Abstract

Radial variation in water concentration from outer to inner lamellae is one of the characteristic features of annulus fibrosus (AF). In addition, water concentration changes are also associated with intervertebral disc (IVD) degeneration. Such changes alter the chemo-mechanical interactions among the biomolecular constituents at molecular level, affecting the load-bearing nature of IVD. This study investigates mechanistic impacts of water concentration on the collagen type I microfibrils in AF using molecular dynamics simulations. Results show, in axial tension, that increase in water concentration (WC) from 0% to 50% increases the elastic modulus from 2.7 GPa to 3.9 GPa. This is attributed to combination of shift in deformation from backbone straightening to combined backbone stretching– intermolecular sliding and subsequent strengthening of tropocollagen–water (TC-water-TC) interfaces through water bridges and intermolecular electrostatic attractions. Further increase in WC to 75% reduces the modulus to 1.8 GPa due to shift in deformation to polypeptide straightening and weakening of TC-water-TC interface due to reduced electrostatic attraction and increase in the number of water molecules in a water bridge. During axial compression, increase in WC to 50% results in increase in modulus from 0.8 GPa to 4.5 GPa. This is attributed to the combination of the development of hydrostatic pressure and strengthening of the TC-water-TC interface. Further increase in WC to 75% shifts load-bearing characteristic from collagen to water, resulting in a decrease in elastic modulus to 2.8 GPa. Such water-mediated alteration in load-bearing properties acts as foundations toward AF mechanics and provides insights toward understanding degeneration-mediated altered spinal stiffness.

References

1.
Raj
,
P. P.
,
2008
, “
Intervertebral Disc: Anatomy-Physiology-Pathophysiology-Treatment
,”
Pain Pract.
,
8
(
1
), pp.
18
44
.10.1111/j.1533-2500.2007.00171.x
2.
Cassidy
,
J. J.
,
Hiltner
,
A.
, and
Baer
,
E.
,
1989
, “
Hierarchical Structure of the Intervertebral Disc
,”
Connect. Tissue Res.
,
23
(
1
), pp.
75
88
.10.3109/03008208909103905
3.
Holzapfel
,
G. A.
,
Schulze-Bauer
,
C. A. J.
,
Feigl
,
G.
, and
Regitnig
,
P.
,
2005
, “
Single Lamellar Mechanics of the Human Lumbar Anulus Fibrosus
,”
Biomech. Model. Mechanobiol.
,
3
(
3
), pp.
125
140
.10.1007/s10237-004-0053-8
4.
Liang
,
T.
,
Che
,
Y. J.
,
Chen
,
X.
,
Li
,
H. T.
,
Yang
,
H. L.
, and
Luo
,
Z. P.
,
2019
, “
Nano and Micro Biomechanical Alterations of Annulus Fibrosus After In Situ Immobilization Revealed by Atomic Force Microscopy
,”
J. Orthop. Res.
,
37
(
1
), pp.
232
238
.10.1002/jor.24168
5.
Lees
,
S.
,
Pineri
,
M.
, and
Escoubes
,
M.
,
1984
, “
A Generalized Packing Model for Type I Collagen
,”
Int. J. Biol. Macromol.
,
6
(
3
), pp.
133
136
.10.1016/0141-8130(84)90053-9
6.
Petruska
,
J. A.
, and
Hodge
,
A. J.
,
1964
, “
A Subunit Model for the Tropocollagen Macromolecule
,”
Proc. Natl. Acad. Sci. U. S. A.
,
51
(
5
), pp.
871
876
.10.1073/pnas.51.5.871
7.
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
.10.1042/bj1570267
8.
Buckwalter
,
J. A.
, 1995,
1976
, “
Spine Update: Aging and Degeneration of the Human Intervertebral Disc
,”
Spine (Phila. Pa)
,
20
(
11
), pp.
1307
1314
.10.1097/00007632-199506000-00022
9.
Iatridis
,
J. C.
,
MacLean
,
J. J.
,
O'Brien
,
M.
