Modelling the Influence of Heterogeneous Annulus Material Property Distribution on Intervertebral Disk Mechanics

Abstract

Accurate modeling of the annulus fibrosus (AF) is a crucial aspect to study spine mechanics in silico. Numerical models require validation at both the microscale and organ level to be representative of the real system. Although the AF presents distributed material properties, its response is often modeled with a homogeneous stiffness distribution. The aim of this study was to investigate the influence of different modeling approaches on the numerical response of disk models, based on lamellae mechanics. A material mapping strategy was developed to define element-wise the local annulus material properties, based on prior findings of single-lamella mechanics and collagen distribution. Three modeling approaches were compared: homogeneous, radial and radial-circumferential distribution of material properties. The simulations showed a strong influence of the chosen modeling approach on the disk's tissue- and organ-scale mechanics. A homogeneous model with uniform, average lamellae stiffness predicted a substantially different internal stress distribution and organ-level response, compared to a model with heterogeneous material properties of the annulus lamellae. Finally, the study has indirectly highlighted that the organization of the mature disks could be a consequence of adaptation to the stresses induced by the applied loads, in order to evenly distribute the load over the entire structure.

Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus

“…Actually, the AF can be modeled as a reinforced matrix fiber. Particularly, the matrix or ground substance has been modeled using the energy functions of Mooney-Rivlin [13][14][15][16][17][18] and Yeoh [19][20][21][22][23][24][25][26]. However, we did not find any study that supported the use of these energy functions and how they affect the mechanical behavior of the AF.…”

3D Printing of Materials with Tunable Failure via Bioinspired Mechanical Gradients

“…Printing and Testing of Artificial IVDs : The geometry used for the artificial IVD was based on the cross section of an IVD model published by Marini and Ferguson . This 2D geometry was extruded in the z ‐direction to form a 3D object and scaled down to increase the number of specimens tested.…”

“…Besides these examples of interfacial attachment, gradients are also used in biological materials to optimize the stress distribution and minimize failure of a wide variety of load‐bearing structures ranging from trees and plant stems to fish scales and bone . An illustrative example of such structures is the human intervertebral disc (IVD), where a mechanical gradient leads to an alteration of the stress distribution within the disc to presumably improve its mechanical performance . Also for such structural applications, additional studies are needed to shed light on the design criteria, constraints and function that these gradients are optimized for.…”

“…To withstand the compressive stresses generated during locomotion, the intervertebral disc shows a complex architecture consisting of a gel‐like core, the nucleus pulposus, encased in a fibrous tissue, and the annulus fibrosus. The annulus fibrosus is compositionally graded and shows a higher stiffness on the outside as compared to the inside . Numerical simulations have shown that the radial gradient profile of IVDs of 13–18 year old patients leads to maximum principal stresses at the outside of the IVD when compressed.…”

Derivation of inter-lamellar behaviour of the intervertebral disc annulus

“…An understanding of the mechanical properties of the different constituent tissues, their interactions, and their role in the functional mechanics of the intervertebral disc is of major importance in the development of such models. In the last decade, many constitutive models of the annulus fibrosus have been proposed, most considering the solid phase of the annulus to be composed of two sets of fibres with oblique-counter oblique orientations and an isotropic elastic matrix ( Elliott and Setton, 2000; Eberlein et al, 2001; Noailly et al, 2011; Galbusera et al, 2011; Cortes et al, 2013; Marini and Ferguson, 2014 ), with a number also accounting for some of the secondary structures between adjacent lamellae ( Peng et al, 2006; Caner et al, 2007; Guerin and Elliott, 2006; Hollingsworth and Wagner, 2011; Reutlinger et al, 2014; Labus et al, 2014 ). The nature of inter-lamellar connectivity has only recently been studied, focussing mainly on the additional shear strength that it provides to the overall structure ( Iatridis and Gwynn, 2004; Gregory et al, 2011, 2014; Kirking et al, 2014; Labus et al, 2014 ).…”