

ORIGINAL ARTICLE 

Year : 2018  Volume
: 9
 Issue : 4  Page : 246249 


On the linear sizes of vertebrae and intervertebral discs of children in the beginning of puberty
Mikhail Dudin^{1}, Yuri Baloshin^{2}, Igor Popov^{2}, Nikita Lisitsa^{2}, Stepan Bober^{1}
^{1} Center for Rehabilitation for Children's Orthopaedic Diseases, St. Petersburg, Russia ^{2} Department of Higher Mathematics, ITMO University, Kronverkskiy, St. Petersburg, Russia
Date of Web Publication  21Jan2019 
Correspondence Address: Prof. Igor Popov Department of Higher Mathematics, ITMO University, Kronverkskiy, 49, St. Petersburg 197101 Russia
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jcvjs.JCVJS_91_18
Abstract   
Study Design: We collected experimental data concerning vertebrae sizes and performed an investigation of these data for different patient ages by methods of mathematical statistics. Purpose: The standard dimensions of vertebrae and intervertebral discs are of major importance for obtaining a comprehensive understanding of spine diseases and their successful treatment. The purpose is to study these sizes for children at the age of 9–14 years. Overview of Literature: Unfortunately, this issue is poorly presented in the corresponding literature. There are no systematic results. Only particular cases are presented. Materials and Methods: Experimental is based on the: results of Xray investigations of children spines. Theoretical background is given by methods of mathematical statistics. Results: Systematic description of vertebrae sizes for children of age 9–14 is given. This specific age interval is the most common period of initiation of various pathological deformations of human spine. Conclusions: The acquired data both reflect the process of spine growth and can serve for building correct mathematical models of a healthful or diseased spine.
Keywords: Scoliosis, spine, vertebrae
How to cite this article: Dudin M, Baloshin Y, Popov I, Lisitsa N, Bober S. On the linear sizes of vertebrae and intervertebral discs of children in the beginning of puberty. J Craniovert Jun Spine 2018;9:2469 
How to cite this URL: Dudin M, Baloshin Y, Popov I, Lisitsa N, Bober S. On the linear sizes of vertebrae and intervertebral discs of children in the beginning of puberty. J Craniovert Jun Spine [serial online] 2018 [cited 2019 Sep 15];9:2469. Available from: http://www.jcvjs.com/text.asp?2018/9/4/246/250486 
Introduction   
Pathological deformations of a human spine can be regarded as stable deviations of its shape from the normal state. Like any disease, this deviation begins from minimal changes in the homeostasis. On the one hand, this preclinical stage is the most subtle to diagnose, but on the other hand, the most opportune for the treatment or prevention of the disease. This is also true for idiopathic scoliosis.
Based on the broad information on the anatomic and functional properties of the human spine, repeatedly confirmed under various clinical studies,^{[1],[2],[3],[4],[5],[6],[7]} a mathematical modeling problem was formulated.^{[8]} Attempts at solving this problem described^{[9],[10],[11],[12]} the process of formation of a threedimensional deformation of the twocolumn human spine in the framework of theoretical mechanics. The modeling revealed a strict sequence of stages of deformation identical to the observed clinical picture.
However, the models developed suffer from lack of concrete numerical values of the linear dimensions of the components of a spine, which prevents from applying them further to obtain the precise conditions of the transition from a normal to a scoliotic spine.
To address this issue, we analyzed Xray images of children's spines at different ages to reveal the real values of these parameters and their growth rates.
Materials and Methods   
It is hard to measure the linear dimensions of spine components directly due to its anatomic complexity. One of the available methods consists in examining Xray images of the spine of patients of the Center for Rehabilitation for Children's Orthopedic Diseases “Ogonek” (Saint Petersburg). Two groups of patients were considered: one with spinal compression fracture and the other with flat back posture and with idiopathic lordoscoliosis of the first degree with deformation angle 5°–7°.
Compressed vertebrae were ignored in the measurements. Furthermore, the low deformation magnitude in the second group when measured in the axial projection does not affect the observed linear dimensions of the vertebrae.
A total of 497 Xray images were used. The detailed information on the numbers of images is presented in [Table 1].
