A Robust Multiscale and Multiphasic Structure-Based Modeling Framework for the Intervertebral Disc

Abstract

A comprehensive understanding of multiscale and multiphasic intervertebral disc mechanics is crucial for designing advanced tissue engineered structures aiming to recapitulate native tissue behavior. The bovine caudal disc is a commonly used human disc analog due to its availability, large disc height and area, and similarities in biochemical and mechanical properties to the human disc. Because of challenges in directly measuring subtissue-level mechanics, such as in situ fiber mechanics, finite element models have been widely employed in spinal biomechanics research. However, many previous models use homogenization theory and describe each model element as a homogenized combination of fibers and the extrafibrillar matrix while ignoring the role of water content or osmotic behavior. Thus, these models are limited in their ability in investigating subtissue-level mechanics and stress-bearing mechanisms through fluid pressure. The objective of this study was to develop and validate a structure-based bovine caudal disc model, and to evaluate multiscale and multiphasic intervertebral disc mechanics under different loading conditions and with degeneration. The structure-based model was developed based on native disc structure, where fibers and matrix in the annulus fibrosus were described as distinct materials occupying separate volumes. Model parameters were directly obtained from experimental studies without calibration. Under the multiscale validation framework, the model was validated across the joint-, tissue-, and subtissue-levels. Our model accurately predicted multiscale disc responses for 15 of 16 cases, emphasizing the accuracy of the model, as well as the effectiveness and robustness of the multiscale structure-based modeling-validation framework. The model also demonstrated the rim as a weak link for disc failure, highlighting the importance of keeping the cartilage endplate intact when evaluating disc failure mechanisms in vitro. Importantly, results from this study elucidated important fluid-based load-bearing mechanisms and fiber-matrix interactions that are important for understanding disease progression and regeneration in intervertebral discs. In conclusion, the methods presented in this study can be used in conjunction with experimental work to simultaneously investigate disc joint-, tissue-, and subtissue-level mechanics with degeneration, disease, and injury.

Torque- and Muscle-Driven Flexion Induce Disparate Risks of In Vitro Herniation: A Multiscale and Multiphasic Structure-Based Finite Element Study

“…Boundary and loading conditions were defined in FEBioStudio, and the fully developed models were solved by FEBio (FEBioStudio 1.5) [Maas et al, 2012]. Our prior work validated that proportional scaling did not significantly alter model predictions [Zhou et al, 2021a]. Thus, the disc joint was modeled at a 1:5 scale (~2.1 million tetrahedral elements) for 1 Corresponding author: Grace D. O'Connell -g.oconnell@berkeley.edu computational efficiency due to limited accessible computing power (maximum of ~200 million nonzero entries in the stiffness matrix can be evaluated).…”

“…Finite element models of the bovine caudal disc motion segment were created based on our previous work (Figure 1A) [Zhou et al, 2021a]. To replicate motion segment samples prepared for most in vitro experiments, posterior structures, including facets joints and ligaments, were not included.…”

“…However, many of these models rely on singlephasic or poroelastic material descriptions that are not capable of describing Donnan equilibrium [Shirazi-Adl et al, 1984;Kurowski and Kubo, 1986;Kim et al, 1991 To address these limitations, we recently developed and validated a novel structure-based triphasic model for the bovine caudal motion segment. Model parameters were determined based on known physical or biochemical properties reported in the literature (e.g., collagen fiber stiffness, fixed charge density) [Zhou et al, 2021a]. The model accurately predicted disc mechanics across the joint, tissue, and subtissue scales and helped elucidate important load-bearing mechanisms between tissue phases (e.g., between fluid and solid phases) or tissue subcomponents (e.g., between fibers and the extrafibrillar matrix), which are essential for understanding and assessing disc failure behavior under multiaxial mechanical loading.…”

Regulating the fate of stem cells for regenerating the intervertebral disc degeneration

“…The onset of the IVDD is believed to be mainly in the NP[ 41 ]. The decline of the key essential proteoglycan, aggrecan[ 42 ], reduces additional ECM production in the NP, and causes decreased hydration[ 43 ], a deficit of IVD height, and general failure to resist compressive burden[ 44 ]. Compression pressures are hence dispensed through the NP to the adjacent AF, which leads to altered biomechanical function of AF and structural failure with radial and circumferential tears in the AF[ 45 ].…”

A Facile Approach for Anisotropic Hydrogel with Light‐Regulated Stiffness and Its Application to Achieve Mechanical Toughening

“…[11][12][13] For example, many natural tissues such as intervertebral disk, mussel byssus, and squid beaks exhibit obvious mechanical heterogeneity, in which the modulus can be varied over one order of magnitude at a centimeter-length scale. [14,15] By spatially controlling the composition and modulus at macroscale, these tissues gain mechanical enhancement and anisotropy, as well as the corresponding functionalities. [16][17][18] This reality inspires new ideas for the design of tough soft materials.…”