Finite element modelling of innovative interspinous process spacers for the lumbar spine. Biomedical Engineering

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Finite element modelling of innovative interspinous

process spacers for the lumbar spine

Valentina da Silva Carvalho

Thesis to obtain the Master of Science Degree in

Biomedical Engineering

Supervisor(s): Prof. André Paulo Galvão de Castro

Eng. Miguel Seabra

Examination Committee

Chairperson: Prof. Patrícia Margarida Piedade Figueiredo

Supervisor:Prof. André Paulo Galvão de Castro

Members of the Committee: Prof. Luís Alberto Gonçalves de Sousa

Dr. Manuel José Tavares de Matos

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Preface

The work presented in this thesis was performed at the Department of Mechanical Engineering of Instituto Superior Técnico (Lisboa, Portugal), during the period February-October 2019, under the supervision of Prof. André Castro and Eng. Miguel Seabra.

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Declaration

I declare that this document is an original work of my own authorship and that it fulfills all the requirements of the Code of Conduct and Good Practices of the Universidade de Lisboa.

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Agradecimentos

Porque nada se constrói sozinho, um muito obrigado aos meus orientadores, André Castro e Miguel Seabra. Um agradecimento especial também aos professores Paulo Fernandes, João Folgado, Carlos Quental que sempre se mostraram prontos a ajudar e a opinar. Um obrigado também ao Doutor Joaquim Pedro Correia, que possibilitou a assistência a uma cirurgia à coluna lombar e sempre se disponibilizou para tirar qualquer tipo de dúvida.

Gostava também de agradecer aos meus colegas e amigos do gabinete. Ao Tiago por sempre se mostrar tão pronto a ajudar qualquer um, à Joana Paulino por entrar sempre no gabinete com um sorriso na cara contagiante, à Joana Real pelo bom trabalho em equipa, que ajudou imenso para que tudo fosse mais fácil, à Mônica por ser sempre tão divertida e querida, ao Rafa e ao Marta por ajudarem sempre no que podiam e por fazerem com que me torna-se hoje mais simpática, e ao Alex por nunca se ter cansado de mim, após 4 anos, um Erasmus e 8 meses de gabinete.

Um obrigado aos Tugas e ao Marina, que sempre funcionaram como bolha de apoio e de carinho para mim, e me fizeram acreditar que uma base solida é a melhor forma de chegar ao topo. À minha mãe, pai que sempre me inspiraram a querer mais e sempre me fizeram acreditar que nada pode falhar quando acreditas e trabalhas para ela. À Aurora, por ser uma irmã tão diferente de mim e me faz ver as coisas sempre de outra forma, por ser tão encorajadora e por me ter feito tantas vezes o jantar neste último ano! E a toda a minha restante família, que me apoia em qualquer decisão e me faz acreditar que o nosso amor funciona à semelhança da Silva e de um Carvalho, impenetrável e duradouro.

Ao João, um grande obrigado por me ensinar a querer ser grande, ao nível dele. A todo o amor e paciência nos últimos 4 anos. E um obrigado final por me levar a almoçar, e me aturar até GOT sair.

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ix Abstract

Low back pain is an emerging problem in society. This occurs as lumbar spine is a leaning site for spinal diseases to occur. Their diagnostic and treatment have a large impact in countries’ economics.

The number of spinal fusion surgeries for treatment of spinal diseases as herniation, stenosis and spondylolisthesis has increased. Interspinous posterior fixation has been proposed as a less invasive alternative to older systems for these spinal procedures. The motivation for this thesis comes directly from that fact, the surgical procedure can be not efficient, thus new design proposals can be achieved with this type of studies, to facilitate whole process.

This study had two main objectives that were achieved with the development of a new Finite Element model of L3-L5 spinal segment: i) study spinal degeneration process; ii) evaluation of a new design of innovative interspinous spacer to be inserted with lower risk for the patient, while having the same biomechanical performance as the existing device, Axle®.

The FE analysis have shown that new devices designs can be considered without resulting in a lower biomechanical performance, confirming that the study and development of a new interspinous devices can be extremely important, as spinal surgery can become less invasive and facilitated procedure. This thesis has also achieved to add more knowledge to the spinal degeneration process studies. All these results can be an important basis for the future research on new models of degenerative spinal process, as in the study of new designs and/or improvements of Axle device.

Keywords: Low Back Pain; Spinal Fusion; Interverbal Disc; Interspinous Posterior Fixation; Spinal Degeneration; Finite Elements.

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xi Resumo

A lombalgia é um problema emergente na sociedade. Isto porque a coluna é uma região sensível a doenças da coluna vertebral, e o seu diagnóstico e tratamento têm grande impacto na economia dos países.

A taxa de cirurgias de fusão espinhal para o tratamento de doenças como protusão do disco intervertebral, estenose e espondilolistese têm vindo a aumentar. A fixação posterior interespinhosa tem sido proposta como uma alternativa menos invasiva aos procedimentos mais antigos. Desta forma, a motivação desta tese advém deste facto, os procedimentos cirúrgicos feitos até então podem não ser as mais eficientes, portanto propostas de novos dispositivos podem ser uma opção para facilitar todo processo cirúrgico.

Este estudo teve por base dois grandes objetivos, que foram conseguidos devido ao desenvolvimento de um modelo de Elementos Finitos de um segmento espinhal L3-L5: i) estudo do processo de degeneração da coluna e seus efeitos e ii) avaliação de um novo design de fixador posterior interespinhoso, com menores riscos para o paciente, na altura da sua inserção no segmento pretendido, igualando o desempenho biomecânico do já existente, Axle®.

A análise de elementos finitos mostrou que novos designs podem ser considerados, não diminuindo o desempenho, confirmando que estudos e desenvolvimento de novos dispositivos interespinhosos pode ser uma mais valia. Assim, considera-se que este trabalho acrescenta mais informação ao que anteriormente já se conhecia da simulação do processo de degeneração. Todas estes resultados podem servir como base para futuras pesquisas quer da modelação do processo degenerativo quer para o estudo do aprimoramento de dispositivos para lá do conhecido Axle.

