Abstract

Total disk arthroplasty (TDA) using an artificial disk (AD) is an attractive surgical technique for the treatment of spinal disorders, since it can maintain or restore spinal motion (unlike interbody fusion). However, adverse surgical outcomes of contemporary lumbar TDAs have been reported. We previously proposed a new mobile-bearing AD design concept featuring a biconcave ultrahigh-molecular-weight polyethylene (UHMWPE) mobile core. The objective of this study was to develop an artificial neural network (NN) based multiobjective optimization framework to refine the biconcave-core AD design considering multiple TDA performance metrics, simultaneously. We hypothesized that there is a tradeoff relationship between the performance metrics in terms of range of motion (ROM), facet joint force (FJF), and polyethylene contact pressure (PCP). By searching the resulting three-dimensional (3D) Pareto frontier after multiobjective optimization, it was found that there was a “best-tradeoff” AD design, which could balance all the three metrics, without excessively sacrificing each metric. However, for each single-objective optimum AD design, only one metric was optimal, and distinct sacrifices were observed in the other two metrics. For a commercially available biconvex-core AD design, the metrics were even worse than the poorest outcomes of the single-objective optimum AD designs. Therefore, multiobjective design optimization could be useful for achieving native lumbar segment biomechanics and minimal PCPs, as well as for improving the existing lumbar motion-preserving surgical treatments.

References

References
1.
Galbusera
,
F.
,
Bellini
,
C. M.
,
Zweig
,
T.
,
Ferguson
,
S.
,
Raimondi
,
M. T.
,
Lamartina
,
C.
,
Brayda-Bruno
,
M.
, and
Fornari
,
M.
,
2008
, “
Design Concepts in Lumbar Total Disc Arthroplasty
,”
Eur. Spine J.
,
17
(
12
), pp.
1635
1650
.10.1007/s00586-008-0811-x
2.
Park
,
P.
,
Garton
,
H. J.
,
Gala
,
V. C.
,
Hoff
,
J. T.
, and
McGillicuddy
,
J. E.
,
2004
, “
Adjacent Segment Disease After Lumbar or Lumbosacral Fusion: Review of the Literature
,”
Spine (Phila. Pa. 1976).
,
29
(
17
), pp.
1938
1944
.10.1097/01.brs.0000137069.88904.03
3.
Marchi
,
L.
,
Oliveira
,
L.
,
Coutinho
,
E.
, and
Pimenta
,
L.
,
2012
, “
The Importance of the Anterior Longitudinal Ligament in Lumbar Disc Arthroplasty: 36-Month Follow-Up Experience in Extreme Lateral Total Disc Replacement
,”
Int. J. Spine Surg.
,
6
(
1
), pp.
18
23
.10.1016/j.ijsp.2011.09.002
4.
Mobbs
,
R. J.
,
Julian Li
,
J. X.
, and
Phan
,
K.
,
2017
, “
Anterior Longitudinal Ligament Reconstruction to Reduce Hypermobility of Cervical and Lumbar Disc Arthroplasty
,”
Asian Spine J.
,
11
(
6
), pp.
943
950
.10.4184/asj.2017.11.6.943
5.
Kurtz
,
S. M.
,
Toth
,
J. M.
,
Siskey
,
R.
,
Ciccarelli
,
L.
,
MacDonald
,
D.
,
Isaza
,
J.
,
Lanman
,
T.
,
Punt
,
I.
,
Steinbeck
,
M.
,
Goffin
,
J.
, and
van Ooij
,
A.
,
2012
, “
The Latest Lessons Learned From Retrieval Analyses of Ultra-High Molecular Weight Polyethylene, Metal-on-Metal, and Alternative Bearing Total Disc Replacements
,”
Semin. Spine Surg.
,
24
(
1
), pp.
57
70
.10.1053/j.semss.2011.11.011
6.
Willing
,
R.
, and
Kim
,
I. Y.
,
2012
, “
Quantifying the Competing Relationship Between Durability and Kinematics of Total Knee Replacements Using Multiobjective Design Optimization and Validated Computational Models
,”
J. Biomech.
,
45
(
1
), pp.
141
147
.10.1016/j.jbiomech.2011.09.008
7.
Willing
,
R.
