Research Papers

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

[+] Author and Article Information
Ghislain Maquer, Marc Laurent

Institute of Surgical
Technology and Biomechanics,
University of Bern,
Bern CH-3014, Switzerland

Vaclav Brandejsky

Department of Clinical Research,
University of Bern,
Bern CH-3010, Switzerland

Michael L. Pretterklieber

Center of Anatomy and Cell Biology,
Department of Applied Anatomy,
Medical University of Vienna,
Vienna 1090, Austria

Philippe K. Zysset

Institute of Surgical
Technology and Biomechanics,
University of Bern,
Stauffacherstrasse 78,
Bern CH-3014, Switzerland
e-mail: philippe.zysset@istb.unibe.ch

1Corresponding author.

Manuscript received September 17, 2013; final manuscript received March 6, 2014; accepted manuscript posted March 26, 2014; published online April 21, 2014. Assoc. Editor: James C. Iatridis.

J Biomech Eng 136(6), 061003 (Apr 21, 2014) (11 pages) Paper No: BIO-13-1434; doi: 10.1115/1.4027300 History: Received September 17, 2013; Revised March 06, 2014; Accepted March 26, 2014

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

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Fig. 1

The parameter study involved four sets of five FE models with various dimensions. Compression (C), torsion (right/left), lateral bending (right/left), and flexion (F)/extension (E) were simulated with two different material properties.

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Fig. 2

First, MRI scans were performed on 14 human intervertebral discs in saline water. Morphological parameters (cross-sectional area CSA, polar moment of inertia J, moment of inertia Ixx, Iyy, and height H) were computed from the segmented volumes. Then, stiffness of each specimen was calculated from the load–deflection data of four mechanical tests (compression (C), torsion (right/left), lateral bending (right/left), and flexion (F)/extension (E)) and normalized by the morphological parameters.

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Fig. 3

An exponential function or a double sigmoid (Exp fit) was fitted to the experimental data (Exp data). Ki, Kf and Kt were computed as the initial slope (NZ stiffness), final slope of the curves and load applied over the deflection. To include even the stiffest discs, Kf and Kt were calculated at 15% strain in compression or a ±3 deg angle for the flexibility tests (here lateral bending). BR: bending right (moment > 0) and BL: bending left (moment < 0).

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Fig. 4

Effect of CSA, J, Ixx, Iyy, and normalization on FE stiffness. CVs of the distinct stiffnesses and normalized stiffnesses are listed on top of each graph.

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Fig. 5

Effect of height and normalization on FE stiffness. CVs of the distinct stiffnesses and normalized stiffnesses are listed on top of each graph.

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Fig. 6

Variability of the stiffness prior to and after normalization was assessed via CV. CVs of measured (K), linearly normalized (KNormL) and nonlinearly normalized (KNormNL) stiffnesses (Ki, Kf, Kt) are presented for each loadcase (compression, torsion, bending, flexion, extension). “All tests” presents the average CVs of Ki, Kf, and Kt when accounting for all loadcases. “All stiffnesses” presents the average CVs of measured and normalized data for all stiffnesses and loadcases with the associated p values.



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