Abstract

Finite element modeling is a popular method for predicting kinematics and kinetics in spine biomechanics. With the advancement of powerful computational equipment, more detailed finite element models have been developed for the various spine segments. In this study, five detailed finite element models of the cervical spine are developed and validated. The geometric boundaries of the vertebrae are determined from computed tomography (CT) scans of five female subjects. The models include the C2–C7 vertebrae, intervertebral discs, nuclei, endplates, and five major ligaments (anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), ligamentum flavum (LF), interspinous ligament (ISL), and capsular ligament (CL)). The ligaments follow nonlinear stress–strain curves whereas all other parts adopt linear material properties. All the material properties are taken from existing literature. The mesh convergence test is performed under flexion/extension. For flexion/extension motion, a pure moment is applied at the top surface of the odontoid process of the C2 vertebra while nodes at the bottom surface of the C7 vertebra are fixed in all directions. The models are extensively validated in flexion/extension, lateral bending, and axial rotation against experimental and finite element studies in the literature. Intervertebral rotation and range of motion are studied under different loading conditions found in the literature. This research also investigates intersubject variability for the cervical spine among five finite element models from five different subjects. Predicted angular displacements and ranges of motion of the current models are consistent with the literature. The validated models are expected to be applicable to simulate neck-related trauma like whiplash and high-g acceleration, among other scenarios.

References

1.
Mustafy
,
T.
,
Moglo
,
K.
,
Adeeb
,
S.
, and
El-Rich
,
M.
,
2016
, “
Injury Mechanisms of the Ligamentous Cervical C2–C3 Functional Spinal Unit to Complex Loading Modes: Finite Element Study
,”
J. Mech. Behav. Biomed. Mater.
,
53
, pp.
384
396
.
2.
Panjabi
,
M. M.
,
1998
, “
Cervical Spine Models for Biomechanical Research
,”
Spine
,
23
(
24
), pp.
2684
2700
.
3.
Nightingale
,
R. W.
,
Chancey
,
V. C.
,
Ottaviano
,
D.
,
Luck
,
J. F.
,
Tran
,
L.
,
Prange
,
M.
, and
Myers
,
B. S.
,
2007
, “
Flexion and Extension Structural Properties and Strengths for Male Cervical Spine Segments
,”
J. Biomech.
,
40
(
3
), pp.
535
542
.
4.
Juarez
,
M. G.
,
Botti
,
V. J.
, and
Giret
,
A. S.
,
2021
, “
Digital Twins: Review and Challenges
,”
ASME J. Comput. Inf. Sci. Eng.
,
21
(
3
), p.
030802
.
5.
Phanden
,
R. K.
,
Sharma
,
P.
, and
Dubey
,
A.
,
2021
, “
A Review on Simulation in Digital Twin for Aerospace, Manufacturing and Robotics
,”
Mater. Today Proc.
,
38
(
1
), pp.
174
178
.
6.
Bomström
,
H.
,
Annanperä
,
E.
,
Kelanti
,
M.
,
Xu
,
Y.
,
Mäkelä
,
S. M.
,
Immonen
,
M.
, and
Päivärinta
,
T.
,
2022
, “
Digital Twins About Humans—Design Objectives From Three Projects
,”
ASME J. Comput. Inf. Sci. Eng.
,
22
(
5
), p.
050907
.
7.
He
,
X.
,
Qiu
,
Y.
,
Lai
,
X.
,
Li
,
Z.
,
Shu
,
L.
,
Sun
,
W.
, and
Song
,
X.
,
2021
, “
Towards a Shape-Performance Integrated Digital Twin for Lumbar Spine Analysis
,”
Digit. Twin
,
1
(
8
), p.
8
.
8.
Panjabi
,
M. M.
,
Crisco
,
J. J.
,
Vasavada
,
A.
,
Oda
,
T.
,
Cholewicki
,
J.
,
Nibu
,
K.
, and
Shin
,
E.