, and
Kim
,
I. Y.
,
2011
, “
Design Optimization of a Total Knee Replacement for Improved Constraint and Flexion Kinematics
,”
J. Biomech.
,
44
(
6
), pp.
1014
1020
.10.1016/j.jbiomech.2011.02.009
8.
Kim
,
I. Y.
, and
De Weck
,
O. L.
,
2005
, “
Adaptive Weighted-Sum Method for Bi-Objective Optimization: Pareto Front Generation
,”
Struct. Multidiscip. Optim.
,
29
(
2
), pp.
149
158
.10.1007/s00158-004-0465-1
9.
Kim
,
I. Y.
, and
De Weck
,
O. L.
,
2006
, “
Adaptive Weighted Sum Method for Multiobjective Optimization: A New Method for Pareto Front Generation
,”
Struct. Multidiscip. Optim.
,
31
(
2
), pp.
105
116
.10.1007/s00158-005-0557-6
10.
Messac
,
A.
, and
Mattson
,
C. A.
,
2004
, “
Normal Constraint Method With Guarantee of Even Representation of Complete Pareto Frontier
,”
AIAA J.
,
42
(
10
), pp.
2101
2111
.10.2514/1.8977
11.
Messac
,
A.
,
Ismail-Yahaya
,
A.
, and
Mattson
,
C. A.
,
2003
, “
The Normalized Normal Constraint Method for Generating the Pareto Frontier
,”
Struct. Multidiscip. Optim.
,
25
(
2
), pp.
86
98
.10.1007/s00158-002-0276-1
12.
Das
,
I.
, and
Dennis
,
J. E.
,
1998
, “
Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems
,”
SIAM J. Optim.
,
8
(
3
), pp.
631
657
.10.1137/S1052623496307510
13.
Garijo
,
N.
,
Martínez
,
J.
,
García-Aznar
,
J. M.
, and
Pérez
,
M. A.
,
2014
, “
Computational Evaluation of Different Numerical Tools for the Prediction of Proximal Femur Loads From Bone Morphology
,”
Comput. Methods Appl. Mech. Eng.
,
268
, pp.
437
450
.10.1016/j.cma.2013.10.005
14.
Taylor
,
M.
,
Perilli
,
E.
, and
Martelli
,
S.
,
2017
, “
Development of a Surrogate Model Based on Patient Weight, Bone Mass and Geometry to Predict Femoral Neck Strains and Fracture Loads
,”
J. Biomech.
,
55
, pp.
121
127
.10.1016/j.jbiomech.2017.02.022
15.
Chao
,
C.-K.
,
Lin
,
J.
,
Putra
,
S. T.
, and
Hsu
,
C.-C.
,
2010
, “
A Neurogenetic Approach to a Multiobjective Design Optimization of Spinal Pedicle Screws
,”
ASME J. Biomech. Eng.
,
132
(
9
), p.
091006
.10.1115/1.4001887
16.
Chen
,
Y.
,
Zhou
,
S.
, and
Li
,
Q.
,
2011
, “
Microstructure Design of Biodegradable Scaffold and Its Effect on Tissue Regeneration
,”
Biomaterials
,
32
(
22
), pp.
5003
5014
.10.1016/j.biomaterials.2011.03.064
17.
Nguyen-Thien
,
T.
, and
Tran-Cong
,
T.
,
1999
, “
Approximation of Functions and Their Derivatives: A Neural Network Implementation With Applications
,”
Appl. Math. Model.
,
23
(
9
), pp.
687
704
.10.1016/S0307-904X(99)00006-2
18.
Zhou
,
C.
, and
Willing
,
R.
,
2019
, “
Development of a Biconcave Mobile-Bearing Lumbar Total Disc Arthroplasty Concept Using Finite Element Analysis and Design Optimization
,”
J. Orthop. Res.
, 37(8), pp.
1805
1816
.10.1002/jor.24315
19.
Rundell
,
S. A.
,
Day
,
J. S.
,
Isaza
,
J.
,
Guillory
,
S.
, and
Kurtz
,
S. M.
,
2012
, “
Lumbar Total Disc Replacement Impingement Sensitivity to Disc Height Distraction, Spinal Sagittal Orientation, Implant Position, and Implant Lordosis
,”
Spine
,
37
(
10
), pp.
E590
E598
.10.1097/BRS.0b013e318241e415
20.
Kurtz
,
S. M.
,
Peloza
,
J.
