Soft tissue structures of the L4-L5 level of the human lumbar spine are represented in finite-element (FE) models, which are used to evaluate spine biomechanics and implant performance. These models typically use average properties; however, experimental testing reports variation up to 40% in ligament stiffness and even greater variability for annulus fibrosis (AF) properties. Probabilistic approaches enable consideration of the impact of intersubject variability on model outputs. However, there are challenges in directly applying the variability in measured load–displacement response of structures to a finite-element model. Accordingly, the objectives of this study were to perform a comprehensive review of the properties of the L4-L5 structures and to develop a probabilistic representation to characterize variability in the stiffness of spinal ligaments and parameters of a Holzapfel–Gasser–Ogden constitutive material model of the disk. The probabilistic representation was determined based on direct mechanical test data as found in the literature. Monte Carlo simulations were used to determine the uncertainty of the Holzapfel–Gasser–Ogden constitutive model. A single stiffness parameter was defined to characterize each ligament, with the anterior longitudinal ligament (ALL) being the stiffest, while the posterior longitudinal ligament and interspinous ligament (ISL) had the greatest variation. The posterior portion of the annulus fibrosis had the greatest stiffness and greatest variation up to 300% in circumferential loading. The resulting probabilistic representation can be utilized to include intersubject variability in biomechanics evaluations.

References

References
1.
Guan
,
Y.
,
Yoganandan
,
N.
,
Zhang
,
J.
,
Pintar
,
F.
,
Cusick
,
J.
,
Wolfla
,
C.
, and
Maiman
,
J.
,
2006
, “
Validation of a Clinical Finite Element Model of the Human Lumbosacral Spine
,”
Med. Biol. Eng. Comput.
,
44
(
8
), pp.
633
641
.
2.
Schmidt
,
H.
,
Kettler
,
A.
,
Heuer
,
F.
,
Simon
,
U.
,
Claes
,
L.
, and
Wilke
,
H.
,
2007
, “
Intradiscal Pressure, Shear Strain, and Fiber Strain in the Intervertebral Disc Under Combined Loading
,”
Spine
,
32
(
7
), pp.
748
755
.
3.
Wong
,
C.
,
Gehrchen
,
P.
,
Darvann
,
T.
, and
Kaer
,
T.
,
2003
, “
Nonlinear Finite-Element Analysis and Biomechanical Evaluation of the Lumbar Spine
,”
IEEE Trans. Med. Imaging
,
22
(
6
), pp.
742
746
.
4.
Eberlein
,
R.
,
Holzapfel
,
G.
, and
Frohlich
,
M.
,
2004
, “
Multi-Segment FEA of the Human Lumbar Spine Including the Heterogeneity of the Annulus Fibrosus
,”
Comput. Mech.
,
34
(
2
), pp.
147
163
.
5.
Ayturk
,
U.
, and
Puttlitz
,
C.
,
2011
, “
Parametric Convergence Sensitivity and Validation of a Finite Element Model
,”
Comput. Methods Biomech. Biomed. Eng.
,
14
(
8
), pp.
695
705
.
6.
Ezquerro
,
F.
,
Vacas
,
G.
,
Postigo
,
S.
,
Prado
,
M.
, and
Simon
,
A.
,
2011
, “
Calibration of the Finite Element Model of a Lumbar Functional Spinal Unit Using an Optimization Technique Based on Differential Evolution
,”
Med. Eng. Phys.
,
33
(
1
), pp.
89
95
.
7.
Dooris
,
A.
,
Goel
,
V.
,
Grosland
,
N.
,
Gilbertson
,
L.
, and
Wilder
,
D.
,
2001
, “
Load-Sharing Between Anterior and Posterior Elements in a Lumbar Motion Segment Implanted With an Artificial Disc
,”
Spine
,
26
(
6
), pp.
E122
E129
.
8.
Rohlmann
,
A.
,
Zander
,
T.
, and
Bergmann
,
G.
,
2005
, “
Effect of Total Disc Replacement With ProDisc on Intersegmental Rotation of the Lumber Spine
,”
Spine
,
30
(
7
), pp.
738
743
.
9.
Chiang
,
M.
,
Zhong
,
Z.
,
Chen
,
C.
,
Cheng
,
C.
, and
Shih
,
S.
,
2006
, “
Biomechanical Comparison of Instrumented Posterior Lumbar Interbody Fusion With One or Two Cages by Finite Element Analysis
,”
Spine
,
31
(
19
), pp.
E682
E689
.
10.
Bono
,
C.
,
Khandha
,
A.
