The annulus fibrosus (AF) of the intervertebral disc (IVD) consists of a set of concentric layers composed of a primary circumferential collagen fibers arranged in an alternating oblique orientation. Moreover, there exists an additional secondary set of radial translamellar collagen fibers which connects the concentric layers, creating an interconnected fiber network. The aim of this study was to investigate the mechanical role of the radial fiber network. Toward that goal, a three-dimensional (3D) finite element model of the L3–L4 spinal segment was generated and calibrated to axial compression and pure moment loading. The AF model explicitly recognizes the two heterogeneous networks of fibers. The presence of radial fibers demonstrated a pronounced effect on the local disc responses under lateral bending, flexion, and extension modes. In these modes, the radial fibers were in a tensile state in the disc region that subjected to compression. In addition, the circumferential fibers, on the opposite side of the IVD, were also under tension. The local stress in the matrix was decreased in up to 9% in the radial fibers presence. This implies an active fiber network acting collectively to reduce the stresses and strains in the AF lamellae. Moreover, a reduction of 26.6% in the matrix sideways expansion was seen in the presence of the radial fibers near the neutral bending axis of the disc. The proposed biomechanical model provided a new insight into the mechanical role of the radial collagen fibers in the AF structure. This model can assist in the design of future IVD substitutes.

References

References
1.
Wade
,
K. R.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2011
, “
A Fresh Look at the Nucleus-Endplate Region: New Evidence for Significant Structural Integration
,”
Eur. Spine J.
,
20
(
8
), pp.
1225
1232
.
2.
Bogduk
,
N.
,
2005
,
Clinical Anatomy of the Lumbar Spine and Sacrum
,
4th ed.
,
Elsevier, Amsterdam
,
The Netherlands
.
3.
Rodrigues
,
S. A.
,
Wade
,
K. R.
,
Thambyah
,
A.
, and
Broom
,
N. D.
,
2012
, “
Micromechanics of Annulus-End Plate Integration in the Intervertebral Disc
,”
Spine J.
,
12
(
2
), pp.
143
150
.
4.
Marchand
,
F.
, and
Ahmed
,
A. M.
,
1990
, “
Investigation of the Laminate Structure of Lumbar Disc Anulus Fibrosus
,”
Spine
,
15
(
5
), pp.
402
410
.
5.
Holzapfel
,
G. A.
,
Schulze-Bauer
,
C.
,
Feigl
,
G.
, and
Regitnig
,
P.
,
2005
, “
Single Lamellar Mechanics of the Human Lumbar Anulus Fibrosus
,”
Biomech. Model. Mechanobiol.
,
3
(
3
), pp.
125
140
.
6.
Schollum
,
M. L.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2010
, “
How Age Influences Unravelling Morphology of Annular Lamellae—A Study of Interfibre Cohesivity in the Lumbar Disc
,”
J. Anat.
,
216
(
3
), pp.
310
319
.
7.
Schollum
,
M. L.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2009
, “
A Microstructural Investigation of Intervertebral Disc Lamellar Connectivity: Detailed Analysis of the Translamellar Bridges
,”
J. Anat.
,
214
(
6
), pp.
805
816
.
8.
Schollum
,
M. L.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2008
, “
ISSLS Prize Winner: Microstructure and Mechanical Disruption of the Lumbar Disc Annulus—Part I: A Microscopic Investigation of the Translamellar Bridging Network
,”
Spine
,
33
(
25
), pp.
2702
2710
.
9.
Han
,
S. K.
,
Chen
,
C. W.
,
Wierwille
,
J.
,
Chen
,
Y.
, and
Hsieh
,
A. H.
,
2015
, “
Three Dimensional Mesoscale Analysis of Translamellar Cross‐Bridge Morphologies in the Annulus Fibrosus Using Optical Coherence Tomography
,”
J. Orthop. Res.
,
33
(
3
), pp.
304
311
.
10.
Smith
,
L. J.
, and
Elliott
,
D. M.
,
2011
, “
Formation of Lamellar Cross Bridges in the Annulus Fibrosus of the Intervertebral Disc Is a Consequence of Vascular Regression
,”
Matrix Biol.
,
30
(
4
), pp.
