Hybrid composite pedicle screw - finite element modelling with parametric optimization

Informatics in Medicine Unlocked 18 (2020) 100290

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Hybrid composite pedicle screw - finite element modelling with parametric optimization Yves Nicolas Becker *, Nicole Motsch, Joachim Hausmann, Ulf Paul Breuer Institut für Verbundwerkstoffe GmbH, Erwin-Schr€ odinger-Str. 58, 67663, Kaiserslautern, Germany

A R T I C L E I N F O

A B S T R A C T

Keywords: Composite pedicle screw Parametric optimization CF-PEEK Finite element analysis

As a result of population aging, the number of spine surgeries steadily increases. Metallic pedicle screw systems are commonly used to achieve spinal fusion, and to correct spine misalignments. However, certain disadvantages are linked to these metallic systems: stress shielding can lead to bone degeneration and adjacent disc disease, artefacts prevent precise diagnosis during CT, MRI, or X-ray medical imaging, radiotherapy is complicated due to backscattering, and patient comfort is reduced due to the implant weight. These disadvantages have led to the development of carbon fibre reinforced polyether ether ketone (CF-PEEK) pedicle screws. Carbon fibres improve the structural mechanical properties of the PEEK matrix so that the me­ chanical requirements of an implant are met. However, with existing CF-PEEK screws the relative motion be­ tween screw and bone is increased due to discontinuous fibre reinforcement. Discontinuous fibre reinforced screws complicate precise stiffness control. In this study, a novel screw design consisting of a reinforcing element in the screw centre, and discontinuous short fibre reinforced CF-PEEK in the screw thread and head is presented. By this concept, the stiffness of the pedicle screw can be controlled and tailored by adapting the reinforcing element. This first study concerning hybrid pedicle screws is based upon numerical investigations to optimize hybrid composite screw stability in human bone. Parametric finite element (FE) models of screw and bone were developed. The main purpose of the study was to obtain design recommendations from the optimization, which will be used for future manufacturing of hybrid composite screws. It is further shown that stress shielding could be significantly reduced with this hybrid pedicle screw design as compared to titanium screws, despite the reinforcing element. Additionally, it is confirmed that the worst-case scenario with the highest risk of composite pedicle screw pull-out is shortly after surgery, when osseointegration is still poor. In future studies, mechanical, functional, and visibility tests of the hybrid composite pedicle screw will be conducted.

1. Introduction In the 1990s, the biocompatibility and in-vivo stability of carbon fibre reinforced polyether ether ketone (CF-PEEK) was characterized [1–4], which led to increased medical applications of this composite material. Due to its radiolucency [2,4–7], artefacts in medical imaging technologies (computer tomography (CT) scan, magnetic resonance imaging (MRI) or X-ray), commonly observed with metallic implants, are reduced [3,6,8–10]. Advantageously, implant complications can be detected more easily [8], the actual implant position and integrity can be superiorly evaluated [5,10], and the assessment of the fusion process is facilitated [3,6] with the use of CF-PEEK implants. Additionally,

backscattering and soft tissue shielding are avoided during radiotherapy [8,11–13]. For metal implants, both backscattering and soft tissue shielding are oftentimes observed [10]. CF-PEEK has excellent long term stability [2], a minimal toxicity [4], and a high resistance to gamma and electron beam radiation [2,14]. Moreover, no deep infections or un­ wanted tissue reactions due to the formation of corrosion products and release of metal ions emerge from composite implant applications [5, 15–18]. Another important advantage of CF-PEEK concerning medical applications is its processability without any additives [19]. These outstanding material properties motivated the development of various medical CF-PEEK applications such as hip endoprosthesis [11,20–22], knee prostheses [23], spinal cages [10,11], implants for osteosynthesis

