A Non-linear Finite Element Model for Assessment of Lumbar Spinal

Injury Due to Dynamic Loading

Alexander Tsouknidas

1, 2

, Savvas Savvakis

, Nikolaos Tsirelis

Antonios Lontos

and Nikolaos Michailidis

Mechanical Engineering Department, Fredereick University, Nicosia, Cyprus

Laboratory of Physical Metallurgy, Mechanical Engineering Department, Aristoteles University of Thessaloniki,

Thessaloniki, Greece

BETA CAE Systems S.A., Thessaoniki, Greece

Keywords: Lumbar Spine, Non-linear FEA, Critical Stress Development.

Abstract: In this paper a highly detailed model of an adult lumbar spine (L1-L5) was recreated based on Computed

Tomography. Next to the viscoelastic deformation of the intervertebral discs, cortical and cancellous bone

anisotropy was considered, while seven types of ligaments were simulated either by solid or cable elements.

The dynamic behaviour of the spine segment was assessed through stress-strain curves, provoking a non-

linear response of all implicated tissues’ material properties. The model was subjected to dynamic loading

to determine abnormalities in the anatomy’s stress equilibrium that could provoke gait disturbances. Results

indicated the introduced methodology as an effective alternative to in vitro investigations, capable of

providing valuable insight on critical movements and loads of potential patients, as the model can be

employed to optimize therapeutic training or threshold kinematics of any given lumbar spine pathology.

1 INTRODUCTION

The lumbar spine is arguably one of the most

important structural elements of our musculoskeletal

system and as such, dominates complaints received

by orthopaedics. Epidemiologic studies indicate that

lumbar spine pathologies in industrialized

environments have a life-time prevalence of about

70% (Waters et al., 1993), ranging from low back

pain to disc protrusion and spinal fractures, which

can occur during every day activities such as

running.

Finite Element (FE) models of the lumbar spine

become increasingly popular during preoperative

preparation of complex surgeries, customized

implant design and recently optimization of non-

invasive therapeutic intervention. This can be

attributed to the capacity of FE to visualize stress

distributions over the entirety of the examined

anatomy and indicate critical regions.

Linear elastic 3D FE models of spine parts,

simulating their biomechanical response (Little et

al., 2010), (Wang et al., 2006) or investigate trauma

related surgical treatment (Ashish and Pramod,

2009), have been repeatedly introduced over the last

years. To describe however, the biomechanics of

spinal injury, non-linear properties should be

considered (Xiao et al., 2011); (Schmidt et al.,

2006).

Models are conventionally recovered though

Computed Tomography (CT) which is considered as

the golden standard in spine reconstruction (Klinder

et al, 2009) while intervertebral discs were reverse

engineered based on the scanned anatomical

characteristics (Tsouknidas et al., 2012). The

majority of available investigations consider the

remaining connective tissue (ligaments) as cable

elements, able of enduring only tension (Davidson-

Jebaseelan et al., 2010). Even at a non-linear state,

two node link elements are not capable of reflecting

biomechanical alterations of the tissue i.e.

degeneration or fracture. These are however highly

important, as deterioration of ligamentous properties

foster several spine pathogenesies due to increased

range of motion within a spinal unit. El-Rich et al.,

(2009) introduced a two vertebral spine model with

three- and four-nodal elements whereas three

dimensional solid elements were also considered in

studies with simplified geometrical characteristics

292

Tsouknidas A., Savvakis S., Tsirelis N., Lontos A. and Michailidis N..

A Non-linear Finite Element Model for Assessment of Lumbar Spinal Injury Due to Dynamic Loading.

DOI: 10.5220/0004236902920295

In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2013), pages 292-295

ISBN: 978-989-8565-35-8

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

and linear properties (Tsuang et al., 2008).

In this investigation, a bio-realistic model of an

entire lumbar spine with regard to non-linear

material properties and partially solid ligaments, is

introduced, in an effort to allow the quantification of

the effect of mobility and/or loading scenarios on the

occurring spine biomechanics.

2 ANALYTICAL MODEL

During the reconstruction of the lumbar spine (L1-

L5) high resolution CT were the imaging modality

of choice due to their ability to demonstrate high

inherent image contrast between bone and soft

tissue. This enabled relatively unhindered

segmentation of the bone from soft tissue. In order

to achive the reconstruction of the desired bony

tissue, consecutive CT scan slices, were overlayed

(Tsouknidas et al., 2012); (Kobayashi et al., 2009).

Based on this concept, a patients lumbar spine was

scanned in its entirety from below the lower

boundaries of L1 to the upper limit of L5 ensuring

the full 3D representation of the examined area.

Data acquisition was in accordance to DICOM

(Digital Imaging and Communications in Medicine)

and interpolation of the CT information ensured an

isotropic data set. Although this process did not

result in higher resolution of the reconstructed set of

vertebra, it lead to smoother representation allowing

the distinct removal of the remaining soft tissue in

close proximity to the bone.

