Wear in ceramic on ceramic type lumbar total disc replacement: Effect of radial clearance

Abstract

The wear of the bearing surfaces of total disc replacement (TDR) is a key problem leads to reduction in the lifetime of the prosthesis and it mainly occurs due to the range of clearances of the articulating surface between the superior plate and core. The objective of this paper is to estimate the wear using finite element concepts considering the different radial clearances between the articulating surfaces of ceramic on ceramic type Lumbar Total Disc Replacement (LTDR). The finite element (FE) model was subjected to wear testing protocols according to loading profile of International Standards Organization (ISO) 18192 standards through 10 million cycles. The radial clearance value of 0.05 mm showed less volumetric wear when compared with other radial clearance values. Hence, low radial clearance values are suitable for LTDR to minimize the wear.

Keywords

Wear total disc replacement ceramic on ceramic radial clearance finite element method

1. Introduction

Degenerative disc disease (DDD) is the gradual deterioration of the disc causing loss of its functions which leads to pain [1]. The most common surgical procedure is spinal fusion and the motion of the joint is drastically reduced [2,3]. However, in recent years, Total disc replacement (TDR) has been introduced to improve upon spinal fusion by restoring the motion [4]. There are different designs of LTDR devices, but most common one is ball-and-socket combination (ProDisc-L and Maverick), with a metal-on-polymer [MOP] or metal-on-metal [MOM] bearing surface. Ceramic on Ceramic [COC] is relatively a new design [5] used instead of MOP and MOM due to its excellent biocompatibility, wear resistance, corrosion resistance and strength [6]. In COC, alumina and zirconia are the two major types used in orthopedic applications.

Over a long period of usage, all implantable mechanical devices exhibits wear [5]. Relative motion under load at the articulating surfaces cause wear in implants [7]. This could induce the inflammatory reaction, can result in loosening of an implant and may lead to pain [8]. Experimental wear study on MOM lumbar disc conducted by Lee et al. [4] showed that the wear rate of MOM bearing surfaces is less than MOP combinations. The wear rate can be minimized when COC material combination is used for TDR [9].

Wear debris evaluations for TDR devices are done in wear simulators using the currently published ASTM/ISO loading profiles. However, it was too complex, expensive and difficult to conduct. FE models based on Archard’s wear formulation is an alternative method that can also be used for wear assessment of TDR implants. This formulation has been used by several authors for THR, TKR and TDR implants for the last decade [10–13]. The radial clearance between the articulating surfaces can vary the contact pressure and may affect the wear. Radial clearance was one of the important parameter to assess the wear and the effect of radial clearance between the articulating surfaces of COC artificial discs was not investigated so for.

The aim of this study was to apply the finite element method to analyze how the different radial clearances influence the wear and contact pressure of LTDR device. Thus, the present study helps in selecting the suitable radial clearance which minimizes the wear. FE implanted model was subjected to loading and displacement parameter for wear testing as per ISO 18192 over 10 million cycles.

2. Methods and materials

2.1. Modeling of TDR implant

The three dimensional ProDisc-L (PDL) model was developed using Pro-E Wildfire 4.0 (PTC, Inc., USA) and dimensions were obtained from the previous work [10]. The PDL implant model includes a superior metallic endplate, a convex polyethylene (PE) core and an inferior metallic endplate. The present study involves COC disc design. Therefore, both endplates and polyethylene core was replaced with alumina (Al₂O₃). The core was fixed into the inferior endplate, creating the ball and socket joint that articulates the surface of superior endplate. The PDL model was simplified by eliminating endplates keel and spikes for further meshing and analysis. The radial clearance between the articulating bearing surfaces was considered as 0.05 mm, 0.1 mm, 0.2 mm and the 2D systematic representation of radial clearance between the articulating surfaces was shown in Fig. 1.

Fig. 1.

