In nowadays, an important area in medicine is the early preclinical identification of the parameters deviations from the norm, where mathematical modeling can help, which should be used to calculate individual linear parameters of internal structures based on external parameters of the body. The aim of the study was to calculate the individual total linear measures of the lumbar intervertebral discs in juniors and men of the first adulthood (17-28 years) in norm. The total size of the each intervertebral discs were calculated a sum of the anterior-posterior diameter, frontal diameter and vertical sizes of each lumbar intervertebral discs, which were measured by MRI. The next step was to calculate the relative proportional nonlinear somato-disc rates (based on body weight and body length) for each individual examined. Mathematical processing of the measured parameters and the relative values of the somato-disc relationships was carried out by the statistical data processing program “STATISTICA 6.1” using parametric methods. The correct distribution of the variational series indicators, mean values and their standard errors were evaluated. Based on relative values the mathematical model was created to obtain individual values of the TS of the lumbar intervertebral discs. Subsequently, we compared the measured total discs sizes of the anterior-posterior, frontal diameters and vertical sizes of the lumbar intervertebral discs with a mathematically calculated value for each lumbar intervertebral discs. The significant difference between the mathematically calculated and measured values of the total intervertebral discs’ sizes of the didn’t exceed 10%. Determination of the standard linear dimensions of the intervertebral discs of the lumbar spine using CT and MRI and comparison with theoretically calculated indices will make it possible to diagnose early manifestations of the lumbar intervertebral discs pathology.

The research for new vertebro-somatometric correlations will significantly improve the possibilities of methods for individualizations of the normal parameters and will accelerate the introduction of scientific developments into the daily practice of clinicians, radiologists, neurosurgeons and other specialists. The aim of research is to investigate the peculiarities of relationships between partial linear dimensions of the lumbar intervertebral discs, their total sizes and relative indicators with somatometric parameters in the youth and young adult males in norm. The linear dimensions of the lumbar intervertebral discs (height, sagittal and transverse sizes) were measured noninvasively on the MRI images in the axial, sagittal and coronal plains. The somatometric investigation was performed individually with measuring of the general (length and weight of body) and particular sizes (the longitudinal sizes, the transverse sizes, the circumferences, pelvic sizes and skinfolds thickness). The bony, muscle and fat components of the body mass were calculated. Correlation analysis was performed in the «Statistica 6.1» license package. The arithmetic means of absolute correlation coefficients between particular and total individual sizes of IVDL1-L2, IVDL2-L3, IVDL3-L4, IVDL4-L5 and relative quantity with somatometric parameters were calculated with following results: arithmetic means of absolute correlation coefficients for particular individual sizes are within 0.080 – 0.150; for total sizes – 0.240; for ratio of the total sizes to the mass-growth coefficient – 0.490. Analysis of arithmetic mean values of absolute correlations with somatometric parameters in youth and young adult males in the norm (17-28 years) showed a gradual increase in the values of correlation coefficients and an increase in the number of significant correlations with maximum values in relative indicators. Thus, in youth and young adult males aged 18-28 years, the features of the relationship of somato-anthropometric parameters with the linear dimensions of the intervertebral discs of the lumbar spine in the norm were studied. The numerous relationships between the partial (height, sagittal and transverse sizes) linear dimensions and total sizes of the lumbar intervertebral discs in the youth and young adult males in norm (17-28 years) with their somatometric parameters were found. Thus, the use of relative indicators can be more acceptable in the subsequent mathematical modeling of individual indicators, in particular, the parameters of the intervertebral discs.

The relationships between linear dimensions of the lumbar intervertebral discs (IVDL1-L2, IVDL2-L3, IVDL3-L4, IVDL4-L5) and somatometric parameters in girls and females of the first adulthood were investigated. The numerous relationships between the partial (height, sagittal and transverse sizes) linear dimensions and total sizes of the lumbar intervertebral discs in girls and women of the first adulthood (16-26 years) with their somatometric parameters were found. The linear dimensions of the lumbar intervertebral discs (height, sagittal and transverse sizes) were measured on the MRI images in the axial, sagittal and coronal plains. The arithmetic means of absolute correlation coefficients between particular and total individual sizes of IVDL1-L2, IVDL2-L3, IVDL3-L4, IVDL4-L5 and relative quantity with somatometric parameters were calculated with following results: arithmetic means of absolute correlation coefficients for particular individual sizes are within 0,120 - 0,170; for total sizes – 0,190; for ratio of the total sizes to the mass-growth coefficient – 0,507.

