Shape and function of the diaphysis of the human tibia

Abstract

There is an agreement about the principle that bones are optimized to resist daily loads. This has never been ascertained for the human tibia. One of the main load components in the tibia in vivo is a cantilever load (with a linearly varying bending moment, with its largest component in the sagittal plane). investigated if the cross-section of the diaphysis and its variation along the tibia make it an optimized structure with respect to such loads. Six cadaveric tibias were CT-scanned. The geometry and material properties were extracted from the CT-scans, and analyzed along the tibias. A linear variation along the tibia was found for the second moments of area and inertia, and the section modulus in the sagittal plane (slightly less linear in the frontal plane). Conversely, the other properties (polar moments and cross-section are) were much less linear. This suggests that the structure is optimized to resist a bending moment that varies linearly along the tibia. The tibias were instrumented with 28 triaxial straingauges each. Strain was measured under cantilever loading in the sagittal and frontal planes, under quasi-constant-bending in the sagittal and frontal planes, under torsional loading, and with an axial force. The strain distribution was remarkably uniform when cantilever loading was applied in the sagittal plane and slightly less uniform when cantilever loading was applied in the frontal plane. Strain variations were one order of magnitude larger for all other loading configurations. This shows that the tibia is a uniform-stress structure (i.e. optimized) for cantilever loading.

Keywords: A; A(E); A1, A2…A7; BL; BW; Bending; CT; Cross-section; DICOM; Diaphysis; HU; Hounsfield unit; Human tibia; I(E_sagittal), I(E_frontal); I(sagittal), I(frontal); J(E_polar); J(polar); L1, L2…L7; M1, M2…M7; Mechanical strain; Moment of area; Optimization; P1, P2…P7; S(E_sagittal), S(E_frontal); S(sagittal), S(frontal); angle of the principal planes (counter-clockwise); area of the cross-section (Table 1); area of the cross-section, weighted by the local material properties (Table 1); biomechanical length of the tibia; body weight; computed tomography; digital imaging and communications in medicine (it is a standard for handling, storing, and transmitting medical images); maximum principal strain; minimum principal strain; polar moment of area (Table 1); polar moment of inertia (Table 1); second moments of area (Table 1); second moments of inertia (Table 1); section modulus (Table 1); section modulus, weighted by the local material properties (Table 1); strain gauges on the anterior side, from proximal to distal; strain gauges on the lateral side, from proximal to distal; strain gauges on the medial side, from proximal to distal; strain gauges on the posterior side, from proximal to distal; ε(1); ε(2); θ(p).