267
274
.
11.
Pezowicz
,
C. A.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2006
, “
The Structural Basis of Interlamellar Cohesion in the Intervertebral Disc Wall
,”
J. Anat.
,
208
(
3
), pp.
317
330
.
12.
Yu
,
J.
,
Tirlapur
,
U.
,
Fairbank
,
J.
,
Handford
,
P.
,
Roberts
,
S.
,
Winlove
,
C. P.
,
Cui
,
Z.
, and
Urban
,
J.
,
2007
, “
Microfibrils, Elastin Fibres and Collagen Fibres in the Human Intervertebral Disc and Bovine Tail Disc
,”
J. Anat.
,
210
(
4
), pp.
460
471
.
13.
Yu
,
J.
,
Peter
,
C.
,
Roberts
,
S.
, and
Urban
,
J. P.
,
2002
, “
Elastic Fibre Organization in the Intervertebral Discs of the Bovine Tail
,”
J. Anat.
,
201
(
6
), pp.
465
475
.
14.
Melrose
,
J.
,
Smith
,
S. M.
,
Appleyard
,
R. C.
, and
Little
,
C. B.
,
2008
, “
Aggrecan, Versican and Type VI Collagen Are Components of Annular Translamellar Crossbridges in the Intervertebral Disc
,”
Eur. Spine J.
,
17
(
2
), pp.
314
324
.
15.
Tavakoli
,
J.
,
Elliott
,
D. M.
, and
Costi
,
J. J.
,
2016
, “
The Structure and Mechanical Function of the Inter-Lamellar Matrix of the Annulus Fibrosus in the Disc
,”
J. Orthop. Res.
,
34
(
8
), pp.
1307
1315
.
16.
Tavakoli
,
J.
, and
Costi
,
J. J.
,
2018
, “
New Insights Into the Viscoelastic and Failure Mechanical Properties of the Elastic Fiber Network of the Inter-Lamellar Matrix in the Annulus Fibrosus of the Disc
,”
Acta Biomater.
,
77
, pp. 292–300.
17.
Tavakoli
,
J.
,
Elliott
,
D. M.
, and
Costi
,
J. J.
,
2017
, “
The Ultra-Structural Organization of the Elastic Network in the Intra- and Inter-Lamellar Matrix of the Intervertebral Disc
,”
Acta Biomater.
,
58
, pp.
269
277
.
18.
Yu
,
J.
,
Schollum
,
M. L.
,
Wade
,
K. R.
,
Broom
,
N. D.
, and
Urban
,
J. P.
,
2015
, “
ISSLS Prize Winner: A Detailed Examination of the Elastic Network Leads to a New Understanding of Annulus Fibrosus Organization
,”
Spine
,
40
, pp.
1149
1157
.
19.
Vernon-Roberts
,
B.
,
Fazzalari
,
N. L.
, and
Manthey
,
B. A.
,
1997
, “
Pathogenesis of Tears of the Anulus Investigated by Multiple‐Level Transaxial Analysis of the T12‐L1 Disc
,”
Spine
,
22
(
22
), pp.
2641
2646
.
20.
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
674
.
21.
Schmidt
,
H.
,
Kettler
,
A.
,
Rohlmann
,
A.
,
Claes
,
L.
, and
Wilke
,
H.-J.
,
2007
, “
The Risk of Disc Prolapses With Complex Loading in Different Degrees of Disc Degeneration—A Finite Element Analysis
,”
Clin. Biomech.
,
22
(
9
), pp.
988
998
.
22.
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
.
23.
Dreischarf
,
M.
,
Zander
,
T.
,
Shirazi-Adl
,
A.
,
Puttlitz
,
C.
,
Adam
,
C.
,
Chen
,
C.
,
Goel
,
V. K.
,
Kiapour
,
A.
,
Kim
,
Y. H.
,
Labus
,
K. M.
,
Little
,
J. P.
,
Park
,
W. M.
,
Wang
,
Y. H.
,
Wilke
,
H.-J.
,
Rohlmann
,
A.
, and
Schmidt
,
H.
,
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
.
24.
Moramarco
,
V.
,
del Palomar
,
A. P.
,
Pappalettere
,
C.
