Multiphasic Intervertebral Disc Mechanics Theory

Authors: Nils Karajan

Publish Date: 2012/05/19

Volume: 19, Issue: 2, Pages: 261-339

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Abstract

The human spine is the flexible support structure of our body Its geometric shape is a result of the human evolutionary history where especially the lumbar spine area L1–L5 is most at risk of causing discomfort resulting from mechanical stresses Herein the intervertebral discs IVD between the vertebral bodies are the most susceptible elements as these avascular structures have to provide the flexibility It is widely accepted that the IVD are often the trigger for back pain In the context of biomechanical research it is therefore important to develop a model for the human lumbar spine with particular focus on the IVDThe objective of the presented work is to subject the IVD of the lumbar spine to continuumbiomechanical research Herein a threedimensional 3d finiteelement model is developed that allows to estimate the influence of lumbar spine motion ie bending torsion and compression on the resulting stressfield inside the IVD Following this the model can be utilised to detect inappropriate or excessive loading of the spine The theoretical description of the IVD is based on a multiphase continuum approach in the framework of the wellknown “Theory of Porous Media” TPM This is a natural choice resulting from the avascular composition of the IVD In general IVD tissue is categorised as charged hydrated material with mechanical and electrochemical internal coupling mechanisms In order to capture these couplings the underlying model incorporates an extracellular matrix ECM with fixed negative charges which is saturated by a mixture of a liquid solvent and ions Following the basic concept of the TPM a volumetric averaging process is prescribed leading to volume fractions for the pore space and the solid skeleton as well as molar concentrations for the ion species in the pore fluidIn detail the IVD exhibits a gelatinous core known as the nucleus pulposus NP and an onionlike surrounding structure consisting of anisotropic crosswise fibrereinforced lamellae the annulus fibrosus AF Both regions are seamlessly merging into each other and consist of mostly collagen fibres of varying strength and direction as well as proteoglycans with adhering negative charges As a result of these fixed negative charges and the fact that the interstitial fluid carries positively and negatively charged ions a model is created that describes the mutually coupled behaviour of solid deformation and fluid flow To illustrate the resulting coupled swelling and shrinkage process it is sufficient to recall that the size of the human body is reduced by roughly 2 centimetres during the waking phase of the day This change in height is triggered by mechanical loads stemming from the body weight which squeezes the interstitial fluid out of the IVD thereby losing altitude Simultaneously an electrochemical imbalance is generated which is compensated during the nocturnal resting phase where the interstitial fluid is driven back into the IVD due to osmotic effectsIn summary the presented paper provides a review on IVD mechanics and can be understood as a compilation of relevant information giving valuable guidance to researchers starting to work in this challenging field In this regard the paper opens with anatomical and chemical fundamentals of IVD tissue with a particular focus on the inherent inhomogeneities This is followed by an introduction to the continuummechanical fundamentals including an overview of the TPM as well as the inelastic nonlinear kinematics and the balance equations of the resulting porous continua Thereafter the constitutive modelling process is illustrated with a particular focus on the thermodynamically consistent modelling process of the intrinsic viscoelasticity of the ECM as well as the inhomogeneous characteristics of the embedded collagen fibres and the viscous pore fluid The resulting system of coupled partial differential equations is then numerically discretised using the finiteelement method which finally allows the simulation of deformation processes of the IVD using either single or multiprocessor machines Moreover an automated computation scheme is presented to systematically capture the inhomogeneities of the IVD The paper is closed with several sample applications which embrace the capabilities of the presented computational model on the one hand and give advice for further validation in terms of the applied material parameters

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