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Research Papers

Plastic Energy Dissipation in Lumbar Spine Implants: A Contact Mechanics Point of View

[+] Author and Article Information
M. Hodaei

Graduate Program in Biomedical Engineering;
Sound and Vibration Laboratory,
Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB R3T 2N2, Canada

A. Bahari, V. Rabbani

Sound and Vibration Laboratory,
Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB R3T 2N2, Canada

P. Maghoul

Graduate Program in Biomedical Engineering;
Department of Civil Engineering,
University of Manitoba,
Winnipeg, MB R3T 2N2, Canada

Manuscript received July 20, 2018; final manuscript received October 8, 2018; published online January 18, 2019. Assoc. Editor: Shijia Zhao.

ASME J of Medical Diagnostics 2(2), 021005 (Jan 18, 2019) (8 pages) Paper No: JESMDT-18-1032; doi: 10.1115/1.4041702 History: Received July 20, 2018; Revised October 08, 2018

In this study, an elastoplastic contact model is developed for L1–L5 lumbar spine implants. Roughness effect is included to estimate energy loss which is an indication of wear and subsequently the issue of metal debris in body. A Gaussian function is assumed for the distribution of asperities. The contact surfaces of the implants are assumed to be spherical caps. Subsequently, a least-square approach is applied to obtain an approximate expression for the contact force using the data from integration over contact zone. The energy loss is calculated, next, which is due to plastic deformations of asperities. The numerical results indicate that for a given loading–unloading condition, the amount of energy dissipation increases in L1–L4 lumbar spine implants, while it decreases from L4 to L5 implants. The implants geometrical specifications are chosen to cover a wide range of patients' age. Finally, a closed-form expression is obtained for the plastic energy dissipation per cycle in terms of plasticity index for the lumbar spine L4, as the worst-case scenario. Such a function can serve as a very useful tool for implant designers and manufacturers.