Palavras-Chave: Lombalgia; Fusão Espinhal; Disco Intervertebral; Fixação Posterior

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List of Figures

2.1 Posterior and anterior views of the curvature of the vertebral column and its different constituents.. . . 6 2.2 Description of the lumbar vertebrae. . . 6 2.3 Structure of the healthy IVD (a) Sagittal cut of the spine showing the inside of the disc and its different structures (b) Cut out portion of the disc. . . .7

2.4 Anatomical distribution of the spinal ligaments in the column. (a) Sagittal view showing ISL, SSL, ALL and PLL. (b) Anterior view showing FL. . . 8 2.5 Morphology alterations related with IVD degeneration (a) Transverse view of the degenerative IVD. (b) Sagittal view of the degenerative IVD. . . 10 3.1 Illustration of Dynesys® dynamic system, that uses flexible materials to stabilize the affected lumbar region. . . 12 3.2 Photographs of various existing interspinous posterior fusion devices. (a) SPIRE spinous process plate. (b) S-plate. (c) Coflex-F. (d) Tadpole. (e) Aspen. (f) Affix (g) Prisma LOK (h) Axle. . . 13 3.3 3D non-linear model of the L2-L3 disc body unit. Because of symmetry, only a quarter of the joint was modelled, with symmetry about sagittal plane and mid-horizontal plane. . . .14 3.4 Entire lumbar model developed by Breau et al. . . .15 3.5 Step by step FE model creation developed and validated by Naserkhaki et al. . . 16 3.6 Spinal model and two concepts of posterior spinal fixation devices. (a) 3D intact segment model. (b) Easy®, a rigid screw/rod. (c) Twinflex®, a dynamic system. . . 17 3.7 Study of new designs for spinal fusion devices (a) FE intact lumbar spine model. (b) Spine model with PEEK cage and pedicle screw implemented by posterior lumbar interbody fusion method(c) Spine model with PEEK cage and interspinous process compressor systems. . . .18 4.1 3D Model of two single parts of the L3-L5 segment. (a) L3-L5 IVD 3D Model. (b) L5 vertebra 3D Model. . . .22 4.2 Diagram that represents the process for the FE model construction. . . .23 4.3 Boundary conditions representation of the FE Model. (a) Model assigned with the inferior surface of the L5 vertebral body completely constrained and the loads applied in the top surface of the L3. The solid arrow represents the pre-load applied to the reference point and the dashed arrow refers to the applied moment, which in this particular case refers to flexion movement. (b) Coupling of the reference point to the L3 surface. . . 26 4.4 FE model with some of the ligaments represented. . . 26 4.5 Illustration of the Axle® device implemented into spinal segment. . . .30 4.6 Boundary conditions applied to Device 1 for mechanical tests. (a) Representation for the compression test. (b) Representation for the shear test. . . .31

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4.7 Boundary conditions applied to Device 2 for mechanical tests. (a) Representation for the compression test. (b) Representation for the shear test. . . .33

5.1 Minimum stress value (S33) at the model depending on the number of nodes of the segment…40 5.2 Maximum stress value (S22) at the Device 1 model depending on the number of nodes of the segment. . . .41 5.3 Minimum stress value (S22) at the Device 2 model depending on the number of nodes of the segment. . . .42 6.1 Mechanical tests results. (a) Compression test result for Device 1. (b) Compression test result for Device 2. (c) Shear test result for Device 1. (d) Shear test result for Device 2. . . .43 6.2 RoM values (in degrees) of the Cases 1, 2, 3 and 4 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . .45

6.3 RoM values (in degrees) of the Cases 1, 2, 5 and 6, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . .46 6.4 Stress Values at the NP center of the Cases 1, 2, 3 and 4, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . . 47

6.5 Stress Values at the Posterior AF of the Cases 1, 2, 3 and 4, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . . .48 6.6 Illustration of bulging phenomena. (a) Lateral bending of a healthy spinal segment. (b) Lateral bending of a degenerate spinal segment. . . .49 6.7 Stress Values at the Posterior AF of the Cases 1, 2, 3 and 4, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . . .49 6.8 RoM values (in Degrees) of the Cases 1, 2, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . . .51 6.9 RoM values (in Degrees) of the Cases 1, 3, Device 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . . .52 6.10 RoM values (in Degrees) of the Cases 1, 4, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . . .53 6.11 Stress Values at the center of NP of the Cases 1, 2, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 53

6.12 Stress Values at the posterior portion of AF of the Cases 1, 2, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments . . . .54

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6.13 Stress values at the center portion of NF of the Cases 1, 3, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 55

6.14 Stress values at the posterior portion of AF of the Cases 1, 3, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments . . . .55 6.15 Stress values at the center portion of NP of the Cases 1, 4, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 56 6.16 Stress values at the posterior portion of AF of the Cases 1, 4, Device 1 and 2, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 56

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List of Tables

4.1 Dimension of the vertebral body.. . . 22

4.2 Dimension of the two IVDs . . . 23

4.3 Material properties for the FE analysis. . . .24

4.4 Materials properties for the spinal ligaments. . . 27

4.5 Cases for the different degeneration’s stages considered in the study. . . 27

4.6 Material properties of the AF and NP for the considered degeneration stages . . . .29

4.7 Dimensions of the Axle® 3D model. . . .30

4.8 Material properties of the Axle® FE model. . . .30

4.9 Dimensions of the Device 2 3D model. . . .32

4.10 Resume of all models that were constructed to guarantee the goal achievements for the study. . . . .35

5.1 Material Properties for the spinal ligaments before verification . . . 38

5.2 Material Properties for the spinal ligaments after verification .. . . .38

5.3 RoM values (in degrees) of the model for extension, flexion, lateral bending and axial rotation moments. The values that correspond to the Heuer et al. study are the minimum, the maximum and the median values observed over the 8 specimens. . . .39

6.1 Compression test results for both devices regarding their critical zones of interest. . . .44

6.2 Shear test results for both devices regarding their critical zones of interest. . . 44

6.3 Stress results of a ligaments set for the four movements. . . .50

6.4 Stress values for a critical node of the interface device-bone. . . 57

6.5 Stress results of a ligaments set for the four movements and for Case 1 and 2, intact and instrumented. . . 58

Table A.1 Stress Values at the anterior portion of AF of the Cases 1, 2, 3 and 4, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 69

Table A.2 Stress Values at the anterior portion of AF of the Cases 1, 2, 5 and 6, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . .69

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Table A.3 Stress Values at the left portion of AF of the Cases 1, 2, 3 and 4, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 69

Table A.4 Stress Values at the left portion of AF of the Cases 1, 2, 5 and 6, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 70

Table A.5 Stress Values at the right portion of AF of the Cases 1, 2, 3 and 4, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 70

Table A.6 Stress Values at the right portion of AF of the Cases 1, 2, 5 and 6, at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 70

Table A.7 Stress Values at the anterior portion of AF of the Cases 1, 2 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 70 Table A.8 Stress Values at the left portion of AF of the Cases 1, 2 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 71 Table A.9 Stress Values at the right portion of AF of the Cases 1, 2 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 71 Table A.10 Stress Values at the anterior portion of AF of the Cases 1, 3 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 71 Table A.11 Stress Values at the left portion of AF of the Cases 1, 3 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 72 Table A.12 Stress Values at the right portion of AF of the Cases 1, 3 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 72 Table A.13 Stress Values at the anterior portion of AF of the Cases 1, 4 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 72 Table A.14 Stress Values at the left portion of AF of the Cases 1, 4 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 73 Table A.15 Stress Values at the right portion of AF of the Cases 1, 4 and both with devices 1 and 2 at the different loading conditions: Lateral Bending (LB), Flexion (FL), Extension (E) and Axial Rotation (AR) for L3-L4 and L4-L5 segments. . . 73

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Acronyms

AF ALL LBP CL FE ISL ITL IVD LF NP PLL RoM S SSL Annulus Fibrosus.