, and
Doblaré
,
M.
,
2010
, “
An Accurate Validation of a Computational Model of a Human Lumbosacral Segment
,”
J. Biomech.
,
43
(
2
), pp.
334
342
.
25.
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
.
26.
Peng
,
X.
,
Guo
,
Z.
, and
Moran
,
B.
,
2006
, “
An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus
,”
ASME J. Appl. Mech.
,
73
(
5
), pp.
815
824
.
27.
Caner
,
F. C.
,
Guo
,
Z.
,
Moran
,
B.
,
Bažant
,
Z. P.
, and
Carol
,
I.
,
2007
, “
Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus
,”
ASME J. Biomech. Eng.
,
129
(
5
), pp.
632
641
.
28.
Hollingsworth
,
N. T.
, and
Wagner
,
D. R.
,
2011
, “
Modeling Shear Behavior of the Annulus Fibrosus
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
7
), pp.
1103
1114
.
29.
Reutlinger
,
C.
,
Bürki
,
A.
,
Brandejsky
,
V.
,
Ebert
,
L.
, and
Büchler
,
P.
,
2014
, “
Specimen Specific Parameter Identification of Ovine Lumbar Intervertebral Discs: On the Influence of Fibre–Matrix and Fibre–Fibre Shear Interactions
,”
J. Mech. Behav. Biomed. Mater.
,
30
, pp.
279
289
.
30.
Eberlein
,
R.
,
Holzapfel
,
G. A.
, and
Schulze-Bauer
,
C. A.
,
2001
, “
An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies
,”
Comput. Methods Biomech. Biomed. Eng.
,
4
, pp.
209
229
.
31.
Shirazi-Adl
,
S. A.
,
Shrivastava
,
S. C.
, and
Ahmed
,
A. M.
,
1984
, “
Stress Analysis of the Lumbar Disc-Body Unit in Compression. A Three-Dimensional Nonlinear Finite Element Study
,”
Spine
,
9
(
2
), p.
120
.
32.
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
.
33.
Mengoni
,
M.
,
Luxmoore
,
B. J.
,
Wijayathunga
,
V. N.
,
Jones
,
A. C.
,
Broom
,
N. D.
, and
Wilcox
,
R. K.
,
2015
, “
Derivation of Inter-Lamellar Behaviour of the Intervertebral Disc Annulus
,”
J. Mech. Behav. Biomed. Mater.
,
48
, pp.
164
172
.
34.
Labus
,
K. M.
,
Han
,
S. K.
,
Hsieh
,
A. H.
, and
Puttlitz
,
C. M.
,
2014
, “
A Computational Model to Describe the Regional Interlamellar Shear of the Annulus Fibrosus
,”
ASME J. Biomech. Eng.
,
136
(
5
), p.
051009
.
35.
Luxmoore
,
B.
,
Wijayathunga
,
V.
,
Rehman
,
S.
,
Wade
,
K.
,
Rodrigues
,
S.
,
Broom
,
N.
, and
Wilcox
,
R. K.
,
2012
, “
Investigating the Mechanical Role of Cross-Bridging in the Annulus Fibrosus Using Finite Element Analysis
,”
58th Annual Meeting of Orthopaedic Research Society, San Francisco, CA
, p.
2164
.
36.
Luxmoore
,
B. J.
,
2013
,
Computational Simulation of the Intervertebral Disc
,
The University of Leeds
,
Leeds, UK
.
37.
Mengoni
,
M.
,
Wijayathunga
,
V. N.
,
Jones
,
A. C.
, and
Wilcox
,
R. K.
,
2013
, “
Structural Modelling of the Annulus Fibrosus-an Anisotropic Hyperelastic Model Approach at the Lamellar Level
,”
Third International Conference on Mathematical and Computational Biomedical Engineering
(
CMBE
), Hong Kong, China, Dec. 16–18.https://www.researchgate.net/publication/260122074_Structural_modelling_of_the_annulus_fibrosus_-_an_anisotropic_hyperelastic_model_approach_at_the_lamellar_level
38.
Yusupov
,
R.
,
2011
,
Nonlinear Finite Element Analysis for Normal and Pathological Mechanical Behavior of the Lumbar Spine
,
Tel Aviv University
,
Tel-Aviv, Israel
.