,
Vadapalli
,
S.
,
Holekamp
,
S.
,
Goel
,
V.
, and
Garfin
,
S. R.
,
2007
, “
Residual Sagittal Motion After Lumbar Fusion: A Finite Element Analysis With Implications on Radiographic Flexion-Extension Criteria
,”
Spine
,
32
(
4
), pp.
417
422
.
11.
Xiao
,
Z.
,
Wang
,
L.
,
Gong
,
H.
, and
Zhu
,
D.
,
2012
, “
Biomechanical Evaluation of Three Surgical Scenarios of Posterior Lumbar Interbody Fusion by Finite Element Analysis
,”
Biomed. Eng. Online
,
11
(
31
) (Published online).
12.
Bowden
,
A.
,
Guerin
,
H.
,
Villarraga
,
M.
,
Patwardhan
,
A.
, and
Ochao
,
J.
,
2008
, “
Quality of Motion Considerations in Numerical Analysis of Motion Restoring Implants of the Spine
,”
Clin. Biomech.
,
23
(
5
), pp.
536
544
.
13.
Lee
,
K. K.
, and
Teo
,
E. C.
,
2005
, “
Material Sensitivity Study on Lumbar Motion Segment (L2-L3) Under Sagittal Plane Loadings Using Probabilistic Method
,”
J. Spinal Disord. Tech.
,
18
(
2
), pp.
163
170
.
14.
Barnes
,
K.
,
Armstrong
,
J.
,
Agarwala
,
A.
, and
Petrella
,
A.
,
2011
, “
Probabilistic Study of a Lumbar Motion Segment: Sensitivity to Material and Anatomic Variability
,”
ASME
Paper No. SBC2011-53846.
15.
Rohlmann
,
A.
,
Boustani
,
H.
,
Bergmann
,
G.
, and
Zander
,
T.
,
2010
, “
A Probabilistic Finite Element Analysis of the Stresses in the Augmented Vertebral Body After Vertebroplasty
,”
Eur. Spine J.
,
19
(
9
), pp.
1585
1595
.
16.
Ahmad
,
Z.
,
Ariffin
,
A. K.
, and
Akramin
,
M. R. M.
,
2010
, “
Probabilistic Stress Analysis of the Human Lumbar Spine Extended Finite Element Method
,”
The 14th Asia Pacific Regional Meeting of International Foundation for Production Research
, Melaka, Malaysia, Dec. 7–10.
17.
Zulkifli
,
A.
,
Ariffin
,
A. K.
,
Ismail
,
A. E.
,
Daud
,
R.
, and
Akramin
,
M. R. M.
,
2011
, “
Stress and Probabilistic Study of the Lumbar Vertebra Under Compression Loading
,”
Appl. Mech. Mater.
,
52–54
, pp.
1394
1399
.
18.
Rohlmann
,
A.
,
Mann
,
A.
,
Zander
,
T.
, and
Bergmann
,
G.
,
2009
, “
Effect of an Artificial Disc on Lumbar Spine Biomechanics: A Probabilistic Finite Element Study
,”
Eur. Spine J.
,
18
(
1
), pp.
89
97
.
19.
Baldwin
,
M.
,
Laz
,
P.
,
Stowe
,
J.
, and
Rullkoetter
,
P.
,
2009
, “
Efficient Probabilistic Representation of Tibiofemoral Soft Tissue Constraint
,”
Comput. Methods Biomech. Biomed. Eng.
,
12
(
6
), pp.
651
659
.
20.
Neumann
,
P.
,
Keller
,
T. S.
,
Ekstrom
,
L.
,
Perry
,
L.
,
Hansson
,
T. H.
, and
Spengler
,
M.
,
1992
, “
Mechanical Properties of the Human Lumbar Anterior Longitudinal Ligament
,”
J. Biomech.
,
25
(
10
), pp.
1185
1194
.
21.
Pintar
,
F. A.
,
Yoganandan
,
N.
,
Myers
,
T.
,
Elhagediab
,
A.
, and
Sances
,
A.
, Jr.
,
1992
, “
Biomechanical Properties of Human Lumbar Spine Ligaments
,”
J. Biomech.
,
25
(
11
), pp.
1351
1356
.
22.
Chazal
,
J.
,
Tanguy
,
M.
,
Bourges
,
M.
,
Gaurel
,
G.
,
Escande
,
G.
,
Guilot
,
M.
, and
Vanneuville
,
G.
,
1985
, “
Biomechanical Properties of Spinal Ligaments and a Histological Study of the Supraspinal Ligament in Traction
,”
J. Biomech.
,
18
(
3
), pp.
