Machine Learning in Model-free Mechanical Property Imaging: Novel Integration of Physics With the Constrained Optimization Process

Cameron Hoerig, Jamshid Ghaboussi, Yiliang Wang, Michael F. Insana

Research output: Contribution to journalReview articlepeer-review


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.

Original languageEnglish (US)
Article number600718
JournalFrontiers in Physics
StatePublished - Jul 30 2021


  • elasticity
  • finite element analysis
  • Inverse problem
  • neural network constitutive model
  • ultrasound

ASJC Scopus subject areas

  • Biophysics
  • Materials Science (miscellaneous)
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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