Anterior Longitudinal Ligament. Low Back Pain.

Capsular Ligament. Finite Element. Interspinous Ligament. Intertransverse Ligament. Intervertebral Disc. Ligament Flavum. Nucleus Pulposus.

Posterior Longitudinal Ligament. Range of Motion.

Stress

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Nomenclature

𝐸 𝑣 𝐷1, 𝐶10, 𝐶01 𝐾 𝐾1, 𝐾2, 𝐾𝑎𝑝𝑝𝑎 Young’s Modulus Poisson’s Ratio

Material Parameters from the Mooney-Rivlin’s Model Bulk Modulus

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Chapter 1 Introduction

Motivation

Low back pain (LBP) affects a large portion of the population, resulting in high care costs for therapy and treatment, especially in western societies. Currently, this problem is one of the major reasons for work absenteeism and productivity decrease, denoting itself to be an alert for society [1]. The big portion of clinical low back pain is explained by the aging of the population and how age is associated with degenerative spinal diseases that can cause spinal stenosis.

Today’s, treatments of degenerative spinal diseases are mainly physical and medical, although these traditional methods may fail to cure the diseases and acts only to symptoms relieve. Therefore, surgical approaches should be applied to recover healthy functionality of the spine [2].

The causes for the degeneration of the spine are still unclear. Many of correlations with the intervertebral disc degeneration, facet joints and ligaments hypertrophy has been documented. The lack of an accepted explanatory models limits the understanding of this disease, and retards the development of effective therapies [3].

Surgery for spinal stenosis generally consists of decompression of the nerves that are being compressed. This method can cause spine instability and consequently it is often followed by the introduction of some type of biomechanical device, in order to stabilize the spine, as well as to replace any kind of structure that have demonstrated to be very degenerated [4].

During the surgery intervention, specific attention should be paid to nerve root. Therefore, there is a high need to develop a less invasive spinal surgery technique. Thus, instrumentation is one of the main factors for design constraints and approaches of biomechanical devices, as fixation and fusion devices for stabilization of human spine [4].

A variety of interspinous fusion systems have been designed as minimally invasive devices after specific decompression surgeries. Different materials and models are available in the medical market, for example the Axle® device, an interspinous fusion system of X-Spine Systems, Inc.

However, the main goal of todays is to create the ideal device that can provide robust posterior fixation with adjustable length. This type of mechanism could enable device-expansion and compression, allowing not only an easier device implementation, but also providing immobilization and stabilization of the spine, preserving the natural anatomy [5-7].

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Biomechanical testing and understanding the effects spinal ligaments, muscles and all involved with spinal mechanism are a prerequisite for the development of new surgical approaches and recommendations for postoperative treatment of spinal injuries [8]. Three different types of methods are currently available: in vivo, in vitro and in silico studies. The last one, resorts to finite element (FE) model, has the advantage of easily modifying the geometry, properties and test different conditions without the need for cadaveric or animal specimens. Thus, the finite element method has been used widely for analyzing biomechanical problems, reporting successfully approaches and results in many studies on lumbar spine [9].

Objectives

Spinal fusion was reported as one of the most frequent procedures for the treatment of human spine diseases. Its implementation ensures immobilization and stability, preventing undesired intersegmental motions[10].

There are a lot of devices in the market that can guarantee spinal fusion. However, in the past years, there has been some progression in order to simplify the device implementation, minimize natural anatomy damages, and guarantee high efficiency of the spinal fusion procedure. Accordingly, the two main objectives of this study focus on:

1. Simulate different spinal degenerations stages and analyze its effects for the spinal column. For that, it was necessary to develop and validate a new FE model of a L3-L5 segment.

2. Study of a new spinal fusion device, that could be more easily implemented without compromising its biomechanical performance, and mechanical comparison with an existing one, Axle.

Thesis Outline

This thesis is divided into 7 chapters, namely: “Introduction”, “Anatomy of the human spine”, “State of the art”, “Methods”, “Validation of the finite element model”, “Results and Discussion”, and “Conclusions and future work”.

The first Chapter includes a brief introduction and motivation for this works and its objectives. In Chapter 2, the anatomical characteristics of the human spine are described, as well as the spinal degenerative mechanisms and consequent treatment process.

The Chapter 3 consist of a description of previous spine and interspinous fixators models, highlighting the most significant models available in the literature.

Chapter 4 describes all the detailed methodology for the development of a new spinal model. Materials properties, interactions, loads and boundary conditions are also described in this Chapter as well as the development of the devices geometrical models are explained. The mesh generation is detailed in the Chapter 5 with a convergence analysis to support the mesh size choice.

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The sixty Chapter comprises the complete FE analysis results of all models developed in the study. Here, the more relevant outcomes are discusses based on the different characteristics of each model, to study the biomechanical effects of each device, along different spinal degeneration stages.

The final Chapter, the seventh, includes not only the generalized conclusions of this work, but also some suggestions for future work.

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Chapter 2 Anatomy of the Human spine

The human spine is a modular structure. Its function is to protect neural elements of the spinal cord, support the trunk in the upright position and allow daily moments. Capacities as strength and flexibility allow it to rotate and move forward, backward and sideways [11].

In a human´s vertebral spine there are thirty-three vertebrae, that are distributed as follows: • 7 cervical vertebrae in the neck region (C1-C7);

• 12 thoracic vertebrae posterior to the thoracic cavity (T1-T12); • 5 lumbar vertebrae support the lower back (L1-L5);

• 5 fused sacral vertebrae that consists the sacrum (S1-S5); • 4 fused coccygeal vertebrae that define the coccyx (Tailbone).

While the sacrum and coccyx are immovable and fused, the upper twenty-four vertebrae are movable, articulating and separated from each other by fibrocartilaginous segments, the 23 intervertebral discs (IVD). These vertebrae are also anchored by ligaments and muscles so that the vertebral column remains aligned and stabilized [12,13].

