Strain Heterogeneity in the Anterior Cruciate Ligament and Constitutive Modeling with Full-Field Methods

Abstract

Anterior cruciate ligament (ACL) injury rates are rising, particularly for women and young people. These injuries are debilitative; they typically require surgical reconstruction and lead to osteoarthritis within ten years. Still, there is little consensus about what puts someone at risk for an ACL injury, and this knowledge is critical to the development of injury prevention strategies. Finite element models provide an effective platform for systemically determining the effect of proposed injury risk factors on ACL strain concentrations, and thus, determining whether they predispose an individual to injury. However, the accuracy of a finite element model relies on the accuracy of the material models used in its construction.

Initially, I examined how the shape of the ligament-bone attachment (enthesis) might affect injury risk. Two factors were found to increase effective strain concentrations: more acute attachment angles and more concave enthesis shapes, both of which are more common in women. However, I also discovered that enthesis shape significantly affects the macroscopic (global) mechanical response of the model ligament. As such, I concluded that enthesis geometry (and the deformation heterogeneity it creates) would need to be considered in the construction of material models.

I also explored the effect of collagen fiber splay (material direction heterogeneity) on the macroscopic mechanical response of the ACL bundles and the patellar tendon (PT), a commonly used graft for ACL reconstruction. Using analytical, computational, and experimental approaches, results clearly demonstrate that splay geometry significantly affects the macroscopic mechanical response of ligaments. Since material properties are, by definition, independent of geometry, this indicates fiber splay is a structural property that prevents the identification of true material properties with standard modeling techniques.

Hence, in the finale of this work, I used displacement-encoded magnetic resonance imaging (MRI) to measure full-volume deformation fields of the ovine PT and both ACL bundles under tension. I then employed the virtual fields method (VFM) -- a full-field inverse method -- to calibrate material models with this data, accounting for strain heterogeneity, material direction heterogeneity (fiber splay), and enthesis shape. Most constitutive parameters were consistent among all specimen groups, demonstrating the universality of ligament material constituents. A material parameter describing the degree of anisotropy, or collagen fiber alignment, however, showed statistically significant differences between groups. It indicated that collagen fibers in the anteromedial (AM) bundle of the ACL were significantly more aligned than those in the posterolateral (PL), which is congruent with optical measurements. My work demonstrates that (when strain heterogeneity and structural properties are accounted for) ligament material microstructure is detectable with measures of mechanical function.