,
2001
, “
Mechanical Properties of the Human Cervical Spine As Shown by Three-Dimensional Load–Displacement Curves
,”
Spine
,
26
(
24
), pp.
2692
2700
.
9.
Yoganandan
,
N.
,
Kumaresan
,
S. C.
,
Liming
,
V.
,
Pintar
,
F. A.
, and
Larson
,
S. J.
,
1996
, “
Finite Element Modeling of the C4–C6 Cervical Spine Unit
,”
Med. Eng. Phys.
,
18
(
7
), pp.
569
574
.
10.
Panzer
,
M. B.
,
Fice
,
J. B.
, and
Cronin
,
D. S.
,
2011
, “
Cervical Spine Response in Frontal Crash
,”
Med. Eng. Phys.
,
33
(
9
), pp.
1147
1159
.
11.
Erbulut
,
D. U.
,
Zafarparandeh
,
I.
,
Lazoglu
,
I.
, and
Ozer
,
A. F.
,
2014
, “
Application of an Asymmetric Finite Element Model of the C2–T1 Cervical Spine for Evaluating the Role of Soft Tissues in Stability
,”
Med. Eng. Phys.
,
36
(
7
), pp.
915
921
.
12.
Merrill
,
T.
,
Goldsmith
,
W.
, and
Deng
,
Y. C.
,
1984
, “
Three-Dimensional Response of a Lumped Parameter Head–Neck Model Due to Impact and Impulsive Loading
,”
J. Biomech.
,
17
(
2
), pp.
81
95
.
13.
Deng
,
Y. C.
, and
Goldsmith
,
W.
,
1987
, “
Response of a Human Head/Neck/Upper-Torso Replica to Dynamic Loading—I. Physical Model
,”
J. Biomech.
,
20
(
5
), pp.
471
486
.
14.
Saito
,
T.
,
Yamamuro
,
T.
,
Shikata
,
J.
,
Oka
,
M.
, and
Sutsumi
,
S.
,
1991
, “
Analysis and Prevention of Spinal Column Deformity Following Cervical Laminectomy I: Pathogenetic Analysis of Postiaminectomy Deformities
,”
Spine
,
16
(
5
), pp.
494
502
.
15.
Luo
,
Z.
, and
Goldsmith
,
W.
,
1991
, “
Reaction of a Human Head/Neck/Torso System to Shock
,”
J. Biomech.
,
24
(
7
), pp.
499
510
.
16.
Zafarparandeh
,
I.
,
Erbulut
,
D. U.
,
Lazoglu
,
I.
, and
Ozer
,
A. F.
,
2014
, “
Development of a Finite Element Model of the Human Cervical Spine
,”
Turk. Neurosurg.
,
24
(
3
), pp.
312
318
.
17.
Maurel
,
N.
,
Lavaste
,
F.
, and
Skalli
,
W.
,
1997
, “
A Three-Dimensional Parameterized Finite Element Model of the Lower Cervical Spine. Study of the Influence of the Posterior Articular Facets
,”
J. Biomech.
,
30
(
9
), pp.
921
931
.
18.
Kumaresan
,
S.
,
Yoganandan
,
N.
, and
Pintar
,
F. A.
,
1999
, “
Finite Element Analysis of the Cervical Spine: A Material Property Sensitivity Study
,”
Clin. Biomech.
,
14
(
1
), pp.
41
53
.
19.
Voo
,
L. M.
,
Kumaresan
,
S.
,
Yoganandan
,
N.
,
Pintar
,
F. A.
, and
Cusick
,
J. F.
,
1997
, “
Finite Element Analysis of Cervical Facetectomy
,”
Spine
,
22
(
9
), pp.
964
969
.
20.
Kumaresan
,
S.
,
Yoganandan
,
N.
, and
Pintar
,
F. A.
,
1998
, “
Finite Element Modeling Approaches of Human Cervical Spine Facet Joint Capsule
,”
J. Biomech.
,
31
(
4
), pp.
371
376
.
21.