One healthy spine forms a S-shaped curve when on the sagittal plane, four slight bends called normal curves: two convex anteriorly and concave posteriorly curves at the neck and low back (cervical and lumbar, respectively) and two concave anteriorly and convex posteriorly curves at the chest and pelvis (thoracic and sacrococcygeal, respectively) [13,14]. This peculiar anatomy has an important role since it allows the maintenance of balance and stability in the upright position, increasing flexibility and absorbing the shocks during daily movements [12]. This description is illustrated in Figure 2.1.

2.1 Vertebra

According to each spinal column region, the vertebrae are different in size, shape and detail. Nevertheless, all are similar in relation to global structure and function [12]. The size and mass of the vertebrae increases from the first cervical to the last lumbar vertebra. This anatomic characteristic corresponds to a mechanical adaptation to the progressively increasing compression loads to which the vertebrae are subjected [11,13].

The vertebra consists of an anterior block of bone, the vertebral body, and a posterior bony ring, known as the neural arch, containing the articular, transverse and spinous processes. The hole between the vertebral arch and body contains the spinal cord and is called vertebral foramen [12,13]. All vertebra components mentioned can be observed in the Figure 2.2.

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The vertebral body is roughly cylindrical mass of cancellous bone contained in a thin shell of cortical bone, that supports most of the compression tensions applied in the vertebra. Its superior and inferior surfaces, the endplates are slightly concave. The neural arch extends backwards from the body of the vertebra and it consists of two short thick processes, the pedicles, which project backwards from the body to unite with the laminae. The laminae end in a single sharp, projection called spinous process. At the point where the lamina and pedicle join, a transverse process extend laterally on each side. These three processes work as point of attachment for muscles. There are four remaining processes, the articular, that form joints with another vertebra above or below. The smooth articulating surfaces of the articular processes, called facets, are covered with hyaline cartilage [12,14].

Figure 2.1: Posterior and anterior views of the curvature of the vertebral column and its different constituents. Retrieved from [2].

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2.2 The interverbal disc

The IVD is a complex joint which allows flexible motion within the spine while working as a shock absorber, this particularity prevents excessive motion and maintains the mechanical stability of the spine. It is composed of cartilage, making regeneration process more difficult since this tissue is avascular. Thus, due to its property, nutrient transport and waste removal are done across the vertebral endplate, one of the three structural components of the IVD [12]. The intervertebral disc, illustrated in Figure 2.3, is composed by the vertebral endplate, an outer fibrous ring, the annulus fibrosus (AF), which surrounds an inner gel-like center, the nucleus pulposus (NP):

• The annulus fibrosus consists of successive layers of collagen fibers, made out of both type I and type II collagen. These fibers are positioned obliquely on the disc, and each layer has the opposite direction from its adjacent ones. This configuration confers greater resistance to torsion loads. Additionally, resistance to shear forces is exerted exclusively by the annulus. The stiff laminae can withstand compressive loads. All these properties prevent the development of stress concentrations which could cause damage to the underlying vertebrae or the endplates [11].

• The nucleus pulposus, the center part of the IVD, is made out of high-water content, type II collagen, chondrocyte-like cells and proteoglycans. These components help the NP to be elastic, allowing it to be flexible under tension and resistant to compression. The high density of proteoglycans gives it a high charge density which causes the NP to absorb water and swell. This gelatinous mechanical property allows the nucleus pulposus to take the stress placed on the spine and redistribute it to the annulus fibrosus and the cartilaginous endplates, being the responsible for maintaining the disc pressurized [11,15,16].

• The cartilaginous endplate is composed by a thin layer of hyaline cartilage and a layer of cortical bone of the same thickness. This structure constitutes a string docking surface for the annulus fibers. The surface of cartilage is semi-permeable allowing the diffusion of water and solutes to and from the IVD [11].

Figure 2.3: Structure of the healthy IVD; (a) Sagittal cut of the spine showing the inside of the disc and its different structures; (b) Cut out portion of the disc. Adapted from [6].

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2.3 Ligaments and Muscles

Ligaments and muscles play an important role in the stability as well as mobility of the spinal column. Along with their mechanical action, they also establish organs of proprioception. Hence, the spine maintains its balance, performs complex movements but also protects itself from excessive or abnormal motion [11,17].

There are seven different ligaments involved in holding the vertebrae together, stabilize and protect the discs. Some of them are illustrated in Figure 2.4. The strong fibrous bands constrain the spine parts and limit the range of motion in all directions. Due to their elasticity, they passively help return the spine back to the neutral position [17].

The three major ligaments of the spine are ligamentum flavum (FL), anterior longitudinal ligament (ALL), and posterior longitudinal ligament (PLL). The ALL and PLL are continuous bands that run from the top to the bottom of the spinal column along the vertebral bodies. The FL attaches between the lamina of each vertebra. These three allow flexion and extension of the spine while keeping the bones aligned. The other four ligaments connect all the posterior elements of the vertebra. The intertransverse ligament (ITL) connects the transverse processes, the interspinous ligament (ISL) connects the opposing edges of the spinous processes, the supraspinous ligament (SSL) connects the peaks of the spinous processes and the capsular ligament (CL) connects the circumferences of the joining articular facet joints [18].

2.4 Spinal Diseases

The chance of an adult experiencing LBP is higher than 50% in a lifetime with about 18% prevalence at any time [19]. Aging of the spine tends to result in a number of painful disorders. The pain experienced Figure 2.4: Anatomical distribution of the spinal ligaments in the column; (a) Sagittal view showing ISL, SSL, ALL and PLL; (b) Anterior view showing FL. Retrieved from [18].

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can be quite ambiguous considering that can be cause for a lot of spinal diseases. And their symptoms tend to overlap, and one may cause others [20].

LBP is commonly associated with IVD herniation, where NP tissues extrude through defects in the AF resulting in back pain, leg numbness and weakness [21]. This association results from the fact that IVD is positioned in one of the most sensitive locations of the human body, next to the spinal canals in close proximity to its nerve roots. Consequently, any changes in its morphology or physiology can lead to a compression of the nerves resulting in pain [15]. Numerous changes in disc have been described by literature. One of the defended origins is the biomechanical wear and tear as well as the disturbance of physiological cellular behavior, mainly focuses on a loss of nutrition. These two possible causes do not exclude each other, in the fact the dichotomy between biology and mechanics is crucial, since cellular physiology is affected by its mechanical environment [3].

