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.

References

References
1.
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
.
2.
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
.
3.
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
.
4.
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.
5.
Heneghan
,
C.
,
Langton
,
D.
, and
Thompson
,
M.
,
2012
, “
Ongoing Problems With Metal-on-Metal Hip Implants
,”
BMJ
,
344
, p.
e1349
.
6.
Wu
,
J.-J.
,
2000
, “
Simulation of Rough Surfaces With FFT
,”
Tribol. Int.
,
33
(
1
), pp.
47
58
.
7.
Patir
,
N.
,
1978
, “
A Numerical Procedure for Random Generation of Rough Surfaces
,”
Wear
,
47
(
2
), pp.
263
277
.
8.
Watson
,
W.
, and
Spedding
,
T. A.
,
1982
, “
The Time Series Modelling of Non-Gaussian Engineering Processes
,”
Wear
,
83
(
2
), pp.
215
231
.
9.
Majumdar
,
A.
, and
Bhushan
,
B.
,
1991
, “
Fractal Model of Elastic-Plastic Contact Between Rough Surfaces
,”
ASME J. Tribol.
,
113
(
1
), pp.
1
11
.
10.
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
.
11.
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
.
12.
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
.
13.
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
.
14.
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
.
15.
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
.
16.
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
.
17.
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
.
18.
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
.
19.
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
.
20.
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
.
21.
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
.
22.
Greenwood
,
J.
, and
Williamson
,
J. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London A
,
295
(
1442
), pp.
300
319
.
23.
Greenwood
,
J. A.
, and
Tripp
,
J. H.
,
1967
, “
The Elastic Contact of Rough Spheres
,”
ASME J. Appl. Mech.
,
34
(
1
), pp.
153
159
.
24.
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
.
25.
Bush
,
A.
,
Gibson
,
R.
, and
Keogh
,
G.
,
1979
, “
Strongly Anisotropic Rough Surfaces
,”
ASME J. Lubr. Technol.
,
101
(
1
), pp.
15
20
.
26.
McCool
,
J. I.
,
1986
, “
Comparison of Models for the Contact of Rough Surfaces
,”
Wear
,
107
(
1
), pp.
37
60
.
27.
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
.
28.
Polycarpou
,
A. A.
, and
Etsion
,
I.
,
1999
, “
Analytical Approximations in Modeling Contacting Rough Surfaces
,”
ASME J. Tribol.
,
121
(
2
), pp.
234
239
.
29.
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
.
30.
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
.
31.
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
.
32.
Sepehri
,
A.
, and
Farhang
,
K.
,
2007
, “
An Extension of Ceb Elastic-Plastic Contact Model
,”
ASME
Paper No. IJTC2007-44362.
33.
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
.
34.
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
.
35.
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
.
36.
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
.
37.
Shirazi-Adl
,
A.
,
1994
, “
Biomechanics of the Lumbar Spine in Sagittal/Lateral Moments
,”
Spine
,
19
(
21
), pp.
2407
2414
.
38.
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
.
39.
Wu
,
H.-C.
, and
Yao
,
R.-F.
,
1976
, “
Mechanical Behavior of the Human Annulus Fibrosus
,”
J. Biomech.
,
9
(
1
), pp.
1
7
.
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