* Corresponding author. E-mail addresses: [email protected] (Y.N. Becker), [email protected] (N. Motsch), [email protected] (J. Hausmann), ulf. [email protected] (U.P. Breuer). https://doi.org/10.1016/j.imu.2020.100290 Received 12 December 2019; Received in revised form 10 January 2020; Accepted 11 January 2020 Available online 14 January 2020 2352-9148/© 2020 The Authors. Published by Elsevier Ltd. This is an open (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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[5,11] or as a component for vertebral body replacement [8]. Recently, also CF-PEEK pedicle screws are available on the market [24,25]. The practical method of pedicle screw fixation of the spine was first popularized by Roy Camille leading to increased applications [26]. Pedicle screw systems are used to align the spine, preserve its stability or achieve fusion for patients subjected to fractures, spondylolisthesis, degenerative arthritis, tumour or scoliosis [27]. Titanium, which is the standard material for medical implants, is typically used for these sys­ tems nowadays. It can promote osseointegration [18,28], and shows superior structural mechanical properties [7]. However, the stiffness of titanium is several decades higher compared to bone, which leads to the effect of stress shielding and a potential degeneration of bone according to Wolff’s law [2,15–18,29–31]. The effect of stress shielding is reduced for CF-PEEK implants because its stiffness is closer to the one of human bone [3–5,7,11,16,32]. Thus, the biomechanics of the spine are better approximated with composite pedicle screw systems [33]. Available composite pedicle screws consist of discontinuous carbon fibres embedded in a PEEK matrix with no distinct fibre orientation. In contrast, this paper introduces a novel approach for CF-PEEK pedicle screws. A hybrid screw is developed, which is composed of two parts: (1) discontinuous fibres embedded in a PEEK matrix, which form thread and head of the screw, and (2) a reinforcing element in the centre of the screw, which increases the strength and stiffness of the screw compared to completely discontinuous fibre reinforced composite pedicle screws. Other authors have studied the behaviour of metallic pedicle screws [30,33–40]. However, only limited knowledge about CF-PEEK pedicle screws is available [41] and only few systems exist on the market such as the pedicle screw systems VADER® and LIGHTMORE® from Icotec AG. These systems are composed of CF-PEEK screws with titanium tulips, titanium locking screws and CF-PEEK or titanium rods.1 The Icotec composite screws contain continuous carbon fibres. However, the fibres are discontinuously distributed due to manufacturing by composite flow moulding [13]. Another manufacturer is CarboFix Orthopedics Ltd. which distributes an entirely non-metallic pedicle screw system [42,43]. This system is comparable to standard metallic pedicle screw systems in terms of intraoperative complications and recovery of stability [42]. However, several disadvantages concerning this system were reported such as difficult positioning, a fixed rod contour and a special tool which is required for system installation [42]. Due to a reduced torsional resistance of the CarboFix CF-PEEK screws, a proper pre-hole prepara­ tion with tapping has to be considered [42]. The studies presented in this paper base on a powerful parametric finite element model to investigate the behaviour of a hybrid CF-PEEK pedicle embedded in bone. The main purpose was to find the best ge­ ometry of the pedicle screw in terms of pull-out resistance by parametric optimization. The final design recommendations will be used for future manufacturing and extensive laboratory tests.

investigations [44]. By executing the parametric script, developed for this study, 2D or 3D models of a pedicle screw embedded in a bone block were automatically generated. 2.1.1. 2D model 2.1.1.1. Geometry. Bone was assumed to be a rectangular block with a length lbone of 45 mm and a width wbone of 65 mm. It was divided into two parts: (1) the upper part represented the cortical bone material with a length lcortical of 11 mm and (2) the lower part represented spongious bone (cf. Fig. 2). The present 2D model of the composite screw was not axisymmetric but showed an offset of half of the pitch pthread between the left and right thread edges. With this offset, the thread pitch was indicated. A buttress thread was used for the composite pedicle screw thread design. To decrease the number of design variations, certain variables were stan­ dardized. The outer diameter Do of the screw was 6.5 mm, and its total length lscrew 50.74 mm from the top to the tip of the screw. The pitch of the thread pthread was standardized with 2.4 mm, and the screw con­ sisted of a thread number nthread of 15. To avoid sharp edges between head and shaft, and shaft and tip, fillets were applied. The length of the tip was 2.2 mm, and it was modelled sharp. The head of the screw was modelled spherical, and showed a radius rhead of 3.55 mm. All other variables, which were necessary to build up the geometry of the FEmodel, could be modified. Fig. 1 illustrates the buttress thread with its significant design parameters on the left. Besides the standardized pitch pthread and the outer diameter Do, the modifiable variables are shown: inner shaft diameter Di, distal root radius rdist, proximal root radius rprox, length of the thread flank lflank, distal half angle αdist, and proximal half angle αprox. The thread was partitioned into two halves separated by the variable Θ, which defines the number of threads, at which the partition was realized. Both the upper and lower shaft could independently be designed conically or cylindrically. The variables Φ and Ψ symbolize the conical angle of the upper and lower part respectively. Furthermore, two low different thread flanks lup flank and lflank could be used independently for the

two parts (cf. Fig. 1 on the right). The standardized and modifiable geometry variables of the screw are listed in Table 1. In the table, the variable Dcore describes the diameter of the reinforcing element in the centre of the screw. To investigate the influence of increasing osseointegration and of better bone properties, nine 2D screw-bone models with different conical shaft angles were developed (cf. Table 2). In this investigation, the variable χ describes the sum of the upper and lower conical angle Φ and ψ.

