Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical property–density relationships have presented results for the superior–inferior (SI), or “on-axis” direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) density-dependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCT-based apparent density of HVTB and its apparent compressive mechanical properties— elastic modulus (Eapp), yield strength (σy), and yield strain (εy)—in the SI and TR directions for future clinical QCT-based continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, ρCT. Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, ρapp, showed significant correlation with ρCTCT = 1.0568 × ρapp, r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (Eapp) and yield strength (σy) were linearly related to the ρCT in the axial direction [ESI = 1493.8 × (ρCT), r = 0.77, p < 0.01; σY,SI = 6.9 × (ρCT) − 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [ETR = 3349.1 × (ρCT)1.94, r = 0.89, p < 0.01; σY,TR = 18.81 × (ρCT)1.83, r = 0.83, p < 0.01]. No significant correlation was found between εy and ρCT in either direction. Eapp and σy in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, εy exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CT-based densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.

References

References
1.
Crawford
,
R. P.
,
Cann
,
C. E.
, and
Keaveny
,
T. M.
,
2003
, “
Finite Element Models Predict in Vitro Vertebral Body Compressive Strength Better Than Quantitative Computed Tomography
,”
Bone
,
33
(
4
), pp.
744
750
.10.1016/S8756-3282(03)00210-2
2.
Mosekilde
,
L.
,
Mosekilde
,
L.
, and
Danielsen
,
C. C.
,
1987
, “
Biomechanical Competence of Vertebral Trabecular Bone in Relation to Ash Density and Age in Normal Individuals
,”
Bone
,
8
(
2
), pp.
79
85
.10.1016/8756-3282(87)90074-3
3.
Nicholson
,
P. H. F.
,
Cheng
,
X. G.
,
Lowet
,
G.
,
Boonen
,
S.
,
Davie
,
M. W. J.
,
Dequeker
,
J.
, and
Van der
Perre
,
G.
,
1997
, “
Structural and Material Mechanical Properties of Human Vertebral Cancellous Bone
,”
Med. Eng. Phys.
,
19
(
8
), pp.
729
737
.10.1016/S1350-4533(97)00030-1
4.
Banse
,
X.
,
Devogelaer
,
J. P.
,
Munting
,
E.
,
Delloye
,
C.
,
Cornu
,
O.
, and
Grynpas
,
M.
,
2001
, “
Inhomogeneity of Human Vertebral Cancellous Bone: Systematic Density and Structure Patterns Inside the Vertebral Body
,”
Bone
,
28
(
5
), pp.
563
571
.10.1016/S8756-3282(01)00425-2
5.
Hulme
,
P. A.
,
Boyd
,
S. K.
, and
Ferguson
,
S. J.
,
2007
, “
Regional Variation in Vertebral Bone Morphology and Its Contribution to Vertebral Fracture Strength
,”
Bone
,
41
(
6
), pp.
946
957
.10.1016/j.bone.2007.08.019
6.
Wegrzyn
,
J.
,
Roux
,
J. P.
,
Arlot
,
M. E.
,
Boutroy
,
S.
,
Vilayphiou
,
N.
,
Guyen
,
O.
,
Delmas
,
P. D.
,
Chapurlat
,
R.
, and
Bouxsein
,
M. L.
,
2010
, “
Role of Trabecular Microarchitecture and Its Heterogeneity Parameters in the Mechanical Behavior of Ex Vivo Human L3 Vertebrae
,”
J. Bone Miner. Res.
,
25
(
11
), pp.
2324
2331
.10.1002/jbmr.164
7.
Nazarian
,
A.
,
Stauber
,
M.
,
Zurakowski
,
D.
,
Snyder
,
B. D.
, and
Muller
,
R.
,
2006
, “
The Interaction of Microstructure and Volume Fraction in Predicting Failure in Cancellous Bone
,”
Bone
,
39
(
6
), pp.
1196
1202
.10.1016/j.bone.2006.06.013
8.
Matsuura
,
M.
,
Eckstein
,
F.
,
Lochmuller
,
E. M.
, and
Zysset
,
P. K.
,
2008
, “
The Role of Fabric in the Quasi-Static Compressive Mechanical Properties of Human Trabecular Bone From Various Anatomical Locations
,”
Biomech. Model Mechanobiol.
,
7
(
1
), pp.
27
42
.10.1007/s10237-006-0073-7
9.
Chevalier
,
Y.
,
Charlebois
,
M.
,
Pahra
,
D.
,
Varga
,
P.
,
Heini
,
P.
,
Schneider
,
E.
, and
Zysset
,
P.