Goel
,
V. K.
, and
Clausen
,
J. D.
,
1998
, “
Prediction of Load Sharing Among Spinal Components of a C5–C6 Motion Segment Using the Finite Element Approach
,”
Spine
,
23
(
6
), pp.
684
691
.
22.
Camacho
,
D. L. A.
,
Nightingale
,
R. W.
, and
Myers
,
B. S.
,
1999
, “
Surface Friction in Near-Vertex Head and Neck Impact Increases Risk of Injury
,”
J. Biomech.
,
32
(
3
), pp.
293
301
.
23.
Stemper
,
B. D.
,
Kumaresan
,
S.
,
Yoganandan
,
N.
, and
Pintar
,
F. A.
,
2000
, “
Head–Neck Finite Element Model for Motor Vehicle Inertial Impact: Material Sensitivity Analysis
,”
Biomed. Sci. Instrum.
,
36
, pp.
331
335
. https://europepmc.org/article/med/10834254
24.
Meyer
,
F.
,
Bourdet
,
N.
,
Deck
,
C.
,
Willinger
,
R.
, and
Raul
,
J. S.
,
2004
, “
Human Neck Finite Element Model Development and Validation Against Original Experimental Data
,”
SAE Technical Papers.
25.
Kallemeyn
,
N.
,
Gandhi
,
A.
,
Kode
,
S.
,
Shivanna
,
K.
,
Smucker
,
J.
, and
Grosland
,
N.
,
2010
, “
Validation of a C2–C7 Cervical Spine Finite Element Model Using Specimen-Specific Flexibility Data
,”
Med. Eng. Phys.
,
32
(
5
), pp.
482
489
.
26.
Kallemeyn
,
N. A.
,
Tadepalli
,
S. C.
,
Shivanna
,
K. H.
, and
Grosland
,
N. M.
,
2009
, “
An Interactive Multiblock Approach to Meshing the Spine
,”
Comput. Methods Programs Biomed.
,
95
(
3
), pp.
227
235
.
27.
Ng
,
H. W.
,
Teo
,
E. C.
, and
Zhang
,
Q. H.
,
2004
, “
Biomechanical Effects of C2–C7 Intersegmental Stability Due to Laminectomy With Unilateral and Bilateral Facetectomy
,”
Spine
,
29
(
16
), pp.
1737
1745
.
28.
Ha
,
S. K.
,
2006
, “
Finite Element Modeling of Multi-level Cervical Spinal Segments (C3–C6) and Biomechanical Analysis of an Elastomer-Type Prosthetic Disc
,”
Med. Eng. Phys.
,
28
(
6
), pp.
534
541
.
29.
Wheeldon
,
J. A.
,
Stemper
,
B. D.
,
Yoganandan
,
N.
, and
Pintar
,
F. A.
,
2008
, “
Validation of a Finite Element Model of the Young Normal Lower Cervical Spine
,”
Ann. Biomed. Eng.
,
36
(
9
), pp.
1458
1469
.
30.
del Palomar
,
A. P.
,
Calvo
,
B.
, and
Doblaré
,
M.
,
2008
, “
An Accurate Finite Element Model of the Cervical Spine Under Quasi-static Loading
,”
J. Biomech.
,
41
(
3
), pp.
523
531
.
31.
Zhang
,
J. G.
,
Wang
,
F.
,
Zhou
,
R.
, and
Xue
,
Q.
,
2011
, “
A Three-Dimensional Finite Element Model of the Cervical Spine: An Investigation of Whiplash Injury
,”
Med. Biol. Eng. Comput.
,
49
(
2
), pp.
193
201
.
32.
Lee
,
S. H.
,
Im
,
Y. J.
,
Kim
,
K. T.
,
Kim
,
Y. H.
,
Park
,
W. M.
, and
Kim
,
K.
,
2011
, “
Comparison of Cervical Spine Biomechanics After Fixed- and Mobile-Core Artificial Disc Replacement: A Finite Element Analysis
,”
Spine
,
36
(
9
), pp.
700
708
.
33.
Dong
,
L.