The nucleus and annulus behave as one. Its efficiency depends on the integrity of each constituent. Disc degeneration begins when the balance between synthesis and degradation of the matrix is altered. This include loss of water and glycoproteins and disruption of collagen fibers organization which results in a dehydration of the disc and therefore a higher stiffness as well as the loss of tensile strength of fibers that constitute the annulus fibrosus [3,22]. These modifications bring macroscopic anatomical alterations that can be observed in Figure 2.5. The loss of water content causes a reduction of disc height. The nucleus´s ground matrix is replaced by collagen fibers and the boundary between the nucleus and the annulus becomes blurred. Due to these alterations, the disc can either buckle, bulge as whole or protrude through weak points. This causes bulging or herniations, possibly resulting in spinal canal stenosis. The degeneration of the intravertebral disc can result in initial relative instability and hypermobility of the facet joints, leading to their hypertrophy, particularly in the superior articular process, resulting in reduced spinal canal dimensions, once again providing the compression of neural elements [4]. Furthermore, it also has implications on the transmission of loads which any modifications can alter the bone remodeling procedure [11].

Another possible cause of spinal diseases is the hypertrophy of the ligaments. Age advance leads to an increase of collagen instead of elastin, increased cross-linking collagen fibers and a reduction in elasticity and strength of ligaments. The loss of elasticity can compromise the anchorage of the vertebrae, leading to instability and unwanted displacements. These can lead to spinal diseases as spondylolisthesis [11,23]. FL, in particular, can lead to its fold into the spinal canal, which leads the compression of the nerve roots, resulting in a spinal canal stenosis. The thickness of FL was found to increase with age, especially on the L3-L5 segment, probably because of large mechanical stress at these levels [23].

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The combination of IVD bulging and its height reduction, facet joints and ligamentum hypertrophy contributes to the pathogenesis of spinal stenosis. There are other factors that can contribute to the narrowing of the spinal canal, trauma and tumors are some few examples, and it is important that these factors are considered as well [23].

Figure 2.5: Morphology alterations related with IVD degeneration; (a) Transverse view of the degenerative IVD; (b) Sagittal view of the degenerative IVD. Adapted from [24,25].

The most common procedures (individually or combined, depending on the pathology) for the treatment of herniation and/or spinal stenosis are:

• Lumbar Decompression: in this technique, a portion of herniated disc is removed to relieve the pressure on the spinal cord or one or more compressed nerve roots passing through the spinal column. The two primary lumbar decompression procedures are microdiscectomy and laminectomy.

• Lumbar Spinal Fusion: this technique joins two or more vertebrae, preventing any movement between them. The spinal fusion involves the total or partial removal of the IVD between the two consecutive vertebrae and the use of bone grafting or an implant to fuse and stabilize the segment.

• Lumbar Total Disc Arthroplasty: it is the procedure in which a degenerated intervertebral disc is replaced with medical implants in the spine. This non-biological device mimics the functions of the original structure, such as stability, shock-absorption and motion.

The surgery type is always dependent of the patient pathology and anatomy. The three mentioned can be performed separately or combined. The surgeon opinion and experience can be an important factor that contributes for the surgery type chosen [26]. Computer simulation can also be very helpful to understand which options are the best in certain clinical cases.

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Chapter 3 State of the art

3.1 Interspinous Fixators for Spinal Fusion

The spinal fusion was initially introduced by Hibbs Albee in 1911 [10]. After that, this technique has been one of the most frequent mechanisms for treating spine diseases as deformity, trauma, degenerative disc disease and spondylolisthesis. The fusion procedure ensures stability and immobilization, preventing undesired intersegmental motions. There are a lot of devices in the market that can guarantee this fusion. These devices must provide enough stiffness for spinal fusion and also must have an uncomplicated and safe process of insertion. This last requirement is very important, since this type of medical instrumentation may have some unfavorable complications, such as paraspinal muscle dissection and retraction, screw mal positioning, neurologic risk and long operative time that can result in blood loss.

In order to minimize these possibilities and guarantee the efficiency of spinal fusion devices, there have been some progressions in the past years regarding their design and material composition.

Rigid fixation systems are the gold standard in the surgical management of spinal disorders with LBP. These are designed to provide immediate stability after surgery until the fusion mass takes over. Pedicle screw systems are one of the first and current techniques used in this particular type of spinal fusion. These pedicle screws are placed above and below the vertebrae, the screws are inserted through the pedicles and into the vertebral body, one on each side.

Several types of pedicle screw systems have been used in lumbar spine fusion. The first systems were made of stainless steel, but titanium-alloy devices have recently been developed and available on the market [27,28].

More recently, some authors have associated the pedicle screw systems to several drawbacks, such as imposing high mechanical stress on the adjacent segment due to the high restriction of the natural mobility which often leads to long-term degenerative changes, resulting in a need for additional fusion surgery [27,28]. Loosening and failure of some pedicle screws has also been reported. For these reasons, some investigators and surgeons defend the dynamic systems as an alternative to rigid systems for spinal treatment, due to the mimicking of natural spine movements [28]. One of the dynamic examples studied is illustrated in Figure 3.1. The dynamic systems consist of titanium alloy pedicle screws, polyester cords and polycarbonate urethane spacers. These set of materials are designed to improve load sharing while providing enough segmental stability and pain relief. Therefore, some authors defend that this mechanism reduces and can even eliminate degenerative effects on adjacent segments, being an advantage of dynamic fixation systems.

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However, published clinical evidence for dynamic systems remains limited, and the medical opinions are still controversial [29].

The need for less invasive techniques and instrumentation has great importance in the fusion implants design constraints and approaches. Therefore, more recently, a variety of interspinous spacers have been proposed as minimally invasive devices that are promoted either as stabilization or fusion devices after specific decompression surgeries [5]. However, these interspinous devices are recommended only for a minimal decompression surgery such as laminotomies. For instance, in cases of spondylolisthesis (grade I and II) the pedicle screw system implantation may be an excessive correction for micro decompression surgery and could potentially generate unnecessary risks.

Some studies affirm that by comparing interspinous posterior fusion devices with the pedicle screw system, the first ones have an advantage for minimally invasive treatment, analyzing parameters as estimated blood loss, surgery time and hospital length of stay [10].

There are already some examples of interspinous posterior fusion devices available on the market. Some of these examples are shown in Figure 3.2.

The Axle Interspinous Fusion System of X-spine Systems, Inc©. represented in Figure 3.2 (h), is one of the devices commonly used for internal fixation of the lumbar spine. Axle is used for plate fixation and attachment to spinous processes. Several sizes of this implant are available becoming possible a good adaptation to consider the pathology and anatomy of the patients.

The device is made of titanium alloy. The Axle as well as other types of interspinous fusion systems is intended for single use only. However, some studies suggest that more computational studies are needed to strongly support the recommendation of an interspinous fusion device as a supplemental fixation to a posterior interbody cage in the lumbar spine [5,6].