2.1.1.2. Properties. Two bone materials were defined to account for the different bone properties of cortical and spongious bone. Furthermore,

2. Finite element analysis and parametric optimization Parametric finite element models (FE-models) have been developed for the numerical analysis and the design optimization of the composite pedicle screw. For the calculation, the finite element solver Abaqus 2018 (Simulia, Dassault Syst�emes) was used. 2.1. Finite element model Two-dimensional (2D) models typically contain much lower numbers of elements and nodes than the corresponding three dimen­ sional (3D) counterparts. Therefore, efficient simulations can be con­ ducted with 2D models due to low computation times. However, the results of the 2D analysis should only be used for comparative 1 https://www.icotec-medical.com/de/implantate/lumbale-wirbelsaeule/pe dicle-systems.html, accessed October 30, 2019.

Fig. 1. Design parameters describing the buttress thread (left) and the parti­ tioned screw shaft (right). 2

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Fig. 2. Local seeds for mesh control with boundary conditions for the pull-out loading case (left) and mesh detail (right).

bone is stiffer along the diaphyseal axis [45] (longitudinal direction) compared to the radial or transverse direction and transverse isotropic behaviour can be assumed. The 1-axis of the cortical material was assumed to be collinear with the screw axis. For the anisotropic material description, the properties E11, E22, ν12, G12, G13 and G23 were defined. The value G23 was calculated by

Table 1 Geometry variable definition. Standardized

Modifiable

lscrew in mm

50.74

Di in mm

DO in mm

6.5

Φ in

pthread in mm

2.4

Ψ in �

rhead in mm

3.55 15

lcortical in mm

11

Θ rprox in mm

wbone in mm

65

lbone in mm

�

G23 ¼

(1)

The properties of bone differ dependent on the age of the patient, the bone mineral density, and other factors such as health condition or gender [45]. In this study, they were modelled linear elastic. The main difference between good and poor bone quality lays in the stiffness value of spongious bone. To analyse the influence of healthier and stronger bone on the pull-out behaviour, the Young’s modulus Espong of the spongious bone was increased from 100 MPa (poor bone quality) to 1000 MPa (good bone quality). Relative variations in spongious bone stiffness are typically higher than for cortical bone [32,46,47]. Increasing the spongious bone stiffness by a factor of 10 was assumed to significantly change the hybrid composite screw pull-out behaviour. The stiffness of cortical bone remained constant for direct comparison. To compare different models, the axial screw pull-out displacements were analysed. Table 3 informs about the material properties of screw and bone used for these studies.

rdist in mm

45

E22 2ð1 þ ν23 Þ

αprox in � αdist in �

lup flank in mm llow flank in mm

Dcore in mm

three screw materials were defined to examine the differences in the pull-out behaviour: (1) a titanium screw, (2) a pure injection moulded short carbon fibre reinforced CF-PEEK screw (sCF-screw), and (3) a hybrid screw consisting of the reinforcing element in the screw centre and short carbon fibre PEEK (sCF-PEEK) material for screw thread and head (uCF-screw). Loads were chosen in a way so that linear elastic material behaviour could be assumed for the screws. For the compara­ tive studies presented here, material data provided by the manufacturers was used. The script allows isotropical or anisotropical modelling of cortical bone. In many studies [30,34–40], no difference between cortical and spongious bone was made or isotropic material behaviour was assumed for cortical bone, especially when bone geometry was simplified. However, anisotropic cortical bone behaviour accounts for more real­ istic properties. Therefore, elastic anisotropic behaviour was assumed for cortical bone in this study. To properly assign the anisotropy of the cortical bone, a local coordinate system (LCOS) was defined. Cortical

2.1.1.3. Interaction and solver option. Osseointegration capability of PEEK implants is typically poor. However, coatings can be used to achieve osseointegration following sufficient time after surgery. Three different contact states between screw and bone were modelled depending on the time after surgery: 1. Short time after surgery (hours): There is no significant osseointe­ gration and roughly no friction interaction between implant and

Table 2 Conical shaft study - model overview. Φ in � ψ in � χ in �

Model-1

Model-2

Model-3

Model-4

Model-5

Model-6

Model-7

Model-8

Model-9

0 0 0

0 1.0 1.0

0 2.5 2.5

0.5 0.5 1.0

0.5 1.0 1.5

1.0 1.0 2.0

1.0 1.5 2.5

1.5 1.5 3.0

1.5 2.0 3.5

3

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Table 3 Material properties. Cortical bone Reinforcing element of uCF-screw Spongious bone Titanium sCF-PEEK a b

E11

E22

E33

V12

V13

V23

G12

G13

G23

Ref.

17900 MPa 170200 MPa

10100 MPa 9400 MPa

10100 MPa 9400 MPa

0.40 0.34

0.40 0.34

0.62 0.40

3300 MPa 5460 MPa

3300 MPa 5460 MPa

3117 MPa 3357 MPa

[45]

E

v

Ref.