, and
Stokes
,
I. A. F.
,
2007
, “
Measurements of Proteoglycan and Water Content Distribution in Human Lumbar Intervertebral Discs
,”
Spine (Phila. Pa. 1976)
,
32
(
14
), pp.
1493
1497
.10.1097/BRS.0b013e318067dd3f
10.
Antoniou
,
J.
,
Steffen
,
T.
,
Nelson
,
F.
,
Winterbottom
,
N.
,
Hollander
,
A. P.
,
Poole
,
R. A.
,
Aebi
,
M.
, and
Alini
,
M.
,
1996
, “
The Human Lumbar Intervertebral Disc: Evidence for Changes in the Biosynthesis and Denaturation of the Extracellular Matrix With Growth, Maturation, Ageing, and Degeneration
,”
J. Clin. Invest.
,
98
(
4
), pp.
996
1003
.10.1172/JCI118884
11.
Watanabe
,
A.
,
Benneker
,
L. M.
,
Boesch
,
C.
,
Watanabe
,
T.
,
Obata
,
T.
, and
Anderson
,
S. E.
,
2007
, “
Classification of Intervertebral Disk Degeneration With Axial T2 Mapping
,”
Am. J. Roentgenol.
,
189
(
4
), pp.
936
942
.10.2214/AJR.07.2142
12.
Ellingson
,
A. M.
,
Mehta
,
H.
,
Polly
,
D. W.
,
Ellermann
,
J.
, and
Nuckley
,
D. J.
,
2013
, “
Disc Degeneration Assessed by Quantitative T2* (T2 Star) Correlated With Functional Lumbar Mechanics
,”
Spine (Phila. Pa. 1976)
,
38
(
24
), pp.
E1533
E1540
.10.1097/BRS.0b013e3182a59453
13.
Ebara
,
S.
,
Iatridis
,
J. C.
,
Setton
,
L. A.
,
Foster
,
R. J.
,
Van Mow
,
C.
, and
Weidenbaum
,
M.
,
1996
, “
Tensile Properties of Nondegenerate Human Lumbar Anulus Fibrosus
,”
Spine (Phila. Pa. 1976)
,
21
(
4
), pp.
452
461
.10.1097/00007632-199602150-00009
14.
Pandit
,
P.
,
Talbott
,
J. F.
,
Pedoia
,
V.
,
Dillon
,
W.
, and
Majumdar
,
S.
,
2016
, “
T1ρ and T2-Based Characterization of Regional Variations in Intervertebral Discs to Detect Early Degenerative Changes
,”
J. Orthop. Res.
,
34
(
8
), pp.
1373
1381
.10.1002/jor.23311
15.
Werbner
,
B.
,
Spack
,
K.
, and
O'Connell
,
G. D.
,
2019
, “
Bovine Annulus Fibrosus Hydration Affects Rate-Dependent Failure Mechanics in Tension
,”
J. Biomech.
,
89
, pp.
34
39
.10.1016/j.jbiomech.2019.04.008
16.
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
.10.1007/s10439-012-0525-4
17.
O'Connell
,
G. D.
,
Sen
,
S.
, and
Elliott
,
D. M.
,
2012
, “
Human Annulus Fibrosus Material Properties From Biaxial Testing and Constitutive Modeling Are Altered With Degeneration
,”
Biomech. Model. Mechanobiol.
,
11
(
3–4
), pp.
493
503
.10.1007/s10237-011-0328-9
18.
Żak
,
M.
, and
Pezowicz
,
C.
,
2016
, “
Analysis of the Impact of the Course of Hydration on the Mechanical Properties of the Annulus Fibrosus of the Intervertebral Disc
,”
Eur. Spine J.
,
25
(
9
), pp.
2681
2690
.10.1007/s00586-016-4704-0
19.
Cortes
,
D. H.
, and
Elliott
,
D. M.
,
2012
, “
Extra-Fibrillar Matrix Mechanics of Annulus Fibrosus in Tension and Compression
,”
Biomech. Model. Mechanobiol.
,
11
(
6
), pp.
781
790
.10.1007/s10237-011-0351-x
20.
