Treherne Paige, Lee Erin C S, Rainbow Michael J, Kelly Luke A
School of Human Movement and Nutrition Science, The University of Queensland, Brisbane, Australia.
Department of Mechanical and Materials Engineering, Queen's University, Kingston, Canada.
R Soc Open Sci. 2025 Mar 19;12(3):241828. doi: 10.1098/rsos.241828. eCollection 2025 Mar.
If human skeletal shape increases proportionally with size (isometric scaling), we would expect exponential increases in joint contact stress as individuals become larger. However, if skeletal shape changes as a function of size (allometric scaling), this can mitigate increases in joint contact stress by changing the surface area (SA)-to-volume ratio. Here, we explored whether human foot bones scale with allometry and, if so, to identify the shape features that are associated with bone size. Computed tomography scans of the two largest foot bones (talus, calcaneus) were obtained from 36 healthy individuals. We implemented a scaling analysis for each joint articular surface and bone. We performed a Procrustes ANOVA to establish the shape features associated with bone size. In line with our hypothesis, articular surfaces on the calcaneus scaled with positive allometry relative to bone volume, whereas total bone SA scaled with negative allometry. This indicates that articular surfaces grew at a faster rate than the overall bone SA. Interestingly, the calcaneus appeared more cube-like with increasing size. This may be important for the mitigation of internal bone stresses with increasing skeletal size. Our findings suggest distinct but varied scaling strategies within the foot. This may reflect the requirement to maintain healthy joint contact and internal bone stresses with increasing size.
如果人类骨骼形状随尺寸成比例增加（等距缩放），那么随着个体变大，我们预计关节接触应力会呈指数增加。然而，如果骨骼形状随尺寸变化（异速生长缩放），这可以通过改变表面积与体积比来减轻关节接触应力的增加。在这里，我们探讨了人类足部骨骼是否按照异速生长进行缩放，如果是，确定与骨骼大小相关的形状特征。从36名健康个体获取了两块最大足部骨骼（距骨、跟骨）的计算机断层扫描图像。我们对每个关节面和骨骼进行了缩放分析。我们进行了普氏方差分析以确定与骨骼大小相关的形状特征。与我们的假设一致，跟骨关节面相对于骨体积呈正异速生长缩放，而总骨表面积呈负异速生长缩放。这表明关节面的生长速度比整体骨表面积快。有趣的是，随着尺寸增加，跟骨看起来更像立方体。这对于随着骨骼尺寸增加减轻内部骨应力可能很重要。我们的研究结果表明足部存在不同但多样的缩放策略。这可能反映了随着尺寸增加维持健康关节接触和内部骨应力的需求。