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References

Brodner, W. , Bitzan, P. , Meisinger, V. , Kaider, A. , Gottsauner-Wolf, F. , and Kotz, R. , 1997, “ Elevated Serum Cobalt With Metal-on-Metal Articulating Surfaces,” J. Bone Jt. Surg. Br., 79(2), pp. 316–321. [CrossRef]
Caicedo, M. S. , Pennekamp, P. H. , McAllister, K. , Jacobs, J. J. , and Hallab, N. J. , 2010, “ Soluble Ions More Than Particulate Cobalt-Alloy Implant Debris Induce Monocyte Costimulatory Molecule Expression and Release of Proinflammatory Cytokines Critical to Metal-Induced Lymphocyte Reactivity,” J. Biomed. Mater. Res., Part A, 93(4), pp. 1312–1321.
Langton, D. , Jameson, S. , Joyce, T. , Hallab, N. , Natu, S. , and Nargol, A. , 2010, “ Early Failure of Metal-on-Metal Bearings in Hip Resurfacing and Large-Diameter Total Hip Replacement: A Consequence of Excess Wear,” J. Bone Jt. Surg., 92(1), pp. 38–46. [CrossRef]
Hothi, H. , Duncan, C. , Garbuz, D. , Henckel, J. , Skinner, J. , and Hart, A. , 2017, “ Wear Analysis of Tapers From Failed Metal-on-Polyethylene Hips Provides First Data on Clinically Significant Doses of Cobalt and Chromium for Adverse Reaction to Metal Debris,” Orthop. Proc., 99-B(S12), p. 9.
Heneghan, C. , Langton, D. , and Thompson, M. , 2012, “ Ongoing Problems With Metal-on-Metal Hip Implants,” BMJ, 344, p. e1349.
Wu, J.-J. , 2000, “ Simulation of Rough Surfaces With FFT,” Tribol. Int., 33(1), pp. 47–58. [CrossRef]
Patir, N. , 1978, “ A Numerical Procedure for Random Generation of Rough Surfaces,” Wear, 47(2), pp. 263–277. [CrossRef]
Watson, W. , and Spedding, T. A. , 1982, “ The Time Series Modelling of Non-Gaussian Engineering Processes,” Wear, 83(2), pp. 215–231. [CrossRef]
Majumdar, A. , and Bhushan, B. , 1991, “ Fractal Model of Elastic-Plastic Contact Between Rough Surfaces,” ASME J. Tribol., 113(1), pp. 1–11. [CrossRef]
Hodaei, M. , and Farhang, K. , 2016, “ Energy Absorption in a Load–Unload Cycle of Knee Implant Using Fractal Model of Rough Surfaces,” Fractals, 24(2), p. 1650020. [CrossRef]
Graindorge, S. L. , and Stachowiak, G. W. , 2000, “ Changes Occurring in the Surface Morphology of Articular Cartilage During Wear,” Wear, 241(2), pp. 143–150. [CrossRef]
Smyth, P. A. , Rifkin, R. E. , Jackson, R. L. , and Reid Hanson, R. , 2012, “ The Fractal Structure of Equine Articular Cartilage,” Scanning, 34(6), pp. 418–426. [CrossRef] [PubMed]
Smyth, P. A. , Rifkin, R. E. , Jackson, R. L. , and Hanson, R. R. , 2012, “ A Surface Roughness Comparison of Cartilage in Different Types of Synovial Joints,” ASME J. Biomech. Eng., 134(2), p. 021006. [CrossRef]
Smyth, P. , Rifkin, R. , Jackson, R. , and Hanson, R. , 2014, “ The Average Roughness and Fractal Dimension of Articular Cartilage During Drying,” Scanning, 36(3), pp. 368–375. [CrossRef] [PubMed]
Yilmaz, S. , Arici, A. A. , and Feyzullahoglu, E. , 2011, “ Surface Roughness Prediction in Machining of Cast Polyamide Using Neural Network,” Neural Comput. Appl., 20(8), pp. 1249–1254. [CrossRef]
Çaydaş, U. , and Hascalik, A. , 2008, “ A Study on Surface Roughness in Abrasive Waterjet Machining Process Using Artificial Neural Networks and Regression Analysis Method,” J. Mater. Process. Technol., 202(1–3), pp. 574–582. [CrossRef]
Belytschko, T. , Kulak, R. , Schultz, A. , and Galante, J. , 1974, “ Finite Element Stress Analysis of an Intervertebral Disc,” J. Biomech., 7(3), pp. 277–285. [CrossRef] [PubMed]
Adam, C. , Pearcy, M. , and McCombe, P. , 2003, “ Stress Analysis of Interbody Fusion—Finite Element Modelling of Intervertebral Implant and Vertebral Body,” Clin. Biomech., 18(4), pp. 265–272. [CrossRef]
Zhong, Z.-C. , Wei, S.-H. , Wang, J.-P. , Feng, C.-K. , Chen, C.-S. , and Yu, C.-h. , 2006, “ Finite Element Analysis of the Lumbar Spine With a New Cage Using a Topology Optimization Method,” Med. Eng. Phys., 28(1), pp. 90–98. [CrossRef] [PubMed]
Godest, A. , Beaugonin, M. , Haug, E. , Taylor, M. , and Gregson, P. , 2002, “ Simulation of a Knee Joint Replacement During a Gait Cycle Using Explicit Finite Element Analysis,” J. Biomech., 35(2), pp. 267–275. [CrossRef] [PubMed]
Fregly, B. J. , Sawyer, W. G. , Harman, M. K. , and Banks, S. A. , 2005, “ Computational Wear Prediction of a Total Knee Replacement From In Vivo Kinematics,” J. Biomech., 38(2), pp. 305–314. [CrossRef] [PubMed]
Greenwood, J. , and Williamson, J. P. , 1966, “ Contact of Nominally Flat Surfaces,” Proc. R. Soc. London A, 295(1442), pp. 300–319. [CrossRef]
Greenwood, J. A. , and Tripp, J. H. , 1967, “ The Elastic Contact of Rough Spheres,” ASME J. Appl. Mech., 34(1), pp. 153–159. [CrossRef]
Whitehouse, D. J. , and Archard, J. , 1970, “ The Properties of Random Surfaces of Significance in Their Contact,” Proc. R. Soc. London A, 316(1524), pp. 97–121. [CrossRef]
Bush, A. , Gibson, R. , and Keogh, G. , 1979, “ Strongly Anisotropic Rough Surfaces,” ASME J. Lubr. Technol., 101(1), pp. 15–20. [CrossRef]
McCool, J. I. , 1986, “ Comparison of Models for the Contact of Rough Surfaces,” Wear, 107(1), pp. 37–60. [CrossRef]
Chang, W. , Etsion, I. , and Bogy, D. B. , 1987, “ An Elastic-Plastic Model for the Contact of Rough Surfaces,” ASME J. Tribol., 109(2), pp. 257–263. [CrossRef]
Polycarpou, A. A. , and Etsion, I. , 1999, “ Analytical Approximations in Modeling Contacting Rough Surfaces,” ASME J. Tribol., 121(2), pp. 234–239. [CrossRef]
Hodaei, M. , Farhang, K. , and Maani, N. , 2014, “ A Contact Mechanics Model for Ankle Implants With Inclusion of Surface Roughness Effects,” J. Phys. D, 47(8), p. 085502. [CrossRef]
Hodaei, M. , and Farhang, K. , 2017, “ Effect of Rough Surface Asymmetry on Contact Energy Loss in Hip Implants,” J. Mech. Med. Biol., 17(1), p. 1750023. [CrossRef]
Hodaei, M. , and Farhang, K. , 2015, “ Connection of Surface Roughness to Hysteresis Loss in Spine Implants,” J. Biomech. Sci. Eng., 10(2), p. 14–00443. [CrossRef]
Sepehri, A. , and Farhang, K. , 2007, “ An Extension of Ceb Elastic-Plastic Contact Model,” ASME Paper No. IJTC2007-44362.
Gocmen-Mas, N. , Karabekir, H. , Ertekin, T. , Edizer, M. , Canan, Y. , and Duyar, I. , 2010, “ Evaluation of Lumbar Vertebral Body and Disc: A Stereological Morphometric Study,” Int. J. Morphol., 28(3), pp. 841–847. [CrossRef]
Moghadas, P. , Mahomed, A. , Hukins, D. W. , and Shepherd, D. E. , 2012, “ Friction in Metal-on-Metal Total Disc Arthroplasty: Effect of Ball Radius,” J. Biomech., 45(3), pp. 504–509. [CrossRef] [PubMed]
Pintar, F. A. , Yoganandan, N. , Myers, T. , Elhagediab, A. , and Sances, A. , 1992, “ Biomechanical Properties of Human Lumbar Spine Ligaments,” J. Biomech., 25(11), pp. 1351–1356. [CrossRef] [PubMed]
Shirazi-Adl, A. , and Parnianpour, M. , 2000, “ Load-Bearing and Stress Analysis of the Human Spine Under a Novel Wrapping Compression Loading,” Clin. Biomech., 15(10), pp. 718–725. [CrossRef]
Shirazi-Adl, A. , 1994, “ Biomechanics of the Lumbar Spine in Sagittal/Lateral Moments,” Spine, 19(21), pp. 2407–2414. [CrossRef] [PubMed]
Goel, V. , Monroe, B. , Gilbertson, L. , and Brinckmann, P. , 1995, “ Interlaminar Shear Stresses and Laminae Separation in a Disc: Finite Element Analysis of the L3-L4 Motion Segment Subjected to Axial Compressive Loads,” Spine, 20(6), pp. 689–698. [CrossRef] [PubMed]
Wu, H.-C. , and Yao, R.-F. , 1976, “ Mechanical Behavior of the Human Annulus Fibrosus,” J. Biomech., 9(1), pp. 1–7. [CrossRef] [PubMed]