Figure 3.1: Illustration of Dynesys® dynamic system, that uses flexible materials to stabilize the affected lumbar region. Adapted from [2].

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3.2 FE Models

3.2.1 Intact Models

Since the first application of FE analysis in biomechanics by Brekelmans et al. in 1972, the number of assessments of the human spine without resorting to animal and cadaveric experiments has increased [30]. This application has countless benefits to health and biomedical researches. As the human spine is a complex system, the modelling simplifications and the easiness of changing the geometry, material properties and boundary conditions can lead to many important conclusions regarding spinal health, diseases, degenerations, trauma, surgery processes and spinal instrumentation.

The first three-dimensional finite element model of a vertebra was obtained through sectioning and direct measurement. The model was constructed by Hakim and King. The intravertebral disc was represented by simple linear axial elements [30].

Some improvements were done by Bozic et al, developing a solid three-dimensional FE vertebra from a CT image [31]. This process represented an advantage of their approach since the bony density of each voxel was obtained from the CT data, and Young modulus and strength of each elements varied accordingly. In this model, springs were used to represent the adjacent discs [30,31].

Belytschko et al. were the first to represent in detail a FE analysis of a spinal segment, in 1974 [32]. They assumed rotational symmetry with respect to a vertical centerline that passes in the middle of the segment and axial symmetry with a horizontal plane of symmetry that passes in the middle of the IVD. These two symmetries enabled a geometric simplification for the FE analysis. The model did not include the posterior elements since an assumption was made by the authors, that there were no loads transmission to these structures. The trabecular and cortical bone and the endplates were simulated as Figure 3.2: Photographs of various existing interspinous posterior fusion devices; (a) SPIRE spinous process plate; (b) S-plate; (c) Coflex-F; (d) Tadpole; (e) Aspen; (f) Affix; (g) Prisma LOK; (h) Axle. Adapted from [10].

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isotropic and homogenous materials. The NP was considered incompressible and the AF was assumed to be linear orthotropic [32,33].

The same symmetric model was posteriorly extended by Kulak et al., assuming that the AF had non-linear orthotropic properties. The parameters were derived by comparison with experimental measurements [30].

Ten years later, Shirazi-Adl et al. made one significant contribution to the modelling of intervertebral discs. In 1984, they developed a three-dimensional nonlinear FE model of the lumbar disc body unit. The model is illustrated in Figure 3.3, and it consisted of cortical bone, trabecular bone, endplate and intervertebral disc. The AF was modelled as a complex of collagenous fibers embedded in a matrix of ground substance, and the NP was represented by an incompressible inviscid fluid. Axial elements were used to model the fibers of the AF, arranged in a crisscross pattern and defined as non-linear properties to express the softening of the fibers at higher tensions [30].

This model was developed to include contact at facet joints and to study their geometry effects. Analysis of the motions segment under pure sagittal plane moments and under combinations of more complex loading conditions were also one of the goals of the study [10,30].

Figure 3.3: 3D non-linear model of the L2-L3 disc body unit. Because of symmetry, only a quarter of the joint was modelled, with symmetry about sagittal plane and mid-horizontal plane. Retrieved from [10].

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In 1991, an entire lumbar segment model was developed by Breau et al., by resorting a segmentation method on a cadaveric specimen subject [34]. As illustrated in Figure 3.4, the model consisted in six vertebrae, five IVD and the spinal ligaments were also introduced. In this model the AF and the NP were modelled as Shirazi-Adl et al considered in their work [7]. The ligaments were modelled using uniaxial elements aligned with the directions of the collagen fibers. The number of elements that represented each ligament was different accordingly with each interconnecting spinal ligament.

Posteriorly, Natarajan et al. developed FE models of the L3-L4 spinal segments of intact and unhealthy spines [35]. The authors have become an important reference in the field since the purpose of their study was to determine the different pathways and mechanical influences for IVD degeneration and the biomechanical consequences for the spinal segment.

More recently, in 2015, Naserkhaki et al. developed and validated a 3D (three-dimensional) nonlinear detailed FE model of lumbosacral spine, illustrated in the Figure 3.5, with realistic geometry, using wide range of numerical and experimental data [36]. This model was subjected to 500N compressive follower load combined with flexion and extension moments of 7.5Nm. The bony structures and endplates were assumed to be linear elastic while AF and NP were governed by hyperelastic material law using the Mooney-Rivlin formulation. The ligaments springs were designed as Rohlmann et al, reported in their work in 2006, with nonlinear force displacement curves, resisting tension only [29]. The fibres of the AF had nonlinear force displacement relationship with stiffness increasing from inner to outer lamella.

More versions of the Naserkhaki et al. model were built to simulate geometries of the spinal structures and sagittal curvature of the lumbar spine in order to understand how the sagittal curvature variation affects the spinal load-sharing [19].

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3.2.2 Implanted Models

Many studies have been performed to better understand the biomechanical effects and influence of the posterior fixation devices in the vertebral spine. The design and materials are parameters that are important to evaluate in order to achieve the best performance possible and guarantee the best functionality of the human spine. The adjacent segments to the fixation device placement are also an important factor to understand, elucidating how the degeneration of the IVD proceeds along the spinal segments.

In 1998, Templier et al. did a numerical comparison using FE analysis of two different concepts of posterior spinal fixation devices when implanted in the human spine. The devices are illustrated in Figure 3.6. One is a rigid screw/rod system (a), and other is a dynamic twin rod system (b). This study was done regarding the opinion of some authors that excessive stiffness of spinal implants could be detrimental to bone graft consolidation and induce overstressed bone-implant interfaces [37].

At first, a 3D FE model of an L3-Sacrum segment was developed and validated. After that, a geometric and mechanical model of each implant were then constructed, before being inserted in the spinal segment model. Both devices were modelled with the mechanical characteristics of stainless steel.

The insertion of the screws into the pedicles and into the body of the vertebrae was simulated by considering the already existing nodes pertaining to the vertebra and corresponding to the location of the screws.

The results concluded that displacement values for both devices were quite similar but the stress values in the implants were not. A concentration of stresses was found in the rigid element. The final conclusion was that this stress concentration could be theoretically responsible for the stress shielding phenomenon observed following the application of rigid implants [37].

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In 2006, Zander et al. implemented a more realistic 3D FE model of the lumbar spine, with the IVD L3-L4 degenerated, inserted with a rigid fixator and bone graft in the segment L2-L3 and an additional paired dynamic posterior implemented at level L3-L4. The purpose of the study was to show that dynamic the implant reduces the disc loads at the level implanted and preserve the disc function, restraining the progression of the disc degeneration. However, even though the dynamic fixator was able to reduce the facet joint forces at the L3-L4 level, the disc loads were not significantly reduced by this peculiar implant [29].

