A direct fiber approach to model sclera collagen architecture and biomechanics

Abstract

Sclera collagen fiber microstructure and mechanical behavior are central to eye physiology and pathology. They are also complex, and are therefore often studied using modeling. Most models of sclera, however, have been built within a conventional continuum framework. In this framework, collagen fibers are incorporated as statistical distributions of fiber characteristics such as the orientation of a family of fibers. The conventional continuum approach, while proven successful for describing the macroscale behavior of the sclera, does not account for the sclera fibers are long, interwoven and interact with one another. Hence, by not considering these potentially crucial characteristics, the conventional approach has only a limited ability to capture and describe sclera structure and mechanics at smaller, fiber-level, scales. Recent advances in the tools for characterizing sclera microarchitecture and mechanics bring to the forefront the need to develop more advanced modeling techniques that can incorporate and take advantage of the newly available highly detailed information. Our goal was to create a new modeling approach that can represent the sclera fibrous microstructure more accurately than with the conventional continuum approach, while still capturing its macroscale behavior. In this manuscript we introduce the new modeling approach, that we call direct fiber modeling, in which the collagen architecture is built explicitly by long, continuous, interwoven fibers. The fibers are embedded in a continuum matrix representing the non-fibrous tissue components. We demonstrate the methodology by modeling a rectangular patch of the posterior sclera. The direct fiber model presented incorporated specimen-specific fiber orientations derived from polarized light microscopy data of histological cryosections. The fibers were modeled using a Mooney-Rivlin model, and the matrix using a Neo-Hookean model. The fiber parameters were determined by inversely matching experimental equi-biaxial tensile data from the literature. After reconstruction, the direct fiber model orientations agreed well with the microscopy data both in the coronal plane (adjusted R2=0.8234) and in the sagittal plane (adjusted R2=0.8495) of the sclera. With the estimated fiber properties (C10=5746.9 MPa; C01=-5002.6MPa, matrix shear modulus 200kPa), the model`s stress-strain curves simultaneously fit the experimental data in radial and circumferential directions (adjusted R2`s 0.9971 and 0.9508, respectively). The estimated fiber elastic modulus at 2.16% strain was 5.45GPa, in reasonable agreement with the literature. During stretch, the model exhibited stresses and strains at sub-fiber level, with interactions among individual fibers which are not accounted for by the conventional continuum methods. Our results demonstrate that direct fiber models can simultaneously describe the macroscale mechanics and microarchitecture of the sclera, and therefore that the approach can provide unique insight into tissue behavior questions inaccessible with continuum approaches.

Fibrous finite element modeling of the optic nerve head region

“…Fourth, the proposed FFE model simulated the fibrous collagen structures in the ONH region without a hydrated matrix, but the collagen fiber bundles in actual tissues are embedded in a hydrated matrix. Our rationale is that the hydrated matrix is much softer, and the IOP-induced load is primarily carried by the collagen fiber bundles as observed in our previous sclera model [28]. In other models of the sclera, the matrix phase is generally included as a continuum structure, and the collagen fibers are embedded in the matrix [52].…”

“…PLM imaging data of a porcine eye used to construct the model geometry was acquired based on our previous work [10,28]. Details of eye preparation, histological processing, PLM imaging, and post-processing methods are described elsewhere [9,29].…”

“…The circumferential bundles were assumed to have circular cross-sections with a constant diameter of 20 μm. Finally, the inter-penetrations of fiber bundles were resolved as in our previous work [28,31]. The algorithm iteratively moved bundle segments in the through-thickness direction to remove the bundle-bundle interpenetrations.…”

“…1b). Experimental data from the PLM images were obtained using the image processing algorithms described in our previous works [28,38].…”

“…Our long-term goal is to understand the complex role of the fibrous collagen structure on ONH biomechanics at all levels of IOP. In this direction, we have developed a novel finite element modeling framework that directly incorporates discrete collagen fiber bundles, their 3D spatial organization derived from polarized light microscopy (PLM) data, interactions between fiber bundles, and long-range strain transmission along fiber bundles [28]. We have recently demonstrated that with the right hyperelastic material properties, a model can predict the nonlinear response of a small rectangular specimen, 2.00mm x 1.91mm, of the posterior sclera in biaxial tensile experiments [28].…”