Each image was processed to measure only the distinctly seen dimensions, mainly the vertebrae C_{7}–L_{5}. The measured parameters were as follows:
 Width of vertebrae bodies (wb)
 Anterior–posterior size of vertebrae (aps)
 Vertebrae height (vh)
 Intervertebral discs height (hd).
These parameters are depicted on [Figure 1].  Figure 1: 1 – The measured vertebrae parameters, 2 – Width of vertebrae bodies (wb), 3 – Anterior–posterior size of vertebrae (aps), 4 – vertebrae height (vh), and 5 – intervertebral discs height (hd)
Click here to view 
The obtained data arrays are plotted in [Figure 2], [Figure 3], [Figure 4], [Figure 5].  Figure 3: Anterior–posterior size of vertebrae (aps), cm (initial data array)
Click here to view 
Results   
The mean values of linear dimensions of vertebrae for different ages were obtained through the method of polynomial regression.^{[13]} As a result, we obtained the averaged form of a linear dependency of vertebrae height and anterior–posterior size and an averaged quadratic dependency of vertebrae width and intervertebral discs height from the vertebra index. The vertebrae indices increase from top to bottom of the spine, vertebra Th_{1} having index #6, while vertebra L_{5} having index #23. The numerical formulas of these dependencies are presented in [Table 2] (“N” is the vertebra index).  Table 2: Vertebrae height, anteriorposterior size, vertebrae width and intervertebral discs height for different children ages
Click here to view 
These dependencies are plotted graphically in [Figure 6], [Figure 7], [Figure 8], [Figure 9].  Figure 7: Anterior–posterior size of vertebrae (aps), cm (linear regression)
Click here to view 
Discussion   
The initial data for the study come from Xray investigations of children spines. It allows one to find only geometric characteristics of vertebrae and intervertebral discs. Other, mechanical, parameters of the biomechanical system which are needed for creation of a mathematical model should be determined by other experimental methods. Systematic description of vertebrae sizes for children of age 9–14 is given. This specific age interval is the most common period of initiation of various pathological deformations of the human spine. These data are necessary, for example, for socalled twocolumn model of spine explaining the scoliosis reasons and evolution (e.g.,).^{[3],[8],[9],[11]}
Conclusions   
This work revealed simple yet informative approximations of the values of linear sizes of the components of the spine for children in the first half of puberty. These values can be used as a reference for building dynamic mathematical models of a normal spine, as well as models of its pathological deformations.
Financial support and sponsorship
The work was partly supported by the grant 0808 of the Government of the Russian Federation.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Bagnall K. How can we achieve success in understanding the aetiology of AIS? Stud Health Technol Inform 2008;135:6174. 
2.  Bagnall KM. Using a synthesis of the research literature related to the aetiology of adolescent idiopathic scoliosis to provide ideas on future directions for success. Scoliosis 2008;3:5. 
3.  DuvalBeaupere G, Dubousset J, Queneau P, Grossiord A. For a unique theory of scoliosis evolution. Presse Med 1970;78:11416. 
4.  Dudin MG, Pinchuk DY. Idiopathic Scoliosis: Diagnosis, Pathogenesis. St. Petersburg: Chelovek; 2009. 
5.  Dudin MG, Pinchuk DY. Idiopathic Scoliosis: Neurophysiology, Neurochemistry. St. Petersburg: Chelovek; 2013. 
6.  Dudin MG. Idiopathic Scoliosis: Prevention, Conservative Treatment. St. Petersburg: Chelovek; 2017. 
7.  Kapandzi AI. Spine: Physiology of the Joints. Moscow: Eksmo; 2009. 
8.  Roth M. Idiopathic scoliosis caused by a short spinal cord. Acta Radiol Diagn (Stockh) 1968;7:25771. 
9.  Dudin MG, Sinitskii YF. On the mechanism of torsion changes in scoliosis. J Orthop Traumatol Prosthet 1981;2:336. 
10.  Dudin M, Olnev M. The threeaxes model of vertebral column deformation. In: Stokes IA, editor. Research into Spinal Deformities. Vol. 2. University of Vermont, Burlington, VT, USA: IOS Press: Technology and Informatics; 1999. p. 6972. 
11.  Dudin MG, Baloshin YU, Bober SV, Pomortsev IY. Mathematical modeling of threeplane deformation of the human spine. Russ J Biomech 2016;20:27282. 
12.  Lisitsa N, Popov I, Baloshin Y, Dudin M, Bober S. Variational model of scoliosis. Theoretical and Applied Mechanics. 2018;45:16775. DOI 10.2298/TAM170818012P. 
13.  LewisBeck MS. Applied Regression: An Introduction. New York: SAGE Publications; 1980. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9]
[Table 1], [Table 2]