In the past years, the 3D FE analysis of new interbody fusion cages with established fixation techniques haves been intensely investigated. This started since the use of stand-alone interbody fusion cage to replace degenerated IVD, treat back pain and restore the spine functionality has not been successfully realized [29].

Chen et al. constructed an interbody fusion cage spinal model with and without pedicle screws fixation to investigate the relative importance and influence of the screws on the spinal segmental. The biomedical instrumentation was defined as titanium alloy. This comparison was made evaluating the contact stress on the facet joints, displacements of the cage on the endplate and rotational angle of the upper vertebra under different loading conditions. The results concluded that the posterior fixation devices provided the stability required for interbody fusion [38].

Other studies with the same purpose as Chen et al. work were conducted. More recently, in 2011, Galbusera et al. considered the application of a cage complied with posterior pedicular screws and rods. To conclude about the performance of the posterior fixation, residual spinal flexibilitity, the force transmitted through the cage, the contact pressure at the cage-endplate interface, the cage movement and the force in the facet joints were measured and evaluated [38,39].

Figure 3.6: Spinal model and two concepts of posterior spinal fixation devices; (a) 3D intact segment model; (b) Easy®, a rigid screw/rod; (c) Twinflex®, a dynamic system. Adapted from [33].

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The study was done using a FE model of L4-L5 spine segment that was previously constructed and validated. This model included vertebral bodies, posterior structures, the IVD, and seven ligaments (ALL, PLL, FL, CL, ISL, SSL and ITL). The ligaments and the annular fibers were represented by membrane fiber-reinforced elements. In the AF, eight criss-cross fiber layers were defined in the radial direction and each layer contained tension-only fibers. Also, the facet joints were defined by using a frictionless surface-to-surface contact. All solid materials were modelled as linear elastic isotropic and modelled as quadratic hexahedral elements.

The screws were modelled as a network of stiff beam elements, not allowing any relative displacement or rotation movements between the pedicles and the rod attachment. The rods were defined as beams with circular cross section. The elastic modulus of the rods was variable, between 19 and 210 000 MPa, with a fixed Poisson ration of 0.4 [39].

Conclusions of the Galbusera et al. work were similar to Chen et al. investigation results. The posterior fixation reduces the spinal flexibility and cage movement, having a beneficial effect in promoting bony fusion [38,39].

Others recent studies were conducted in order to investigate new possible designs for the spinal fusion. In 2016, Choin et al. apply their research at biomechanical effects in surgical and adjacent lumbar spine segments of a newly interspinous process compressor and compared with a traditional pedicle screw fixation. The three finite element models of the lumbar spine studied are represented in the Figure 3.7. The biomechanical effects were evaluated, measuring the range of motion (ROM) and the facet contact forces. Also, the stress in adjacent intervertebral discs were analyzed.

The results had shown that the newly proposed fusion device had similar fusion effects at surgical level and biomechanical effects at adjacent segments with those of pedicle screw fixation system [40].

Figure 3.7: Study of new designs for spinal fusion devices; (a) FE intact lumbar spine model; (b) Spine model with PEEK cage and pedicle screw implemented by posterior lumbar interbody fusion method; (c) Spine model with PEEK cage and interspinous process compressor systems. Adapted from [40].

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Topology optimization have been also a useful process to achieve better designs and to obtain better materials for interspinous devices. In 2017, Guo et al. proposed a new version of the Coflex-F device for the interspinous stabilization, using topology optimization. A new device with reduced volume were achieved. The authors tested the biomechanical performance of the new and old Coflex-F design, and the results had shown that both devices provided stability in all motion at the surgical segment. Also, the advantage of Coflex-New was that it can decrease the stress of the implant structure in some motions. Additionally, the stress spinous process with Coflex-NEW was well-distributed [41].

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Chapter 4 Methods

4.1 Geometric Model

For this study, it was developed a new FE model of segment L3-L5 of the spine-human. This segment was chosen, since it is in this spine region where there is the biggest load support and rotational movements that allow the daily routines actions [42]. Thus, in these segments, there is a higher sensitivity to spinal problems, as the higher load support makes the degeneration of spinal structures and fractures more likely to occur, making this region a region of real interest to study. The goal of the intact model, the healthy L3-L5 segment, was to be the most robust and realistic possible, being also easily computed.

4.1.1 Implanted Models

The model was constructed from CT images through image segmentation, using the software ITK-SNAP® (University of Pennsylvania and University of Utah, USA) [43]. CT images from a healthy 40-year women were obtained from the xVertSeg Database from the Laboratory of Imaging Technologies (University of Ljubljana, Faculty of Electrical Engineering, Slovenia)1_{[44]. ITK-SNAP software permitted} the image processing and segmentation. The images were segmented based on X-ray attenuation to separate soft tissue from the hard tissue by thresholding. The segmented, digitalized images provided a 3D volume.

4.1.2 IVD and Facet Joints construction

A 3D model, in STL format, was obtained and imported to SolidWorks® (Dassault Systèmes SolidWorks Corp., USA), as a solid model. Here, the two IVD were constructed through the interpolation of the vertebrae L3-L4 and L4-L5, since they were not obtained in the segmentation as the IVD density is lower when compared to bone.

In order to accomplish this, a transverse plane was defined slightly below the inferior vertebra of L3 onto which the spaced outline of the L3 vertebra was sketched. A new, 3D prismatic part was then created from the sketch, by extruding it in direction to the plane created slightly above of L4. A split

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operation, first with the L3 vertebra, and then with the L4 vertebra was used to define the superior and inferior surfaces of the new part, which represented the intervertebral disc. This procedure was repeated for the other segment L4-L5, thus creating three new parts: two IVDs and the vertebrae [45]. One of each is represented in the Figure 4.1.

The two IVDs were also divided into nucleus pulposus and annulus fibrous, representing 70% and 30% of the disc, respectively, and can also be observe in Figure 4.1(a) [18].

Using SolidWorks software, it was also possible to design the facet joint, since the 3D volume of the vertebrae provided from the segmentation was considered as one single piece, which it is not anatomically correct. Thus, a gap with 2 mm was created mimicking the joint between the inferior articular process and the superior articular process of the subsequent vertebrae [45].

The final model was then imported as Parasolid into FE solver ABAQUS® (Dassault Systèmes Simulia Corp., USA), in order to perform the FE analysis. As the model was constructed through image segmentation, its dimensions were consistent to the real spinal anatomy as presented in Tables 4.1 and 4.2.

