System reliability analysis of the scoliosis disorder

Nouri et al. BMC Musculoskeletal Disorders https://doi.org/10.1186/s12891-020-03230-4 (2020) 21:199 RESEARCH ARTICLE Open Access System reliability analysis of the scoliosis disorder Fatemeh Nouri1, S. Hooman Ghasemi1,2* and Ji Yun Lee2 Abstract Background: Scoliosis is a spine abnormal deviation, which is an idiopathic disorder among children and adolescents. As a matter of the fact, distribution of loads on the patient’s spine and load-carrying capacity of the vertebral column are both random variables. Therefore, the probabilistic approach may consider as a sophisticated method to deal with this problem. Method: Reliability analysis is a probabilistic-based approach to consider the uncertainties of load and resistance of the vertebral column. The main contribution of this paper is to compare the reliability level of a normal and scoliosis spinal. To do so, the numerical analyses associated with the inherent random parameters of bones and applied load are performed. Then, the reliability indices for all vertebrae and discs are determined. Accordingly, as the main innovation of this paper, the system reliability indices of the spinal column for both normal and damaged backbone systems are represented. Results: Based on the required reliability index for normal spinal curvature the target system reliability level for scoliosis disorder is proposed. Conclusion: Since the proposed target reliability index is based on the strength limit state of the vertebral column, it can be considered as a reliability level for any proposed treatment approaches. Keywords: Target reliability, Scoliosis, Vertebral column, System reliability, Statistical parameters Background Scoliosis is a common disease that affects many children and adolescents. In a simple definition, scoliosis is a onesided bending of the spine. Scoliosis is a serious malformation in which the spine abnormally changes with spinal rotation in three directions [26]. This abnormality progresses throughout growth, and the asymmetric loads due to spinal deformation cause more deformation, resulting in increased asymmetric loads, and this cycle continues [31]. In most cases, the growth of the spine has been observed in pre-puberty [28]. Spinal deformation in the idiopathic scoliosis abnormality is generally described as the * Correspondence: 1 Department of Civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin 14778-93855, Iran 2 Department of Civil and Environmental Engineering, Washington State University, Pullman, USA lateral deformity caused by the lateral spine curvature [30]. The deformity caused by the spine in this disorder involves deformation and displacement in three directions and the spinal axis rotation [17]. The effective treatment for the curvature of the spine is to install the rod and curvature correction by loading force. The rod that is mounted on the spine is responsible for bearing the forces created by the spine and skeletal deformation. For this reason, it is very important to estimate the forces needed to be loaded on the rod used in scoliosis curvature repair in a way that does not cause bone failure [26]. Measuring the forces involved in the spine in a living tissue environment is difficult, and numerous studies have been done to measure the distribution of force on the spine and this information is available. In 1989, Stokes examined the spine of 40 patients with idiopathic scoliosis in adults to examine the relationship between the vertebral spinal cord and © The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Nouri et al. BMC Musculoskeletal Disorders (2020) 21:199 deviant and lateral curvature in the spinal column in scoliosis and indicated that spinal rotation had a close relationship with deviation. Then, Stokes defined the relationship between the vertebral rotation and lateral curvature in the spine. In 2011, Shi et al. examined the association between the progression of idiopathic anomalies in adults and the anomalous development of the anterior part of the spine and indicated that the rate of growth stimulated the progression and increased risk of scoliosis. Salmingo et al. [26] presented a force method based on a finite element analysis to estimate spinal force inputs in a living tissue environment by examining the shape deformation used in the treatment of scoliosis abnormality curvature correction using 3D imaging. They showed that bending stresses depend directly on the curvature angle on the deformed rod. In 2013, Salmingo et al. measured the amount of bar deformation used in the treatment of surgery before and after treatment. They found the correlation between the intensity of the force and the angle of correction by measuring the applied force. Little et al. [19] tried to find out how deformation was affected by the severity of corrective forces to predict the severity of the tension required to treat spinal curvature in scoliosis abnormalities. Their research showed that there is a direct relationship between the compressive forces of the connections used and the degree of curvature change. In 2015, Abe et al. analyzed the amount of force that is necessary to correct the spinal cord by limited finite element analyzes and examining 20 patients who underwent spinal cord correction surgery between 2009 and 2011. Schlösser et al. [27] examined the relationship between the three-dimensional displacements of the vertebrae. In 2015, Cheuk et al. evaluated the mechanical properties of the spinal bones using finite element analysis. However, the applied load and the structural resistance of the backbone system are both random variables which involved the uncertainties. Therefore, there is a need for a probabilistic approach to estimate the load-carrying capacity of the scoliosis disorder. To do so, in this study, first, it is attempted to collect the inherent uncertainties parameters impacting on the load-carrying capacity of the vertebral column. The (...truncated)