,
2008
, “
A Patient-Specific Finite Element Methodology to Predict Damage Accumulation in Vertebral Bodies Under Axial Compression, Sagittal Flexion and Combined Loads
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
5
), pp.
477
487
.10.1080/10255840802078022
10.
Chevalier
,
Y.
, and
Zysset
,
P. K.
,
2012
, “
A Patient-Specific Computer Tomography-Based Finite Element Methodology to Calculate the Six Dimensional Stiffness Matrix of Human Vertebral Bodies
,”
ASME J. Biomech. Eng.
,
134
(
5
), p.
051006
.10.1115/1.4006688
11.
Mosekilde
,
L.
,
Ebbeson
,
E. N.
,
Tornvig
,
L.
, and
Thomson
,
J. S.
,
2000
, “
Trabecular Bone Structure and Strength -Remodelling and Repair
,”
J. Musculoskeletal Neuronal Interact.
,
1
, pp.
25
30
.
12.
Keller
,
T. S.
,
1994
, “
Predicting the Compressive Mechanical Behavior of Bone
,”
J. Biomech.
,
27
(
9
), pp.
1159
1168
.10.1016/0021-9290(94)90056-6
13.
Keaveny
,
T. M.
,
Pinilla
,
T. P.
,
Crawford
,
R. P.
,
Kopperdahl
,
D. L.
, and
Lou
,
A.
,
1997
, “
Systematic and Random Errors in Compression Testing of Trabecular Bone
,”
J. Orthop. Res.
,
15
(
1
), pp.
101
110
.10.1002/jor.1100150115
14.
Kopperdahl
,
D. L.
, and
Keaveny
,
T. M.
,
1998
, “
Yield Strain Behavior of Trabecular Bone
,”
J. Biomech.
,
31
(
7
), pp.
601
608
.10.1016/S0021-9290(98)00057-8
15.
Morgan
,
E. F.
, and
Keaveny
,
T. M.
,
2001
, “
Dependence of Yield Strain of Human Trabecular Bone on Anatomic Site
,”
J. Biomech.
,
34
(
5
), pp.
569
577
.10.1016/S0021-9290(01)00011-2
16.
Ashman
,
R. B.
,
Corin
,
J. D.
, and
Turner
,
C. H.
,
1987
, “
Elastic Properties of Cancellous Bone: Measurement by an Ultrasonic Technique
,”
J. Biomech.
,
20
(
10
), pp.
979
983
, 985–986.10.1016/0021-9290(87)90327-7
17.
Turner
,
C. H.
,
Anne
,
V.
, and
Pidaparti
,
R. M. V.
,
1997
, “
A Uniform Strain Criterion for Trabecular Bone Adaptation: Do Continuum-Level Strain Gradients Drive Adaptation?
,”
J. Biomech.
,
30
(
6
), pp.
555
563
.10.1016/S0021-9290(97)84505-8
18.
Currey
,
J. D.
,
1984
,
The Mechanical Adaptations of Bones
,
Princeton University Press
Princeton, NJ
.
19.
Silva
,
M. J.
,
Keaveny
,
T. M.
, and
Hayes
,
W. C.
,
1998
, “
Computed Tomography-Based Finite Element Analysis Predicts Failure Loads and Fracture Patterns for Vertebral Sections
,”
J. Orthop. Res.
,
16
(
3
), pp.
300
308
.10.1002/jor.1100160305
20.
Kopperdahl
,
D. L.
,
Roberts
,
A. D.
, and
Keaveny
,
T. M.
,
1999
, “
Localized Damage in Vertebral Bone is Most Detrimental in Regions of High Strain Energy Density
,”
ASME J. Biomech. Eng.
,
121
(
6
), pp.
622
628
.10.1115/1.2800864
21.
Wachtel
,
E. F.
, and
Keaveny
,
T. M.
,
1997
, “
Dependence of Trabecular Damage on Mechanical Strain
,”
J. Orthop. Res.
,
15
(
5
), pp.
781
787
.10.1002/jor.1100150522
22.
Keaveny
,
T. M.
,
Morgan
,
E. F.
,
Niebur
,
G. L.
, and
Yeh
,
O. C.
,
2001
, “
Biomechanics of Trabecular Bone
,”
Annu. Rev. Biomed. Eng.
,
3
(
1
), pp.
307
333
.10.1146/annurev.bioeng.3.1.307
23.
Cowin
,
S. C.
,
1986
, “
Wolff's Law of Trabecular Architecture at Remodeling Equilibrium
,”
ASME J. Biomech. Eng.
,
108
(
1
), pp.
