Mechanical behavior of shark vertebral centra at biologically relevant strains

Cartilaginous shark skeletons experience axial deformation at the intervertebral joints, but also within the mineralized cartilaginous centrum, which can compress to between 3% and 8% of its original length in a free-swimming shark. Previous studies have focused on shark centra mechanical properties when loaded to failure; our goal was to determine properties when compressed to a biologically relevant strain. We selected vertebrae from six shark species and from the anterior and posterior regions of the vertebral column. Centra were X-radiographed to measure double cone proportion and apex angles, and were mechanically tested at three displacement rates to 4% strain. We determined the variation in toughness and stiffness of vertebral centra among shark species and ontogenetic stages, testing strain rates, and compared anterior and posterior regions of the vertebral column. Our results suggest that toughness and stiffness, which are positively correlated, may be operating in concert to support lateral body undulations, while providing efficient energy transmission and return in these swift-swimming apex predators. We analyzed the contribution of double cone proportion and apex angle to centra mechanical behavior. We found that the greatest stiffness and toughness were in the youngest sharks and from the posterior body, and there was significant interspecific variation. Significant inverse correlations were found between mechanical properties and double cone apex angle suggesting that properties can be partially attributed to the angle forming the double cone apex. These comparative data highlight the importance of understanding cartilaginous skeleton mechanics under a wide variety of loading conditions representative of swimming behaviors seen in the wild.