Chandran
,
P. L.
, and
Horkay
,
F.
,
2012
, “
Aggrecan, an Unusual Polyelectrolyte: Review of Solution Behavior and Physiological Implications
,”
Acta Biomater.
,
8
(
1
), pp.
3
12
.10.1016/j.actbio.2011.08.011
21.
Comper
,
W. D.
, and
Laurent
,
T. C.
,
1978
, “
Physiological Function of Connective Tissue Polysaccharides
,”
Physiol. Rev.
,
58
(
1
), pp.
255
315
.10.1152/physrev.1978.58.1.255
22.
Urban
,
J. P. G.
, and
Roberts
,
S.
,
1995
, “
Development and Degeneration of the Intervertebral Discs
,”
Mol. Med. Today
,
1
(
7
), pp.
329
335
.10.1016/S1357-4310(95)80032-8
23.
Adams
,
M. A.
, and
Roughley
,
P. J.
,
2006
, “
What is Intervertebral Disc Degeneration, and What Causes It?
,”
Spine (Phila. Pa. 1976)
,
31
(
18
), pp.
2151
2161
.10.1097/01.brs.0000231761.73859.2c
24.
Ashinsky
,
B. G.
,
Gullbrand
,
S. E.
,
Wang
,
C.
,
Bonnevie
,
E. D.
,
Han
,
L.
,
Mauck
,
R. L.
, and
Smith
,
H. E.
,
2020
, “
Degeneration Alters Structure-Function Relationships at Multiple Length-Scales and Across Interfaces in Human Intervertebral Discs
,”
J. Anat.
,
238
(
4
), pp.
986
998
.10.1111/joa.13349
25.
Antoniou
,
J.
,
Pike
,
G. B.
,
Steffen
,
T.
,
Baramki
,
H.
,
Poole
,
A. R.
,
Aebi
,
M.
, and
Alini
,
M.
,
1998
, “
Quantitative Magnetic Resonance Imaging in the Assessment of Degenerative Disc Disease
,”
Magn. Reson. Med.
,
40
(
6
), pp.
900
907
.10.1002/mrm.1910400616
26.
Trattnig
,
S.
,
Stelzeneder
,
D.
,
Goed
,
S.
,
Reissegger
,
M.
,
Mamisch
,
T. C.
,
Paternostro-Sluga
,
T.
,
Weber
,
M.
,
Szomolanyi
,
P.
, and
Welsch
,
G. H.
,
2010
, “
Lumbar Intervertebral Disc Abnormalities: Comparison of Quantitative T2 Mapping With Conventional MR at 3.0 T
,”
Eur. Radiol.
,
20
(
11
), pp.
2715
2722
.10.1007/s00330-010-1843-2
27.
Messner
,
A.
,
Stelzeneder
,
D.
,
Trattnig
,
S.
,
Welsch
,
G. H.
,
Schinhan
,
M.
,
Apprich
,
S.
,
Brix
,
M.
,
Windhager
,
R.
, and
Trattnig
,
S.
,
2017
, “
Does T2 Mapping of the Posterior Annulus Fibrosus Indicate the Presence of Lumbar Intervertebral Disc Herniation? A 3.0 Tesla Magnetic Resonance Study
,”
Eur. Spine J.
,
26
(
3
), pp.
877
883
.10.1007/s00586-016-4873-x
28.
Kettler
,
A.
,
Rohlmann
,
F.
,
Ring
,
C.
,
Mack
,
C.
, and
Wilke
,
H. J.
,
2011
, “
Do Early Stages of Lumbar Intervertebral Disc Degeneration Really Cause Instability? Evaluation of an In Vitro Database
,”
Eur. Spine J.
,
20
(
4
), pp.
578
584
.10.1007/s00586-010-1635-z
29.
Lee
,
S. H.
,
Daffner
,
S. D.
, and
Wang
,
J. C.
,
2014
, “
Does Lumbar Disk Degeneration Increase Segmental Mobility In Vivo?: Segmental Motion Analysis of the Whole Lumbar Spine Using Kinetic MRI
,”
J. Spinal Disord. Tech.
,
27
(
2
), pp.