,
Li
,
G.
,
Mao
,
H.
,
Marek
,
S.
, and
Yang
,
K. H.
,
2013
, “
Development and Validation of a 10-Year-Old Child Ligamentous Cervical Spine Finite Element Model
,”
Ann. Biomed. Eng.
,
41
(
12
), pp.
2538
2552
.
34.
Östh
,
J.
,
Brolin
,
K.
,
Svensson
,
M. Y.
, and
Linder
,
A.
,
2016
, “
A Female Ligamentous Cervical Spine Finite Element Model Validated for Physiological Loads
,”
ASME J. Biomech. Eng.
,
138
(
6
), p.
061005
.
35.
Wang
,
Z.
,
Zhao
,
H.
,
ming Liu
,
J.
,
wen Tan
,
L.
,
Liu
,
P.
, and
hua Zhao
,
J.
,
2016
, “
Resection or Degeneration of Uncovertebral Joints Altered the Segmental Kinematics and Load-Sharing Pattern of Subaxial Cervical Spine: A Biomechanical Investigation Using a C2–T1 Finite Element Model
,”
J. Biomech.
,
49
(
13
), pp.
2854
2862
.
36.
Zhang
,
Q. H.
,
Teo
,
E. C.
,
Ng
,
H. W.
, and
Lee
,
V. S.
,
2006
, “
Finite Element Analysis of Moment-Rotation Relationships for Human Cervical Spine
,”
J. Biomech.
,
39
(
1
), pp.
189
193
.
37.
Herron
,
M. R.
,
Park
,
J.
,
Dailey
,
A. T.
,
Brockmeyer
,
D. L.
, and
Ellis
,
B. J.
,
2020
, “
Febio Finite Element Models of the Human Cervical Spine
,”
J. Biomech.
,
113
, p.
110077
.
38.
Wang
,
X. D.
,
Feng
,
M. S.
, and
Hu
,
Y. C.
,
2019
, “
Establishment and Finite Element Analysis of a Three-Dimensional Dynamic Model of Upper Cervical Spine Instability
,”
Orthop. Surg.
,
11
(
3
), pp.
500
509
.
39.
Finley
,
S. M.
,
Astin
,
J. H.
,
Joyce
,
E.
,
Dailey
,
A. T.
,
Brockmeyer
,
D. L.
, and
Ellis
,
B. J.
,
2021
, “
Febio Finite Element Model of a Pediatric Cervical Spine
,”
J. Neurosurg. Pediatr.
,
29
(
2
), pp.
218
224
.
40.
Hoffmann
,
C. M.
,
2005
, “
Constraint-Based Computer-Aided Design
,”
ASME J. Comput. Inf. Sci. Eng.
,
5
(
3
), pp.
182
187
.
41.
Biswas
,
J. K.
,
Malas
,
A.
,
Majumdar
,
S.
, and
Rana
,
M.
,
2022
, “
A Comparative Finite Element Analysis of Artificial Intervertebral Disc Replacement and Pedicle Screw Fixation of the Lumbar Spine
,”
Comput. Methods Biomech. Biomed. Eng.
,
25
(
16
), pp.
1812
1820
.
42.
Davis
,
R. J.
,
Nunley
,
P. D.
,
Kim
,
K. D.
,
Hisey
,
M. S.
,
Jackson
,
R. J.
,
Bae
,
H. W.
, and
Stone
,
M. B.
,
2015
, “
Two-Level Total Disc Replacement With Mobi-C Cervical Artificial Disc Versus Anterior Discectomy and Fusion: A Prospective, Randomized, Controlled Multicenter Clinical
,”
J. Neurosurg.
,
22
(
1
), pp.
15
25
.
43.
Carstensen
,
T. B. W.
,
Frostholm
,
L.
,
Oernboel
,
E.
,
Kongsted
,
A.
,
Kasch
,
H.
,
Jensen
,
T. S.
, and
Fink
,
P.
