Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016

Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

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PAPER REF: 6337

BIOMECHANICS OF LUMBAR SPINE

Catarina S. Mendes1, Luísa C. Sousa

2 (*), Marco Parente

2, Renato Natal Jorge

2, João M. Gonçalves

3,

Rolando Freitas4

1Universidade do Porto, Porto, Portugal 2Instituto de Engenharia Mecânica e Gestão Industrial (INEGI), Universidade do Porto, Porto, Portugal 3Serviço de Ortopedia, Hospital da Arrábida, Vila Nova de Gaia, Portugal 4Departmento de Cirurgia da Coluna, Serviço de Ortopedia - C. H. de Vila Nova de Gaia, Portugal (*)Email: lcsousa@fe.up.pt

ABSTRACT

The main goal of the presented study is to understand the mechanical behaviour of a lumbar

functional spine unit (FSU) L4-L5 with spondylolisthesis pathology. For the study of the

healthy FSU the process includes the 3D reconstruction of the lumbar spine geometry from

computer tomography (CT) images, finite element (FE) mesh definition and simulation of the

spine mechanics under different load cases. The pathological model was built applying a

posterior displacement of 6.81mm. The study of the two FE models, one healthy and the other

with pathology, allowed identifying significant differences on the mechanical behaviour.

Keywords: Biomechanics, finite elements method, lumbar spine, vertebrae L4-L5,

spondylolisthesis.

INTRODUCTION

Low back pain is the most diffuse pathology and represents one of the top causes of missed

work. This pain is a universal human experience as almost everyone has it at some point.

Fortunately, low back pain often gets better on its own. When it doesn't, there are effective

treatments.

Some authors (Weinstain, 2010; Moramarco, 2010) explain that low back pain can arise due

to idiopathic degeneration of any mechanical component of the column spine, like discs,

ligaments and facet joints. In most cases, surgery is the unique effective solution to the

problem. Surgery should only be considered if a patient's ability to participate in everyday

activities is unacceptably reduced and a concerted effort to relieve symptoms through non

operative techniques has been unproductive. Any treatment of lumbar spine injuries aims at

returning to a more active and pain free lifestyle, decreasing of any neurological deficit and

prevention of further disability. Furthermore, surgical treatment has some advantages like the

immediate stability and the possibility for early mobilization.

Nowadays most of the orthopaedic surgeries are essentially based on the experience of the

surgeon, who demands the best situation for each patient (Moramarco, 2010). Although CT

and magnetic resonance techniques allow the doctor to observe the current state of the patient

spine degeneration, it is not possible to predict the behaviour of the spine after surgery. The

use of computer models to study the biomechanical alterations of the cervical spine is a

powerful tool to understand the mechanisms of injury. The finite element method is an

excellent tool for studying the biomechanical behaviour of the spine, as it allows spine motion

analysis(Guan, 2006; Little, 2007); it makes possible to find the best solutions helping

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clinicians to make the best decision in planning surgical interventions. In the last years,

several models were created, with the goal to create prosthesis for a particular problem,

(Eberlein, 2001; Guan, 2006; Little, 2007; Moramarco, 2010; Rodrigues 2012; , 2013).

The main goal of this study is to perform the development of a non-invasive method to obtain

truly dynamic behaviour of the spine under specific loads. A heathy model of a lumbar L4-L5

FSU is created and an iterative calibration process was performed in order to find an ideal but

realistic combination of mechanical properties. Then a pathological model is built applying a

posterior displacement equal to 6.81 mm, corresponding to a lumbar spondylolisthesis. Using

the commercial software Abaqus Explicit, the characterization of each FSU model is made in

order to compare the behaviour of the heathy and non-health FE models under different

loading types; results show that for the same load, stresses of the non-healthy intervertebral

disc are higher, which can lead to greater disc injury.

METHODS

The spinal segment L4-L5 under consideration consists of two vertebral bodies, the

intervertebral disc, spinal ligaments and facet joints. The intervertebral disc and ligaments

contribute to the general flexibility of this spinal segment, having an important role in the

spine kinematics. For the definition of the healthy FSU geometry, vertebrae, intervertebral

discs (nucleus pulpous, annulus fibrosus and fibres), endplates, ligaments and facet joints

were considered (Little, 2007).

The construction of the vertebrae was established using CT scan data, and the finite element

mesh of the vertebrae was created using the commercial finite element package Abaqus/Cae

(Rodrigues, 2012).

The intervertebral disc was designed with its components, such as nucleus pulposus and

annulus fibrosus bounded by two endplates (Jieun, 2012; Rodrigues, 2012). Due to its lower

density, the intervertebral discs are not visible in a CT and disc geometry was defined using

the lower surface of L4 and the upper surface of L5. Fig. 1 shows the disc geometry with the

two different regions, the inner nucleus pulposus and the peripheral annulus fibrosus taking

into account the volumetric ratio 3:7.