Table 4.1: Dimension of the vertebral body.

Vertebra Lateral diameter

(mm) Sagittal diameter (mm) Anterior height (mm) Posterior height (mm) L3 41 32 24 24 L4 44 34 25 25 L5 45 34 25 25

Figure 4.1: 3D Model of two single parts of the L3-L5 segment; (a) L3-L5 IVD 3D Model; (b) L5 vertebra 3D Model.

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Table 4.2: Dimension of the two IVDs

Level Anterior height

(mm) Posterior height (mm) Total cross-sectional area (mm2₎ NP´s cross-sectional area (mm2₎ L3-L4 10 10 1360 373 L4-L5 10 10 1368 418

All procedures performed to create the L3-L5 spinal model and proceed with its 3D analysis are outlined in the diagram of Figure 4.2. Each document formats used as input for the different software are also clear, so that such a process can be easily mimicked.

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4.2 FE Non-instrumented Model

4.2.1 Intact Model

In Abaqus, it was necessary to assign the set of properties of each constitutive parts of the model. The properties parameters chosen for the FE analysis are showed in Table 4.3. These parameters were used as the first stage in order to achieve an optimal solution to model validation.

Table 4.3: Material properties for the FE analysis.

Material Formulation Parameters Reference

Cortical Bone Linear Elastic E=1200 Mpa [8]

v=0.3

Nucleus Pulposus Hyperelastic C10=0.12 [8]

Isotropic C01=0.03 (Mooney-Rivlin) D1=0.6667 Annulus Fibrosus C10=0.315 [46] Hyperelastic D1=0.2540 Anisotropic K1=12 MPa [46] (Holzapfel) K2= 300 Kappa= 0.1 [46]

As the annulus fibrosus was defined as hypereslatic anisotropic material following the Holzapfel formulation, it was necessary define the local directions that characterizes the constituent’s fibers, to identify the preferred direction. The fibers were placed in 35º angle and 145º angle in relation to the axial plane [19]. According to the Holzapel formulation described in Equation 4.1 and 4.2, the matrix stiffness and compressibility are defined by C10 and D1 parameters. The material parameter K1 has dimension of stress and is related to the stiffness of fibers, and K2 is a dimensionless material property that is related to fiber non-linear behavior. Finally, kappa parameter is related to how the fibers are oriented, it ranges from 1/3, for the randomly oriented fibers, to 0, for aligned fibers [19,47]. All these five parameters are temperature-dependent material values. The U is the strain energy per unit of reference volume, N is the number of fibers , I1 is the first deviatoric strain invariant, Jel_{is the elastic volume ratio denominated} as thermal expansion and I4 are pseudo-invariants [48].

The NP behaves as a nonlinear elastic stress-strain (hyperelasticity) material. The formulation used in this work was the Mooney-Rivlin model, that presents the strain energy function as linear combination of two variants of the left Cauchy-Green deformation tensor. The Equation 4.3 describes its form.

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with, Eα= kappa(I1− 3) + (1 − 3 × kappa)(I4(αα)− 1)

(4.2) 𝑈 = 𝐶10(𝐼1− 3) + 𝐶01(𝐼2− 3) + 1 𝐷1(𝐽 𝑒𝑙_{− 1)} (4.3)

The vertebrae were not separated into cortical and trabecular bone, and the endplates were not considered as well, since this division would not add more relevant information to the wanted results. Furthermore, it would only add more complexity to the analysis.

The interactions between all parts of the model (three vertebrae and respective IVDs) were considered rigidly bonded using the tool merge geometry (selecting the option retain intersecting bound). The contacts between the facet joints were defined as surface-to-surface, soft contact with exponential-pressure-overclosure option available in ABAQUS. This option was based on the literature, the contact parameters were adapted until reach the optimal values. Pressure of 50 N/mm2 _{and clearance of 1 mm} were the parameters that better fit the model under study [45].

In the top surface of the L3, it was defined a reference point which was coupled to all surface. This

allowed that the loads were uniformly distributed on the surface. The applied loads were chosen according to the Heuer et al. study, as this was the study used as benchmark for the validation of the intact model [8]. This validation analysis is described in more detail later in Chapter 5. Regarding the boundary conditions, of the FE model, the inferior surface of the L5 vertebral body was completely constrained, meaning that all degrees of freedom of the surface nodes were completely fixed [8]. The Figure 4.3 illustrates the boundary conditions and loads applied in the model.

After the mesh generation, the complete model consisted of 311 128 nodes and 210 235 elements that represented the L3-L5 segment of the lumbar spine. The number of elements was stipulated according to a convergence analysis that is presented later in this thesis in the Chapter 5. The element type chosen was quadratic tetrahedral with ten nodes (C3D10) mesh to comply with mesh accuracy requirements while reconstructing a model from medical images.

As previously mentioned in the description of the human spine anatomy, in the lumbar spine there are seven different ligaments: ALL, PLL, FL, ITL, ISL, SSL, CL. Each ligament displays restricted effects in the spinal motion, so their considerations in this study considered to be relevant to the motion analysis. Thus, all ligaments were modelled in ABAQUS as lines between two nodes (ligaments origin and insertion points were not personalized, their selection was selected based on anatomical and histological findings) with linear elastic behaviors and only tension response. The design of each ligament was done based on the literature: the ALL and the PLL were represented by single set of eleven serial elements, the ITL was represented by two elements, FL and the SSL were each represented by sets of three elements, the ISL was represented by a set of four elements and finally, the CL was represented by a set of eight elements [18,19]. Figure 4.4 shows some of these ligaments’ representations.

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Although ligaments represent nonlinear elastic behavior, in this model they were considered as linear elastic to guarantee the simplicity of the simulation. Material properties and cross-sectional areas were adopted from literature as described in Table 4.4. [49-51]. Its achievement was accomplished through a material verification described in Chapter 5. Since all ligaments are attached along the spine, it was crucial necessary to define the local areas where the ligaments were attached to the vertebrae and IVD. The delimitation of these areas was made so that there was a strict agreement between the computational model and the anatomical reference. Thus, the nodes used to create the ligaments were

Figure 4.4: FE model with some of the ligaments represented.

Figure 4.3: Boundary conditions representation of the FE Model; (a) Model assigned with the inferior surface of the L5 vertebral body completely constrained and the loads applied in the top surface of the L3. The solid arrow represents the pre-load applied to the reference point and the dashed arrow refers to the applied moment, which in this particular case refers to flexion movement; (b) Coupling of the reference point to the L3 surface.

Finite element modelling of innovative interspinous process spacers for the lumbar spine. Biomedical Engineering