111
116
.10.1097/BSD.0b013e3182a1ddef
30.
Zirbel
,
S. A.
,
Stolworthy
,
D. K.
,
Howell
,
L. L.
, and
Bowden
,
A. E.
,
2013
, “
Intervertebral Disc Degeneration Alters Lumbar Spine Segmental Stiffness in All Modes of Loading Under a Compressive Follower Load
,”
Spine J.
,
13
(
9
), pp.
1134
1147
.10.1016/j.spinee.2013.02.010
31.
Muriuki
,
M. G.
,
Havey
,
R. M.
,
Voronov
,
L. I.
,
Carandang
,
G.
,
Zindrick
,
M. R.
,
Lorenz
,
M. A.
,
Lomasney
,
L.
, and
Patwardhan
,
A. G.
,
2016
, “
Effects of Motion Segment Level, Pfirrmann Intervertebral Disc Degeneration Grade and Gender on Lumbar Spine Kinematics
,”
J. Orthop. Res.
,
34
(
8
), pp.
1389
1398
.10.1002/jor.23232
32.
Rohlmann
,
A.
,
Zander
,
T.
,
Schmidt
,
H.
,
Wilke
,
H. J.
, 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
.10.1016/j.jbiomech.2005.07.026
33.
Gautieri
,
A.
,
Pate
,
M. I.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Buehler
,
M. J.
,
2012
, “
Hydration and Distance Dependence of Intermolecular Shearing Between Collagen Molecules in a Model Microfibril
,”
J. Biomech.
,
45
(
12
), pp.
2079
2083
.10.1016/j.jbiomech.2012.05.047
34.
Zhang
,
D.
,
Chippada
,
U.
, and
Jordan
,
K.
,
2007
, “
Effect of the Structural Water on the Mechanical Properties of Collagen-Like Microfibrils: A Molecular Dynamics Study
,”
Ann. Biomed. Eng.
,
35
(
7
), pp.
1216
1230
.10.1007/s10439-007-9296-8
35.
Grant
,
C. A.
,
Brockwell
,
D. J.
,
Radford
,
S. E.
, and
Thomson
,
N. H.
,
2009
, “
Tuning the Elastic Modulus of Hydrated Collagen Fibrils
,”
Biophys. J.
,
97
(
11
), pp.
2985
2992
.10.1016/j.bpj.2009.09.010
36.
Depalle
,
B.
,
Qin
,
Z.
,
Shefelbine
,
S. J.
, and
Buehler
,
M. J.
,
2015
, “
Influence of Cross-Link Structure, Density and Mechanical Properties in the Mesoscale Deformation Mechanisms of Collagen Fibrils
,”
J. Mech. Behav. Biomed. Mater.
,
52
, pp.
1
13
.10.1016/j.jmbbm.2014.07.008
37.
Bhattacharya
,
S.
, and
Dubey
,
D. K.
,
2020
, “
Effect of Aggrecan Degradation on the Nanomechanics of Hyaluronan in Extra-Fibrillar Matrix of Annulus Fibrosus: A Molecular Dynamics Investigation
,”
J. Mech. Behav. Biomed. Mater.
, 107, p.
103752
. 10.1016/j.jmbbm.2020.103752
38.
Buehler
,
M. J.
,
2006
, “
Atomistic and Continuum Modeling of Mechanical Properties of Collagen: Elasticity, Fracture, and Self-Assembly
,”
J. Mater. Res.
,
21
(
8
), pp.
1947
1961
.10.1557/jmr.2006.0236
39.
Lorenzo
,
A. C.
, and
Caffarena
,
E. R.
,
2005
, “
Elastic Properties, Young's Modulus Determination and Structural Stability of the Tropocollagen Molecule: A Computational Study by Steered Molecular Dynamics
,”
J. Biomech.
,
38
(
7
), pp.
1527
1533
.10.1016/j.jbiomech.2004.07.011
40.
Vesentini
,
S.
,
Fitié
,
C. F. C.
,
Montevecchi
,
F. M.
, and
Redaelli
,
A.
