Modeling Components of Lumbar Spine Using an Optimization Algorithm Developed for Passive Exoskeletons

This work describes a rst attempt to model the passive components of the lumbar spine during a simple movement of lateral bending. This approach adopts an adapted version of an algorithm that was developed for the design of a passive exoskeleton for the rehabilitation of upper and lower limbs. The aim of this work is to assess the capability of this approach to deal with more complex structures. This approach is structured in two sections: the rst one deals with the design of a human lumbar spine by integrating geometrical data taken from literature with intervertebral joint angles measured on human lumbar spines. In particular, the model is composed by 3D images of lumbar vertebrae obtained from CT scans performed on cadaver specimens while their orientation is given by values of intervertebral angles measured on healthy patients. In order to properly arrange all the vertebrae in the space, geometrical assumptions have been considered and implemented. The second part of the work focuses on the algorithm cited above; in particular, it describes the di erences respect to the original one and its implementation to the virtual lumbar spine. Instead of having elements that are simpli ed as beams that perform movements in a plane, the algorithm deals with the morphologies of the vertebrae that are moving in space. Therefore, the developed code has been structured in order to arrange a network of linear springs for each functional spinal unit; these elastic elements would represent passive tissues such as intervertebral discs and ligaments. For each pair of vertebrae, the algorithm tunes the characteristics of these springs in order to guarantee the torque equilibrium with respect to external loads that are acting on the vertebral body centroid of the upper vertebra; indeed, this is able to rotate around a spherical joint placed between the lower endplate of the upper vertebra and the upper endplate of the lower vertebra. The results show that this is a theoretical framework that could be used to apply the Exonet as an hypotetical assistive device