## 7 Conclusions  
The main objective of this study was to perform stress-strain computational analyses and an experimental analysis for the determination of the axial force generated during osteosynthesis with a headless Herbert screw (Ti: 4.0/1.4 \(\times\) 30/7 mm, Medin a.s., Czech Republic). This screw is intended for the osteosynthesis of fragments of the fifth metatarsal fracture. Such implants are commonly used in medical practice. Due to the different pitches of the threads on both ends of the screw, the bone fragments are drawn to each other and compressed at the fracture site, which facilitates the process of fracture healing. The analytical (deterministic) calculation was defined as a tension-compression problem. This problem was statically indeterminate to the first degree, which required the use of an additional deformation boundary condition. The relationships derived from the analytical calculation were used for the stochastic (probabilistic) approach, which, through pseudo-random values generation from defined histograms, allows us to respect the real variability of the input and output data and to perform a probabilistic reliability assessment. Here, the Monte Carlo method was used for the solution and evaluation of 10\({}^{6}\) pseudo-random simulations. In addition, an experiment (10 measurements) aimed at determining the compressive normal forces acting on the [PERSON] screw during tightening was performed. This experiment revealed the average force required to shear the thread in the bone to be 204 N. This is an important finding for headless screw designers and for surgeons developing new surgical techniques. Next, a suitable function sufficiently approximating the measured values from the experiments was searched for. The excellent quality of the fit of the regression model to the experimental data was demonstrated using the coefficient of determination R\({}^{2}\). Finally, the results of all approaches were compared. As the approximation of the experiment using a cosine power function (F = \(\frac{\mathrm{F_{F}}}{2^{6}}\)\([1-\cos\left(\frac{\mathrm{m}}{\mathrm{n_{e}}}\right)]^{m}\)) is suitable and provided sufficient accuracy, it is obvious that the task can be solved analytically as a second-order differential equation, which subsequently leads to a significantly simpler and computationally less demanding solution than the use of the FEM approaches. Our model also enables a relatively simple application of the probabilistic approach, which is advantageous, as it allows respecting the real variability of input and output variables, which is typical of the real world. This paper also briefly mentions the numerical solution based on FEM. The results of all four approaches to the solution (i.e., deterministic, stochastic, experimental, and numerical) are in sufficient agreement and confirm the suitability of the examined screw for clinical use. This combined algorithm can be used as a basis for implant certification or recommendations for clinical testing of various types/applications of headless Herbert screws in medical or veterinary practice, as well as for the modification or change of screw design. The acquired data on axial forces in osteosynthesis of the fifth metatarsal were determined in an original and novel way in this study. From this perspective, the paper significantly contributes to the field of fracture biomechanics. The applications and conclusions obtained in this paper can be used in other fields as well--even in the construction industry in the analysis of joints in wooden structures [24; 30; 31]. **Author Contributions:** Supervision, K.F. and L.P.; Writing--original draft, K.V. and K.F. ; Writing--review & editing, V.B., J.D., L.P., M.H., J.P., R.M., J.K., P.K., P.O., K.C., E.O. and J.V. All authors have read and agreed to the published version of the manuscript.