finite element investigation of the loadin grate effect on the spinal load-sharing changes under...

7/27/2019 Finite Element Investigation of the Loadin Grate Effect on the Spinal Load-sharing Changes Under Impact Conditions

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Finite element investigation of the loading rate effect on the spinalload-sharing changes under impact conditions

Marwan El-Rich a,b, Pierre-Jean Arnoux a,, Eric Wagnac a,b, Christian Brunet a, Carl-Eric Aubin b

a Laboratoire de Biomecanique Appliquee (LBA-INRETS), Marseille, Franceb Department of Mechanical Engineering, Ecole Polytechnique, Montreal, Quebec, Canada

a r t i c l e i n f o

Article hi story:

Accepted 11 March 2009

Keywords:

High-speed impact

Lumbar spine

Stress

Bone fracture

Injury

Finite-element analysis

a b s t r a c t

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause

spinal injuries. This study aimed to investigate the rotation rate effect on the L2L3 motion segmentload-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the

failure may initiate?

Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to

analyze the responses of the soft tissues and the bony structures until possible fractures. The structural

response was markedly different under the highest velocity that caused high peaks of stresses in the

segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at

the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower

endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and

fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle

region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure

was higher under flexion and decreased when the endplate was fractured, while the contact forces were

greater under extension and decreased when the facet surface was cracked. The highest ligaments

stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and

facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can

result at sagittal rotation velocity exceeding 0.51

/ms.&2009 Elsevier Ltd. All rights reserved.

1. Introduction

Epidemiologic and biomechanical studies have shown the role

of the mechanical loads acting on the human spine during daily

activities in the onset of low back pain (LBP) disorders and

symptoms (Damkot et al., 1984; Kelsey et al., 1984). Among the

various loading conditions, impact loading at high-velocity

rate releases important energy over a short time period and can

induce spinal fractures. Although spinal fractures (burst fracture,

disc protrusion and narrowing of the spinal canal by bone

fragment) are of immense clinical significance (Tran et al., 1995;Wilcox et al., 2004), the biomechanics of spinal injury has been

insufficiently analyzed under dynamic loadings.

Under high-velocity impact, the spine can be injured with

small displacement and angulation compared with a low-velocity

injury (Neumann et al., 1995, 1996). For a short duration of impact,

the high dynamic stiffness increases the stability of the spinal

segment against the impact load (Lee et al., 2000). However, the

corresponding increase in stresses within the vertebral body and

endplate may induce fractures. Yingling et al. (1997) found that

failure at low load rates occurred exclusively in the endplate,

whereas failure of the vertebral body appeared more frequently at

higher load rates. In healthy spine, the excessive pressurization of

nucleus under high dynamic loading can cause endplate fracture

(Brown et al., 2008).

Numerous studies investigating the effect of loading rate on

the biomechanical properties of the boneligamentbone com-

plex have reported an increase in failure load, failure strain,

stiffness and energy absorbed to failure with increasing loading

rate (Panjabi et al., 1998; Bass et al., 2007). High loading rateincreased the intradiscal pressure (IDP), resistant bending mo-

ment, ligament stress and annulus fiber stress (Wang et al., 2000).

However, the pressure is independent of the impact duration and

depends only on the magnitude of the impact force (Lee et al.,

2000).

The lumbar spine component (L2L3) mobility seems to be

responsible for many severe injuries such as bone fractures

(Sances et al., 1984). Mechanisms postulated in trauma situations

(vehicle crash, aircraft ejection) are related to flexion/extension of

the spinal unit. From these previous works, we assumed that the

lumbar motion segment could demonstrate diverse mechanical

behaviors leading to trauma under different loading velocities.

ARTICLE IN PRESS

Contents lists available atScienceDirect

journal homepage: www.elsevier.com/locate/jbiomechwww.JBiomech.com

Journal of Biomechanics

0021-9290/$- see front matter& 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jbiomech.2009.03.036

Corresponding author. Tel.: +334 9165 80 00; fax: +334 9165 8019.

E-mail address: [email protected] (P.-J. Arnoux).