39.
Platzer
,
W.
,
2009
,
Color Atlas of Human Anatomy: Locomotor System
,
6th ed.
,
Theime
,
New York
.
40.
Schünke
,
M.
,
Schulte
,
E.
, and
Schumacher
,
U.
,
2006
,
General Anatomy and Musculoskeletal System (THIEME Atlas of Anatomy)
,
1st ed.
,
Thieme Medical Pblishers
,
New York
, pp.
100
142
.
41.
White
,
A. A.
, and
Panjabi
,
M. M.
,
1990
,
Clinical Biomechanics of the Spine
,
Lippincott
,
Philadelphia, PA
.
42.
Clemente
,
C. D.
,
1997
,
Anatomy: A Regional Atlas of the Human Body
,
4th ed.
,
Williams & Wilkins
,
Baltimore, MA
, p.
132
.
43.
Jaumard
,
N. V.
,
Welch
,
W. C.
, and
Winkelstein
,
B. A.
,
2011
, “
Spinal Facet Joint Biomechanics and Mechanotransduction in Normal, Injury and Degenerative Conditions
,”
ASME J. Biomech. Eng.
,
133
(
7
), p.
071010
.
44.
Goto
,
K.
,
Tajima
,
N.
,
Chosa
,
E.
,
Totoribe
,
K.
,
Kuroki
,
H.
,
Arizumi
,
Y.
, and
Arai
,
T.
,
2002
, “
Mechanical Analysis of the Lumbar Vertebrae in a Three-Dimensional Finite Element Method Model in Which Intradiscal Pressure in the Nucleus Pulposus Was Used to Establish the Model
,”
J. Orthop. Sci.
,
7
(
2
), pp.
243
246
.
45.
Humzah
,
M.
, and
Soames
,
R.
,
1988
, “
Human Intervertebral Disc: Structure and Function
,”
Anat. Rec.
,
220
(
4
), pp.
337
356
.
46.
Wade
,
K. R.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2012
, “
On the Extent and Nature of Nucleus-Annulus Integration
,”
Spine
,
37
(
21
), pp.
1826
1833
.
47.
Taylor
,
T.
,
Ghosh
,
P.
, and
Bushell
,
G.
,
1981
, “
The Contribution of the Intervertebral Disc to the Scoliotic Deformity
,”
Clin. Orthop. Relat. Res.
,
156
, pp.
79
90
.
48.
Tsuji
,
H.
,
Hirano
,
N.
,
Ohshima
,
H.
,
Ishihara
,
H.
,
Terahata
,
N.
, and
Motoe
,
T.
,
1993
, “
Structural Variation of the Anterior and Posterior Anulus Fibrosus in the Development of Human Lumbar Intervertebral Disc—A Risk Factor for Intervertebral Disc Rupture
,”
Spine
,
18
(
2
), pp.
204
210
.
49.
Baek
,
G. H.
,
Carlin
,
G. J.
,
Vogrin
,
T. M.
,
Woo
,
S. L.
, and
Harner
,
C. D.
,
1998
, “
Quantitative Analysis of Collagen Fibrils of Human Cruciate and Meniscofemoral Ligaments
,”
Clin. Orthop. Relat. Res.
,
357
, pp.
205
211
.
50.
Han
,
W. M.
,
Nerurkar
,
N. L.
,
Smith
,
L. J.
,
Jacobs
,
N. T.
,
Mauck
,
R. L.
, and
Elliott
,
D. M.
,
2012
, “
Multi-Scale Structural and Tensile Mechanical Response of Annulus Fibrosus to Osmotic Loading
,”
Ann. Biomed. Eng.
,
40
(
7
), pp.
1610
1621
.
51.
Sharabi
,
M.
,
Wade
,
K. R.
,
Galbusera
,
F.
,
Rasche
,
V.
,
Haj-Ali
,
R.
, and
Wilke
,
H.-J.
,
2018
, “
Three-Dimensional Microstructural Reconstruction of the Ovine Intervertebral Disc Using Ultra-High Field MRI
,”
Spine J.
(in press).
52.
