Toward Patient Specific Models of Pediatric IVDs: A Parametric Study of IVD Mechanical Properties

Three-dimensional fiber patterning in the annulus fibrosus can be derived from vertebral endplate topography

Introduction

The annulus fibrosus (AF) of the Intervertebral disc (IVD) is composed of concentric lamellae of helically wound collagen fibers. Understanding the spatial variation of collagen fiber orientations in these lamellae, and the resulting material anisotropy, is crucial to predicting the mechanical behavior of the complete IVD.

Methods

This study builds on a prior model predicated on path-independent displacement of fiber endpoints during vertebral body growth to predict a complete, three-dimensional annulus fibrosus fiber network from a small number of subject-independent input parameters and vertebral endplate topographies obtained from clinical imaging. To evaluate the model, it was first fit to mid-plane fiber orientations obtained using polarized light microscopy in a population of bovine caudal discs for which computed tomography images vertebral endplates were also available. Additionally, the model was used to predict the trajectories based on human lumbar disc geometries and results were compared to previously reported data. Finally, the model was employed to investigate potential disc-related variations in fiber angle distributions.

Results

The model was able to accurately predict experimentally measured fiber distributions in both bovine and human discs using only endplate topography and three input parameters. Critically, the model recapitulated previously observed asymmetry between the inclinations of right- and left-handed fibers in the posterolateral aspect of the human AF. Level to level variation of disc height and aspect ratio in the human lumbar spine was predicted to affect absolute values of fiber inclination, but not this asymmetry.

Conclusion

Taken together these results suggest that patient-specific distributions of AF fiber orientation may be readily incorporated into computational models of the spine using only disc geometry and a small number of subject-independent parameters.

Muscle-driven forward dynamic active hybrid model of the lumbosacral spine: combined FEM and multibody simulation

Most spine models belong to either the musculoskeletal multibody (MB) or finite element (FE) method. Recently, coupling of MB and FE models has increasingly been used to combine advantages of both methods. Active hybrid FE-MB models, still rarely used in spine research, avoid the interface and convergence problems associated with model coupling. They provide the inherent ability to account for the full interplay of passive and active mechanisms for spinal stability. In this paper, we developed and validated a novel muscle-driven forward dynamic active hybrid FE-MB model of the lumbosacral spine (LSS) in ArtiSynth to simultaneously calculate muscle activation patterns, vertebral movements, and internal mechanical loads. The model consisted of the rigid vertebrae L1-S1 interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, facet joints, and force actuators representing the muscles. Morphological muscle data were implemented via a semi-automated registration procedure. Four auxiliary bodies were utilized to describe non-linear muscle paths by wrapping and attaching the anterior abdominal muscles. This included an abdominal plate whose kinematics was optimized using motion capture data from upper body movements. Intra-abdominal pressure was calculated from the forces of the abdominal muscles compressing the abdominal cavity. For the muscle-driven approach, forward dynamics assisted data tracking was used to predict muscle activation patterns that generate spinal postures and balance the spine without prescribing accurate spinal kinematics. During calibration, the maximum specific muscle tension and spinal rhythms resulting from the model dynamics were evaluated. To validate the model, load cases were simulated from -10° extension to +30° flexion with weights up to 20 kg in both hands. The biomechanical model responses were compared with in vivo literature data of intradiscal pressures, intra-abdominal pressures, and muscle activities. The results demonstrated high agreement with this data and highlight the advantages of active hybrid modeling for the LSS. Overall, this new self-contained tool provides a robust and efficient estimation of LSS biomechanical responses under in vivo similar loads, for example, to improve pain treatment by spinal stabilization therapies.

Modelling of Intervertebral Disc (IVD) with Structured Mesh and Crosswise Collagen Fibers

The highly organized collagen network of human lumbar annulus fibrosus (AF) is fundamental to preserve the mechanical integrity of the intervertebral discs. In the healthy AF, fibers are embedded in a hydrated matrix and arranged in a crosswise fashion, giving an anisotropic structure capable to undergo large strains. For finite element analysis (FEA) of spine, modelling a realistic intervertebral disc geometry has always been a challenge. This paper proposes a simple yet efficient workflow details for generating structured mesh of the ground substance of the AF and the method for generating collagen fibers with controllable angles that are embedded in AF.Clinical Relevance- The biomechanical response of spine is usually studied by finite element analysis (FEA) of the assembly of vertebra and IVD and other components. The FEA results are always dependent on the correct generation of the geometry and the material of the components. For IVD, creating structured mesh with crosswise collagen fibers with adjustable angles will provide a better control over the anisotropic property definitions of the IVD and approaching a more realistic simulation.

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.

Influence of structural and material property uncertainties on biomechanics of intervertebral discs - Implications for disc tissue engineering

This study investigated how variations of structural and material properties of human intervertebral discs (IVDs) affect the biomechanical responses of the IVDs under simulated physiological loading conditions using a stochastic finite element (SFE) model. An SFE method, which combined an anatomic FE model of human lumbar L3-4 segment and probabilistic analysis of its structural and material properties, was used to generate a dataset of 500 random disc samples with varying structural and material properties. The sensitivity of the biomechanical responses, including intervertebral displacements/rotations, intradiscal pressures (IDP), fiber stresses and matrix strains of annulus fibrosus (AF), were systematically quantified under various physiological loading conditions, including a 500N compression and 7.5Nm moments in the 3 primary rotations. Significant variations of the IDPs, IVD displacements/rotations, and stress/strain distributions were found using the dataset of 500 ramdom disc samples. Under all the loading conditions, the IDPs were positively correlated with the Poisson's ratio of the NP (r = 0.46 to 0.75, p = 0.004-0.001) and negatively with the Young's modulus of the annulus matrix (r = -0.48 to -0.65, p = 0.003-0.001). The primary intervertebral rotations were significantly affected by the Young's modulus of the annulus matrix (r = -0.44 to -0.71, p = 0.001-0.032) and the orientations of the annular fibers (r = -0.45 to -0.69, p = 0.001-0.029). The heterogeneity of structures and material properties of the IVD had distinct effects on the biomechanical performances of the IVD. These data could help improve our understanding of the intrinsic biomechanics of the IVD and provide references for optimal design of tissue engineered discs by controlling structural and material properties of the disc components.