83
88
.10.1115/1.3138584
24.
Chang
,
W. C. W.
,
Christensen
,
T. M.
,
Pinilla
,
T. P.
, and
Keaveny
,
T. M.
,
1999
, “
Uniaxial Yield Strains for Bovine Trabecular Bone Are Isotropic and Asymmetric
,”
J. Orthop. Res.
,
17
(
4
), pp.
582
585
.10.1002/jor.1100170418
25.
Turner
,
C. H.
,
1989
, “
Yield Behavior of Bovine Cancellous Bone
,”
ASME J. Biomech. Eng.
,
111
(
3
), pp.
256
260
.10.1115/1.3168375
26.
Bevill
,
G.
,
Farhamand
,
F.
, and
Keaveny
,
T. M.
,
2009
, “
Heterogeneity of Yield Strain in Low-Density Versus High-Density Human Trabecular Bone
,”
J. Biomech.
,
42
(
13
), pp.
2165
2170
.10.1016/j.jbiomech.2009.05.023
27.
Jones
,
D. B.
,
Broeckmann
,
E.
,
Pohl
,
T.
, and
Smith
,
E. L.
,
2003
, “
Development of a Mechanical Testing and Loading System for Trabecular Bone Studies for Long Term Culture
,”
Eur. Cells Mater.
,
15
, pp.
48
60
.
28.
Smith
,
E. L.
, and
Jones
,
D.
,
2001
, “
Combined Perfusion and Mechanical Loading System for Explanted Bone
,” U.S. Patent No. US 6,171,812 B1.
29.
Davies
,
C. M.
,
Jones
,
D. B.
,
Stoddart
,
M. J.
,
Koller
,
K.
,
Smith
,
E. L.
,
Archer
,
C. W.
, and
Richards
,
R. G.
,
2006
, “
Mechanically Loaded Ex Vivo Bone Culture System ‘Zetos’: Systems and Culture Preparation
,”
Eur. Cells Mater.
,
11
, pp.
57
75
.
30.
Garcia-Rodriguez
,
S.
,
Smith
,
E. L.
, and
Ploeg
,
H.-L.
,
2008
, “
A Calibration Procedure for a Bone Loading System
,”
J. Med. Devices
,
2
(
1
), pp.
1
6
.10.1115/1.2889059
31.
Endres
,
S.
,
Kratz
,
M.
,
Wunsch
,
S.
, and
Jones
,
D. B.
,
2009
, “
Zetos: A Culture Loading System for Trabecular Bone. Investigation of Different Loading Signal Intensities on Bovine Bone Cylinders
,”
J. Musculoskeletal Neuronal Interact.
,
9
(
3
), pp.
173
183
.
32.
Vivanco
,
J.
,
Garcia
,
S.
,
Ploeg
,
H. L.
,
Alvarez
,
G.
,
Cullen
,
D.
, and
Smith
,
E. L.
,
2013
, “
Apparent Elastic Modulus of Ex Vivo Trabecular Bovine Bone Increases With Dynamic Loading
,”
Proc. Inst. Mech. Eng., Part H
,
227
(
8
), pp.
904
912
.
33.
Dumas
,
V.
,
Perrier
,
A.
,
Malaval
,
L.
,
Laroche
,
N.
,
Guignandon
,
A.
,
Vico
,
L.
, and
Rattner
,
A.
,
2009
, “
The Effect of Dual Frequency Cyclic Compression on Matrix Deposition by Osteoblast-Like Cells Grown in 3D Scaffolds and on Modulation of VEGF Variant Expression
,”
Biomaterials
,
30
(
19
), pp.
3279
3288
.10.1016/j.biomaterials.2009.02.048
34.
Mann
,
V.
,
Huber
,
C.
,
Kogianni
,
G.
,
Jones
,
D.
, and
Noble
,
B.
,
2006
, “
The Influence of Mechanical Stimulation on Osteocyte Apoptosis and Bone Viability in Human Trabecular Bone
,”
J. Musculoskeletal Neuronal Interact.
,
6
(
4
), pp.
408
417
.
35.
Harrigan
,
T. P.
,
Jasty
,
M.
,
Mann
,
R. W.
, and
Harris
,
W. H.
,
1988
, “
Limitations of the Continuum Assumption in Cancellous Bone
,”
J. Biomechanics
,
21
(
4
), pp.
269
275
.10.1016/0021-9290(88)90257-6
36.
Morgan
,
E. F.
,
Yeh
,
O. C.
,
Chang
,
W. C.
, and
Keaveny
,
T. M.
,
2001
, “
Nonlinear Behavior of Trabecular Bone at Small Strains
,”
ASME J. Biomech. Eng.