,
Siskey
,
R.
, and
Villarraga
,
M. L.
,
2005
, “
Analysis of a Retrieved Polyethylene Total Disc Replacement Component
,”
Spine J.
,
5
(
3
), pp.
344
350
.10.1016/j.spinee.2004.11.011
21.
Rundell
,
S. A.
,
Auerbach
,
J. D.
,
Balderston
,
R. A.
, and
Kurtz
,
S. M.
,
2008
, “
Total Disc Replacement Positioning Affects Facet Contact Forces and Vertebral Body Strains
,”
Spine
,
33
(
23
), pp.
2510
2517
.10.1097/BRS.0b013e318186b258
22.
Panjabi
,
M. M.
,
Goel
,
V.
,
Oxland
,
T.
,
Takata
,
K.
,
Duranceau
,
J.
,
Krag
,
M.
, and
Price
,
M.
,
1992
, “
Human Lumbar Vertebrae: Quantitative Three-Dimensional Anatomy
,”
Spine
,
17
(
3
), pp.
299
306
.10.1097/00007632-199203000-00010
23.
Panjabi
,
M. M.
,
Oxland
,
T.
,
Takata
,
K.
,
Goel
,
V.
,
Duranceau
,
J.
, and
Krag
,
M.
,
1993
, “
Articular Facets of the Human Spine Quantitative Three-Dimensional Anatomy
,”
Spine
,
18
(
10
), pp.
1298
1310
.10.1097/00007632-199308000-00009
24.
Schmidt
,
H.
,
Galbusera
,
F.
,
Rohlmann
,
A.
,
Zander
,
T.
, and
Wilke
,
H. J.
,
2012
, “
Effect of Multilevel Lumbar Disc Arthroplasty on Spine Kinematics and Facet Joint Loads in Flexion and Extension: A Finite Element Analysis
,”
Eur. Spine J.
,
21
(
S5
), pp.
663
S674
.10.1007/s00586-010-1382-1
25.
Van Der Houwen
,
E. B.
,
Baron
,
P.
,
Veldhuizen
,
A. G.
,
Burgerhof
,
J. G. M.
,
Van Ooijen
,
P. M. A.
, and
Verkerke
,
G. J.
,
2010
, “
Geometry of the Intervertebral Volume and Vertebral Endplates of the Human Spine
,”
Ann. Biomed. Eng.
,
38
(
1
), pp.
33
40
.10.1007/s10439-009-9827-6
26.
Zhou
,
C.
,
Cha
,
T.
, and
Li
,
G.
,
2019
, “
An Upper Bound Computational Model for Investigation of Fusion Effects on Adjacent Segment Biomechanics of the Lumbar Spine
,”
Comput. Methods Biomech. Biomed. Eng.
, 22(14), pp.
1126
1134
.
27.
Schmidt
,
H.
,
Heuer
,
F.
,
Simon
,
U.
,
Kettler
,
A.
,
Rohlmann
,
A.
,
Claes
,
L.
, and
Wilke
,
H. J.
,
2006
, “
Application of a New Calibration Method for a Three-Dimensional Finite Element Model of a Human Lumbar Annulus Fibrosus
,”
Clin. Biomech.
,
21
(
4
), pp.
337
344
.10.1016/j.clinbiomech.2005.12.001
28.
Bergström
,
J. S.
,
Rimnac
,
C. M.
, and
Kurtz
,
S. M.
,
2003
, “
Prediction of Multiaxial Mechanical Behavior for Conventional and Highly Crosslinked UHMWPE Using a Hybrid Constitutive Model
,”
Biomaterials
,
24
(
8
), pp.
1365
1380
.10.1016/S0142-9612(02)00514-8
29.
Schmidt
,
H.
,
Heuer
,
F.
,
Claes
,
L.
, and
Wilke
,
H. J.
,
2008
, “
The Relation Between the Instantaneous Center of Rotation and Facet Joint Forces—A Finite Element Analysis
,”
Clin. Biomech.
,
23
(
3
), pp.
270
278
.10.1016/j.clinbiomech.2007.10.001
30.
Goel
,
V. K.
,
Grauer
,
J. N.
,
Patel
,
T. C.
,
Biyani
,
A.
,
Sairyo
,
K.
,
Vishnubhotla
,
S.
,
Matyas
,
A.
,
Cowgill
,
I.