Journal of Biomechanics 42 (2009) 12521262
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We developed a refined three-dimensional finite-element model

(FEM) of the L2L3 segment enriched by advanced visco-elastic,

hyper-elastic and elasto-plastic material properties (Garo et al.,

2007) to evaluate the rotation rate effect on the load-sharing

changes among the segment components during rapid sagittal

movements. These movements could result from sudden decel-

eration, frontal or rear impact configurations and lead to potential

damage in the structure. The current study aimed particularly to

identify which spinal component is at risk of failure and at whatvelocity the failure may occur.

2. Methods

2.1. Model description

The geometry of the vertebrae was reconstructed from 0.6-mm-thick CT-scan

slices of a 50th percentile healthy male with no recent back complication (Fig. 1).

The vertebral bodies and posterior elements were modeled by taking into account

the separation of the cortical shell (including bony endplate and facet joints) and

cancellous bone using 3-nodes shell and 4-nodes solid elements, respectively.

All shell elements had 0.7mm thickness and characteristic length close to 0.5 mm.

The intervertebral disc was created between the intervening endplates. It was

subdivided into nucleus pulposus and annulus fibrosus with a proportion

according to the histological findings (44%_nucleus, 56%_annulus). The disc

was filled with 5 layers of 8-nodes solid elements and the annulus was

reinforced in the radial direction by 8 collagenous fiber layers using

unidirectional springs organized in concentric lamellae with crosswise pattern

ARTICLE IN PRESS

Annulus Matrix

Collagenous Fibers

ALL

ITL

FL

JC

Contact Facet

Nucleus

SSL

ISL

PLL

Bony Endplate

Cancellous Bone

Cortical Shell

191000 elements40300 nodes

Fig. 1. L2L3 finite-element model.

Fig. 2. JohnsonCook elasto-plastic material law used to model the structural

behavior of the bone structure.

M. El-Rich et al. / Journal of Biomechanics 42 (2009) 12521262 1253


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close to 7351 ( Schmidt et al., 2007). Fiber stiffness increased by 110% from the

center to the middle layers and by 150% from the center to the outer layers of the

annulus (Shirazi-Adl et al., 1986;Cheung et al., 2003).

The surrounding ligaments, the anterior (ALL) and posterior (PLL) longitudinal

ligaments, intertransverse (ITL), flavum (FL), capsular (JC) and intertransverse (ITL)

ligaments were represented by envelops of 1 mm uniform thickness. The

geometrical properties were taken from the literature (Pintar et al., 1992). All

ligaments were modeled with 4- and 3-nodes (JC) shell elements.

Tied contact interfaces were used to ensure the disc and ligament attachment

to the vertebrae and to prevent any relative movement during the simulations.

Frictionless contact interfaces were assumed between the diverse parts of themodel to avoid any possible penetration. This interface was also used between the

facet surfaces to calculate the contact forces.

The bone structure was assumed as a homogeneous material. It was modeled

with a symmetric elasto-plastic material law (JohnsonCook) allowing computing

von Mises hardening with ductile damage until potential rupture ( Fig. 2). In this

law, the material behaves as linear elastic when equivalent stress is lower than the

yield stress and as plastic for higher values of stress. When the maximum stress is

reached during computation, the stress remains constant while the elements

deformation continues until the plastic strain reaches the maximum value.

Element rupture occurs if the plastic strain reaches the maximum value. If the

element is a shell, the ruptured element is deleted. If the element is a solid, the

ruptured element has its deviatoric stress tensor permanently set to zero, but the

element is not deleted. Therefore, the material rupture is modeled without any

damage effect. The plastic strain threshold used in the model is ranged from 1% to

3% (Schileo et al., 2008; Kimpara et al., 2006; Arnoux et al., 2005). Strain-rate

dependency of the bone structure was investigated through a sensitivity analysis.