167
176
.
23.
White
,
A.
, and
Panjabi
,
M.
,
1990
,
Clinical Biomechanics of the Spine
,
Lippincott Williams & Wilkins
,
Philadelphia, PA
.
24.
Iida
,
T.
,
Abumi
,
K.
,
Kotani
,
Y.
, and
Kaneda
,
K.
,
2002
, “
Effects of Aging and Spinal Degeneration on Mechanical Properties of Lumbar Supraspinous and Interspinous Ligaments
,”
Spine J.
,
2
(
2
), pp.
95
100
.
25.
Robertson
,
D.
,
Willardson
,
R.
,
Parajuli
,
D.
,
Cannon
,
A.
, and
Anton
,
E.
,
2013
, “
The Lumbar Supraspinous Ligament Demonstrates Increased Material Stiffness and Strength on Its Ventral Aspect
,”
J. Mech. Behav. Biomed. Mater.
,
17
, pp.
34
43
.
26.
Fujita
,
Y.
,
Duncan
,
N.
, and
Lotz
,
J.
,
1997
, “
Radial Tensile Properties of the Lumbar Annulus Fibrosis Are Site and Degeneration Dependent
,”
J. Orthop. Res.
,
15
(
6
), pp.
814
819
.
27.
Guerin
,
H.
, and
Elliott
,
D.
,
2006
, “
Degeneration Affects the Fiber Reorientation of Human Annulus Fibrosus Under Tensile Load
,”
J. Biomech.
,
39
(
8
), pp.
1410
1418
.
28.
O'Connell
,
G.
,
Guerin
,
H.
, and
Elliott
,
D.
,
2009
, “
Theoretical and Uniaxial Experimental Evaluations of Human Annulus Fibrosis Degeneration
,”
ASME J. Biomech. Eng.
,
131
(
11
), p.
111007
.
29.
Wagner
,
D.
, and
Lotz
,
J.
,
2004
, “
Theoretical Model and Experimental Results for the Nonlinear Elastic Behavior of Human Annulus Fibrosus
,”
J. Orthop. Res.
,
22
(
4
), pp.
901
909
.
30.
Ebara
,
S.
,
Iatridis
,
J.
,
Setton
,
L.
,
Foster
,
R.
,
Mow
,
V.
, and
Weidenbaum
,
M.
,
1996
, “
Tensile Properties of Nondegenerate Human Lumbar Anulus Fibrosis
,”
Spine
,
21
(
4
), pp.
452
461
.
31.
Holzapfel
,
G. A.
,
Schulze-Bauer
,
C. A.
,
Feigl
,
G.
, and
Regitnig
,
P.
,
2005
, “
Single Lamellar Mechanics of the Human Lumbar Anulus Fibrosus
,”
Biomech. Model. Mechanobiol.
,
3
(
3
), pp.
125
140
.
32.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Ogden
,
R. W.
,
2000
, “
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,”
J. Elasticity
,
61
(
1
), pp.
1
48
.
33.
Gasser
,
T. C.
,
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
,
2006
, “
Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations
,”
J. R. Soc. Interface
,
3
(
6
), pp.
15
35
.
34.
Coombs
,
D. J.
,
Bushelow
,
M.
,
Laz
,
P. J.
,
Rao
,
M.
, and
Rullkoetter
,
P. J.
,
2013
, “
Stepwise Validated Finite Element Model of the Human Lumbar Spine
,”
ASME
Paper No. FMD2013-16167.
35.
Shahraki
,
N. M.
,
Fateme
,
A.
,
Goel
,
V. K.
, and
Agarwal
,
A.
,
2015
, “
On the Use of Biaxial Properties in Modeling Annulus as a Holzapfel-Gasser-Ogden Material
,”
Front. Bioeng. Biotechnol.
,
3
, p.
69
.
36.
Simulia Dassault Systemes
,
2012
, “
Hyperelastic Behavior of Rubberlike Materials: abaqus Users Guide (Release 6.12)
,” Simulia Dassault Systemes, Vélizy-Villacoublay Cedex - France, Chap. 22.5.1.
37.
Rohlmann
,
A.
,
Zander
,
T.
,
Schmidt
,
H.
,
Wilke
,
H.
, and
Bergmann
,
G.
,
2006
, “
Analysis of the Influence of Disc Degeneration on the Mechanical Behaviour of a Lumbar Motion Segment Using the Finite Element Method
,”
J. Biomech.
,
39
(
13
), pp.
2484
2490
.
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