100 MPa or 1000 MPab 110000 MPa 18000 MPa

0.20 0.30 0.44

[37,45,46,48] [36,49–51] [52,53]

a

Material data provided by project partner. A stiffness value of 100 MPa was chosen to represent poor bone quality and 1000 MPa was chosen to represent good bone quality.

surrounding bone. In the model, the tangential contact behaviour was assumed to be frictionless. 2. Medium time after surgery (days, weeks): There is osseointegration and friction interaction between implant and surrounding bone. In the model, the tangential contact behaviour was assumed to have a friction coefficient μ of 0.2.2 3. Long time after surgery (several months): The level of osseointe­ gration is high and there is a connection between implant and sur­ rounding bone. In the model, the interaction was assumed to be a tie constraint.

a force load was applied. The load was chosen in the way that the ma­ terial behaviour of screw and bone was in the linear elastic range. Furthermore, left and right bone edges were clamped so that the dis­ placements uX and uY in the global coordinate system were restricted (cf. Fig. 2). 2.1.1.6. Parametric optimization. The parametric script written in Py­ thon enables the use of a parametric optimizer. With the optimizer LSOPT 5.2.1 from DYNAmore GmbH, the parametric optimization was conducted. The aim of the optimization was the determination of a screw shaft and thread design, which showed the highest resistance against a specified constant pull-out force of 100 N. The load was chosen in such a way that the material behaviour remains in the elastic region. The pull-out case was chosen here because the screw shaft and thread design highly affect the pull-out behaviour. Dependent on the screw design, the resultant screw pull-out displacements vary. The aim of the design optimization is the reduction of the pull-out displacements, so that the risk of pulling out the screw is reduced. Lower pull-out dis­ placements increase the possibility of osseointegration and long-term screw stability. Thus, a good design yields low pull-out displacements, a bad design results in higher pull-out displacements. Generally, an excellent shaft and thread design is crucial to prevent the screw from pulling out [34,54–60]. As mentioned in section 2.1.1.1., some variables were standardized and were not included in the optimization process. In this study, the screw was modelled with the reinforcing core, the cortical bone was modelled anisotropically, and a force controlled pullout loading condition was used. The interaction between screw and bone was modelled as frictionless. The screw head geometry as well as the fillet between head and body, body and tip, and at the tip itself did not change within the optimization procedure. The parametric script was adapted so that the optimizer could identify the variables which should be changed within the specific optimization procedure. The script was read by the FE-software Abaqus, the calculation was done, and output was produced. This optimization loop continued until all defined screw designs were calculated or until the optimum was found within the required accuracy. After the opti­ mization procedure, the results could be post-processed and visualized by other programs. This process of optimization is illustrated in Fig. 3. For the optimization, the displacement of one specific node was

A surface-to-surface contact with a finite sliding formulation was implemented in the model. There was neither need for slave adjustment nor for surface smoothing. If short or medium time after surgery was modelled, the tangential contact behaviour was defined. It could either be frictionless (short time) or based on a penalty formulation (medium time). In both cases, the normal contact behaviour, which is based on a penalty formulation, was assumed to be a hard contact with a linear behaviour and a normal contact stiffness of 8000 MPa. This value was chosen to be lower than the stiffness of sCF-PEEK to promote conver­ gence. Separation after contact was allowed. 2.1.1.4. Mesh. The Abaqus 8-node quadratic quadrilateral plane stress elements CPS8R and the 6-node quadratic triangular plane stress ele­ ments CPS6 were used for the FE-analysis. The core of the screw was structurally meshed with local seed assignment whereas the rest of the head and the area close to the thread were meshed freely. For the screw core, a slightly coarser mesh was used compared to the mesh at the outer edges of the screw. For the bone, the area close to the screw cavity showed a free mesh with small elements to account for the screw-bone interaction. The remaining bone parts were structurally meshed with coarser elements towards the left and right outer edges. Fig. 2 highlights edges used for mesh control showing the example of a uCF-screw with its combination of the reinforcing core (C) and sCF-PEEK material (B). The screw is embedded in bone, which consists of a cortical shell (A) and a spongious bone part (D). A detailed view of the mesh is shown in Fig. 2 on the right. The boundary conditions, which will be described in the following section, are shown as well. Due to the 2D character of the FE-model, the number of elements was quite low. Around 16000 elements each were used for the mesh of screw and bone. Roughly 98% of the elements were CPS8R. The remaining elements were CPS6. Certainly, these numbers depended on the actual screw and bone geometry. 2.1.1.5. Loads and boundary conditions. A pull-out loading condition was used for the numerical analysis. The pull-out load was applied to the lower edges of the screw head. The model could be constructed with a displacement or force load. For the comparative studies presented here,

2 This value was assumed for a medium osseointegration state in between no and full osseointegration. In Ref. [74], a friction coefficient μ of 0.2 was used between bone and a stainless steel implant.