The ligaments and the disc were governed by visco-elastic (generalized

MaxwellKelvinVoigt; Fig. 3) and hyper-elastic (MooneyRivlin) material

laws, respectively, while the fibers were modeled using nonlinear elastic

material (Table 1). Damage occurrence of soft tissues is usually described in

terms of ultimate strain levels. Therefore, ligament failure was based on straincriterions based onPintar et al. (1992) findings. Ultimate strain levels were thus

calculated for all ligaments and used to identify their potential failure. All

simulations were performed using the explicit dynamic finite-element solver

Radioss (Version 4.4, Altair HyperWorks Inc.).

2.2. Model validation under quasi-static loading conditions

The calculated quasi-static compressive stiffness of the disc was compared

with the in-vitro values obtained on cadaveric samples (three women donors:

ARTICLE IN PRESS

Table 1

Summary of the material properties used for the modeling.

Material properties Vertebra components

Density (kg/mm3) 1.83E-06 (Lee et al., 2000) 0.17E-06 (Kopperdahl and

Keaveny, 1998)

1.06E-06 (Kasra et al., 1992)

Young modulus,

E(MPa)

14000 (Kopperdahl and Keaveny,

1998;Wirtz et al., 2000)

291 (Kopperdahl and

Keaveny, 1998)

10000 (Lee et al., 2000)

Poisson ratio, n 0.3 (Qiu et al., 2006) 0.25 (Qiu et al., 2006) 0.3 (Qiu et al., 2006)Yield stress a(MPa) 110 (Kopperdahl and Keaveny,

1998,Wirtz et al., 2000)

1.92 (Kopperdahl and

Keaveny, 1998)

6 (Ochia et al., 2003)

Hardening modulus

b(MPa)

100 20 100

Hardening exponent,

n

0.1 1 1

Failure plastic strain,

ep

9.68E-03 14.5E-03 (Kopperdahl and

Keaveny, 1998)

0.02

Maximum stress,

(MPa)

155 (Kopperdahl and Keaveny,

1998,Wirtz et al., 2000)

2.23 (Kopperdahl and

Keaveny, 1998)

7.5 (Ochia et al., 2003)

Strain rate coefficient,

c

1 1 3

Disc components

Nucleus pulposus Annulus matrix References Collagenous fibers Reference

Density (kg/mm3) 1.00E-06 1.20E-06 (Lee et al., 2000) Nonlinear elastic curve (ShiraziAdl et al., 1986)

Poisson ratio, n 0.495 0.45 (Schmidt et al., 2007)C10 0.12 0.18 (Schmidt et al., 2007)

C01 0.03 0.045 (Schmidt et al., 2007)

Ligaments

ALL PLL ITL ISL LF SSL JC References

Density (kg/mm3) 1.0E-06 1.0E-06 1.0E-06 1.0E-06 1.0E-06 1.0E-06 1.0E-06

Young modulus, E(MPa) 11.4 9.12 11.4 4.56 5.7 8.55 22.8 (Yang et al. 1998)

Poisson ratio, n 0.4 0.4 0.4 0.4 0.4 0.4 0.4 (Yang et al. 1998)Tangent modulus, Et(MPa) 10.0 9.0 11.0 4.0 5.0 8.0 22.0

Tangent poisson ratio, nt 0.42 0.42 0.42 0.42 0.42 0.42 0.42 Viscosity coefficient,Z0 28 28 28 28 28 28 28 Naviers constant, l 1.0E06 1.0E06 1.0E06 1.0E06 1.0E06 1.0E06 1.0E06

ke += , ke +=

E

e = ,

t

vk

E

= ,

v

=k

tE

E

k

ke

+=+=

, kt

E +=

k

tt

EEEEE ++=

)(

Fig. 3. Generalized MaxwellKelvinVoigt visco-elastic material law used to model the structural behavior of the spinal ligaments.

M. El-Rich et al. / Journal of Biomechanics 42 (2009) 125212621254


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subject1: 85years, 177 cm, 86 kg; subject2: 55years, 156cm, 38 kg; subject3: 80years,

159cm, 69 kg). These samples containing the disc and adjacent endplates (Fig. 4a)

were taken from T9 to L4. The disc was loaded until damage (over 60% of axial strain)

by applying an axial compressive displacement on the lower endplate of the proximal

vertebra at a constant velocity of 1.267mm/s, while the upper endplate of the distal

vertebra was fixed (Fig. 4b). These endplates were embedded with a rigid resin.

