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First published online June 16, 2004
Journal of Experimental Biology 207, 2577-2588 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01065
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Ontogenetic patterns of limb loading, in vivo bone strains and growth in the goat radius

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



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Fig. 1. Representative principal strains recorded from the cranial and caudal surfaces of the radius and axial strains from the medial surface for an intermediate-sized goat during two strides at a gallop (3.57 m s–1). Principal tensile strains are in green and compressive (both principal and axial) strains are in red. Shaded bars represent the stance phase during the locomotor cycle. Silhouettes of the goat at the top show five phases during stance (0, 25, 50, 75 and 100%), with the recorded limb in white.

 


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Fig. 2. Mean peak principal bone strains from the (A) cranial and (B) caudal surfaces, and (C) mean peak axial strains from the medial surface recorded at the midshaft of the radius for the small, intermediate and adult groups at a walk, trot and gallop. Error bars represent ±1 S.D. Medial axial strains are not present for the adult group, as they were not collected in Biewener and Taylor (1986Go).

 


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Fig. 3. Axial and bending strains in the radius determined from the cranio-caudal longitudinal principal strain data based on means for the individual trials at a given speed and gait for all small and intermediate animals. (A) Axial strain ({epsilon}ax), (B) bending strain ({epsilon}b) and (C) percentage of total strain due to bending plotted versus speed. Data for the small and intermediate groups are represented by circles and squares, respectively. Data for walking, trotting and galloping trials are represented by open, filled and open with a dot symbols, respectively. The solid regression line is fit to the data for the small group. The broken line is fit to the data for the intermediate group. In A, the equations of the regression lines (±95% CI for the slope, r2) for the small and intermediate groups are y=–49.7–60.8x (±22.5, r2=0.48) and y=–186.9–48.6x (±89.7, r2=0.04), respectively. In B, small, y=44.3+241.3x (±58.8, r2=0.68); intermediate, y=312.5+147.2x (±53.0, r2=0.54). In C, small, y=69.0+2.4x (±3.7, r2=0.05); intermediate, y=65.0+2.3x (±6.5, r2=0.02). The mean percentage of strain due to bending observed for the adult group is indicated at 89% (Biewener and Taylor, 1986Go). Due to the large variation among individuals within each size/age group, trends from the small and intermediate groups are not significantly different. One goat from the small group (triangles) exhibited tensile axial strains and, although shown, was not included in the analyses of loading mode. The outlying tensile axial strains of this animal resulted from a strain distribution in which both the cranial and caudal surfaces were loaded in longitudinal tension and were near the neutral axis of bending, corresponding to the low strains that were recorded at the time of peak strain on the two surfaces.

 


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Fig. 4. Cross-sectional longitudinal strain distributions in the radius from the same intermediate-sized goat during a gallop (3.57 m s–1) as shown in Fig. 1. Five phases are shown as percentage of time through stance: (A) 0%, (B) 25%, (C) 50%, (D) 75% and (E) 100%. Anatomical axes are labeled in A. The position of the neutral axis is indicated by the heavy black line. The outline of the ulna is included for reference, located caudo-lateral to the radius. The scale for the color gradient goes from red for negative (compressive) strains to yellow near zero strain and toward green for positive (tensile) strains.

 


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Fig. 5. Normalized peak vertical ground reaction forces (GRF) against gait for the small, intermediate and adult groups. Peak vertical forces (Fv) were normalized by dividing the forces by the body weight (BW) of the goat. Error bars represent ±1 S.D.

 


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Fig. 6. Cranio-caudal and medio-lateral longitudinal curvature of the radius plotted against body mass on logarithmic axes. Data for the small, intermediate and adult groups are represented by circles, squares and diamonds, respectively. Cranio-caudal (C-C) and medio-lateral (M-L) data are represented by filled and open symbols, respectively. C-C, y=0.81x0.12±0.14 (r2=0.13); M-L, y=0.32x0.05±0.18 (r2=0.02).

 


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Fig. 7. (A) Cross-sectional area and (B) cranio-caudal and medio-lateral second moments of area (I) of the radius at the midshaft plotted against body mass on logarithmic axes. Data for the small, intermediate and adult groups are represented by circles, squares and diamonds, respectively. Cranio-caudal (ICC) and medio-lateral (IML) data are represented by filled and open symbols, respectively. In A, y=13.4x0.53±0.07 (r2=0.92). In B, ICC, y=26.6x0.84±0.16 (r2=0.85); IML, y=52.3x1.03±0.12 (r2=0.94). The broken lines represent isometry in each case (slope: A, 0.67; B, 1.33) and are positioned to facilitate comparison with the regression lines (solid lines).

 


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Fig. 8. Percentage mineral ash weight against body mass. Data from the small, intermediate and adult groups are represented by circles, squares and diamonds, respectively. y=55.4+0.21x (±0.07, r2=0.68).

 





© The Company of Biologists Ltd 2004