Optimization of Taylor spatial frame half-pins diameter for bone deformity correction: Application to femur

Using external fixtures for bone deformity correction takes advantages of less soft tissue injury, better bone alignment and enhances strain development for bone formation on cutting section, which cause shorter healing time. Among these fixtures, Taylor spatial frame is widely used and includes two rings and six adjustable struts developing 6 degrees of freedom, making them very flexible for this type of application. The current study describes a method to optimize Taylor spatial frame pin-sizes currently chosen from the surgeon's experiences. A three-dimensional model of femur was created from computed tomography images; segmentation of the medical images was made based on the Hounsfield unit (gray scale) in order to allocate adequate mechanical properties into cortical and trabecular bone sections. Both the cortical and trabecular sections were assumed to be isotropic and homogeneous. The diameter optimization of Taylor spatial frame's half-pins was carried out by coupling genetic algorithm and finite element analysis. The finite element analysis was based on a static mechanical load corresponding to a standing person's body weight. Finite element analysis results were validated with experimentally measured strains obtained from bone compression tests. A cost function, based on the developed bone stresses, was defined close to the Taylor spatial frame's half-pins. The calculated cost function showed a decrease of over 33% from the initial half-pin selection by the surgeon and the genetic algorithm optimization. Consequently, the maximum stresses experienced by the bone in the connected location of the half-pins decreased from 121.4 MPa in the surgeon's selection to 73.07 MPa as a result of the optimization process.