The IDP changes under a follower preload simulating gravity (Rohlmann et al.,

2006) and a combination of a preload and moments in the principal planes were

also evaluated and compared with the published values. These loads were 500N of

preload combined with 7.5 N m in the principal planes (Schmidt et al., 2007) and

1000 N of preload combined with 20Nm in the sagittal plane (Shirazi-Adl andDrouin, 1988).

The ligaments strains were compared within-vitrovalues measured on L3L4

and L4L5 segments under 15 N m of physiological moments (Panjabi et al., 1982).

These deformations were calculated as the percentage change in length with

respect to the original length (shortest distance between the insertion points of the

ligaments), and an average value was considered.

2.3. Loading rate investigation

Five degrees of flexion and extension were applied on the L2 upper endplate

at three rates (0.05, 0.5 and 51/ms) while the model was fixed in the L3 lower

endplate. These endplates were considered as rigid and the rest of the structures as

flexible bodies. The IDP changes in the nucleus and von Mises stress in the annulus

were calculated. The ligaments stresses were evaluated in their fibers directions

and the contact forces were assessed in the facet joints. Equivalent stress and

plastic strain in the bone until possible fracture were also evaluated.

3. Model validation results

The calculated forcedeformation curve of the disc showed a

nonlinear compressive behavior and a stiffness increase with load.

The curve falls within the experimental corridor (Fig. 4c), however

the modeled disc appeared stiffer than the corresponding

experimental one, and the decrease in stiffness seen in the

experimental curves was not obtained by the model.

The IDP was in agreement with the previous results ofShirazi-Adl and Drouin (1988)(Fig. 5a) andSchmidt et al. (2007)(Fig. 5b).

Ligament strains that were inside the experimental range was

defined byPanjabi et al. (1982)(Table 2). In flexion all ligaments

were recruited except ALL while only ALL and JC ligaments were

recruited under extension. The right bending generated greater

deformation than the left one. In the axial plane, the deformation

was similar under the right and left rotations and the greatest

values were obtained for the JCligaments (Table 2).

4. Loading rate investigation results

The structural response was markedly different under the

highest velocity (Figs. 6 and 7). It exhibited vibrations and caused

ARTICLE IN PRESS

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Axial Displacement (mm)

CompressiveForce(N)

L2_L3_FEM

T11-T12 (Sub_1)

T9-T10 (Sub_1)

L1-L2 (Sub_1)

L3-L4 (Sub_1)

L2-L3 (Sub_2)

T10-T11 (Sub_2)

T12-L1 (Sub_2)

L1-L2 (Sub_3)

T12-L1 (Sub_3)

0.0 0.5 1.0 1.5 2.0 2.5

Fig. 4. (a) Experimental set up for quasi-static compressive testing of the disc, (b) finite-element simulation of the compressive testing and (c) the compressive

forcedisplacement curve of the disc: FE model of the lumbar L2L3 level versus experimental curves of several thoracic, thoraco-lumbar and lumbar levels of the three

postmortem human subjects (Sub_1, Sub_2, Sub_3).



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high peaks of stresses in the ligaments, the disc and the bony

structures. The stress and the IDP increased with the rotation rate.

At the faster rotation, the stress and the plastic strain exceeded

the yield and ultimate values, respectively, in L2 vertebra. The

stress was concentrated in the upper and lower pedicle regions

under flexion and extension, respectively (Table 3). Under flexion,

ARTICLE IN PRESS

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Moment (N.m)

IntradiscalPressure(MPa)

Flexion_Shirazi & Drouin, 1988

Flexion_FE Model

Extension_Shirazi & Drouin, 1988

Extension_FE Model

PreloadP = 1000N

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

IDP(MPa)

FEM_L2-L3

Schmidt et al. 2007_L4-L5

500N of preload &7.5Nm of moment

0 2 4 6 8 10 12 14 16 18 20

Flexion Lat. Bending (R)Extension Lat. Bending (L) Ax. Rotation (R)

Fig. 5. IDP changes under combination of preload and moments in the principal planes: (a) 1000 N of preload combined with large sagittal moments and (b) 500 N of

preload combined with 7.5N m of moment in the principal planes.