,
2012
, “
Are There Gender Differences in Coping With Neck Pain Following Acute Whiplash Trauma? A 12-Month Follow-Up Study
,”
Eur. J. Pain.
,
16
(
1
), pp.
49
60
.
44.
Vasavada
,
A. N.
,
Danaraj
,
J.
, and
Siegmund
,
G. P.
,
2008
, “
Head and Neck Anthropometry, Vertebral Geometry and Neck Strength in Height-Matched Men and Women
,”
J. Biomech.
,
41
(
1
), pp.
114
121
.
45.
Dreischarf
,
M.
,
Zander
,
T.
,
Shirazi-Adl
,
A.
,
Puttlitz
,
C. M.
,
Adam
,
C. J.
,
Chen
,
C. S.
,
Goel
,
V. K.
, et al
,
2014
, “
Comparison of Eight Published Static Finite Element Models of the Intact Lumbar Spine: Predictive Power of Models Improves When Combined Together
,”
J. Biomech.
,
47
(
8
), pp.
1757
1766
.
46.
Xu
,
M.
,
Yang
,
J.
,
Lieberman
,
I. H.
, and
Haddas
,
R.
,
2017
, “
Lumbar Spine Finite Element Model for Healthy Subjects: Development and Validation
,”
Comput. Methods Biomech. Biomed. Eng.
,
20
(
1
), pp.
1
15
.
47.
Xu
,
M.
,
Yang
,
J.
,
Lieberman
,
I.
, and
Haddas
,
R.
,
2019
, “
The Effect of Surgical Alignment in Adult Scoliotic Spines on Axial Cyclic Vibration: A Finite Element Study
,”
ASME J. Comput. Inf. Sci. Eng.
,
19
(
2
), p.
021006
.
48.
Wheeldon
,
J. A.
,
Pintar
,
F. A.
,
Knowles
,
S.
, and
Yoganandan
,
N.
,
2006
, “
Experimental Flexion/Extension Data Corridors for Validation of Finite Element Models of the Young, Normal Cervical Spine
,”
J. Biomech.
,
39
(
2
), pp.
375
380
.
49.
Traynelis
,
V. C.
,
Donaher
,
P. A.
,
Roach
,
R. M.
,
Kojimoto
,
H.
, and
Goel
,
V. K.
,
1993
, “
Biomechanical Comparison of Anterior Caspar Plate and Three-Level Posterior Fixation Techniques in a Human Cadaveric Model
,”
J. Neurosurg.
,
79
(
1
), pp.
96
103
.
50.
Cai
,
X. Y.
,
YuChi
,
C. X.
,
Du
,
C. F.
, and
Mo
,
Z. J.
,
2020
, “
The Effect of Follower Load on the Range of Motion, Facet Joint Force, and Intradiscal Pressure of the Cervical Spine: A Finite Element Study
,”
Med. Biol. Eng. Comput.
,
58
(
8
), pp.
1695
1705
.
51.
Pospiech
,
J.
,
Stolke
,
D.
,
Wilke
,
H. J.
, and
Claes
,
L. E.
,
1999
, “
Intradiscal Pressure Recordings in the Cervical Spine
,”
Neurosurgery
,
44
(
2
), pp.
379
385
.
52.
Nightingale
,
R. W.
,
Winkelstein
,
B. A.
,
Knaub
,
K. E.
,
Richardson
,
W. J.
,
Luck
,
J. F.
, and
Myers
,
B. S.
,
2002
, “
Comparative Strengths and Structural Properties of the Upper and Lower Cervical Spine in Flexion and Extension
,”
J. Biomech.
,
35
(
6
), pp.
725
732
.
53.
Fedorov
,
A.
,
Beichel
,
R.
,
Kalpathy-Cramer
,
J.
,
Finet
,
J.
,
Fillion-Robin
,
J.
,
Pujol
,
S.
,
Bauer
,
C.
, et al
,
2012
, “
3D Slicer As an Image Computing Platform for the Quantitative Imaging Network
,”
Magn. Reson. Imaging
,
30
(
9
), pp.
1323
1341
.
