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First published online July 20, 2007
Journal of Experimental Biology 210, 2676-2690 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.004580
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Skeletal strain patterns and growth in the emu hindlimb during ontogeny

Russell P. Main* and Andrew A. Biewener

Concord Field Station, Department of Organismic and Evolutionary Biology, Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA


Figure 1
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  		Fig. 1. A lateral view of the left hindlimb skeleton and pelvis of an adult emu with representative mid-shaft cross-sections for the femur and tibiotarsus (TBT). The gauge positions in the cross-sections and at the femur and TBT mid-shafts are indicated with black rectangles. On the hindlimb skeleton, the gauge position for the medial TBT is indicated by a hatched rectangle on the lateral surface. The kinematic markers analyzed are indicated with black circles and are as follows: the ischium, hip, knee, ankle, tarsometatarsal-phalangeal joint (TMP), and the distal end of the middle toe.

 

Figure 2
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  		Fig. 2. (A) The mean joint angles at mid-stance versus body mass while running with a 0.40 duty factor (DF), for the hip (open circles), knee (closed diamonds), ankle (closed circles) and TMP joints (open squares). The equations for the least-squares regression lines (±95%CI for the slope) are as follows: hip, y=87.3+0.13x (±0.24, R2=0.07); knee, y=88.9+0.04x (±0.30, R2=0.01); ankle, y=127.2+0.06x (±0.17, R2=0.03), and TMP, y=112.0–0.03x (±0.12, R2=0.01). (B) Peak resultant ground reaction forces (FR) normalized by body weight when running with a 0.40DF; y=2.24–0.004x (±0.006, R2=0.08). (C) A scaled stick figure representation of the typical emu hindlimb posture at the time of peak bone strains when running with a 0.40DF. The joint angles (mean ± s.d.) are as follows: hip, 86±9°; knee, 97±12°; ankle, 129±7°; TMP, 120±7°. FR is oriented 1.7° from the vertical axis in the fore–aft plane, passing near the knee. Even though the TMP joint is inclined slightly relative to the toe (9°), the foot was flat on the ground at the time of peak bone strains.

 

Figure 3
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  		Fig. 3. Representative principal and axial bone strains for the (A) femur and (B) TBT for five footfalls from a 36 week old, 27 kg emu running with a 0.41DF at 5.40 m s–1. Principal tensile strains, green; principal compressive strains, red. The axial strains measured from the lateral femur and cranial and medial TBT are in black. The shaded bars represent the stance phase during the locomotor cycle.

 

Figure 4
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  		Fig. 4. Mean peak bone strains versus body mass for the emu femur on logarithmic axes. Mean peak principal tensile and compressive strains for the (A) cranial and (B) caudal surfaces and (C) mean peak tensile axial strains for the lateral surface of the emu femur as the birds ran at a 0.40DF. Tensile strains, circles; compressive strains, squares. In A, the equations for the least-squares regression lines for the peak principal tensile and compressive strains are y=612x0.24±0.16 (R2=0.50, N=14) and y=–482x–0.29±0.17 (R2=0.55), respectively. In B, for principal tension, y=304x0.39±0.28 (R2=0.48, N=11) and principal compression, y=–399x–0.36±0.28 (R2=0.43). In C, for axial tension, y=721x–0.06±0.47 (R2=0.003, N=12). In A and B, the slopes and 95%CIs of the power lines for the principal compressive strains were taken on the absolute values of these strains, but plotted in the figure on the negative compressive values for clarity. As multiple trials at this DF were not collected for all birds, error bars have been omitted for consistency.

 

Figure 5
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  		Fig. 5. Cranial view of the femur and caudal views of the femur and TBT of an adult emu, showing the mean principal strain orientations on the different bone surfaces and the corresponding direction of torsional loading. In the femur (A), the principal tension (black arrows) measured at the bone's mid-shaft is oriented at 37° and 49° relative to the long axis of the bone on the cranial and caudal surfaces, respectively. The principal compression (reverse black arrows) is oriented at 90° to the principal tension. The orientation of the strains in the femur indicate torsional loading of the bone, acting to rotate the proximal end medially about the long axis relative to the distal end (as viewed from the cranial surface, grey arrows). (B) In the TBT (shown with adjacent fibula), the principal compression is oriented at 25° relative to the long axis, indicating a significant torsional component acting to rotate the proximal end medially relative to the distal end (as viewed from the caudal surface, grey arrows). The lengths of the black arrows representing the principal strains are not scaled to the strain magnitudes measured on these bone surfaces.

