Three‐dimensional geometric and structural symmetry of the turkey ulna

Abstract

Structural models of long-bone preparations usually assume left-right symmetry of contralateral bones under normal (baseline) conditions. To obtain insight on how this assumption affects the detection of subtle changes (as from functional adaptation), we formally examined the three-dimensional geometric and structural symmetry of paired long bones, using contemporary image reconstruction and stress analysis techniques. Nine pairs of ulnae from normal male turkeys were reconstructed computationally from serial transverse images obtained by either (a) mechanical sectioning and digital photographic imaging or (b) computed tomography. Computed tomography scans allowed greater precision in reconstruction than did digitally imaged photographs. Left-right comparisons of parameters of geometric symmetry (from computed tomography reconstructions) revealed average differences in whole bone volume and whole bone principal moments of inertia of 3.6 and 3.0%, respectively. Differences in bone curvature were indexed as noncolinearity of left compared with (mirrored) right centroidal axes, giving a disparity of 0.7 ± 0.3 mm. Within the longitudinal central 20% of the diaphysis (the customary region for histomorphometry), average left-right differences in cross-sectional area and area principal moments of inertia for computed tomography images were 4.7 and 5.0%, respectively. The overlap of longitudinally paired cross sections of the mid-diaphysis, aligned at common centroids and oriented in the respective principal inertial directions, was greatest (as much as 95%) in the central 20% of the diaphysis. Paired three-dimensional finite element models demonstrated nearly identical left and right stress/strain fields throughout the ulnar diaphyses for both compressive and torsional loading. Our data suggest that the assumption of contralateral geometric symmetry in long bones should be judged in the context of the specific attribute of symmetry under consideration; however, we conclude that for purposes of finite element modeling the assumption of symmetry is reasonable.