Strain Gradients Correlate with Sites of Periosteal Bone Formation

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Abstract
We examined the hypothesis that peak magnitude strain gradients are spatially correlated with sites of bone formation. Ten adult male turkeys underwent functional isolation of the right radius and a subsequent 4‐week exogenous loading regimen. Full field solutions of the engendered strains were obtained for each animal using animal‐specific, orthotropic finite element models. Circumferential, radial, and longitudinal gradients of normal strain were calculated from these solutions. Site‐specific bone formation within 24 equal angle pie sectors was determined by automated image analysis of microradiographs taken from the mid‐diaphysis of the experimental radii. The loading regimen increased mean cortical area (±SE) by 32.3 ± 10.5% (p = 0.01). Across animals, some periosteal bone formation was observed in every sector. The amount of periosteal new bone area contained within each sector was not uniform. Circumferential strain gradients (r2 = 0.36) were most strongly correlated with the observed periosteal bone formation. SED (a scalar measure of stress/strain magnitude with minimal relation to fluid flow) was poorly correlated with periosteal bone formation (r2 = 0.01). The combination of circumferential, radial, and longitudinal strain gradients accounted for over 60% of the periosteal new bone area (r2 = 0.63). These data indicate that strain gradients, which are readily determined given a knowledge of the bone's strain environment and geometry, may be used to predict specific locations of new bone formation stimulated by mechanical loading.