We 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. Here, 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.
Seidl, Daniel Thomas, et al. "Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging." Inverse Problems in Science and Engineering, vol. 28, no. 2, Apr. 2019. https://doi.org/10.1080/17415977.2019.1603222
Seidl, Daniel Thomas, van Bloemen Waanders, Bart G., & Wildey, Timothy Michael (2019). Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging. Inverse Problems in Science and Engineering, 28(2). https://doi.org/10.1080/17415977.2019.1603222
Seidl, Daniel Thomas, van Bloemen Waanders, Bart G., and Wildey, Timothy Michael, "Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging," Inverse Problems in Science and Engineering 28, no. 2 (2019), https://doi.org/10.1080/17415977.2019.1603222
@article{osti_1515211,
author = {Seidl, Daniel Thomas and van Bloemen Waanders, Bart G. and Wildey, Timothy Michael},
title = {Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging},
annote = {We 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. Here, 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.},
doi = {10.1080/17415977.2019.1603222},
url = {https://www.osti.gov/biblio/1515211},
journal = {Inverse Problems in Science and Engineering},
issn = {ISSN 1741-5977},
number = {2},
volume = {28},
place = {United States},
publisher = {Taylor & Francis},
year = {2019},
month = {04}}
Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, Vol. 224, Issue 2https://doi.org/10.1243/09544119JEIM586