First published online December 14, 2005
Journal of Experimental Biology 209, 57-65 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01971
Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation
H. Pontzer1,*,
D. E. Lieberman1,
E. Momin1,
M. J. Devlin1,
J. D. Polk2,
B. Hallgrímsson3 and
D. M. L. Cooper4
1 Department of Anthropology, Harvard University, Cambridge MA, 02138,
USA
2 Department of Anthropology, University of Illinois, Urbana-Champaign, IL,
USA
3 Department of Cell Biology and Anatomy and the Bone and Joint
Institute
4 Departments of Archaeology and Medical Science, University of Calgary,
Alberta, Canada
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Fig. 2. Gait elements within stance phase for a typical stride. (A) Midstance
elements were defined as follows: foot strike is the first kinematic frame in
which the foot (labeled by the TPj kinematic marker) contacts the trackway;
foot off is the first kinematic frame in which the foot rises from the
trackway; toe off is the first frame in which the foot begins a second, larger
arc about the tip of the phalanges; swing phase is the first frame of swing
phase. Adapted from Gatesy
(1999 ). (B) The timing of
midstance elements relative to peak nGRF for 16 strides. Mean occurrence time
for each gait element is indicated; values are means ± s.e.m. Negative
times indicate the element occurred before peak nGRF, while positive times
indicate it occurred after. Foot off was coincident with peak nGRF (mean
difference 0±0.01 s, N=16 strides).
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Fig. 3. Radon transform analysis. (A) Pixel grayscale values are summed along rows
(in the direction of the green arrows), creating a column of row-intensity
values. This is done iteratively as the image is rotated through 179°. (B)
The resulting set of row-intensity columns is arrayed by rotation angle
(orientation), and these columns are summed to create a density distribution
(C). The peak of the density distribution therefore corresponds to the primary
orientation of objects within the image. (D-G) This method reliably detects
the orientation of radially arrayed struts (D), regardless of induced noise
(E) or the removal of the image center (F), but will not produce a false
signal for pure noise (G).
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Fig. 4. Comparison between mean intercept length (MIL) and radon transform analysis
(RTA) methods for determining predominant trabecular orientation. (A)
Predominant orientations given by the MIL method (red cylinders) and the RTA
method (yellow lines) for all planes (x-y, x-z, y-z) of a
representative femoral head trabecular volume. Top row, volumes analyzed using
MIL, with RTA results superimposed. Bottom row, corresponding planar images
analyzed using the RTA method with predominant orientations shown. (B) Results
from each method for all femoral head volumes (N=4). Filled diamonds,
y-z and z-x results; open circles, x-y results;
solid line, least-squares regression, excluding x-y results
(N=8, r2=0.97, P<0.01). Broken line
indicates unity.
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Fig. 5. Orientation of peak trabecular density (OPTD). (A) Four two-dimensional
(2-D) slices were taken from micro-CT volumes of the right distal femur. (B)
Half-circle regions of interest (ROI), were taken from each 2-D slice, and
these ROIs were converted into circular images for analysis. The center of the
image was removed, leaving only the homogeneous layer of spongiosa for
analysis (see text). (C,D) Density distribution for individual subjects in the
Level condition (C) and Incline condition (D). Initials indicate individual
subjects.
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Fig. 6. Analysis of centerless images using the radon transform analysis (RTA)
method. (A) When analyzing an image in which objects are arrayed radially and
the center is removed, rows along the top and bottom of the image (arrows)
create noise in the intensity-angle matrix, while rows within the center of
the image, indicated by lines, provide useful signal regarding orientation.
Therefore, only the center region of the intensity-angle matrix is summed to
produce the density distribution (B).
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Fig. 7. Trabecular orientation reflects differences in joint flexion. (A) Mean
density distributions for Incline (red), Level (blue) and Control (yellow)
groups show a more posterior orientation of peak trabecular density (OPTD,
crosses in the right panel). (B) Differences in OPTD correspond to differences
in joint angle at peak GRF. (C) Individual OPTD values demonstrate greater
variability in Level and Control subjects. Comparisons between Level and
Incline groups demonstrate that differences in OPTD are significant
(P=0.01, Student's t-test).
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© The Company of Biologists Ltd 2006
) at peak normal ground reaction force (nGRF) oriented perpendicularly
to the track surface. (B) Differences in knee flexion (