 

Figure 6
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  		Fig. 6. Mean peak bone strains versus body mass for the emu TBT on logarithmic axes. Mean peak axial tensile and compressive strains for the (A) cranial and (C) medial surfaces and (B) mean peak principal tensile and compressive strains from the caudal surface of the emu TBT while the birds ran at a 0.40DF. Tensile strains, circles; compressive strains, squares. In A, the equations for the least-squares regression lines for the peak axial tensile and compressive strains are y=179x0.21±0.28 (R2=0.11, N=19) and y=–165x–0.324±0.316 (R2=0.09), respectively. In B, for principal tension, y=400x0.26±0.11 (R2=0.68, N=12) and principal compression, y=–500x–0.32±0.10 (R2=0.75). In C, for axial tension, y=144x0.15±0.25 (R2=0.09, N=18) and axial compression, y=–542x–0.12±0.17 (R2=0.08). The slopes and 95%CIs of the power lines for the compressive strains, were taken on the absolute values of these strains, but plotted in the figure on the negative compressive values for clarity. As multiple trials at this DF were not collected for all birds, error bars have been omitted for consistency.

 

Figure 7
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  		Fig. 7. Representative axial, cranial–caudal and medial–lateral axial bending, and caudal and cranial shear strains for (A) the femur and (B) TBT for three footfalls from a 36-week-old, 27 kg emu running with a 0.41DF at 5.40 m s–1. The shaded bars represent the stance phase during the locomotor cycle. Note that the peak shear strains for the caudal surface of the TBT are negative while those for the femur are positive. This is consistent with the primary torques on these bones acting in opposite directions, where the proximal ends of the femur and TBT experienced medial and lateral torsion, respectively, when viewed from the cranial surfaces of the bones.

 

Figure 8
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  		Fig. 8. Axial compression, cranial–caudal axial bending, and cranial and caudal shear strains versus body mass on logarithmic axes for (A) the femur and (B) TBT. Closed squares, axial compression; closed circles, cranial–caudal axial bending; closed diamonds, cranial shear strains; open diamonds, caudal shear strains. In A, given the non-linearity of the trends for the femur, even on logarithmic axes, regression equations were not calculated. In B, axial compression, y=–46x–0.52±0.27 (R2=0.48, N=14); cranial-caudal axial bending, y=181x0.38±0.30 (R2=0.38, N=14); caudal shear, y=–212x–0.66±0.22 (R2=0.69, N=11). In B, the slopes and 95%CIs of the power lines for the axial compressive and caudal shear strains were taken on the absolute values of these strains, but plotted in the figure on the negative values for clarity. As multiple trials at this DF were not collected for all birds, error bars have been omitted for consistency.

 

Figure 9
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  		Fig. 9. Mid-shaft cross-sectional area (A) and the second moments of area across the x and y axes (Ixx and Iyy, respectively) for the emu (A) femur and (B) TBT versus body mass on logarithmic axes. Femur and TBT mid-shaft cross-sections from an adult bird (>8 years old, 37 kg) demonstrate the anatomical position of the axes about which the second moments of area were typically distributed, where Ixx (closed circles) and Iyy (open circles) are distributed about the x–x and y–y axes, respectively. (A) A: y=32x0.59±0.06 (R2=0.87); Ixx: y=120x1.38±0.07 (R2=0.95); Iyy: y=143x1.43±0.08 (R2=0.90). (B), A: y=26x0.63±0.05 (R2=0.95); Ixx: y=74x1.37±0.08 (R2=0.93); Iyy: y=76x1.45±0.07 (R2=0.92). The scaling patterns for the polar moments of area, J, were omitted for clarity as, being the sum of Ixx and Iyy, they nearly overlie the trends for I and scaled very similarly, JFEMUR: y=264x1.410±0.075 (R2=0.93) and JTBT: y=150x1.41±0.07 (R2=0.93).

 

Figure 10
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  		Fig. 10. Cranial–caudal (CCC) and medial–lateral (CML) longitudinal bone curvature versus body mass on logarithmic axes for the emu (A) femur and (B) TBT. CCC, closed circles; CML, open circles. In A, CCC: y=0.77x–0.20±0.08 (R2=0.57); CML: y=0.82x–0.12±0.06 (R2=0.42). In B, CCC: y=0.71x–0.19±0.14 (R2=0.19); CML: y=0.82x–0.15±0.10 (R2=0.32).

 

Figure 11
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  		Fig. 11. Percent mineral content by mass versus body mass on logarithmic axes for the emu femur (closed circles) and TBT (open circles). Femur: y=52x0.070±0.010 (R2=0.88); TBT: y=54x0.055±0.009 (R2=0.83).

 

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© The Company of Biologists Ltd 2007