Table 2

Ligaments deformation under 15 N m of moment in the principal planes: negative values mean unloaded ligaments (FE Model versusin-vitro data).

Ligament Flexion Extension Right bending Left bending Right rotation Left rotation

FE model In-vitro

studyaFE model In-vitro





studya

ALL 7.9 871.4 7.1 6.771.4 2.6 3.773 1.25 2.672.8 1.9 1.671.4 2.2 2.773.3

PLL 7.2 7.373.3 4.6 4.673.4 7.8 8.873.5 2.9 4.273 0.9 1.170.4 3.7 3.271.6

ITL_R 4.3 7.472.8 4 4.572.6 8.4 6.871.4 10.9 9.971.8 3.3 3.271.7 0 1.171.5

ITL_L 3.7 7.672.7 3.2 3.971.8 12.7 15.973.8 11.9 1273.9 0.9 0.771.3 2.7 4.972.6

FL_R 9.5 9.173.1 6 6.573.1 2.4 2.772.1 1.9 0.971.9 2.1 1.870.8 2.4 2.271.1

FL_L 10.7 9.173.1 7.6 6.372.9 6.8 7.772.9 3.7 3.972.7 1.0 0.970.6 2.8 371.7

JC_R 10.3 10.475 5 672.1 1.3 1.874.7 1.1 1.274.3 7.7 771.8 2.1 3.672.7

JC_L 12.7 1375.5 3.8 3.771.7 9.9 8.875.4 2.9 3.274 3.7 3.372.7 8.2 8.774.3

ISL 17.3 1775.3 4.9 5.172.2 4.6 4.274.2 2.3 0.873.1 4.2 471.7 4.1 5.973.2

SSL 19.2 1874.9 11 13.174.1 1.4 4.473.4 1.1 0.173.5 2.5 3.371.8 2.6 5.272.9

a Mean7SD, Panjabi et al., (1982).



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fractures were initiated in the lower endplate at 2.41 and in the

upper pedicle region at 3.51 (Fig. 6a). Under extension, fractures

were initiated in the left facet joint at 1.51, in the lower endplate at

2.31and in the upper pedicle region at 2.81(Figs. 6b and8). Under

the intermediate and lower flexion, stresses were concentrated in

the same regions as for the fastest flexion except for the stress

in the endplate that was higher in L3 than in L2 (Table 3).

Under the intermediate and lower extension, higher stresses were

concentrated in the L2 cortical shell, L3 cancellous bone and

endplate (Table 3). However, no rupture has resulted at the

intermediate or lower rate.

The fastest rotation of L2 has increased significantly the IDP

(3.1 MPa_flexion) and the stress in the outer annulus (4.6 MPa_ex-

tension, 12.7 MPa_flexion). The fastest extension caused also

important contact forces (920 N of total force) but increased

slightly the IDP (1 MPa). The fracture occurrence in the endplate

and facet surfaces caused decreases in the IDP (Fig. 6a) and the

contact forces (Fig. 6b), respectively.

The fastest flexion caused high stresses in the capsular and

posterior ligaments. Maximal stress was concentrated in the

lower attachment of left JC ligament to the articular facet, in the

middle region of SSL ligament and in the lower posterior

attachment of ISL ligament to the L3 spinous process. Highest

stress was also concentrated in the middle region of the right ITL

ligament, in the lower region of LF ligament and in the upper

attachment ofPLL ligament to the L2 lower endplate. Under the

ARTICLE IN PRESS

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Rotation ()

IDP

(MPa)

5/ms_F

5/ms_E

0.5/ms _F

0,5/ms_E

0.05/ms_F

0.05/ms_E

Fracture of the L2

Lower Endplate

Fracture in the L2 Pedicle Region

0

100

200

300

400

500

600

700

800

900

1000

Rotation ()

