Model Development for Soft Tissue Biomechanics by Full-Field Characterization and Variational System Identification

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Each year hundreds of thousands of people suffer soft tissue injuries that require surgical reconstruction. Anterior Cruciate Ligament (ACL) damage/rupture is the most common injury in athletic individuals. Notably, injury rates are higher in women with a relative risk factor of 4-6 compared to men, and this rises to 10 for women in military training. For grafts of replacement or engineered tissue to be effective and not harmful to the patient in a few years, it is important to be able to precisely characterize their mechanical properties, as well as to develop computational models of their mechanical performance. This project will address the challenge of characterization via novel experimental techniques that can map out the deformation at every point in specimens of ligaments and tendons of the knee. The problem of developing accurate models will be addressed by furthering recent advances in machine learning that can use the three-dimensional data to identify the most appropriate model. This project will provide fundamental knowledge that will enable advances in orthopedic surgery for repair and replacement of ligaments and tendons of the knee and other joints. Experimental and machine learning methods used in this project will be translated into educational modules aimed at high school students and designed to attract these students to study engineering and computation. A new, fully three-dimensional approach to soft material characterization and constitutive modeling is studied in this project. The experimental approach involves in situ mechanical loading in a magnetic field, yielding the finite deformation tensor field throughout the volume of the specimen. This has been coupled with our recent computational advances in inverse modeling to infer the soft tissue mechanics constitutive model that best represents full-field deformation data, from a spectrum of admissible candidate models, with parsimonious representation, accurate coefficients, and uncertainty quantification. This novel combination of approaches overcomes the challenges of identifying material properties of soft tissue in traditional experiments that rely on the assumption of uniform, largely one-dimensional, deformation over regularly shaped test specimens. In this work, characterization of irregular shapes and boundaries is possible with a reduced number of deformation states due to the available full, three-dimensional, finite strain tensor field. Inference techniques assemble the optimal constitutive representation from a library of operators without restriction to only determining the coefficients of a pre-selected model. The full-field approach makes it possible to characterize soft tissues of the knee and infer the physically best-suited and parsimonious mathematical models of their mechanical responses with confidence bounds and uncertainty quantification. Those models are incorporated into computational models of the knee that can simulate injury-inducing loading accurately and with the full strain and stress fields in these tissues during injury-inducing deformations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.