Lu
,
Y. M.
,
Hutton
,
W. C.
, and
Gharpuray
,
V. M.
,
1996
, “
Do Bending, Twisting, and Diurnal Fluid Changes in the Disc Affect the Propensity to Prolapse? A Viscoelastic Finite Element Model
,”
Spine
,
21
(
22
), pp.
2570
2579
.
53.
Goel
,
V. K.
,
Kong
,
W.
,
Han
,
J. S.
,
Weinstein
,
J. N.
, and
Gilbertson
,
L. G.
,
1993
, “
A Combined Finite Element and Optimization Investigation of Lumbar Spine Mechanics With and Without Muscles
,”
Spine
,
18
(
11
), p.
1531
.
54.
Totoribe
,
K.
,
Tajima
,
N.
, and
Chosa
,
E.
,
1999
, “
A Biomechanical Study of Posterolateral Lumbar Fusion Using a Three-Dimensional Nonlinear Finite Element Method
,”
J. Orthop. Sci.
,
4
(
2
), pp.
115
126
.
55.
Wu
,
H.-C.
, and
Yao
,
R.-F.
,
1976
, “
Mechanical Behavior of the Human Annulus Fibrosus
,”
J. Biomech.
,
9
(
1
), pp.
1
7
.
56.
Shirazi-Adl
,
A.
,
Ahmed
,
A.
, and
Shrivastava
,
S.
,
1986
, “
A Finite Element Study of a Lumbar Motion Segment Subjected to Pure Sagittal Plane Moments
,”
J. Biomech.
,
19
(
4
), pp.
331
350
.
57.
Chen
,
C.-S.
,
Cheng
,
C.-K.
,
Liu
,
C.-L.
, and
Lo
,
W.-H.
,
2001
, “
Stress Analysis of the Disc Adjacent to Interbody Fusion in Lumbar Spine
,”
Med. Eng. Phys.
,
23
(
7
), pp.
485
493
.
58.
Chazal
,
J.
,
Tanguy
,
A.
,
Bourges
,
M.
,
Gaurel
,
G.
,
Escande
,
G.
,
Guillot
,
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
.
59.
Wu
,
J.
, and
Chen
,
J.
,
1996
, “
Clarification of the Mechanical Behaviour of Spinal Motion Segments Through a Three-Dimensional Poroelastic Mixed Finite Element Model
,”
Med. Eng. Phys.
,
18
(
3
), pp.
215
224
.
60.
Panjabi
,
M. M.
,
Oxland
,
T.
,
Yamamoto
,
I.
, and
Crisco
,
J.
,
1994
, “
Mechanical Behavior of the Human Lumbar and Lumbosacral Spine as Shown by Three-Dimensional Load-Displacement Curves
,”
J. Bone Jt. Surg.
,
76
(
3
), pp.
413
424
.
61.
Yamamoto
,
I.
,
Panjabi
,
M. M.
,
Crisco
,
T.
, and
Oxland
,
T.
,
1989
, “
Three-Dimensional Movements of the Whole Lumbar Spine and Lumbosacral Joint
,”
Spine
,
14
(
11
), p.
1256
.
62.
Guan
,
Y.
,
Yoganandan
,
N.
,
Moore
,
J.
,
Pintar
,
F. A.
,
Zhang
,
J.
,
Maiman
,
D. J.
, and
Laud
,
P.
,
2007
, “
Moment–Rotation Responses of the Human Lumbosacral Spinal Column
,”
J. Biomech.
,
40
(
9
), pp.
1975
1980
.
63.
Markolf
,
K. L.
, and
Morris
,
J. M.
,
1974
, “
The Structural Components of the Intervertebral Disc
,”
J. Bone Jt. Surg. Am.
,
56
(
4
), pp.
675
687
.
64.
Brinckmann
,
P.
, and
Grootenboer
,
H.
,
1991
, “
Change of Disc Height, Radial Disc Bulge, and Intradiscal Pressure From Discectomy An In Vivo Investigation on Human Lumbar Discs
,”
Spine
,
16
(
6
), pp.
641
646
.
65.
Vergari
,
C.
,
Mansfield
,
J.