2D systematic diagram of radial clearance between the articulating surfaces. R1, radius of superior endplate bearing surface; R2, radius of polymer core bearing surface.

2.2. Finite element analysis of TDR implant

The solid PDL model was meshed with ANSYS. SOLID 187, a 10 node tetrahedral elements were applied to mesh the whole model as shown in Fig. 2. The number of elements within superior endplate, core and inferior endplate were respectively 7279, 15,108, 5067. The moving interface between the superior endplate and the core for implant model was simulated using ANSYS contact elements (CONTA 174 and TARGE 170) with standard contact behavior. The PE core base and inferior endplate upper surface was simulated using same contact element with bonded contact behavior. The contact algorithm used in this analysis was augmented Lagrangian method. The purpose of the augmentation was to reduce the sensitivity to contact stiffness. All things being equal, the augmented Lagrange method will produce less penetration than the pure penalty method. Initially, mesh convergence study was carried out by varying the number of elements to optimize the results. Young’s modulus and Poison’s ratio were obtained from [14] was utilized for the present work.

Fig. 2.

FE model of ProDisc-L. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151544.)

2.3. Boundary and loading conditions

The base of the core was constrained with inferior endplate. Superior endplate was left unconstrained and could freely articulate on the convex surface of core, while inferior endplate was completely fixed at its base. A varying compressive load of 200 to 1750 N as per ISO 18192 [10] was applied through a coupled point on the superior surface of the superior endplate and it was shown in Fig. 3.

Fig. 3.

Phasing of the displacement and axial load curves for wear simulations as per ISO 18192 obtained from Rawlinson et al. [10].

2.4. Wear simulation

Based on Archard’s wear theory [15] the wear rate can be predicted as follows: $V = K F S,$ (1) where V is the total volume of wear debris produced, K is wear coefficient, F is the applied force and S is sliding distance. The incremental sliding distance between the two successive points was obtained using the procedures by Kang et al. [16]. The wear coefficient of 0.2 × 10⁻¹¹ mm³/Nmm is utilized as similar to [11].

2.4.1. Linear wear

The penetration of one component to another leads to linear wear (wear depth) and the formula for linear wear was modified from Eq. (1) as, $V_{L} = \sum K_{w} \times P_{i} \times S_{i} (i = 1, \dots, n),$ (2) where $V_{L}$ is linear wear, $P_{i}$ is the contact pressure. Here $n = 25$ , since the whole load curve is discretized into 25 gait instants as per [10].

2.4.2. Volumetric wear

It is the volume of material removed from the articulating surface. Linear wear is converted into volumetric wear by multiplying it with the contact area of each instant. Therefore, the volumetric wear is given by, $V_{V} = V_{L i} A_{i} (i = 1, \dots, n),$ (3) where $V_{V}$ is volumetric wear, $V_{L i}$ is the linear wear calculated for each instants and $A_{i}$ is the area of contact of the bearing surface.

2.4.3. Updating the geometry

After calculating the wear depth (linear wear) and the amount of material removed (volumetric wear) for first instance, the nodal positions were then updated to change in surface topography. One million cycle of wear was divided into 4 steps, with scaling of 250,000 times occurring at each step [10]. The FE model was simulated for 10 million cycles. The linear wear depth was computed as the average wear depth for the entire mesh. The total cumulative wear depth was calculated at the end of each million cycles.

