  Soft biological tissues often have complex mechanical properties due to
variation in structural components. In this paper, we develop a novel
UNet-based neural network model for inversion in elasticity (El-UNet) to infer
the spatial distributions of mechanical parameters from strain maps as input
images, normal stress boundary conditions, and domain physics information. We
show superior performance, both in terms of accuracy and computational cost, by
El-UNet compared to fully-connected physics-informed neural networks in
estimating unknown parameters and stress distributions for isotropic linear
elasticity. We characterize different variations of El-UNet and propose a
self-adaptive spatial loss weighting approach. To validate our inversion
models, we performed various finite-element simulations of isotropic domains
with heterogenous distributions of material parameters to generate synthetic
data. El-UNet is faster and more accurate than the fully-connected
physics-informed implementation in resolving the distribution of unknown
fields. Among the tested models, the self-adaptive spatially weighted models
had the most accurate reconstructions in equal computation times. The learned
spatial weighting distribution visibly corresponded to regions that the
unweighted models were resolving inaccurately. Our work demonstrates a
computationally efficient inversion algorithm for elasticity imaging using
convolutional neural networks and presents a potential fast framework for
three-dimensional inverse elasticity problems that have proven unachievable
through previously proposed methods.
