Comparing continuum and direct fiber models of soft tissues: An ocular biomechanics example reveals that continuum models may artificially disrupt the strains at both the tissue and fiber levels

Abstract

Collagen fibers are the main load-bearing component of soft tissues but difficult to incorporate into models. Whilst simplified homogenization models suffice for some applications, a thorough mechanistic understanding requires accurate prediction of fiber behavior, including both detailed fiber-level strains and long-distance transmission. Our goal was to compare the performance of a continuum model of the optic nerve head (ONH) built using conventional techniques with a fiber model we recently introduced which explicitly incorporates the complex 3D organization and interaction of collagen fiber bundles [1]. To ensure a fair comparison, we constructed the continuum model with identical geometrical, structural, and boundary specifications as for the fiber model. We found that: 1) although both models accurately matched the intraocular pressure (IOP)-induced globally averaged displacement responses observed in experiments, they diverged significantly in their ability to replicate specific 3D tissue-level strain patterns. Notably, the fiber model faithfully replicated the experimentally observed depth-dependent variability of radial strain, the ring-like pattern of meridional strain, and the radial pattern of circumferential strain, whereas the continuum model failed to do so; 2) the continuum model disrupted the strain transmission along each fiber, a feature captured well by the fiber model. These results demonstrate limitations of the conventional continuum models that rely on homogenization and affine deformation assumptions, which render them incapable of capturing some complex tissue-level and fiber-level deformations. Our results show that the strengths of explicit fiber modeling help capture intricate ONH biomechanics. They potentially also help modeling other fibrous tissues.

Statement of significance

Understanding the mechanics of fibrous tissues is crucial for advancing knowledge of various diseases. This study uses the ONH as a test case to compare conventional continuum models with fiber models that explicitly account for the complex fiber structure. We found that the fiber model captured better the biomechanical behaviors at both the tissue level and the fiber level. The insights gained from this study demonstrate the significant potential of fiber models to advance our understanding of not only glaucoma pathophysiology but also other conditions involving fibrous soft tissues. This can contribute to the development of therapeutic strategies across a wide range of applications.