Form-function relationship between trabecular bone architecture and biomechanical function in the horse humerus

• Cadoret Nicolas
• Julien Chaves-Jacob
• Linares Jean-Marc
• Houssaye Alexandra

• Bio-inspiration
• Bones
• Trabecular Architecture
• Stress Tensor
• Fabric Tensor

In mechanical design, it is a common challenge to design parts with high strength-to-weight ratio. Throughout evolution, natural organisms have faced the same challenge and developed a variety of solutions. One of these is the endoskeleton, composed of bones linked by joints. In long bones, near joints, Nature uses an anisotropic porous material, trabecular bone. This architecture is adapted to the mechanical stresses it undergoes. The aim of this work is to study the relationship between a given trabecular architecture and its biomechanical function. Understanding this relationship allows to predict the natural trabecular architecture that would be optimal to support a given stress field. Trabecular architecture is often characterised through a Fabric Tensor (FT) whose eigenvectors and eigenvalues respectively describe trabecular orientation and anisotropy. A first FT (M_mes) was measured using BoneJ2 in 20 trabecular Regions Of Interest (ROI) identified in a microtomographied horse humerus. In parallel, the stress field in this humerus was calculated using a Finite Elements Analysis (FEA) based on a musculoskeletal model of the horse forelimb during trotting. This FEA was used to obtain a second FT (M_est) for each ROI through an equation from the literature relating FT to stress in the human femur. Difference percentages between M_mes and M_est were calculated and showed that the proposed law is accurate to predict FT from stress in the horse humerus. This law is interesting for the design of mechanical parts bio-inspired from bones, which reproduce the adaptation of trabecular architecture to the mechanical stress it undergoes.