3. Results and discussion

3.1. Contact pressure simulation

The contact pressure values were obtained from ANSYS for each gait instant upto 10 million cycles. The contact pressure distribution of COC material combination for 0.05 mm, 0.1 mm and 0.2 mm radial clearances were shown in Fig. 4. The contact pressure on core decreases, once the gait cycle starts increasing. The contact area increased with consequent cycles as the articulating surface of superior endplate became more conforming with core. Contact area was always concentrated around the pole and within the bearing surface of the core and extending circumferentially with increase in gait cycles. The maximum contact pressure was always at the outer periphery of the core during loading cycles as stated in Rawlinson et al. [10]. The contact pressure of a material combination depends mainly on its material property. Previous study on MOM combination by Wenzel and Shepherd [17] revealed that the contact pressure range in between 63–130 MPa. The present study involves COC material combination which had higher young’s modulus than MOM (Cobalt chromium alloy) couples. Hence, the contact pressure range 75.85–166.39 MPa was obtained which was quite higher than the MOM material combination. The relation between contact pressure distributions at the completion of 10 million cycles against the applied load for different radial clearances were shown in Fig. 5. The contact pressure values of 0.05 mm, 0.1 mm and 0.2 mm were 9.49 MPa, 15.81 MPa and 18.03 MPa respectively. The contact pressure values for 0.05 mm had been validated with the previous works and the validity of finite element simulation results was shown in [18]. The result showed that for increase in radial clearance which tends to increase the maximum contact pressure and this was due to the minimum conformal contact area for increasing radial clearance values.

Fig. 4.

Contact pressure distribution of COC material combination for different radial clearance at 50% gait cycle. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151544.)

Fig. 5.

Contact pressure distribution at the end of 10 million cycles for different radial clearances against applied load. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151544.)

Fig. 6.

Cumulative linear wear for different radial clearance as a function of cycles (million). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151544.)

Fig. 7.

Cumulative volumetric wear for different radial clearance as a function of cycles (million). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151544.)

3.2. Linear wear

The linear wear predicted for 10 million cycles for different radial clearance values were shown in Fig. 6. At the end of 10 million cycles, the linear wear for 0.05 mm radial clearance was 0.0011 mm (validated with the results of [18]) which was quite larger when compared with MOM bearings which showed 0.0045 mm [5]. This was due to the wear coefficient of MOM bearing 1.01 × 10⁻¹¹ mm³/Nmm was much closer to COC combination. Linear wear increased 1.63 times when the clearance was increased from 0.05 mm to 0.1 mm and 1.27 times increased when the clearance was increased from 0.1 mm to 0.2 mm. It clearly showed that increase in radial clearance had a tendency to increase the wear depth. This was due to high contact pressure and less conformal contact area ultimately resulting in increase in linear wear.

3.3. Volumetric wear

The predicted volumetric wear for different radial clearance values up to 10 million cycles were shown in Fig. 7. At the end of 10 million cycles, the volumetric wear for 0.05 mm clearance was 0.113 mm³ (validated with the results of [18]) which was quite higher when compared with MOM combination as 0.275 mm³ [5]. The volumetric wear for 0.1 mm clearance was 0.118 mm³ and for 0.2 mm clearance was 0.13 mm³. The cumulative volumetric wear for different radial clearance values also remained almost constant through 10 million cycles. This reflects the same case as wear prediction of MOP done by Rawlinson et al. [10] but the cumulative volumetric wear at the end of 10 million cycles was 56.7 mm³ which was very much higher than the present result. It clearly showed that the volumetric wear for COC combination was lesser than other two combinations. Hence, low radial clearance value was most suitable to minimize the material removal due to the close conformity of the concave superior endplate surface against convex core surface.

Wear in the total disc replacement (TDR) was a significant clinical concern which reduces the lifetime of prosthesis. It induces the formation of potentially harmful debris and involves the risks of a new surgical operation. Wear was mainly caused due to the contact pressure between the superior plate and polymer core. So, minimizing the wear becomes very essential in biomedical applications. These proposed methodologies were similar to the previous works in hip prosthesis (THR) work which was validated with clinical problems. So, these results can be utilized for developing new design.

