This research involves the development of optimization techniques for the automatic determination of the material properties of deformable solids via modern imaging and scanning technologies (e.g. MRI, CT, etc.) with particular focus on hyper-elastic materials under large deformation, high strain rates and often plasticity. Such materials are characteristic of biological soft tissues (e.g. muscle, fat, skin etc.) and their determination is critical to creating accurate, subject specific simulations of the function of these anatomical structures. Simulation using modern computational techniques is an increasingly reliable tool for answering many questions in biomedical engineering ranging from basic functionality to post-surgical response of complex regions of the anatomy. However, reliable results are only possible when accurate constitutive descriptions of the simulated materials are available. Although much work has been done to develop and determine constitutive models for biological soft tissues, most material parameters have been estimated from cadaveric specimens or from a small group of individuals. This is an unacceptable simplification given the widely established variation in material behavior across subjects and from the material changes inherent in cadaveric specimens. This research will establish techniques for the near-automatic determination of subject specific behavior necessary to continue the relevance and reliability of biomedical simulation of soft tissues. Though motivated by biomedical simulation, the techniques developed in this research transcend the boundaries of biomechanics and will provide a more general framework for determining material properties for engineering applications.
The PI and collaborators will use their combined experience in constitutive modeling, finite element simulation of soft tissues, mesh generation, optimization and medical imaging to formulate and develop methods for the determination of constitutive parameters from imaged behaviors. This task is formulated as an inverse problem of fitting a constitutive model to observed material motion (involving imaging, segmentation and denoising). The PI and collaborators will draw upon their prior experience with similar techniques for estimating muscles activation parameters and muscle material properties from material deformation. The capstone problems to be solved involve accurately tracking material particle trajectories with imaging technologies and approximating the Jacobian of elastic equilibrium configurations of soft tissues with respect to unknown material parameters in a given constitutive model. With this functionality, the PI and collaborators will determine the suitability of established optimization techniques and develop novel approaches (both engendered by the successful solution of previously mentioned capstone problems).