Fig. 3. Process of optimization. 4

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analysed. It was located at the uppermost point of the screw head at the screw axis.

the reinforcing core. The geometry (cf. Table 1) and all other parameters used for the analysis were the same for all models. 100 N were used for the pull-out load. For the sCF- and uCF-screws, the stress in the bone was 22.2% and 11.1% higher than for the metallic screw. Therefore, the risk of stress shielding was reduced for the hybrid composite screws. The stiffer titanium screw showed higher von Mises stresses than the pure sCF-screw and the discontinuous CF reinforced parts of the uCF-screw. Fig. 5 illustrates the contour plots of the three models with different screw materials and compares von Mises stress values at distinct screw locations. In the figure, the underlined numbers refer to bone stresses.

2.1.2. 3D model The parametric script could be used for 2D and 3D studies. By a control variable, 2D or 3D models could be automatically constructed. Although the 3D model is a more realistic representation of the real scenario, computing time efficient studies could only be done with the 2D model. However, the 2D model was only used for comparative studies. The 3D model of screw and bone was built up as a quarter model with an axisymmetric screw and bone. Basically, most of the commands used for building up the 2D model were adopted for the 3D case. The mesh was slightly coarser than in the 2D model to keep the number of ele­ ments in a reasonable range. Moreover, the material definition accounted for the third dimension. The Abaqus elements used for the 3D model were the 20-node quadratic brick element C3D20R with reduced integration and the 10-node quadratic tetrahedron element C3D10. The quarter model consisted of around 147000 nodes and 33000 elements. As for the 2D case, these numbers were dependent on the screw and bone geometry. Symmetry boundary conditions were implemented to define the quarter model properly. The model showed an X-symmetry bound­ ary condition in the ZY-plane and a Z-symmetry boundary condition in the XY-plane.

3.2. Contact formulation results Fig. 6 shows the results of the contact study for different times after surgery and different spongious bone qualities (cf. section 2.1.1.2.). The absolute displacement values uabs of each model listed in Table 2 were cyl

related to the absolute displacement value uabs of the cylindrical refer­ ence model-1 for each contact formulation: urel ¼

uabs ucyl abs

(2)

A cylindrical screw showed the lowest displacement values inde­ pendently of the contact definition or bone quality. The differences in relative pull-out displacements between the models are below 1%. Every parameter optimization only contributes to a small improvement of screw stability. However, the sum of the im­ provements of all parameters contributes to a significant increase of screw stability (cf. section 3.3.). In the case of poor bone quality, the relative displacements urel increased if the conical angles increased. Screws with the same upper conical angle (cf. Table 2) showed the same level of relative displace­ ment. If the upper conical angle increased, the relative displacement increased as well. In contrast, the lower conical angle played a minor role in the cases with poor bone quality. This means that the conical angle Φ of the upper screw part (cortical bone) had a bigger influence on the screw pull-out behaviour than the conical angle ψ of the lower screw part (spongious bone). Most forces between implant and bone were

3. Results 3.1. Stress and strain analysis Analysing the stress regions of the 3D quarter pull-out model, the reinforcing core was subjected to high stresses. In this model, the interaction between screw and bone was modelled frictionless and the screw pull-out displacement load Lu was 0.1 mm so that the material behaviour of screw and bone has still been in the elastic region. More­ over, a perfect bond between the uCF-screw core and the overmoulded sCF-PEEK material was assumed. The equivalent von Mises stress σMises was used to investigate the material behaviour of the overmoulded sCFPEEK material, which was assumed to be isotropic (cf. Fig. 4). Con­ cerning the screw, high stress values were located at areas close to the proximal root radii rprox. The stress was transferred from the screw head to the reinforcement core. A good adhesion between core and overmould is important to guarantee proper load transfer. Generally, the stiffer cortical bone showed higher stresses and lower strains than the spon­ gious bone. The regions of highest von Mises stresses in the bone were located in the cortical part around the first thread and the regions of highest strains were located in the spongious part close to the thread flanks. Three 3D models were designed with different screw materials to study their differences in stress behaviour. One screw was composed of titanium, one was a pure sCF-screw, and one was a uCF-screw containing

Fig. 5. Comparison of von Mises stresses (in MPa) of models with different screw materials.