4. Conclusions

A three dimensional FE analysis was performed to predict the influence of different radial clearance over wear and contact pressure by considering the loading and displacement parameter for wear testing as per ISO 18192 over 10 million cycles. The result showed that the contact pressure increases with increase in radial clearance while the contact area decreases with increase in radial clearance. The cumulative linear wear increases for increase in radial clearance values once the gait cycle starts to increase. Smaller deviation found in volumetric wear for increase in radial clearance values. The predicted linear and volumetric wear was much closer to MOM combination and higher when compared to MOP combination. The radial clearance of 0.05 mm showed less volumetric wear among other radial clearance values. Therefore, COC type implant device with less radial clearance between the articulating surfaces was a superior choice to minimize the wear.

References

[1] Luoma

Riihimaki

Luukkonen

Raininko

Viikari-Juntura

and Lamminen

, Low back pain in relation to lumbar disc degeneration, Spine 15 (2000), 487–492.

[2] Bono

C.M.

and Garfin

S.R.

, History and evolution of disc replacement, Spine J. 6(Suppl.) (2004), S145–S150.

[3] Lee

C.K.

and Goel

V.K.

, Artificial disc prosthesis: Design concepts and criteria, Spine J. 6(Suppl.) (2004), S209–S218.

[4] Lee

J.L.

Billi

Sangiorgio

S.N.

McGarry

Krueger

D.J.

Miller

P.T.

McKellop

and Ebramzadeh

, Wear of an experimental metal-on-metal artificial disc for the lumbar spine, Spine 33 (2008), 597–606.

[5] Bhattacharya

, Predictive finite element modeling of artificial cervical discs in a ligamentous functional spinal unit, Thesis and disertations, The University of Toledo, 2011.

[6] Hsu

S.M.

and Shen

, Wear prediction of ceramics, Wear 256 (2004), 867–878.

[7] Affatato

Spinelli

Zavalloni

Mazzega-Fabbro

and Viceconti

, Tribology and total hip joint replacement: Current concepts in mechanical simulation, Med. Eng. Phys. 30 (2008), 1305–1317.

[8] Amstutz

H.C.

Campbell

Kossovsky

and Clarke

I.C.

, Mechanism and clinical significance of wear debris-induced osteolysis, Clin. Orthop. Relat. Res. 276 (1992), 7–18.

[9] Shaheen

and Shepherd

, Lubrication regimes in lumbar total disc arthroplasty, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 221 (2007), 621–627.

10.

[10] Rawlinson

J.J.

Punga

K.P.

Gunsallus

K.L.

Bartel

D.L.

and Wright

T.M.

, Wear simulation of the ProDisc-L disc replacement using adaptive finite element analysis, J. Neurosurg.-Spine 7 (2007), 165–173.

11.

[11] Uddin

and Zhang

, Predicting the wear of hard-on-hard hip joint prostheses, Wear 301 (2013), 192–200.

12.

[12] Bhattacharya

Vijay

G.K.

Xia

Ali

and Hassan

S.A.

, Models that incorporate spinal structures predict better wear performance of cervical artificial discs, Spine J. 11 (2011), 766–776.

13.

[13] Shankar

and Nithyaprakash

, Wear prediction on silicon nitride bearing couple in human hip prosthesis using finite element concepts, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 228 (2014), 717–724.

14.

[14] Piconi

and Maccauro

, Zirconia as a ceramic biomaterial, Biomaterials 20 (1999), 1–25.

15.

[15] Archard

, Contact and rubbing of flat surfaces, Journal of Applied Physics 24 (2004), 981–988.

16.

[16] Kang

Galvin

A.L.

Jin

Z.M.

and Fisher

, A simple fully integrated contact-coupled wear prediction for ultra-high molecular weight polyethylene hip implants, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 220 (2006), 33–46.

17.

[17] Wenzel

and Shepherd

, Contact stresses in lumbar total disc arthroplasty, Bio-Medical Materials and Engineering 17 (2007), 169–173.

18.

[18] Shankar

and Kesavan

, Wear prediction of the lumbar total disc replacement using finite element method, Journal of Mechanics in Medicine and Biology 16 (2015), 1650004–1650016.