,
Shaw
,
M.
,
Long
,
R.
,
Dick
,
D.
,
Panjabi
,
M. M.
, and
Serhan
,
H.
,
2005
, “
Effects of Charité Artificial Disc on the Implanted and Adjacent Spinal Segments Mechanics Using a Hybrid Testing Protocol
,”
Spine
,
30
(
24
), pp.
2755
2764
.10.1097/01.brs.0000195897.17277.67
31.
Patwardhan
,
A. G.
,
Havey
,
R. M.
,
Meade
,
K. P.
,
Lee
,
B.
, and
Dunlap
,
B.
,
1999
, “
A Follower Load Increases the Load-Carrying Capacity of the Lumbar Spine in Compression
,”
Spine
,
24
(
10
), pp.
1003
1009
.10.1097/00007632-199905150-00014
32.
Dreischarf
,
M.
,
Zander
,
T.
,
Bergmann
,
G.
, and
Rohlmann
,
A.
,
2010
, “
A Non-Optimized Follower Load Path May Cause Considerable Intervertebral Rotations
,”
J. Biomech.
,
43
(
13
), pp.
2625
2628
.10.1016/j.jbiomech.2010.05.033
33.
Fujiwara
,
A.
,
Tamai
,
K.
,
Yamato
,
M.
,
An
,
H. S.
,
Yoshida
,
H.
,
Saotome
,
K.
, and
Kurihashi
,
A.
,
1999
, “
The Relationship Between Facet Joint Osteoarthritis and Disc Degeneration of the Lumbar Spine: An MRI Study
,”
Eur. Spine J.
,
8
(
5
), pp.
396
401
.10.1007/s005860050193
34.
Jin
,
Y.
, and
Sendhoff
,
B.
,
2008
, “
Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies
,”
IEEE Trans. Syst. Man Cybern. Part C
,
38
(
3
), pp.
397
415
.10.1109/TSMCC.2008.919172
35.
Shim
,
C. S.
,
Lee
,
S.-H.
,
Shin
,
H.-D.
,
Kang
,
H. S.
,
Choi
,
W.-C.
,
Jung
,
B.
,
Choi
,
G.
,
Ahn
,
Y.
,
Lee
,
S.
, and
Lee
,
H. Y.
,
2007
, “
CHARITE Versus ProDisc: A Comparative Study of a Minimum 3-Year Follow-Up
,”
Spine
,
32
(
9
), pp.
1012
1018
.10.1097/01.brs.0000260795.57798.a0
36.
Salzmann
,
S. N.
,
Plais
,
N.
,
Shue
,
J.
, and
Girardi
,
F. P.
,
2017
, “
Lumbar Disc Replacement Surgery—Successes and Obstacles to Widespread Adoption
,”
Curr. Rev. Musculoskelet. Med.
,
10
(
2
), pp.
153
159
.10.1007/s12178-017-9397-4
37.
Serhan
,
H.
,
Mhatre
,
D.
,
Defossez
,
H.
, and
Bono
,
C. M.
,
2011
, “
Motion-Preserving Technologies for Degenerative Lumbar Spine: The Past, Present, and Future Horizons
,”
SAS J.
,
5
(
3
), pp.
75
89
.10.1016/j.esas.2011.05.001
38.
Moumene
,
M.
, and
Geisler
,
F. H.
,
2007
, “
Comparison of Biomechanical Function at Ideal and Varied Surgical Placement for Two Lumbar Artificial Disc Implant Designs
,”
Spine
,
32
(
17
), pp.
1840
1851
.10.1097/BRS.0b013e31811ec29c
39.
Kurtz
,
S. M.
,
van Ooij
,
A.
,
Ross
,
R.
,
de Waal Malefijt
,
J.
,
Peloza
,
J.
,
Ciccarelli
,
L.
, and
Villarraga
,
M. L.
,
2007
, “
Polyethylene Wear and Rim Fracture in Total Disc Arthroplasty
,”
Spine J.
,
7
(
1
), pp.
12
21
.10.1016/j.spinee.2006.05.012
40.
Kurtz
,
S. M.
,
Patwardhan
,
A.
,
MacDonald
,
D.
,
Ciccarelli
,
L.
,
van Ooij
,
A.
,
Lorenz
,
M.
,
Zindrick
,
M.
,
O’Leary
,
P.
