Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging

Abstract

ABSTRACTWe present a formulation to simultaneously invert for a heterogeneous shear modulus field and traction boundary conditions in an incompressible linear elastic plane stress model. Our approach utilizes scalable deterministic methods, including adjoint-based sensitivities and quasi-Newton optimization, to reduce the computational requirements for large-scale inversion with partial differential equation (PDE) constraints. We address the use of regularization for such formulations and explore the use of different types of regularization for the shear modulus and boundary traction. We apply this PDE-constrained optimization algorithm to a synthetic dataset to verify the accuracy in the reconstructed parameters, and to experimental data from a tissue-mimicking ultrasound phantom. In all of these examples, we compare inversion results from full-field and sparse data measurements.