TotalContactForce(N)

5/ms_F

5/ms_E

0.5/ms_F

0.5/ms_E

0.05/ms_F

0.05/ms_E

Fracture of the L2

Left Facet Surface

0 1 2 3 4 5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Fig. 6. (a) IDP changes under flexion and extension at different rates and fracture occurrence at different rotation rate levels from 0.05 to 5 1/ms under flexion (_F) and

extension (_E) and (b) total contact force at facet surfaces under flexion and extension at different rotation rate levels from 0.05 to 5 1/ms under flexion (_F) and extension

(_E).



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fastest extension, the highest stress was concentrated in lower

attachment of the left JCligament to the articular facet and in the

left upper attachment of theALL ligament to the lower endplate of

L2 (Fig. 9). No failure was observed in ligaments as the strain level

remained below the ultimate thresholds.

5. Discussion

The current study used a FEM with bio-realistic geometry

and refined mesh. It allowed investigating the different injury

phenomena that could arise under impact loads. This model

ARTICLE IN PRESS

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Stress(MPa)

0.05/ms

0.5/ms

5/ms

Extension () Flexion ()

JC

SSL

PLL

JC

ALL

Fracture of the L2Left Facet Surface

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Stress(MPa)

0.05/ms

0.5/ms

5/ms

Flexion ()

ISL

ITL

FL

0.0 1.0 2.0 3.0 4.0 5.0 6.0

0.5 1.5 2.5 3.5 4.5 5.5 6.5-6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5

Fig. 7. Ligaments stresses evaluated in their fiber directions under flexion (left) and extension (right) at the different rates: (a)JC,SSL,PLLligaments under flexion andJCand

ALL ligaments under extension and (b) ISL, FL and ITL ligaments under flexion.

Table 3

Maximum stress values and locations in the vertebrae at different rotation rates of flexion and extension movements.

Bony location Flexion Extension

Low rate Intermediate rate High rate Low rate Intermediate rate High rate

Cancellous bone 2.2 (L2) 4.5 (L2) 20 (L2) 2.1 (L3) 4.1 (L3) 22 (L2)

Cortical shell 80.5 (L2) 86.5 (L2) 154 (L2) 89 (L2) 91 (L2) 154 (L2)

Endplates 6.5 (L2) 6.6 (L2) 96 (L2) 6.2 (L3) 6.3 (L3) 65 (L2)



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allowed a detailed/realistic evaluation of failure occurrence and

propagation over the bone and not only to define failure risk

regions based on high-stress concentrations (Lee et al., 2000;Qiu

et al., 2006;Wilcox et al., 2004).Kopperdahl and Keaveny (1998)

demonstrated that the cancellous bone in human vertebrae has

similar compressive and tensile mechanical properties expect

the yield strain, which was significantly higher in compression.

Thus, similar compressive and tensile mechanical properties were

considered in modeling the bone. The microstructure and

anisotropy of the cancellous bone were not modeled as well asthe bone fragments at the fracture site. Also, the fracture

depended on the ultimate plastic strain value and location. Such

simplifications were already used in many other studies (Schileo

et al., 2008;Kimpara et al., 2006) and offered acceptable results.

Future work could benefit from the implementation of a user

pseudo-elasto-plastic material law based on energy formulation

that includes unsymmetrical behavior, damage and failure (Jundt

et al., 2007).

Ligament failure was not supported by this model. However,

the ligament stress/strain values were compared with the

published failure data (Pintar et al., 1992). Stress was not

uniformly distributed over the ligaments and was concentrated

in specific region of each ligament. This confirmed the benefit

of the 2D geometrical representation in ligament modeling. Theuse of viscous material properties allowed studying the ligaments

under various loading rates. However, the results depend on the

viscous properties given in the model. Since very limited

information was available on the structural behavior of spinal

ligaments in dynamic loading conditions, the used viscous

parameters were based on the values measured in quasi-static

conditions (Pintar et al., 1992). Consequently, in the present study,

it was assumed that any slight variation in the viscosity

parameters would not modify significantly the results trend and

the observed phenomenon, which is not related to ligaments

injury but to bone fracture. Recent findings (Arnoux et al., 2005)