,
2005
, “
Molecular Assessment of the Elastic Properties of Collagen-Like Homotrimer Sequences
,”
Biomech. Model. Mechanobiol.
,
3
(
4
), pp.
224
234
.10.1007/s10237-004-0064-5
41.
Dubey
,
D. K.
, and
Tomar
,
V.
,
2009
, “
Role of the Nanoscale Interfacial Arrangement in Mechanical Strength of Tropocollagen-Hydroxyapatite-Based Hard Biomaterials
,”
Acta Biomater.
,
5
(
7
), pp.
2704
2716
.10.1016/j.actbio.2009.02.035
42.
Gautieri
,
A.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Buehler
,
M. J.
,
2011
, “
Hierarchical Structure and Nanomechanics of Collagen Microfibrils From the Atomistic Scale Up
,”
Nano Lett.
,
11
(
2
), pp.
757
766
.10.1021/nl103943u
43.
Orgel
,
J. P. R. O.
,
Irving
,
T. C.
,
Miller
,
A.
, and
Wess
,
T. J.
,
2006
, “
Microfibrillar Structure of Type I Collagen In Situ
,”
Proc. Natl. Acad. Sci. U. S. A.
,
103
(
24
), pp.
9001
9005
.10.1073/pnas.0502718103
44.
Iatridis
,
J. C.
,
MacLean
,
J. J.
, and
Ryan
,
D. A.
,
2005
, “
Mechanical Damage to the Intervertebral Disc Annulus Fibrosus Subjected to Tensile Loading
,”
J. Biomech.
,
38
(
3
), pp.
557
565
.10.1016/j.jbiomech.2004.03.038
45.
Huang
,
C. C.
,
Couch
,
G. S.
,
Pettersen
,
E. F.
,
Ferrin
,
T. E.
,
Howard
,
A. E.
, and
Klein
,
T. E.
,
1998
, “
The Object Technology Framework: An Object-Oriented Interface to Molecular Data and Its Application to Collagen
,”
Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing
, Maui, Hawaii, Jan. 4–9, pp.
349
361
.https://www.semanticscholar.org/paper/The-object-technology-framework%3A-an-objectoriented-Huang-Couch/9f3442e40a4e31e0566c79570d94f09716f6c371
46.
Bodian
,
D. L.
,
Radmer
,
R. J.
,
Holbert
,
S.
, and
Klein
,
T. E.
,
2011
, “
Molecular Dynamics Simulations of the Full Triple Helical Region of Collagen Type i Provide an Atomic Scale View of the Protein's Regional Heterogeneity
,” Pacific Symposium on Biocomputing (
PSB 2011)
, Kohala Coast, Hawaii, Jan. 3–7, pp.
193
204
.10.1142/9789814335058_0021
47.
Consortium, T. U.
,
2019
, “
UniProt: A Worldwide Hub of Protein Knowledge the UniProt Consortium
,”
Nucl. Acids Res.
, 47(D1), pp. D506–D515.10.1093/nar/gky1049
48.
Orgel
,
J. P. R. O.
,
Miller
,
A.
,
Irving
,
T. C.
,
Fischetti
,
R. F.
,
Hammersley
,
A. P.
, and
Wess
,
T. J.
,
2001
, “
The In Situ Supermolecular Structure of Type I Collagen
,”
Structures
,
9
(
11
), pp.
1061
1069
.10.1016/S0969-2126(01)00669-4
49.
Humphrey
,
W.
,
Dalke
,
A.
, and
Schulten
,
K.
,
1996
, “
VMD: Visual Molecular Dynamics
,”
J. Mol. Graph.
,
14
(
1
), pp.
33
38
.10.1016/0263-7855(96)00018-5
50.
In 't Veld
,
P. J.
, and
Stevens
,
M. J.
,
2008
, “
Simulation of the Mechanical Strength of a Single Collagen Molecule
,”
Biophys. J.
,
95
(
1
), pp.
33
39
.10.1529/biophysj.107.120659
51.
