关键词：
Wolffs law
trajectory hypothesis
stress trajectories
cancellous bone adaptation
cancellous bone anisotropy
trabecular bone
摘要：
Wolff's "law" of the functional adaptation of bone is rooted in the trajectory hypothesis of cancellous bone architecture. Wolff often used the human proximal femur as an example of a trajectorial structure (i.e. arched trabecular patterns appear to be aligned along tension/compression stress trajectories). We examined two tenets of the trajectory hypothesis;namely, that the trabecular tracts from the tension- and compression-loaded sides of a bending environment will: (1) follow 'lines' (trajectories) of tension/compression stress that resemble an arch with its apex on a neutral axis, and (2) form orthogonal (90 degrees) intersections. These predictions were analysed in proximal femora of chimpanzees and modern humans, and in calcanei of sheep and deer. Compared to complex loading of the human femoral neck, the chimpanzee femoral neck reputedly receives relatively simpler loading (i.e. temporally/spatially more consistent bending), and the artiodactyl calcaneus is even more simply loaded in bending. In order to directly consider Wolff's observations, measurements were also made on two-dimensional, cantilevered beams and curved beams, each with intersecting compression/tension stress trajectories. Results in the calcanei showed: (1) the same nonlinear equation best described the dorsal ("compression") and plantar ("tension") trabecular tracts, (2) these tracts could be exactly superimposed on the corresponding compression/tension stress trajectories of the cantilevered beams, and (3) trabecular tracts typically formed orthogonal intersections. In contrast, trabecular tracts in human and chimpanzee femoral necks were non-orthogonal (mean similar to 70 degrees), with shapes differing from trabecular tracts in calcanei and stress trajectories in the beams. Although often being described by the same equations, the trajectories in the curved beams had lower r(2) values than calcaneal tracts. These results suggest that the trabecular patterns in the calcanei and stress tr
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中文科技期刊
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