-dependent elastic properties
We focus our discussion on quasi-static ultrasound elastography (QUSE), wherein local tissue displacements are estimated from RF echo frames acquired as an ultrasound probe is slowly pressed into the tissue surface
We found that Cartesian neural network constitutive models (CaNNCMs) trained in Autoprogressive Method (AutoP) using only boundary information were unable to recover internal structure away from the surface
Summary
Soft tissues are complex structures that exhibit non-linear, time-dependent elastic properties. Elasticity imaging methods have been developed to fill this niche and directly evaluate the mechanical properties of soft tissue. Estimating material properties from force-displacement measurements constitutes the inverse problem in QUSE. Unlike other data-driven approaches, AutoP combines physical modeling through finite element analysis (FEA) with artificial neural networks (ANNs) to extract the stress-strain relationship embedded within force-displacement measurements. In the context of elasticity imaging, ANNs characterizing the stress-strain behavior of soft tissues can be interrogated to infer material parameters that best summarize the learned mechanical properties. Data acquisition and displacement estimation details are omitted from our discussions, but are available in [24, 25] Even though such details are important in practice and will affect the efficacy of QUSE methods, we wish to compare the operation of AutoP and model-based methods at a more conceptual level
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