Fig. 4. Von Mises stress analysis (in MPa) of screw-bone model with detailed view without reinforcing core. 5

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Fig. 6. Relative displacements in axial screw directions for different times after surgery and bone conditions.

transferred in the upper part, which interacted with cortical bone. The lower part, which was embedded in spongious bone, transferred much less force. Therefore, the influence of the conical angle of the upper screw part was higher compared to the conical angle of the lower screw part. The results of the short time (frictionless modelling) and medium time (μ ¼ 0.2) studies with poor bone quality were very similar. In the long time studies (tie constraint) with poor bone quality, the influence of conicity of the different models on the relative displacement was significantly smaller. In the case of good quality bone, one relative displacement level for each model was reached. This means that not only the upper but also the lower conical angle had a major influence on the pull-out behaviour in the case of good bone quality. Here, the sum of the conical angles Φ and ψ, referred to as cumulated conical angle χ , could be chosen as an indi­ cator. As an example, model-3 had a cumulated angle of 2.5� . The displacement of model-3 rather fitted to the ones of model-6 and model7, which had a cumulated angle of 2� and 2.5� (cf. Table 2). Due to the increased stiffness of spongious bone, more pull-out forces could be transferred in the lower thread part, which was in contact with spon­ gious bone. This study highlights that a special attention has to be given to the design of the lower pedicle screw part when developing screws for patients with good bone properties, such as healthy youths. To examine the differences in absolute axial screw displacements among the different contact studies, the absolute axial screw displace­ model ment uabs; frictionless;

1 100 MPa

Table 4 Comparison of different contact studies. Ratio of axial screw displacements in %

Frictionless contact Friction contact Tie constraint Frictionless contact Friction contact Tie constraint

100

100

100 100 1000

98.60 60.77 36.03

1000 1000

35.72 27.71

3.3. Parametric optimization results As an illustrating example, the distal root radius rdist and the prox­ imal root radius rprox were changed in the interval from 0.1 mm to 1.2 mm for the distal root radius, and from 0.1 mm to 0.4 mm for the proximal root radius. Simultaneously, the distal and proximal half an­ gles αdist and αprox were altered. In Fig. 7, the relative axial screw pullout displacements urel are plotted against the two root radii rdist and rprox. The calculation of the relative axial screw displacement was done by the division of the absolute displacement of each model by the lowest absolute displacement within this study. To illustrate this optimization curve, the distal half angle was held fixed at 35� , and the proximal half angle at 0� . In the figure, the data points are shown by red asterisks. The area in between the data points is interpolated. To extend the study presented in section 3.1, the variables Φ and ψ were varied from 0� to 1.5� and from 0� to 2� in equidistant intervals according to Table 5. They describe the conicity of the upper and lower part of the screw shaft, as mentioned above. To see the influence of each parameter combination, a full factorial study was performed. The relative displacement value, introduced in equation (2), was used for this study. The resulting surface plot of the relative displacement values urel for the poor bone quality case is illus­ trated in Fig. 8. Verifying the results of section 3.1., the completely cylindrical screw showed the lowest displacement values. With a higher degree of conicity, the displacement values increased. The slope of the upper conical angle Φ is steeper than the slope of the lower conical angle ψ in the poor bone quality case. This means that the influence of the upper conical angle was bigger than the influence of the lower conical angle as

of model-1 of the frictionless contact study,

uabs; model 1 ​ model 1 uabs; frictionless; 100 MPa

Stiffness Espong in MPa

poor bone quality highly increased the risk of spinal screw pull-out.

modelled with a spongious bone stiffness of 100 MPa (poor bone qual­ ity), was taken as a reference. The absolute displacement values uabs; model 1 ​ of model-1 of the other contact studies were related to this reference: Ratio of axial screw displacements ¼

Contact definition

(3)

Table 4 contains the corresponding percentage values of the ratio of axial screw displacements. The interaction definition and the spongious bone quality signifi­ cantly influence the pull-out behaviour of the composite pedicle screw. The higher the interaction between screw and bone, the lower the axial pull-out displacement of the screw. More interaction corresponds to a better osseointegration between implant and bone. With increasing time after surgery, the degree of osseointegration increases. The most critical state of the patient with the highest risk of pulling-out the hybrid composite pedicle screw was shortly after surgery when osseointegra­ tion is still poor. Furthermore, if the spongious bone quality was good, the pull-out displacements were significantly reduced. This means that 6

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Informatics in Medicine Unlocked 18 (2020) 100290

Fig. 7. Specific surface plot of the relative axial screw displacement values urel dependent on the thread root radii.

surface shows the relative axial screw displacement for a screw with a core diameter of 1.8 mm, the yellow one for a core diameter of 0.4 mm. The influence of the core diameter was higher than the influence of the conical shaft angles Φ and ψ since the levels of relative axial screw displacements of each surface are different. In the same manner, the optimization has been done for the thread variables distal and proximal half angle αdist and αprox, the inner shaft

Table 5 Parameter range of the upper and lower conical shaft angle Φ and ψ for the design optimization. Φ in

