Ambard, Dominique

Chetoui, Mohamed ,

Lefloch, S.

Royer, Pascale

English

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Submitted on 14 Oct 2019
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Effect of collagen network orientation on the cervical
intervertebral disc response to flexion load
Mohamed Chetoui, Dominique Ambard, Pascale Royer, S. Lefloch
To cite this version:
Mohamed Chetoui, Dominique Ambard, Pascale Royer, S. Lefloch. Effect of collagen network orien-
tation on the cervical intervertebral disc response to flexion load. 44ème Congrès de la Société de
Biomécanique, Oct 2019, Poitiers, France. ￿hal-02315250￿
Effect of collagen network orientation on the cervical intervertebral disc response 
to flexion load 
 
M. A. Chetouia*, D. Ambarda, P. Royera and S. Le Floc’ha 
a LMGC, Univ. Montpellier, CNRS, Montpellier, France 
 
Keywords: Cervical spine; Intervertebral disc; Collagen fibers; Annulus fibrosus; FE analysis 
 
1. Introduction 
Collagen is the most prevalent protein constituting 
the intervertebral disc (IVD) extracellular matrix 
(ECM). Annular collagen constitutes a structured 
network formed by two fiber families oriented about 
±30° with respect to the transverse plane. Local 
measurements have shown that the orientation angle 
decreases from the inner AF to the outer AF (Holzapfel 
et al .2005). The collagen network shape enables the 
mechanical strength of the AF and therefore the tensile 
properties of the IVD. With age the ECM of the IVD 
undergoes several modifications affecting its ability to 
to absorb and to redistribute the applied mechanical 
charges. Among these alterations, collagen network 
looses its organized shape which leads to a loss in IVD 
mechanical properties (Whatley and Wen 2012). 
At the cervical level, IVDs are mostly exposed to 
flexion-extension motion (Mikuckyte and Ostasevisius 
2017). Although lateral bending and axial rotation are 
less frequent, they are always exercised as secondary 
motions during spine flexion-extension. For these 
complex loads, the collagen fiber network seems to be 
the main load bearing in the AF (Ayturk et al. 2010). 
In order to investigate the importance of the collagen 
network structure in the cervical IVD mechanics, we 
propose to perform a parametric study using an 
hyperelastic fiber reinforced finite element (FE) model 
of cervical IVD. The parametric study is carried out by 
varying the collagen fiber orientation. 
This study highlights that the cervical IVD behavior 
is sensitive to collagen network organisation. It also 
shows that axial stress is more affected by modifying 
the fiber orientation than shear stress in flexion motion.  
 
2. Methods  
A 3D geometry of a C6-C7 IVD was constructed to 
carry out the study (Figure 1). A biphasic swelling 
model was used to take into account the internal 
osmotic pressure role in the IVD behavior. The 
permeability of the tissue was taken strain dependent. 
The IVD is assumed to be a saturated porous media 
described by a superposition of two intrinsically 
incompressible phases: an hyperelastic solid for the 
ECM and a fluid phase for the water saturating the 
pores space. The strain energy density of the solid 
phase is composed of an isotropic compressible Neo-
Hookean part for the non-fibrillary matrix and an 
anisotropic part for the fiber network. 
𝑊 = 𝑊𝑁𝐻(𝐶̿) + ∑𝑊𝑓𝑖(𝐶̿, 𝑒𝑖⃗⃗  )
𝑖
 
where for each fiber family i, 𝑒𝑖⃗⃗   denotes the director 
vector of the fiber orientation and 𝑊𝑓𝑖 their anisotropic 
strain energy density (Gasser et al. 2006). In the current 
model, 𝑊𝑓𝑖 was null in the NP and in the cartilaginous 
endplates (CEP). Two families of fibers with the same 
mechanical properties were defined in the AF. 
 
 
Figure 1 Geometry of C6-C7 IVD  
 
In order to study the effect of the collagen network 
orientation under physiological spine flexion, two 
parameters were varied to construct 5 cases. The two 
parameters are the fiber orientation angles in the inner 
AF (IAF) and the outer AF (OAF) respectively 𝛼𝑖 and  
𝛼𝑜 (table 1). Cases 1, 2 and 3 permit to study the effect 
of varying the fiber direction when 𝛼𝑖 = 𝛼𝑜. Cases 3, 
4 and 5 permit to investigate the effect of using a local 
distribution of the fiber orientation (𝛼𝑖 ≠ 𝛼𝑜) with a 
fixed mean angle 𝛼𝑚 = 35°. The remaining model 
parameters were taken from Chetoui et al. 2019. 
The range of motion of the flexion and the secondary 
lateral bending and axial rotation at C6-C7 level were 
taken from in vivo measurement (Anderst et al. 2015). 
  