After the representation of the surfaces the

resulting volumes were generated considering an

outer cortex for each vertebra corresponding to the

cortical bone with a thickness of 0.5mm. The

remaining volume of each vertebra was considered

as cancellous bone.

Due to the severely altering density and the

inhomogeneous tissue of the intervertebral discs,

these were reverse engineered based on the superior

and inferior surface of the connecting vertebral

bodies as described by Tsouknidas et al., (2011).

During the model set up, anterior logitudial

(ALL), posterior logitudial (PLL), intertransverse

ligmante (ITL) and supraspinous ligament (SSL)

were modelled by four uniform layers of hexahedral

elements 0.3mm in thickness each, in order to

encapture their viscoelastic response (Sharma et al.,

1995). The remaining connective tissue, flavum (FL)

and capsular (JC) were considered as two node

tension elements. The simulated geometry,

emphasizing on some of its critical structural

elements, is demonstrated in figure 1.

Figure 1: Meshed lumbar spine model and details of

critical structural elements.

The annulus ground substance of the intervertebral

discs, was meshed by hexahedral elements to

facilitate the implementation of collagen fibers

positioned crosswise within the tetrahedron

structure. The remaining model, nucleus pulposus

and vertebrae, composes of tetrahedral elements and

the unhindered connection at the models contact

areas (hexa - tetrahedral elements interface) was

ensured through the diametrical incision of two

triangles in every rectangle, maintaining the same

nodes throughout the intervertebral disc surface and

the vicinical vertebrae. The same approach was

employed for the solid ligaments (ALL, PLL, ITL

and SSL). These ligaments were modelled through

the stress strain curves illustrated in figure 2

accurate way.

Intrinsic properties were considered for the

remaining ligamentus tissue. Their Young’s module

and poisson ratio as well as the cross sectional area

of each cable element used within the model

originated from literature data (Shirazi-ald et al.,

1984); (Smit et al., 1997).

The annulus fibrosus was considered to exhibit a

incompressible fluid like behaviour in order to

enrapture its hyperelastic response. In order to do so,

the Mooney-Rivlin strain energy density function

was employed as describer by Xiao et al., (2011).

The mechanical properties of bony tissue were

described by the Johnson-Cook elasto-plastic

material law considering strain rate dependent

stress-strain curves.

ANon-linearFiniteElementModelforAssessmentofLumbarSpinalInjuryDuetoDynamicLoading

293

Figure 2: Non-linear properties of solid ligamentus tissue.

To avoid element shear locking and hourglassing

phenomena during the numerical analysis of the

model, second order elements with reduced

integration were employed for all model entities.

Solid ligaments were modelled to comprise of four

layer each, to further supress the appearance of

artificial energy within the model.

Table 1: Mesh related data.

Material type

no. of

Elements

max size

Element

min size

Element

Cortical bone 87.521 1,78 mm 0,08 mm

Cancellous bone 712.361 3,04 mm 0,97 mm

Nucleus pulposus 317.251 2,27 mm 0,72 mm

Annulus 298.657 3,71 mm 1,87 mm

ALL 4260 1,92 mm 1,54 mm

PLL 2100 1,78 mm 1,52 mm

SSL 1420 1,83 mm 1,54 mm

ITL

1380 1,74 mm 1,53 mm

The mesh grid of the spine segment was

generated in ANSA by BETA CAE Systems in order

to ensure anatomic based meshing, leading to a

realistic and isotropic stress transition within the

entire model. Convergence studies were conducted

for every model entity individually, indicating the

optimum mesh density in terms of processing time,

with regard to the results accuracy, related

information are demonstrated in Table 1.

3 RESULTS

Employing the introduced model in for two mobility

scenarios, walking and running, facilitated the

determination of FSU’s biomechanical response to

external stimuli. Corresponding results are presented

in figure 3.

When interpreting these results, it is highly

important to consider that the same scale is used to

indicate stress development of both soft and bony

tissue.

Figure 3: Stress development in the FSU during walking

and running.

Even though stress concentrations are apparent in

the vertebral bodies of both models, these are not

considered as critical as even the highest values

(25.14 and 42.36 respectively) lie below their

strength characteristics. In the running scenario

however, some critical regions can be observed

within intervertebral discs, both qualitative and

quantitative, indicating that health condition of

patients with spinal injuries could be affected

drastically based on everyday activities.

4 CONCLUSIONS

The introduced model facilitates the evaluation of

induced loads on the lumbar spine. Pathological

defects, trauma as well as therapy oriented

intervention can be assessed prior to the actual

practice on the patient. This model may also be a

BIOINFORMATICS2013-InternationalConferenceonBioinformaticsModels,MethodsandAlgorithms

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valuable tool in preoperative evaluation of the

biomechanical response of the system to a function

specific implant.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the Hellenic

General Secretariat for Research and Technology, as

this work was funded in the frame of the BioSpine

grant (#PE8 3227).

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ANon-linearFiniteElementModelforAssessmentofLumbarSpinalInjuryDuetoDynamicLoading

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