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First published online August 8, 2003

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Optimization of bone growth and remodeling in response to loading in tapered mammalian limbs

Daniel E. Lieberman^1,*, Osbjorn M. Pearson², John D. Polk¹, Brigitte Demes³ and A. W. Crompton⁴

¹ Peabody Museum, Harvard University, 11 Divinity Avenue, Cambridge Massachusetts 02138, USA
² Department of Anthropology, University of New Mexico, Albuquerque, New Mexico, 87131, USA
³ Department of Anatomical Sciences, Health Sciences Center, State University of New York, Stony Brook, New York, 11794, USA
⁴ Museum of Comparative Zoology, Harvard University, 26 Oxford St., Cambridge, Massachusetts, 02138, USA

View larger version (17K): [in a new window]   Fig. 1. Optimization model for cortical bone responses to loading. The periosteal modeling rate (PM RATE) is predicted to decrease and the Haversian remodeling rate (HRR) to increase with higher costs of adding mass [roughly proportional to R, the functional distance from each midshaft to the axis of rotation of the hind limb at the hip]. If Haversian remodeling functions to repair or prevent fatigue damage, then HRR is expected to increase as PM RATE activity declines with age for both models.

View larger version (33K): [in a new window]   Fig. 2. Midshaft periosteal modeling rate (left y-axis, circles), and Haversian remodeling rate (right y-axis, squares) versus R, the distance from the midshaft to the hip joint (x-axis) in juveniles (A), subadults (B) and young adults (C). Runners, filled symbols; controls, unfilled symbols. Values are means ±1 S.E.M. The energetic cost of added mass is approximately proportional to the square of R. Modeling rates are higher in proximal than distal bones, and decrease with age, whereas remodeling rates are higher in distal than proximal bones, and increase with age. The effects of exercise are greatest in juveniles, and non-significant in all adults. See Tables 1 and 2 for tests of significance.

View larger version (19K): [in a new window]   Fig. 3. Isoclines of strains () in microstrain (µ) in the midshaft cross section of the tibia (A) and metatarsal (B) of two juvenile sheep at 1.5 m s–1. NA is the neutral axis; positive values are tensile, negative values are compressive. x indicates the location of rosette strain gauges and arrows show the orientation of the principal strain (1°) relative to the bone's long axis. Orientations of strains (solid lines) relative to the long axis of the bone (dotted lines) are indicated by the small figures adjacent to each gauge site. Both bones are bent in the sagittal plane, with neutral axes shifted significantly from the cross-sectional centroid towards the cortex subject to tension.