showed that loading of the ligaments at high strain rate could lead

to a saturation phenomenon (no more viscous effect even when

the strain rate increases). Thus, the objective of this work was

focused on the investigation of injury mechanisms up to bone

failure using a single set of viscous parameters for ligaments

structure behavior. Obviously, further improvements of the

ligaments model (integration of the toe-in region, implementation

of threshold data for damage and failure process in dynamic

loading conditions, extended validation of the strain-rate effects

according to the range of tested velocity, etc.) could be performed

once experimental data will be available.

The fluid-like behavior of the disc was simulated with nearly

incompressible hyper-elastic material (Schmidt et al., 2007;Noailly et al., 2007). The fluid-flow in the disc and porous bone

was not simulated since the current model studied only the

immediate effect of fast movements on the load-sharing changes

over the spinal structures.

The disc stiffness curve obtained by the model under quasi-

static compressive test corroborated the experimental ones.

However, the modeled disc was stiffer than the corresponding

experiments that may be explained by the decrease of the discs

strength related to the donors age (Skrzypiec et al., 2007). The

decrease in stiffness showed by the experimental curves repre-

senting the failure behavior was not demonstrated by the model.

The IDP changes under preload only and a combination of pre-

load and moments followed the same trends as the published

values (Shirazi-Adl and Drouin, 1988; Schmidt et al., 2007). Theligaments strains under physiological moments corroborated the

experimental values (Panjabi et al., 1982) and the differences may

be related to the dissimilarities in geometry and stiffness between

the modeled segment (L2L3) and the experimental ones (L3L4

and L4L5).

The vertebral body failure load under dynamic compressive

tests was previously investigated using the current model (Garo

et al., 2007). These authors have found that under axial displace-

ment test (2.5 m/s), the vertebral body failed when the load

reached 10.4kN, which agrees with the published values of

9699.9372110.63 kN (Ochia et al., 2003). Moreover, a comple-

mentary sensitivity study was performed to investigate the strain

rate effects on the bone structure. The analysis was performed on

the Youngs modulus, the yield stress, the maximum stress and

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At 2.8

At 5.0

At 1.5

Fractures

Propagation

Fractures

Initiation

Top View

Bottom View

Sagittal View

Top View

Fig. 8. Initiation and propagation of fracture in the L2 vertebra under the fastest extension movement.



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the maximum strain of the bony components (endplate, cortical

and cancellous bones) and considered two sets of material

properties. The first one was based on material propertiesmeasured in quasi-static loading conditions (eo1 s1) (Wirtz

et al., 2000;Lee et al., 2000;Kopperdahl and Keaveny, 1998) while

the other set was based on material properties measured in

dynamic loading conditions (e428 s1) (Hansen et al., 2008;Shim

et al., 2005). Accordingly, the values of the parameters provided in

the sensitivity analysis covered a wide range of material proper-

ties, thus providing an alternate method to evaluate the potential

effect of bone viscosity (represented by strain-rate dependency of

the material properties) on spinal injuries. Results showed that for

both flexion and extension, changes in the material properties

of the bony components had no effects on the location of the site

where fractures are occurring, and slight effect on the angle at

which they initiate (o31). Thus, despite a limited validation of the

FE model against experimental data measured in dynamic loading

conditions, the complementary analysis confirmed the conclusion

drawn from the current model.

Faster movement of L2 has increased considerably the IDP inthe nucleus and the stresses over the rest of the structures,

whereas a slight change was found between the intermediate

and lower rates except in the ligaments stress under flexion. This

increase was more significant under faster flexion than extension.

