SHEAR LOADING IS THE WEAKEST LINK FOR FEMORAL NECK TRABECULAR BONE
+*Keaveny, T M (A-NIH, NSF); *Bayraktar, H H (A-NIH); *Kwon, R Y (A-NIH)
+*Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA. (510) 643-8017, Fax: (510) 642-6163,
[email protected]
Shear modulus: Y = 4820 X - 794, R2= 0.66
Tension: Y = 61.9 X - 5.89, R 2= 0.83
40
5000
Shear: Y = 33.6 X - 5.18, R 2= 0.63
Yield Stress (MPa)
35
4000
3000
2000
1000
30
25
20
15
10
5
0
0.15
0.20
0.25
0.30
0.35
0
0.15
0.40
Bone Volume Fraction
0.20
0.25
0.30
0.35
0.40
Bone Volume Fraction
Figure 1: Left: apparent modulus vs. volume fraction. Right: strength vs.
volume fraction for compression, tension, and shear.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Compression
Tension
Shear
Loading Mode
Volume Failed Tissue / Total Tissue (%)
Results: Both Young’s and shear modulus increased in a linear fashion with
increasing volume fraction, but the shear modulus was substantially lower, on
average by a factor 4.98 (Figure 1, left). Analysis of the yield strength
properties revealed that for all volume fractions, the bone was substantially
weaker in shear, (p<0.001) on average being 4.57 and 2.62 times weaker than
in compression and tension, respectively (Figure 1, right). In general,
correlations between modulus or strength and volume fraction were weakest
for shear, suggesting a greater role of architecture in determination of these
properties. The yield strains were greater in shear than in compression or
tension (p<0.003, Figure 2, left). Yield strains displayed little variation across
all 12 specimens, there being slightly more variation in shear than the other
modes (p<0.001). At the apparent yield point, analysis of the amount of failed
tissue revealed that only a small amount of tissue failed in shear (Figure 2,
right). Further, almost all the failed tissue for shear loading occurred from
excessive tissue level tensile strain whereas for the other loading modes
failure at the tissue level was dominated by the applied apparent loading
mode.
Compression: Y=113 X - 11.7, R 2= 0.84
Young's modulus: Y = 15200 X - 1370, R2= 0.82
Elastic Modulus (MPa)
Methods: Twelve 5-mm high-resolution finite element models (52-66 µm
sized elements) were created from 10-22 µm resolution three-dimensional
images of 12 on-axis trabecular bone specimens taken from the neck region of
the proximal femur. The femurs were taken from 11 normal cadavers, mean ±
SD age = 66 ± 9 years, range 51–85. Tissue yielding was defined by a
maximum principal strain criterion, with elastic tensile and compressive
limits, 0.412% and 0.825%, respectively. A comprehensive calibration study
was performed to determine the tissue level elastic modulus for each
specimen, as well as the tissue level yield tensile and compressive yield
strains. Then, using specimen-specific values of tissue modulus, but mean
values of each of the tensile and compressive tissue level yield strains, the
compressive, tensile, and shear 0.2% offset apparent level yield stress and
strain of each specimen were computed. In addition, the amount of tissue that
exceeded the tissue level tensile and compressive yield strains was calculated,
and expressed as a percentage of the total volume of bone tissue within each
specimen. All non-linear finite element analyses were performed on an IBM
SP2 supercomputer, requiring a total of 3600 CPU hours.
3
Discussion: This study establishes that the trabecular bone from the human
femoral neck is very much weaker in shear than in either compression or
tension. In addition, since so little of the tissue fails at the apparent yield point
for shear, the bone is particularly susceptible to damage when loaded in this
manner. These results have important clinical implications since they suggest
that the most sensitive biomechanical assay for detection of osteoporotic bone
in the femoral neck is a shear test, as opposed to the compression test that is
almost universally used. Biologically, our results demonstrate unique damage
patterns for the various loading modes, suggesting differential biological
responses to apparent level compression, tension, and shear loading. While the
bone is quite robust for compressive and even tensile loading, i.e. it can
sustain a large amount of damaged tissue at the yield point, it is very poorly
adapted to shear loading for which bending failure mechanisms become
dominant. We conclude that mechanical events that produce large amounts of
shear on this type of trabecular bone are expected to be catastrophic.
Apparent Yield Strain (%)
Introduction: The relative strength of trabecular bone in compression,
tension, and shear is important for understanding hip fracture etiology since
large off-axis and multiaxial stresses can develop during a sideways fall1.
Knowledge of the “weakest link” loading mode is critical to developing
appropriate biomechanical assays for detection of osteoporotic bone since it is
likely that the bone will maintain as much integrity as possible for habitual
loading in the face of age-related bone loss, but may be particularly degraded
for other loading modes. While it has been demonstrated that bovine
trabecular bone is very weak in shear2, there are no studies available that have
compared compressive, tensile, and shear strengths for any type of human
trabecular bone. With the advent of high-resolution finite element analysis
that can predict the failure behavior of trabecular bone with an outstanding
level of accuracy for multiple loading modes3, it is now possible to directly
compare various strength modes for the same set of trabecular bone
specimens, a task that could not be achieved in a purely experimental setting
due to the destructive nature of any strength test. Thus, we used this
technology to test the hypothesis that human femoral neck trabecular bone is
weakest in shear, and to explore the underlying patterns of failed tissue
associated with various loading modes. Our specific objectives were to: 1) use
a series of validated high-resolution finite element models to compare both
elastic and yield properties for compression, tension, and shear loading; 2)
compare the amount of failed tissue at the yield point for these loading modes.
Tissue Level Failure Mode
tension
compression
25
20
15
10
5
0
Compression
Tension
Shear
Loading Mode
Figure 2: Left: mean apparent yield strain (bar = 1 SD). Right: amount of
failued tissue vs. loading mode. Tissue can fail from excessive tensile or
compressive (black) strain at the microstructural level (n=12 all cases).
Acknowledgements: NIH AR43784; NSF BES-9625030; NRAC UCB266;
Miller Institute for Research in Basic Science, Berkeley. Cadaveric tissue was
obtained from NDRI.
References: 1) Lotz et al., J Biomech Eng, 1991, 113(4): 353-360; 2) Fenech
and Keaveny, J Biomech Eng, 1999, 121: 414-422, 3) Niebur et al.,
J Biomech, 2000, 33: 1575-1583
48th Annual Meeting of the Orthopaedic Research Society
Poster No: 0555