 𝛼𝑖 = 𝛼𝑜 Constant 𝛼𝑚 
case 1 2 3 4 5 
𝛼𝑖 ±25 ±30 ±35 ±45 ±50 
𝛼𝑜 ±25 ±30 ±35 ±25 ±20 
 Table 1 Parameters sets used in the parametric study 
The simulations were performed using the open 
source software LMGC90. Firstly, a preconditioning 
step was performed to set the initial internal fields and 
swelling followed by a 100N creep-compressive load 
step to model the head weight. Finally, to simulate the 
flexion, a displacement-driven load was applied on the 
upper CEP for 10 seconds. The used mesh, obtained 
after a mesh sensitivity analysis, is constituted of 5940 
hexahedral elements (26106 nodes). 
3. Results and discussion 
Each case took about 16 hours of computing time. 
The stress field did not vary qualitatively with the fiber 
orientation. Only the value of the stress was affected. 
With constant fiber orientation, the AF stress increases 
with 𝛼. The AF maximal shear stress is obtained at the 
end of the flexion load step. For 𝛼 = 35°, the maximal 
shear stress 𝜎𝑥𝑧 (z being the axial direction of the IVD) 
reaches 0.954 MPa. A decrease of 10° in the angle 𝛼 
induces a diminution of 1.7% in 𝜎𝑥𝑧 (Figure 2). The 
compressive stress 𝜎𝑧𝑧 drops by a greater rate equal to 
11.7% when 𝛼 decreases from 35° to 25°.  
The AF stress is directy proportional to the value of 
the fiber orientation angle with respect to the 
transverse plane. When collagen fibers direction get 
closer to the axial direction, they become more 
resistant to the disc radial swelling and the axial strain. 
 
 
Figure 2 Maximal AF shear stress with respect to α 
 
In the case where 𝛼𝑖 ≠ 𝛼𝑜, varying the difference 
between the outer AF and the inner AF fiber 
orientation has no significant effect on the maximal 
shear stress. A relative difference of 0.6% is found 
between 𝝈𝒙𝒛 in cases 3 and 5. The difference between 
the maximal compressive stresses 𝝈𝒛𝒛 found with the 
same range of angles is more relevant. 𝝈𝒛𝒛 increases by 
10.7% when 𝛼𝑖 − 𝛼𝑜 drops from 30
o to 0 (Figure 3). 
Varying the fiber orientation spatial distribution 
affects noticeably the value of the axial stress. This 
result highlights the relevance of defining local fiber 
orientations at the AF level in IVD FE analysis. 
In flexion load, the contribution of the collagen fiber 
in the AF shear stress does not seem relevant compared 
to its contribution in the axial stress. By analogy, 
similar results will be found under lateral bending. We  
 
Figure 3 Maximal AF compressive stress with respect 
to the distribution of α 
 
anticipate that the shear stress will be more affected by 
changing the fiber orientation under axial rotation. 
4. Conclusions 
The present work investigated the contribution of the 
collagen network orientation in the cervical IVD 
mechanics under flexion load. The obtained results did 
not only show the importance of the collagen network 
structure for the IVD behavior, but also confirmed that 
simulating the IVD mechanics under non axial loads 
strongly requires the use of a fiber reinforced model. 
 
Acknowledgements 
This work is supported by Labex NUMEV (ANR-10-
LABEX-20 projects 2017-1-27) and by CNRS (AAP 
“Osez l’interdesciplinarité 2018”, MoTiV Project) 
 
References  
Anderst W, Donaldson III W, Lee J, Kang J. 2015. 
Three-dimensional intervertebral kinematics in the 
healthy young adult cervcal spine during dynamic 
functional loading. J Biomech. 48:1286-1293. 
Ayturk UM, Garcia JJ, Puttlitz CM. 2010. The 
Micromechanical role of the annulus fibrosus 
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lumber spine. J Biomech Eng. 132:061007. 
Chetoui M, Boiron O, Ghiss M, Dogui A, Deplano V. 
2019. Assessment of IVD degeneration related 
properties using FE models based on ρH weighted 
MRI data. Biomech Model Mechan 18(1):17-28. 
Gasser T, Ogden R, Holzapfel G. 2006. Hyperelastic 
modelling of arterial layers with distributed 
collagen fibre orientation. J Roy Soc Inter. 3:15-35. 
Holzapfel G, Schulze-Bauer C, Feigl G, Regitnig P. 
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*Corresponding author. Email: Mohamed-amine.chetoui@umontpellier.fr 


Effect of collagen network orientation on the cervical intervertebral disc response to flexion load

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Effect of collagen network orientation on the cervical intervertebral disc response to flexion load

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