Annotation. The use of math algorithms for calculating the anatomical and functional parameters of the organs and systems based on somatometric parameters and allows to individualize and quantify the indicators of the norm. In order to build mathematical models to calculate the size of the lumbar spine intervertebral discs somatometry of almost healthy 80 girls and women aged 16-26 years and 74 juniors and men aged 17-28 years was performed. As well as magnetic resonance imaging of the lumbar spine was used to obtain the MR-images in the axial, sagittal and frontal planes in the T2-TSE mode and to perform MR-morphometry by using the DICOM image processing program. The correlation analysis and estimation of interrelations of somatometric parameters with partial linear sizes of intervertebral disks, the sum of the disks’ sizes and relative somato-disk rate are carried out. Body weight was found to have strong correlations with relative somato-disc rate (mean correlation coefficients for L1-L5 intervertebral discs were 0.803 and 0.821 in women and men, respectively) and weak and very weak correlations with partial disc sizes. When constructing the regression model, as an intermediate stage of the calculation, the somato-disk rate (the ratio of mass-growth coefficient to the sum of the sizes of the intervertebral disc) was used. The simulation of the three sizes’ sum of intervertebral discs L1-L5 segments was ultimately based on weight and body length (coefficient of determination R2 is from 80.4% for the sum of the intervertebral discs L1-L2 in girls and women and boys and men, up to 89.7% for the sum of the size of the intervertebral disc L4-L5 in girls and women). Verification of the obtained mathematical models showed a discrepancy between the calculated and measured indicators of the sums of intervertebral disc sizes in the presence of disc degeneration. The used mathematical algorithm for calculating individualized indicators of linear dimensions of lumbar intervertebral discs on the base of somatometric parameters allowed to determine the absence of objective quantitative changes in unchanged intervertebral discs and avoid overdiagnosis.

An important element of evidence-based medicine is to take into account the individual variability of the indicators of the norm of intervertebral discs, which is undoubtedly the basis for early preclinical detection of their pathology. Mathematical modeling and comprehensive assessment of the parameters of the intervertebral discs can not only predict and determine the early manifestations of pathological changes, but also help to correct them in advance. The aim of the study was to calculate and evaluate the variability of absolute, calculated and relative metric parameters of intervertebral discs in the norm with the subsequent possibility of modeling standards based on individual linear dimensions of intervertebral discs of the lumbar spine and general anthropometric characteristics (body length and weight) in young men and men of the first period of adulthood (17-28 years), both in separate age groups and in the combined group. The series of MRI scans obtained on a Phillips Achieva 1.5T scanner measured the anterior, middle and posterior vertical dimensions, maximum sagittal and frontal dimensions of the intervertebral discs L1-L2, L2-L3, L3-L4, L4-L5 segments of the spine (IVDL1-L2, IVDL2-L3, IVDL3-L4, IVDL4- L5). We calculated the average height of the intervertebral discs, cross-sectional area and volume of intervertebral discs, as well as relative indicators - the ratio of the sum of sagittal and transverse dimensions, the sum of three dimensions, cross-sectional area and volume of intervertebral discs to the average intervertebral disc height. Statistical analysis of the obtained morphometric parameters was performed in the license package “STATISTICA 6.1”. The distribution of variation series indicators, their average values and standard errors, coefficients of variation and asymmetry were evaluated. It was determined that the sums of the transverse and sagittal sizes and the sums of the three sizes increase proportionally in the caudal direction, have a distribution of indicators as close as possible to normal, and their coefficients of variation are many times smaller than for cross-sectional areas and volumes. Indicators of the ratio of the sum of the sagittal and transverse size and the sum of the three sizes to the average height of the intervertebral discs have a variability of less than 10% and correspond to the characteristics of the general population. Body weight and length have significantly higher correlation coefficients with the sums of sagittal and transverse dimensions, the sums of three dimensions and cross-sectional areas than with the partial dimensions of the intervertebral discs.