54.
Grosland
,
N. M.
,
Shivann
,
K. H.
,
Magnotta
,
V. A.
,
Kallemey
,
N. A.
,
DeVries
,
N. A.
,
Tadepalli
,
S. C.
, and
Lisle
,
C.
,
2009
, “
IA-FEMesh: An Open-Source, Interactive, Multiblock Approach to Anatomic Finite Element Model Development
,”
Comput. Methods Programs Biomed.
,
94
(
1
), pp.
96
107
.
55.
Zander
,
T.
,
Rohlmann
,
A.
, and
Bergmann
,
G.
,
2009
, “
Influence of Different Artificial Disc Kinematics on Spine Biomechanics
,”
Clin. Biomech.
,
24
(
2
), pp.
135
142
.
56.
Pitzen
,
T.
,
Pitzen
,
T.
,
Schmitz
,
B.
,
Georg
,
T.
,
Barbier
,
D.
,
Beuter
,
T.
,
Steudel
,
W. I.
, and
Reith
,
W.
,
May 2004
, “
Variation of Endplate Thickness in the Cervical Spine
,”
Eur. Spine J.
,
13
(
3
), pp.
235
240
.
57.
Kim
,
Y. H.
,
Khuyagbaatar
,
B.
, and
Kim
,
K.
,
2018
, “
Recent Advances in Finite Element Modeling of the Human Cervical Spine
,”
J. Mech. Sci. Technol.
,
32
(
1
), pp.
1
10
.
58.
Womack
,
W.
,
Leahy
,
P. D.
,
Patel
,
V. V.
, and
Puttlitz
,
C. M.
,
2011
, “
Finite Element Modeling of Kinematic and Load Transmission Alterations Due to Cervical Intervertebral Disc Replacement
,”
Spine (Phila. Pa. 1976)
,
36
(
17
), pp.
E1126
E1133
.
59.
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
(
5
), pp.
466
473
.
60.
Jones
,
A. C.
, and
Wilcox
,
R. K.
,
2008
, “
Finite Element Analysis of the Spine: Towards a Framework of Verification, Validation and Sensitivity Analysis
,”
Med. Eng. Phys.
,
30
(
10
), pp.
1287
1304
.
61.
Shah
,
C.
,
2002
, “
Mesh Discretization Error and Criteria for Accuracy of Finite Element Solutions
,”
International ANSYS Conference
,
Pittsburgh, PA
,
Apr. 22–24
.
62.
Henak
,
C. R.
,
Ateshian
,
G. A.
, and
Weiss
,
J. A.
,
2014
, “
Finite Element Prediction of Transchondral Stress and Strain in the Human Hip
,”
ASME J. Biomech. Eng.
,
136
(
2
), p.
021021
.
63.
Bright
,
J. A.
, and
Rayfield
,
E. J.
,
2011
, “
The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density
,”
Anat. Rec.
,
294
(
4
), pp.
610
620
.
64.
Guo
,
G. M.
,
Guo
,
G.
,
Li
,
J.
,
Diao
,
Q.
,
Zhu
,
T.
,
Song
,
Z.
,
Guo
,
Y.
, and
Gao
,
Y.
,
2018
, “
Cervical Lordosis in Asymptomatic Individuals: A Meta-Analysis
,”
J. Orthop. Surg. Res.
,
13
(
1
).
65.
Niemeyer
,
F.
,
Wilke
,
H. J.
, and
Schmidt
,
H.
,
2012
, “
Geometry Strongly Influences the Response of Numerical Models of the Lumbar Spine-A Probabilistic Finite Element Analysis
,”
J. Biomech.
,
45
(
8
), pp.
1414
1423
.
66.
Little
,
J. P.
, and
Adam
,
C. J.
,
2015
, “
Geometric Sensitivity of Patient-Specific Finite Element Models of the Spine to Variability in User-Selected Anatomical Landmarks
,”
Comput. Methods Biomech. Biomed. Eng.
,
18
(
6
), pp.
676
688
.
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