Figures

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Fig. 1

Spine lumbar implant components in contact and its associated free-body diagram: (a) spine schematic and (b) implant's free-body diagram

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Fig. 2

Contact force approximation and the associated error versus minimum mean separation, h0: (a) exact and approximate forces and (b) relative error of the approximate contact force

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Fig. 3

Contact force F¯ versus displacement perturbation ε for a loading–unloading cycle in lumbar spine L1 in low plastic zone (ψ = 0.6)

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Fig. 4

Contact force F¯ versus displacement perturbation ε for a loading–unloading cycle in lumbar spine L1 in high plastic zone (ψ = 1.3)

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Fig. 5

Contact force F¯ versus displacement perturbation ε for a loading–unloading cycle in lumbar spine L2 in high plastic zone (ψ = 1.3)

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Fig. 6

Contact force F¯ versus displacement perturbation ε for a loading–unloading cycle in lumbar spine L3 in high plastic zone (ψ = 1.3)

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Fig. 7

Contact force F¯ versus displacement perturbation ε for a loading–unloading cycle in lumbar spine L4 in high plastic zone (ψ = 1.3)

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Fig. 8

Contact force F¯ versus displacement perturbation ε for a loading–unloading cycle in lumbar spine L5 in high plastic zone (ψ = 1.3)

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Fig. 9

Estimated energy loss per one cycle using exact versus linear approximate contact force for the plasticity index of ψ = 1.3 for lumbar spine implants L1L5

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Fig. 10

Loading–unloading contact force difference, (FL − FU), versus plasticity index, ψ, and displacement perturbation, ε, in Lumbar spine L4

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Fig. 11

(a) Energy loss versus plasticity index ψ for Lumbar spine L4. (b) Relative error between the actual computed energy loss values approximate fitted curve of Eq. (23) and versus plasticity index, ψ.

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