Grynpas
,
M. D.
,
Eyre
,
D. R.
, and
Kirschner
,
D. A.
,
1980
, “
Collagen Type II Differs From Type I in Native Molecular Packing
,”
BBA—Protein Struct.
,
626
(
2
), pp.
346
355
.10.1016/0005-2795(80)90129-4
52.
Makarov
,
V.
,
Pettitt
,
B. M.
, and
Feig
,
M.
,
2002
, “
Solvation and Hydration of Proteins and Nucleic Acids: A Theoretical View of Simulation and Experiment
,”
Acc. Chem. Res.
,
35
(
6
), pp.
376
384
.10.1021/ar0100273
53.
Plimpton
,
S.
,
1995
, “
Fast Parallel Algorithms for Short-Range Molecular Dynamics
,”
J. Comput. Phys.
,
117
(
1
), pp.
1
19
.10.1006/jcph.1995.1039
54.
Brooks, B. R., Brooks, C. L., Mackerell, A. D., Nilsson, L., Petrella, R. J., Roux, B., Won, Y., 2009, “CHARMM: The Biomolecular Simulation Program,”
J. Comput. Chem.
, 30(10), pp. 1545–1614.10.1002/jcc.21287
55.
Patel
,
M.
,
Dubey
,
D. K.
, and
Singh
,
S. P.
,
2020
, “
Phenomenological Models of Bombyx Mori Silk Fibroin and Their Mechanical Behavior Using Molecular Dynamics Simulations
,”
Mater. Sci. Eng. C
,
108
, p.
110414
.10.1016/j.msec.2019.110414
56.
Buehler
,
M. J.
,
Keten
,
S.
, and
Ackbarow
,
T.
,
2008
, “
Theoretical and Computational Hierarchical Nanomechanics of Protein Materials: Deformation and Fracture
,”
Prog. Mater. Sci.
,
53
(
8
), pp.
1101
1241
.10.1016/j.pmatsci.2008.06.002
57.
Florová
,
P.
,
Sklenovský
,
P.
,
Banáš
,
P.
, and
Otyepka
,
M.
,
2010
, “
Explicit Water Models Affect the Specific Solvation and Dynamics of Unfolded Peptides While the Conformational Behavior and Flexibility of Folded Peptides Remain Intact
,”
J. Chem. Theory Comput.
,
6
(
11
), pp.
3569
3579
.10.1021/ct1003687
58.
Thompson
,
A. P.
,
Plimpton
,
S. J.
, and
Mattson
,
W.
,
2009
, “
General Formulation of Pressure and Stress Tensor for Arbitrary Many-Body Interaction Potentials Under Periodic Boundary Conditions
,”
J. Chem. Phys.
,
131
(
15
), p.
154107
.10.1063/1.3245303
59.
Zhou
,
M.
,
2003
, “
A New Look at the Atomic Level Virial Stress: On Continuum-Molecular System Equivalence
,”
Proc. R. Soc. A Math. Phys. Eng. Sci.
,
459
(
2037
), pp.
2347
2392
.10.1098/rspa.2003.1127
60.
Black
,
S. D.
, and
Mould
,
D. R.
,
1991
, “
Development of Hydrophobicity Parameters to Analyze Proteins Which Bear Post- or Cotranslational Modifications
,”
Anal. Biochem.
,
193
(
1
), pp.
72
82
.10.1016/0003-2697(91)90045-U
61.
Skaggs
,
D. L.
,
Weidenbaum
,
M.
,
Latridis
,
J. C.
,
Ratcliffe
,
A.
, and
Mow
,
V. C.
,
1994
, “
Regional Variation in Tensile Properties and Biochemical Composition of the Human Lumbar Anulus Fibrosus
,”
Spine (Phila. Pa. 1976
),
19
(
12
), pp.
1310
1319
.10.1097/00007632-199406000-00002
62.
Buehler
,
M. J.
, and
Wong
,
S. Y.
,
2007
, “
Entropic Elasticity Controls Nanomechanics of Single Tropocollagen Molecules
,”
Biophys. J.
,
93
(
1
), pp.