,
123
(
1
), pp.
1
9
.10.1115/1.1338122
37.
Zysset
,
P. K.
,
2003
, “
A Review of Morphology-Elasticity Relationships in Human Trabecular Bone: Theories and Experiments
,”
J. Biomech.
,
36
(
10
), pp.
1469
1485
.10.1016/S0021-9290(03)00128-3
38.
Rincon-Kohli
,
L.
, and
Zysset
,
P. K.
,
2009
, “
Multi-Axial Mechanical Properties of Human Trabecular Bone
,”
Biomech. Model Mechanobiol.
,
8
(
3
), pp.
195
208
.10.1007/s10237-008-0128-z
39.
Fields
,
A. J.
, and
Keaveny
,
T. M.
,
2012
, “
Trabecular Architecture and Vertebral Fragility in Osteoporosis
,”
Curr. Osteoporosis Rep.
,
10
(
2
), pp.
132
140
.10.1007/s11914-012-0097-0
40.
Rho
,
J. Y.
,
Ashman
,
R. B.
, and
Turner
,
C. H.
,
1993
, “
Young's Modulus of Trabecular and Cortical Bone Material: Ultrasonic and Microtensile Measurements
,”
J. Biomech.
,
26
(
2
), pp.
111
119
.10.1016/0021-9290(93)90042-D
41.
Keaveny
,
T. M.
,
Wachtel
,
E. F.
,
Zadesky
,
S. P.
, and
Arramon
,
Y. P.
,
1999
, “
Application of the Tsai–Wu Quadratic Multiaxial Failure Criterion to Bovine Trabecular Bone
,”
ASME J. Biomech. Eng.
,
121
(
1
), pp.
99
107
.10.1115/1.2798051
42.
Gibson
,
L. J.
,
1985
, “
The Mechanical Behaviour of Cancellous Bone
,”
J. Biomech.
,
18
(
5
), pp.
317
328
.10.1016/0021-9290(85)90287-8
43.
Snyder
,
B. D.
,
Piazza
,
S.
,
Edwards
,
W. T.
, and
Hayes
,
W. C.
,
1993
, “
Role of Trabecular Morphology in the Etiology of Age-Related Vertebral Fractures
,”
Calcif. Tissue Int.
,
53
(
0
), pp.
S14
S22
.10.1007/BF01673396
44.
Odgaard
,
A.
, and
Linde
,
F.
,
1991
, “
The Underestimation of Young's Modulus in Compressive Testing of Cancellous Bone Specimens
,”
J. Biomech.
,
24
(
8
), pp.
691
698
.10.1016/0021-9290(91)90333-I
45.
Linde
,
F.
,
Hvid
,
I.
, and
Madsen
,
F.
,
1992
, “
The Effect of Specimen Geometry on the Mechanical Behaviour of Trabecular Bone Specimens
,”
J. Biomech.
,
25
(
4
), pp.
359
368
.10.1016/0021-9290(92)90255-Y
46.
Lievers
,
W. B.
,
Waldman
,
S. D.
, and
Pilkey
,
A. K.
,
2010
, “
Minimizing Specimen Length in Elastic Testing of End-Constrained Cancellous Bone
,”
J. Mech. Behav. Biomed. Mater.
,
3
(
1
), pp.
22
30
.10.1016/j.jmbbm.2009.02.001
47.
Ün
,
K.
,
Bevill
,
G.
, and
Keaveny
,
T. M.
,
2006
, “
The Effects of Side-Artifacts on the Elastic Modulus of Trabecular Bone
,”
J. Biomech.
,
39
(
11
), pp.
1955
1963
.10.1016/j.jbiomech.2006.05.012
48.
Bevill
,
G.
,
Easley
,
S. K.
, and
Keaveny
,
T. M.
,
2007
, “
Side-Artifact Errors in Yield Strength and Elastic Modulus for Human Trabecular Bone and Their Dependence on Bone Volume Fraction and Anatomic Site
,”
J. Biomech.
,
40
(
15
), pp.
3381
3388
.10.1016/j.jbiomech.2007.05.008
49.
Lievers
,
W. B.
,
Petryshyn
,
A. C.
,
Poljsak
,
A. S.
,
Waldman
,
S. D.
, and
Pilkey
,
A. K.
,
2010
, “
Specimen Diameter and “Side Artifacts” in Cancellous Bone Evaluated Using End-Constrained Elastic Tension
,”
Bone
,
47
(
2
), pp.
371
377
.10.1016/j.bone.2010.03.024
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