Muscle forces – Bone deformations Designing an inverse finite element algorithm

Abstract

Bone remodeling and it’s capability to adapt to various environmental conditions is the topic of many present-day research. On Earth, many people suffer from bone atrophy and Osteoporosis with no real treatment available. Additionally, astronauts experience significant bone atrophy during their time in space. Therefore investigations are focusing on understanding the processes behind these effects, mainly in the long bones like the human femur and the tibia. The prime controlling mechanism for bone adaptation is the mechanical loading of the bone. Yet, contrary to common belief, it is not the body weight and its’ momentum that triggers bone adaption. Muscle forces are explicitly needed which, by contracting, exert a force on the bone and therefore a deformation. A descriptive example is shown in the figure on the right hand side: While balancing on the ball of the foot, the muscles exert a force three times larger than the body weight to keep the equilibrium. This force is induced into the tibia on top of the acting force due to the body weight. All of this points lead to the fact, that the muscles play an essential role in bone remodeling and adaption. However, since it is difficult to measure muscle forces in vivo, a novel approach is introduced here. It combines a classical forward Finite Element Analysis (FEA) with a linear optimization algorithm to create an inverse FEA, in order to solve the question: What forces do muscles exert on the bone?