Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and Poisson?s ratio

Elasticity imaging is a technique that discovers the spatial distribution of mechanical properties of tis-sue using deformation and force measurements under various loading conditions. Given the complexity of this discovery, most existing methods approximate only one material parameter while assuming ho-mogeneous distributions for the others. We employ physics-informed neural networks (PINN) in linear elasticity problems to discover the space-dependent distribution of both elastic modulus (E) and Pois-son's ratio (nu) simultaneously, using strain data, normal stress boundary conditions, and the governing physics. We validated our model on three examples. First, we experimentally loaded hydrogel samples with embedded stiff inclusions, representing tumorous tissue, and compared the approximations against ground truth determined through tensile tests. Next, using data from finite element simulation of a rect-angular domain containing a stiff circular inclusion, the PINN model accurately localized the inclusion and estimated both E and nu. We observed that in a heterogeneous domain, assuming a homogeneous nu distribution increases estimation error for stiffness as well as the area of the stiff inclusion, which could have clinical importance when determining size and stiffness of tumorous tissue. Finally, our model ac-curately captured spatial distribution of mechanical properties and the tissue interfaces on data from another computational model, simulating uniaxial loading of a rectangular hydrogel sample containing a human brain slice with distinct gray matter and white matter regions and complex geometrical features. This elasticity imaging implementation has the potential to be used in clinical imaging scenarios to re-liably discover the spatial distribution of mechanical parameters and identify material interfaces such as tumors.Statement of significanceOur work is the first implementation of physics-informed neural networks to reconstruct both material parameters - Young's modulus and Poisson's ratio - and stress distributions for isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model us-ing experimental measurements and synthetic data generated using finite element modeling. Our method can be implemented in clinical elasticity imaging scenarios to improve diagnosis of tumors and for me-chanical characterization of biomaterials and biological tissues in a minimally invasive manner.(c) 2022 The Author(s). Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

Elasticity imaging is a technique to discover the mechanical properties of tissues using deformation and force measurements. We use physics-informed neural networks (PINN) to simultaneously discover the distribution of elastic modulus and Poisson's ratio in linear elasticity problems. Our model is validated through experiments and simulations.