# Stochastic Strength Analyses of Screws for Femoral Neck fractures
## 7 Conclusions  
This paper, as well as our previous one [1], discusses and solves basic medical perspectives on _collum femoris_ fractures with the focus on their treatment via cancellous, i.e., femoral, screws, in particular of subcapital, mediocervical fractures. The new, simple, deterministic, and stochastic (probabilistic) 2D model of a cancellous screw in the femur as a beam on an elastic bilateral Winkler foundation, along with the 2 nd-order theory of small deformations, i.e., bending and compression loading, were applied in the beams. Materials, dimensions, loading, differential equations and their solutions, evaluations, etc., are described. Important biomechanical stochastic evaluations, i.e., evaluations of normal forces, shearing forces, bending moments, deflections, slopes, stresses, probabilistic reliability assessment, and the probability of failure were carried out. Compared to the finite element method, our computational model as a whole is characterized by a quick and easy solution and high variability of possible screw insertion positions. One example of probabilistic reliability assessment of the undesirable situation (i.e., probability of plastic deformations) with results \(P_{RF\leq 0}=2.51\times 10^{-5}\) was presented and discussed in this paper. According to the results, from the biomechanical point of view, the cancellous screws are safe enough and are recommended as a suitable and safe osteosynthetic tool for fracture treatment. Other possibilities for future research and developments, such as material nonlinearities, and experiments are discussed. Hence, together with our former work, this article has presented new ideas and methods and has demonstrated their practical applications in biomechanical engineering, centered around a new simple approach to the solution of cancellous screws with applications in the field of traumatology and orthopedics. Applications of stochastic mechanics, together with probabilistic reliability assessment in biomechanics, are still rare but are in accordance with modern and innovative trends of science. According to our presented simple model, the relatively complicated problems of geometry, dimensions, configurations, way of insertion, reliability assessment, etc., for cancellous screws can be solved. Conceptualization, K.F. ; Project administration, L.P. and K.P.D. ; Resources, M.S., R.M., [PERSON] ([PERSON]) and [PERSON] ([PERSON]); Writing--original draft, K.F., D.C., J.K. ([PERSON]) and D.S. ; Writing--review & editing, [PERSON] ([PERSON]), D.C. and [PERSON]. ([PERSON]). All authors have read and agreed to the published version of the manuscript. SP2021/66 \"Use of experimental and computational modeling problems of elastic and flexible bodies\". CZ.02.1.01/0.0/0.0/17_049/0008441 \"Innovative Therapeutic Methods of Musculoskeletal System in Accident Surgery\". CZ.02.1.01/0.0/17_049/0008407 \"Innovative and additive manufacturing technology--new technological solutions for 3D printing of metals and composite materials\". This article was supported by a project SP2021/66 financed by the Ministry of Education, Youth and Sports of the Czech Republic and by projects CZ.02.1.01/0.0/17_049/0008407 \"Innovative and additive manufacturing technology-new technological solutions for 3D printing of metals and composite materials\" and CZ.02.1.01/0.0/0.0/17_049/0008441 \"Innovative Therapeutic Methods of Musculoskeletal System in Accident Surgery\" within the Operational Programme Research, Development and Education financed by the European Union and from the state budget of the Czech Republic. The authors declare no conflict of interest. List of Symbols