A microstructure-based model for a full lamellar-interlamellar displacement and shear strain mapping inside human intervertebral disc core.

The determinant role of the annulus fibrosus interlamellar zones in the intervertebral disc transversal and volumetric responses and hence on their corresponding three-dimensional conducts have been only revealed and appreciated recently. Their consideration in disc modeling strategies has been proven to be essential for the reproduction of correct local strain and displacement fields inside the disc especially in the unconstrained directions of the disc. In addition, these zones are known to be the starting areas of annulus fibrosus circumferential tears and disc delamination failure mode, which is often judged as one of the most dangerous disc failure modes that could evolve with time leading to disc hernia. For this latter reason, the main goal of the current contribution is to incorporate physically for the first time, the interlamellar zones, at the scale of a complete human lumbar intervertebral disc, in order to allow a correct local vision and replication of the different lamellar-interlamellar interactions and an identification of the interlamellar critical zones. By means of a fully tridimensional chemo-viscoelastic constitutive model, which we implemented into a finite element code, the physical, mechanical and chemical contribution of the interlamellar zones is added to the disc. The chemical-induced volumetric response is accounted by the model for both the interlamellar zones and the lamellae using experimentally-based fluid kinetics. Computational simulations are performed and critically discussed upon different simple and complex physiological movements. The disc core and the interlamellar zones are numerically accessed, allowing the observation of the displacement and shear strain fields that are compared to direct MRI experiments from the literature. Important conclusions about the correct lamellar-interlamellar-nucleus interactions are provided thanks to the developed model. The critical interlamellar spots with the highest delamination potentials are defined, analyzed and related to the local kinetics and microstructure.

A microstructure-based modeling approach to assess aging-sensitive mechanics of human intervertebral disc.

BACKGROUND AND OBJECTIVE: The human body soft tissues are hierarchic structures interacting in a complex manner with the surrounding biochemical environment. The loss of soft tissues functionality with age leads to more vulnerability regarding to the external mechanical loadings and increases the risk of injuries. As a main example of the human body soft tissues, the intervertebral disc mechanical response evolution with age is explored. Although the age-dependence of the intervertebral disc microstructure is a well-known feature, no noticeable age effect on the disc stiffness is evidenced in the in-vitro experimental studies of the literature. So, if the disc intrinsic mechanics remains constant, how to explain the correlation of disc degeneration and disc functionality loss with age. METHODS: A microstructure-based modeling approach was developed to assess in-silico the aging-sensitive mechanics of human intervertebral disc. The model considers the relationship between stress/volumetric macro-response and microstructure along with effective age effects acting at the lamellar and multi-lamellar scales. The stress-stretch and transversal responses of the different disc regions were computed for various age groups (13-18, 36, 58, 69 and 82 years old) and their evolution with age was studied. RESULTS: While matching with in-vitro experimental data, the predicted stiffness was found to increase while passing from adolescent young discs to mature older discs and then to remain almost constant for the rest of life. Important age-related changes in the disc transversal behavior were also predicted affecting the flexibility of the disc, changing its volumetric behavior, and modifying its dimensions. CONCLUSION: The developed approach was found able to bring new conclusions about age-dependent mechanical properties including regional dependency. The disc mechanics in terms of rigidity, radial and axial transversal responses were found to alter going from adolescent to middle age where the disc reaches a certain maturity. After reaching maturity, the mechanical properties undergo very slight changes until becoming almost constant with age.

Interlamellar matrix governs human annulus fibrosus multiaxial behavior.

Establishing accurate structure-property relationships for intervertebral disc annulus fibrosus tissue is a fundamental task for a reliable computer simulation of the human spine but needs excessive theoretical-numerical-experimental works. The difficulty emanates from multiaxiality and anisotropy of the tissue response along with regional dependency of a complex hierarchic structure interacting with the surrounding environment. We present a new and simple hybrid microstructure-based experimental/modeling strategy allowing adaptation of animal disc model to human one. The trans-species strategy requires solely the basic knowledge of the uniaxial circumferential response of two different animal disc regions to predict the multiaxial response of any human disc region. This work demonstrates for the first time the determining role of the interlamellar matrix connecting the fibers-reinforced lamellae in the disc multiaxial response. Our approach shows encouraging multiaxial predictive capabilities making it a promising tool for human spine long-term prediction.

Interlamellar-induced time-dependent response of intervertebral disc annulus: A microstructure-based chemo-viscoelastic model.

The annulus fibrosus of the intervertebral disc exhibits an unusual transversal behavior for which a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency has not yet been developed, and it is hence the aim of the present contribution. A physically-based model is proposed by introducing a free energy function that takes into account the actual disc annulus structure in relation with the surrounding biochemical environment. The response is assumed to be dominated by the viscoelastic contribution of the extracellular matrix, the elastic contribution of the oriented collagen fibers and the osmo-induced volumetric contribution of the internal fluid content variation. The regional dependence of the disc annulus response due to variation in fibers content/orientation allows a micromechanical treatment of the soft tissue. A finite element model of the annulus specimen is designed while taking into consideration the 'interlamellar' ground substance zone between lamellae of the layered soft tissue. The kinetics is designed using full-field strain measurements performed on specimens extracted from two disc annulus regions and tested under different osmotic conditions. The time-dependency of the tissue response is reported on stress-free volumetric changes, on hysteretic stress and transversal strains during quasi-static stretching at different strain-rates and on their temporal changes during an interrupted stretching. Considering the effective contributions of the internal fluid transfer and the extracellular matrix viscosity, the microstructure-based chemo-mechanical model is found able to successfully reproduce the significant features of the macro-response and the unusual transversal behavior including the strong regional dependency from inner to outer parts of the disc: Poisson's ratio lesser than 0 (auxetic) in lamellae plane, higher than 0.5 in fibers plane, and their temporal changes towards usual values (between 0 and 0.5) at chemo-mechanical equilibrium. The underlying time-dependent mechanisms occurring in the tissue are analyzed via the local numerical fields and important insights about the effective role of the interlamellar zone are revealed for the different disc localizations. STATEMENT OF SIGNIFICANCE: The structural complexity of the annulus fibrosus has only been appreciated through recent experimental contributions and a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency of the unusual transversal behavior has not yet been developed. Here, a microstructure-based chemo-viscoelastic model is developed to highlight the interlamellar-induced time-dependent response by means of a two-scale strategy. The model provides important insights about the origin of the time-dependent phenomena in disc annulus along with regional dependency, essential for understanding disc functionality.