analytical solutions; biomechanics; bone; experiments; fifth metatarsal fracture; finite element method; headless screw; Monte Carlo method; orthopedics; osteosynthesis; probabilistic (stochastic) solutions; reliability; steel; tensile and compression loading; traumatology

This paper evaluates the various approaches to strength and stiffness analysis of fracture osteosynthesis using a headless Herbert screw. The problem has been extensively addressed using several scientific approaches, namely the analytical approach, stochastic approach, experimental approach, and (marginally) using the finite elements method. The problem is illustrated on the use of a prototype headless screw Ti: 4.0/1.4 x 30/7 (manufacturer: Medin, Czech Republic) and the surgical treatment of the fifth metatarsal fracture. Mathematical equations for the analytical calculation of the maximum stresses in the screw were established for tensile/compression loading. This problem is also interesting because of its static indetermination in tension and compression; for this reason, it was necessary to use the deformation condition, i.e., the relationship between screw extension and bone contraction. The stochastic (probabilistic) approach, i.e., application of the Monte Carlo method, takes advantage of the mathematical equations derived during the analytical solution by respecting of the natural variabilities and uncertainties. The analytical and stochastic approaches were validated by measurements on porcine bones and by the finite element method. The data measured experimentally were also processed and used for deriving an equation, appropriately approximating the data. The main part of the measurement was to determine the axial force generated during osteosynthesis with a headless screw. The obtained compressional force was used to determine the maximal stress in the screw and bone. Finally, the methods were compared. In this paper, comprehensive and original approaches based on the authors' experience with multiple methods are presented. Obtained results are necessary for headless screw designers during optimalization of the implants and are also useful for surgeons developing new surgical techniques.