However, the faster extension movement generated the highest

contact forces causing facets fractures. This confirmed the distinct

role of the posterior ligaments and facet joints in supporting the

extension moment (Shirazi-Adl and Drouin, 1988). Under flexion,

the substantial increase of the IDP caused the initiation of

fractures in the L2 lower endplate (Brown et al., 2008). The L2

pedicle fractures may result from the posterior ligaments (viscous

structure) resistance to the rapid movement of L2. These results

supported the hypothesis of the inertial and visco-elastic

resistance of the spine when exposed to high-speed traumatic

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Max

Extension

ALL

Max

Extension

JC_RJC_L

Max

Flexion

ISL

Max

Flexion

SSL

Max

Flexion

ITL_RITL_L

Max

Flexion

FL

Max

Flexion

PLL

Max

Flexion

JC_RJC_L

Fig. 9. Ligaments stress (von Mises) distribution under the fastest extension and flexion.



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loading (Viano and Lau,1988). Fractures were initiated in different

regions of L2 at smaller angles, which confirmed the vulnerability

of the segment under high-rate loading (Neumann et al., 1995,

1996). This study confirmed also that rapid movements may

reduce the margin of safety for the spine and increase the risk

of injury (Adams and Dolan, 1996). Results demonstrated also that

under the same rate, fractures may occur at different times and

regions depending on the movement direction and the strength

of these regions (Lee et al., 2000). The facet surfaces, endplatesand pedicle were the weakest regions when the motion segment

moved rapidly in the sagittal plane. Experimental studies have

shown that failure caused by impact loading occurs in the

endplate or posterior region of the cortical shell, (Willen et al.,

1984;Yingling et al., 1997) although there is a lack of consensus as

to which region fails first.

The stress values and distribution in the different ligaments

depended on their stiffness and orientation with respect to the

center of rotation (Panjabi et al., 1982). Stress was mostly

concentrated in the attachment regions of ligaments to the bone

that may lead to ligaments tear. The capsular and posterior

ligaments were highly loaded; however, it is quite speculative at

this time to connect these results to the invocation of pain. We

assumed also that the disc will not fail under the highest stress

obtained in this study based on the failure load values obtained

experimentally under quasi-static compressive tests and the

increase of the disc strength with loading rate (Adams and Dolan,

1996;Kemper et al., 2007).

This study investigated sagittal symmetric movements and did

not consider neuromuscular responses, which may underestimate

the effect on the load-sharing changes over the spinal compo-

nents. The risk of injury increases as a result of the higher stress/

strain caused by additional lateral or axial rotation (Shirazi-Adl,

1989) and/or higher internal loads (Lavander et al., 1999; Marras

and Mirka, 1990; Fathallah et al., 1998). In real life conditions,

more complex loads are present. To our knowledge, no study

quantified precisely those complex loads. This study is a first step

to investigate such mechanical loads and identify the potential

risk of injuries with an increasing loading rate. Future work willaddress more complex types of loading such as combined

rotations and translations that could potentially lead to more

severe injuries due to the early contact between bone components

and to an amplified strain level on ligaments.

6. Conclusion

A detailed FE model of the spinal complex structure was build

to investigate spinal injury mechanisms (location, chronology and

macroscopic failure process) and structure effects in dynamic

loading conditions. The obtained results demonstrated that

sagittal movement of the lumbar spine during sudden decelera-

tion and rear/front impact conditions increased significantly theIDP and the contact forces and generated high stresses in the disc,

ligaments and vertebrae. Flexion generated the highest stresses

while bone fractures were firstly initiated under extension. The

endplate, pedicle and facet surface represented the potential sites

of bone fracture. The ligaments attachment and outer annulus

regions highly loaded were susceptible to failure. These spinal

injuries can result at sagittal rotation velocity exceeding 0.51/ms.

Conflict of interest

There is no conflict of interest. Authors have not received any

payment for conducting this work and are in no conflict of

interest.

Acknowledgements

The authors are particularly grateful to M. Py, C. Regnier and M.

Paglia for the experimental set up and in-vitro samples prepara-

tions. This work was funded by the Fonds de Recherche sur la

Nature et les Technologies of the Government of Quebec.

Appendix A. Supporting Information

Supplementary data associated with this article can be found

in the online version at doi:10.1016/j.jbiomech.2009.03.036.

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