�

0

ψ in �

0

3 14 2 7

6 14 4 7

9 14 6 7

12 14 8 7

15 14 10 7

18 14 12 7

21 14 14 7

low diameter Di, and the upper and lower thread flank lup flank and lflank . With

these studies, the importance of different parameters, which contribute to low pull-out displacements, could be identified. Table 6 contains the optimization results with the recommendations if either a big (↑) or a small value (↓) for the specific design variable should be chosen. Since the screw pull-out was most critical shortly after the surgery, the screw shaft and thread design has been optimized for this worst-case scenario. With the specific parameter ranges listed in Table 6, the difference between the best and the worst screw design in terms of pull-out displacement reduction was around 11.91%. As mentioned above, each parameter optimization only contributed to a small improvement of screw stability. However, the sum of the improvements of all pa­ rameters contributed to a significant increase of screw stability. Fig. 11

far as poor bone properties were assumed for the spongious bone. The same model was built up with a spongious bone stiffness Espong of 1000 MPa to account for the case of stronger bone (good bone quality). The results are shown in Fig. 9. Compared to Fig. 8, the surface is turned slightly clockwise. This means that the influence of the conical angle ψ in the lower thread part became more important in the case of younger and healthier bone (cf. section 3.1.). The influence of different geometry parameters on the pull-out behaviour could also be shown by analysing the variable Dcore, which describes the diameter of the reinforcing element of the hybrid com­ posite screw. Two surfaces are plotted in Fig. 10. Each surface corre­ sponds to one specific value of the diameter of the screw core. The blue

Fig. 8. Surface plot of the relative axial screw displacement values urel dependent on the conicity for the case of poor bone quality. 7

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Informatics in Medicine Unlocked 18 (2020) 100290

Fig. 9. Surface plot of the relative axial screw displacement values urel dependent on the conicity for the case of good bone quality.

Fig. 10. Surface plot of the relative axial screw displacement values urel dependent on the conicity and the diameter of the reinforcing core Dcore.

shows two hybrid composite screws. The screw at the top was designed according to the design recommendations so that a strong resistance against pull-out forces was achieved. In contrast, the screw at the bottom shows a weak resistance against screw pull-out. For a first consistence check, one 3D design study was performed. Qualitatively, the same behaviour as in the 2D case was observed. For a second consistence check, a tie constraint was used to describe the interaction between screw and bone instead of a frictionless description. The design recommendations still counted for this case. Certainly, the manufacturing techniques, and the requirements of the manufacturing process of the screw, limit the design space and the feasible parameter range. The parametric optimization results in recommendations, which have to be checked, up to which limit they can be realized for future manufacturing of the hybrid composite pedicle screw.

Several studies have been published concerning the optimization of metallic pedicle screws. Typically, screw design optimization yields the increase of screw stability in bone and the resistance against pull-out [55]. Pull-out forces lead to shear stresses in bone which have to be lower than bone shear strength. Besides an optimal pedicle screw design, a material stiffness comparable to bone is important to decrease stress shielding and increase implant stability, as described above. Screw stability is also influenced by the structural implant stiffness defined as a product of material stiffness and implant cross-section [55]. Screw stability depends on screw and thread profile design [27,34, 54,55], bone properties [27,34,54], the structural mechanical properties of the screw material [61], the surgical technique [27], and the size of the pilot hole [60,61]. However, numerical models are simplifications of reality and cannot consider all dependencies. The study presented here complements the studies of other authors concerning metallic pedicle screws [34,38,54–56,61] by providing knowledge about hybrid com­ posite pedicle screw design. Pull-out does not replicate the complex and multidirectional in vivo loads of the human spine. However, this loading case is suitable to evaluate screw fixation strength and to compare numerical studies [62]. Pull-out loading was chosen for the numerical studies because thread design is crucial for screw stability in bone under pull-out loads. A pull-out load of 100 N was exemplarily used for the comparative studies

4. Discussion By the design optimization, the stability of a composite pedicle screw subjected to pull-out load could be increased. This effect may contribute to less failure of the pedicle screw system. The stiffness of the screw may further be increased by optimizing the adhesion between the reinforcing core and the sCF-PEEK material during manufacturing of the hybrid composite screw. 8

