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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

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Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation

H. Pontzer^1,*, 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

View larger version (29K): [in a new window]   Fig. 1. Differences in knee flexion between conditions. (A) Level condition subjects were exercised at 0° pitch, whereas Incline subjects were exercised at 20°, resulting in a more acute angle of knee flexion () at peak normal ground reaction force (nGRF) oriented perpendicularly to the track surface. (B) Differences in knee flexion () are expected to result in differences in the orientation of compressive loads (dotted lines) relative to the distal femur in the parasagittal plane, because the joint reaction force (JRF; gray arrow) is transmitted more posteriorly on the femoral condyles. Mean knee flexion at peak GRF: Level, 76.3±1.33°, mean ± s.e.m., N=16 strides; Incline, 62.6±3.52°, N=10 strides; P<0.01, Student's t-test.

View larger version (42K): [in a new window]   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).

View larger version (49K): [in a new window]   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).

View larger version (62K): [in a new window]   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.

View larger version (35K): [in a new window]   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.

View larger version (45K): [in a new window]   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).

View larger version (36K): [in a new window]   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).