Fig. 1 - 3D finite element of the intervertebral disc and Layers 1-2 and 7-8 of collagen fibres

The annulus fibrosus is a viscous substance reinforced by a network of collagen fibres. The

arrangement of the elastic fibres plays a very important role in the overall mechanical

properties of the annulus fibrosus. The stiffness of the fibre proportionally decreased from

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outside to inside for every two fibre layers and the proportion varied from 1 to 0.65 (Xu,

2013). The fibres were modelled as tension-only truss elements, T3D2 and embedded in the

viscous matrix of the respective annulus layer as shown in Fig. 1. The definition of the

cartilaginous plates was performed considering the first and last layer elements, respectively.

With the aim to decrease the thickness of the plate, the nodes were moved.

In order to model the intervertebral joints, facet joints were created in the contact area of the

two vertebrae. These facet joints were treated as a three-dimensional contact problem using

surface-to-surface soft contact with exponential-pressure-over closure option available in

ABAQUS. Finally the anterior longitudinal ligaments (ALL), the posterior longitudinal

ligaments (PLL), the supraspinous ligament (SSL), the interspinous ligaments (ISL), the

intertransverse ligaments (ITL), the ligamentum flavum (LF) and the capsular ligaments (CL)

were considered, and modelled with tension-only spring connector elements (truss elements

T3D2), similar to the definition of the collagen fibres. The complete model is presented in

Fig. 2a).

(a) (b)

Fig. 2 - 3D finite element: (a) healthy model; (b) pathologic model

In FE modelling of spinal motion segments generally it is considered that the segment is

supported rigidly along the inferior endplate of the lower vertebra, L5, and the loads are

applied on the superior endplate of the upper vertebra. The loads can be applied as static or

dynamic loads. In this study static loading situations were considered and all the loads were

applied in the superior surface of L4 through a reference node. The choice of mechanical

properties was performed by an iterative calibration process; considering a compression load

case a realistic combination of mechanical properties was obtained taking into account results

found in literature (Rodrigues, 2012). Elastic behaviour was considered for all FSU elements

(Rodrigues, 2012), except the nucleus pulposus and the viscous annulus that were considered

as hyper elastic materials. The vertebral bodies were taken as rigid bodies, thus there was no

difference between cortical and trabecular bone.

The pathological model, shown in Fig. 2b, was built applying a posterior displacement of 6.81

mm. The characterization of each model was performed using Abaqus Explicit: the two

models were subjected to pure moments and forces in the three anatomical planes. In order to

compare the mechanical behaviour of the two units, the maximum displacement and stress

fields were calculated.

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RESULTS

Two movements were analysed such as flexion and torsion. For each load case the axial

displacement field of the L4-L5 FSU, and the minimum principal stress distribution in the

intervertebral disc were analysed. Considering load cases flexion and torsion, moments of +20

Nm and +11.45 Nm were applied respectively.

(a) (b)

Fig. 3 - Axial displacement field (flexion load): (a) healthy model; (b) pathologic model

Figure 3 shows similar displacement fields for the healthy and non-healthy models,

considering flexion load; the healthy model presented a smaller axial displacement and in

both models the largest axial displacements are observed in vertebrae apophysis.

(a) (b)

Fig. 4 - Stress distribution considering torsion load: (a) healthy model; (b) pathologic model

Figure 4 shows the minimum principal stress distribution on the disc considering load case

flexion for healthy and pathological discs, respectively. As expected results show

compression at the anterior zone and traction at the posterior zone. Considering compression,

the maximum stress values are -0.5607 MPa and -1.238 MPa for the healthy and pathologic

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discs respectively. Concluding, the pathological model presents higher stresses and is more

prone to deformations.

(a) (b)

Fig. 5 - Axial displacement field (torsion load): (a) healthy model; (b) pathologic model

Figures 5 and 6 present the displacement field and the minimum principal stress distribution

considering torsion load. As in the previous load case the healthy model presents smaller axial

displacements. Stress distribution is uniform in the healthy model, however, in the disease

model, the intervertebral disc is under traction on the right side and under compression on the

left side. In both models the critical zone is under compression. The healthy model presents a

maximum value equal to -0.2396 MPa while for the pathological model maximum value is

equal to -0.476 MPa. Once more the FSU model with pathology presents higher stresses

(almost twice) than the healthy one.

(a) (b)

Fig. 6 - Stress distribution considering torsion load: (a) healthy model; (b) pathologic model

CONCLUSIONS

The obtained results, as clinically expected, show that pathologic model present the highest

compressive stresses for the two studied load cases. Concluding patients with

spondylolisthesis will have greater possibility of disc degeneration and herniation.

Furthermore greater deformation of the disc and large axial displacements of contiguous

segments, will lead to neurological injury.

The obtained results with static load conditions allow the prediction of the most loaded parts

of the discs related to the most susceptible zones of damage. Although the finite element

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model developed for this study is still not fully complete, as muscle forces and initial stresses

of the ligaments were not considered it proved to be a useful tool for understanding the

biomechanical behaviour of the cervical spine, and may help clinicians to understand the

initiation and progression of disc degeneration and to treat lumbar discopathy problems even

more effectively.

ACKNOWLEDGMENTS

The authors acknowledge the collaborative work of the medical team of the Centro Hospitalar

de Vila Nova de Gaia and of the Hospital da Arrábida, Vila Nova de Gaia, Portugal.

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