New insights into long-bone biomechanics: Are limb safety factors invariable across mammalian species?

The most common function of limb bones is to provide stiff levers acting against muscles and gravity; however, a general mechanical description is not yet available. This research attempts such a description by modeling the bone's intrinsic biomechanics through elastic stability of solid long cylinders considered in non-critical, transient and critical mechanical regimes distinguished conventionally through maximal resisting elastic strains.The non-critical regime controls bones’ adaptation through the safety factor (bone strength related to the peak functional stress) S⩾2S⩾2. This is ensured by bone-diameter (d=1/3+β)(d=1/3+β) and bone-length (l=1/3-β)(l=1/3-β) scaling exponents generally following from compressive-stress constraints. Prange's index (0<β⪡1)(0<β⪡1) known from long-bone allometry is related to the components of bone-stress tensor. The tensor-stress components depend weakly on body size, whereas the overall peak limb-compressive stress in running animals remains almost weight-independent. The transient regime (1