37
43
.10.1529/biophysj.106.102616
63.
Harley
,
R.
,
James
,
D.
,
Miller
,
A.
, and
White
,
J. W.
,
1977
, “
Phonons and the Elastic Moduli of Collagen and Muscle
,”
Nature
,
267
(
5608
), pp.
285
287
.10.1038/267285a0
64.
Cusack
,
S.
, and
Miller
,
A.
,
1979
, “
Determination of the Elastic Constants of Collagen by Brillouin Light Scattering
,”
J. Mol. Biol.
,
135
(
1
), pp.
39
51
.10.1016/0022-2836(79)90339-5
65.
Svensson
,
R. B.
,
Mulder
,
H.
,
Kovanen
,
V.
, and
Magnusson
,
S. P.
,
2013
, “
Fracture Mechanics of Collagen Fibrils: Influence of Natural Cross-Links
,”
Biophys. J.
,
104
(
11
), pp.
2476
2484
.10.1016/j.bpj.2013.04.033
66.
Van Der Rijt
,
J. A. J.
,
Van Der Werf
,
K. O.
,
Bennink
,
M. L.
,
Dijkstra
,
P. J.
, and
Feijen
,
J.
,
2006
, “
Micromechanical Testing of Individual Collagen Fibrils
,”
Macromol. Biosci.
,
6
(
9
), pp.
699
702
.10.1002/mabi.200600063
67.
Cortes
,
D. H.
,
Han
,
W. M.
,
Smith
,
L. J.
, and
Elliott
,
D. M.
,
2013
, “
Mechanical Properties of the Extra-Fibrillar Matrix of Human Annulus Fibrosus Are Location and Age Dependent
,”
J. Orthop. Res.
,
31
(
11
), pp.
1725
1732
.10.1002/jor.22430
68.
Bruehlmann
,
S. B.
,
Matyas
,
J. R.
, and
Duncan
,
N. A.
,
2004
, “
ISSLS Prize Winner: Collagen Fibril Sliding Governs Cell Mechanics in the Anulus Fibrosus: An In Situ Confocal Microscopy Study of Bovine Discs
,”
Spine (Phila. Pa. 1976
),
29
(
23
), pp.
2612
2620
.10.1097/01.brs.0000146465.05972.56
69.
Tavakoli
,
J.
, and
Costi
,
J. J.
,
2018
, “
Ultrastructural Organization of Elastic Fibres in the Partition Boundaries of the Annulus Fibrosus Within the Intervertebral Disc
,”
Acta Biomater.
,
68
, pp.
67
77
.10.1016/j.actbio.2017.12.017
70.
Cortes
,
D. H.
,
Jacobs
,
N. T.
,
DeLucca
,
J. F.
, and
Elliott
,
D. M.
,
2014
, “
Elastic, Permeability and Swelling Properties of Human Intervertebral Disc Tissues: A Benchmark for Tissue Engineering
,”
J. Biomech.
,
47
(
9
), pp.
2088
2094
.10.1016/j.jbiomech.2013.12.021
71.
Miles
,
C. A.
,
Sims
,
T. J.
,
Camacho
,
N. P.
, and
Bailey
,
A. J.
,
2002
, “
The Role of the Α2 Chain in the Stabilization of the Collagen Type I Heterotrimer: A Study of the Type I Homotrimer in Oim Mouse Tissues
,”
J. Mol. Biol.
,
321
(
5
), pp.
797
805
.10.1016/S0022-2836(02)00703-9
72.
Soler-Crespo
,
R. A.
,
Gao
,
W.
,
Mao
,
L.
,
Nguyen
,
H. T.
,
Roenbeck
,
M. R.
,
Paci
,
J. T.
,
Huang
,
J.
,
Nguyen
,
S. T.
, and
Espinosa
,
H. D.
,
2018
, “
The Role of Water in Mediating Interfacial Adhesion and Shear Strength in Graphene Oxide
,”
ACS Nano
,
12
(
6
), pp.
6089
6099
.10.1021/acsnano.8b02373
73.