,
Isaza
,
J.
, and
Ross
,
R.
,
2008
, “
What Is the Correlation of In Vivo Wear and Damage Patterns With In Vitro TDR Motion Response?
,”
Spine
,
33
(
5
), pp.
481
489
.10.1097/BRS.0b013e318165e3be
41.
Malakoutian
,
M.
,
Volkheimer
,
D.
,
Street
,
J.
,
Dvorak
,
M. F.
,
Wilke
,
H.-J. J.
, and
Oxland
,
T. R.
,
2015
, “
Do In Vivo Kinematic Studies Provide Insight Into Adjacent Segment Degeneration? a Qualitative Systematic Literature Review
,”
Eur. Spine J.
,
24
(
9
), pp.
1865
1881
.10.1007/s00586-015-3992-0
42.
Volkheimer
,
D.
,
Malakoutian
,
M.
,
Oxland
,
T. R.
, and
Wilke
,
H. J.
,
2015
, “
Limitations of Current In Vitro Test Protocols for Investigation of Instrumented Adjacent Segment Biomechanics: Critical Analysis of the Literature
,”
Eur. Spine J.
,
24
(
9
), pp.
1882
1892
.10.1007/s00586-015-4040-9
43.
Huang
,
R. C.
,
Girardi
,
F. P.
,
Cammisa
,
F. P.
, and
Wright
,
T. M.
,
2003
, “
The Implications of Constraint in Lumbar Total Disc Replacement
,”
J. Spinal Disord. Tech.
,
16
(
4
), pp.
412
7
.10.1097/00024720-200308000-00014
44.
Büttner-Janz
,
K.
,
Guyer
,
R. D.
, and
Ohnmeiss
,
D. D.
,
2014
, “
Indications for Lumbar Total Disc Replacement: Selecting the Right Patient With the Right Indication for the Right Total Disc
,”
Int. J. Spine Surg.
,
8
, p.
12
.10.14444/1012
45.
Fattor
,
J. A.
,
Hollenbeck
,
J. F. M.
,
Laz
,
P. J.
,
Rullkoetter
,
P. J.
,
Burger
,
E. L.
,
Patel
,
V. V.
, and
Cain
,
C. M. J.
,
2016
, “
Patient-Specific Templating of Lumbar Total Disk Replacement to Restore Normal Anatomy and Function
,”
Orthopedics
,
39
(
2
), pp.
97
102
.10.3928/01477447-20160304-06
46.
Baldwin
,
M. A.
,
Langenderfer
,
J. E.
,
Rullkoetter
,
P. J.
, and
Laz
,
P. J.
,
2010
, “
Development of Subject-Specific and Statistical Shape Models of the Knee Using an Efficient Segmentation and Mesh-Morphing Approach
,”
Comput. Methods Programs Biomed.
,
97
(
3
), pp.
232
240
.10.1016/j.cmpb.2009.07.005
47.
Bryan
,
R.
,
Surya Mohan
,
P.
,
Hopkins
,
A.
,
Galloway
,
F.
,
Taylor
,
M.
, and
Nair
,
P. B.
,
2010
, “
Statistical Modelling of the Whole Human Femur Incorporating Geometric and Material Properties
,”
Med. Eng. Phys.
,
32
(
1
), pp.
57
65
.10.1016/j.medengphy.2009.10.008
48.
Rao
,
C.
,
Fitzpatrick
,
C. K.
,
Rullkoetter
,
P. J.
,
Maletsky
,
L. P.
,
Kim
,
R. H.
, and
Laz
,
P. J.
,
2013
, “
A Statistical Finite Element Model of the Knee Accounting for Shape and Alignment Variability
,”
Med. Eng. Phys.
,
35
(
10
), pp.
1450
1456
.10.1016/j.medengphy.2013.03.021
49.
Peloquin
,
J. M.
,
Yoder
,
J. H.
,
Jacobs
,
N. T.
,
Moon
,
S. M.
,
Wright
,
A. C.
,
Vresilovic
,
E. J.
, and
Elliott
,
D. M.
,
2014
, “
Human L3L4 Intervertebral Disc Mean 3D Shape, Modes of Variation, and Their Relationship to Degeneration
,”
J. Biomech.
,
47
(
10
), pp.
2452
2459
.10.1016/j.jbiomech.2014.04.014
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