,
Meakin
,
J. R.
, and
Winlove
,
P. C.
,
2016
, “
Lamellar and Fibre Bundle Mechanics of the Annulus Fibrosus in Bovine Intervertebral Disc
,”
Acta Biomater.
,
37
, pp.
14
20
.
66.
Michalek
,
A. J.
,
Buckley
,
M. R.
,
Bonassar
,
L. J.
,
Cohen
,
I.
, and
Iatridis
,
J. C.
,
2009
, “
Measurement of Local Strains in Intervertebral Disc Anulus Fibrosus Tissue Under Dynamic Shear: Contributions of Matrix Fiber Orientation and Elastin Content
,”
J. Biomech.
,
42
(
14
), pp.
2279
2285
.
67.
Gregory
,
D. E.
,
Veldhuis
,
J. H.
,
Horst
,
C.
,
Brodland
,
G. W.
, and
Callaghan
,
J. P.
,
2011
, “
Novel Lap Test Determines the Mechanics of Delamination Between Annular Lamellae of the Intervertebral Disc
,”
J. Biomech.
,
44
(
1
), pp.
97
102
.
68.
Cassidy
,
J.
,
Hiltner
,
A.
, and
Baer
,
E.
,
1989
, “
Hierarchical Structure of the Intervertebral Disc
,”
Connect. Tissue Res.
,
23
(
1
), pp.
75
88
.
69.
Yang
,
B.
, and
O'Connell
,
G. D.
,
2017
, “
Effect of Collagen Fibre Orientation on Intervertebral Disc Torsion Mechanics
,”
Biomech. Model. Mechanobiol.
,
16
(
6
), pp.
2005
2015
.
70.
Eyre
,
D. R.
, and
Muir
,
H.
,
1976
, “
Types I and II Collagens in Intervertebral Disc. Interchanging Radial Distributions in Annulus Fibrosus
,”
Biochem. J.
,
157
(
1
), pp.
267
270
.
71.
Sharabi
,
M.
,
Wade
,
K.
, and
Haj-Ali
,
R.
,
2018
, “
The Mechanical Role of Collagen Fibers in the Intervertebral Disc
,”
Biomechanics of the Spine
,
Elsevier
,
Amsterdam, The Netherlands
, pp.
105
123
.
72.
Pezowicz
,
C. A.
,
Robertson
,
P. A.
, and
Broom
,
N. D.
,
2005
, “
Intralamellar Relationships Within the Collagenous Architecture of the Annulus Fibrosus Imaged in Its Fully Hydrated State
,”
J. Anat.
,
207
(
4
), pp.
299
312
.
73.
Gelse
,
K.
,
Pöschl
,
E.
, and
Aigner
,
T.
,
2003
, “
Collagens—Structure, Function, and Biosynthesis
,”
Adv. Drug Delivery Rev.
,
55
(
12
), pp.
1531
1546
.
74.
Sun
,
S.
, and
Karsdal
,
M. A.
,
2016
,
Type VI Collagen. Biochemistry of Collagens, Laminins and Elastin
,
Elsevier
,
Amsterdam, The Netherlands
, Chap. 6, pp.
49
55
.
75.
Venkatraman
,
S.
,
Boey
,
F.
, and
Lao
,
L. L.
,
2008
, “
Implanted Cardiovascular Polymers: Natural, Synthetic and Bio-Inspired
,”
Prog. Polym. Sci.
,
33
(
9
), pp.
853
874
.
76.
Holzapfel
,
G. A.
,
2001
, “
Biomechanics of Soft Tissue
,”
The Handbook of Materials Behavior Models
, Vol.
3
,
Elsevier
,
Amsterdam, The Netherlands
, pp.
1049
1063
.
77.
Gracovetsky
,
S.
, and
Farfan
,
H.
,
1986
, “
The Optimum Spine
,”
Spine
,
11
(
6
), pp.
543
–5
73
.
78.
Mueller
,
M. J.
, and
Maluf
,
K. S.
,
2002
, “
Tissue Adaptation to Physical Stress: A Proposed ‘Physical Stress Theory’ to Guide Physical Therapist Practice, Education, and Research
,”
Phys. Ther.
,
82
(
4
), pp.
383
403
.
You do not currently have access to this content.