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surgeon uses special drills or instruments to drill a pre-hole into the vertebrae. The pull-out performance of pedicle screws is highly depen­ dent on the size and quality of the pre-hole, especially shortly after surgery. The influence of different pre-hole sizes was not considered here but will be investigated in future laboratory tests. Conical screws can compact spongious bone if pre-holes are sufficiently small [60,66]. Bone compaction increases the required insertion torque values of pedicle screws due to increased friction between bone and screw. However, hybrid composite screws have a reduced torsional stiffness compared to metallic screws. Pre-holes have to be sufficiently large so that hybrid composite screw insertion is possible without damage. Therefore, the effect of bone compaction was supposed to be insignifi­ cant and therefore was not considered in this study. PEEK implants show poor osseointegration capabilities because PEEK is an inert material [2,67] with low surface energy [68]. However, osseointegration can be achieved with coatings composed of calcium phosphate (hydroxyapatite) [2,54,68] or titanium [2,10,68]. Osseoin­ tegration is difficult to simulate by numerical methods because it is a complex process which is dependent on various factors [54,69,70]. In this study, three osseointegration states were modelled with different numerical interaction properties. A friction coefficient of 0.2 was assumed for a medium osseointegration state. This coefficient is dependent on the formation of the screw bone interface ranging from no osseointegration (frictionless contact in the model) to full osseointe­ gration (tie constraint in the model). There are numerous osseointe­ gration states in between. However, only one state was modelled with the friction coefficient used in this study. These approaches are accepted in the literature and also used by others [64,71–73]. To investigate the influence of poor bone quality, spongious bone stiffness was changed. The stiffness of cortical bone remained un­ changed to clearly see the effect on the pull-out behaviour and to pro­ mote the comparability of results. Material data provided by the manufacturer was used for the comparative studies presented here. These data can be different compared to true experimental material data. However, it is believed that no significant change in model behaviour will result from using true experimental material data. Due to material requirements and pur­ chasability, materials for the hybrid composite screw were predefined and material variation was of no use. The hybrid composite pedicle screw was developed to be one part of a composite pedicle screw system intended for lumbar spine applica­ tions. However, the general concept of the screw is not limited to the lumbar spine region only.

Table 6 Recommendations for screw design variables.

Primary effects

Variable

Parameter range

Design recommendation

Inner diameter Di

3.2 mm–5.0 mm 0.4 mm–2.5 mm

↑

5.0� –35.0�

↑

0� –10.0�

↓

0.1 mm–1.2 mm

↓

Proximal root radius rprox

0.1 mm–0.4 mm

↑

Upper thread flank lup flank

0.05 mm–0.4 mm

↑

Lower thread flank

0.05 mm–0.4 mm

↑

Upper conical angle Φ Lower conical angle ψ*

0� –1.5�

↓

0� –2.0�

↓

Core diameter Dcore Secondary effects

Distal half angle

αdist

Proximal half angle

αprox

Distal root radius rdist

llow flank

↑

*The lower conical angle became more important with healthier/younger bone (cf. section 3.1.).

Fig. 11. Hybrid composite screw design with strong (top) and weak resistance against pull-out forces (bottom).

to ensure material behaviour in the elastic regions. This load represents clinically relevant loading, but also higher loads can arise during service life of pedicle screws [34,56]. However, as long as no screw failure is observed, these loads typically deform the implant elastically. So far, the numerical models have not been verified by experimental tests. However, only comparative analyses are presented in this study. In future studies, mechanical pull-out tests will be performed with hybrid composite pedicle screws, and the absolute results of the numerical and experimental study will be compared. The helix angle of the thread can influence the pull-out behaviour of pedicle screws. In this study, the 3D quarter model was modelled axisymmetric and the thread helix angle was ignored for 3D and 2D models. This simplification puts some limitation to the interpretation of the results but is widely used in the literature. Other authors have used axisymmetric 2D models to promote bone screw research [35,55,63,64], especially if simple load cases such as pull-out are investigated [34]. A comparison of the load distribution between an axisymmetric 3D model and a model which considered the thread helix was made in Ref. [65]. It was found that the helical effect did not significantly influence load distribution. Due to the broad acceptance of axisymmetric screw models in the literature, the significant increase in complexity concerning parametrization, and the uncertain increase in accuracy, the helical ef­ fect was neglected in this comparative study. Additionally, the model­ ling of vertebral 3D bone geometry was beyond scope of this study and therefore bone geometry was simplified. The studies presented here are based on the assumption that the bone cavity perfectly fits to the outer shape of the screw. In reality, the

5. Conclusion In this study, a novel hybrid composite screw design was presented. Parametric scripts were used to build up finite element models of a pedicle screw embedded in bone. By parametric optimization, various shaft and thread variables of the hybrid screw were studied to determine the screw design with the highest stability in human bone. The resulting design recommendations will be considered for the manufacturing of the composite pedicle screw. Additionally, stress values of models with different screw materials were compared. It was shown numerically that composite pedicle screws reduce the risk of stress shielding. Further­ more, shortly after surgery, when there is still no relevant effect of osseointegration, the risk of screw pull-out is highest. In future studies, the design recommendations will be used for final hybrid composite screw design. Additionally, mechanical, functional, and visibility tests will be conducted to determine the hybrid pedicle screw stiffness behaviour and to evaluate the promising advantages of hybrid composite screws compared to their metallic and composite counterparts.

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Ethical statement

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