Femoral bone strength in extant quadrupedal animals from Microtus ochrogaster to Loxodonta africana

The femoral bone strength in extant quadrupedal animals from Microtus ochrogaster (meadow mouse) to Loxodonta africana (African elephant) has been studied as a function of mass of the animal. The masses of these animals vary by more than five orders of magnitude. Given the finite resources available, each organ of an animal is as big as it needs to be, but no bigger. In this work, we study what limits the strength of the femur. The femoral cortical area at the narrowest part gives the measure of the strength of the femur to support the longitudinal stress due to the weight of the animal. The femoral section modulus at the narrowest part is a measure of the ability to resist transverse stresses. Both the cortical area and the section modulus are found to be power laws of the mass. The exponent of the power law is about 0.70 for the cortical area and about 1.0 for the section modulus. This suggests that transverse stresses are the limiting factor for the bones of the legs of these quadrupedal animals.