Pradhan
,
S. M.
,
Katti
,
K. S.
, and
Katti
,
D. R.
,
2012
, “
Structural Hierarchy Controls Deformation Behavior of Collagen
,”
Biomacromolecules
,
13
(
8
), pp.
2562
2569
.10.1021/bm300801a
74.
O'Connell
,
G. D.
,
Guerin
,
H. L.
, and
Elliott
,
D. M.
,
2009
, “
Theoretical and Uniaxial Experimental Evaluation of Human Annulus Fibrosus Degeneration
,”
ASME J. Biomech. Eng.
,
131
(
11
), p.
111007
.10.1115/1.3212104
75.
Dvořák
,
J.
,
Panjabi
,
M. M.
,
Chang
,
D. G.
,
Theiler
,
R.
, and
Grob
,
D.
,
1991
, “
Functional Radiographic Diagnosis of the Lumbar Spine: Flexion-Extension and Lateral Bending
,”
Spine (Phila. Pa. 1976)
,
16
(
5
), pp.
562
571
.10.1097/00007632-199105000-00014
76.
Panjabi
,
M. M.
,
Oxland
,
T. R.
,
Yamamoto
,
I.
, and
Crisco
,
J. J.
,
1994
, “
Mechanical Behavior of the Human Lumbar and Lumbosacral Spine as Shown by Three-Dimensional Load-Displacement Curves
,”
J. Bone Jt. Surg. Ser. A
,
76
(
3
), pp.
413
424
.10.2106/00004623-199403000-00012
77.
Dvorak
,
J.
,
Panjabi
,
M. M.
,
Novotny
,
J. E.
, and
Antinnes
,
J. A.
,
1991
, “
In Vivo Flexion/Extension of the Normal Cervical Spine
,”
J. Orthop. Res.
,
9
(
6
), pp.
828
834
.10.1002/jor.1100090608
78.
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 (Phila. Pa. 1976)
,
26
(
24
), pp.
2692
2700
.10.1097/00007632-200112150-00012
79.
Scott
,
J. E.
, and
Haigh
,
M.
,
1986
, “
Proteoglycan-Collagen Interactions in Intervertebral Disc. A Chondroitin Sulphate Proteoglycan Associates With Collagen Fibrils in Rabbit Annulus Fibrosus at the d-e Bands
,”
Biosci. Rep.
,
6
(
10
), pp.
879
888
.10.1007/BF01116241
80.
Roughley
,
P. J.
,
Melching
,
L. I.
,
Heathfield
,
T. F.
,
Pearce
,
R. H.
, and
Mort
,
J. S.
,
2006
, “
The Structure and Degradation of Aggrecan in Human Intervertebral Disc
,”
Eur. Spine J.
, 15, pp.
326
332
.10.1007/s00586-006-0127-7
81.
Quint
,
U.
, and
Wilke
,
H. J.
,
2008
, “
Grading of Degenerative Disk Disease and Functional Impairment: Imaging Versus Patho-Anatomical Findings
,”
Eur. Spine J.
,
17
(
12
), pp.
1705
1713
.10.1007/s00586-008-0787-6
82.
Passias
,
P. G.
,
Wang
,
S.
,
Kozanek
,
M.
,
Xia
,
Q.
,
Li
,
W.
,
Grottkau
,
B.
,
Wood
,
K. B.
, and
Li
,
G.
,
2011
, “
Segmental Lumbar Rotation in Patients With Discogenic Low Back Pain During Functional Weight-Bearing Activities
,”
J. Bone Jt. Surg. Ser. A
,
93
(
1
), pp.
29
37
.10.2106/JBJS.I.01348
83.
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
.10.1016/j.actbio.2018.07.023
84.
Smith
,
L. J.
, and
Fazzalari
,
N. L.
,
2009
, “
The Elastic Fibre Network of the Human Lumbar Anulus Fibrosus: Architecture, Mechanical Function and Potential Role in the Progression of Intervertebral Disc Degeneration
,”
Eur. Spine J.
,
18
(
4
), pp.
439
448
.10.1007/s00586-009-0918-8
You do not currently have access to this content.