Мathematical modeling of reference values of internal organs of mongolians and comparative assessment with ultrasound measurements / Монголын Анагаах Ухаан

ABSTRACT

Objective: Mathematical modeling of reference values of internal organs of Mongolians (in vitro) and compare them with results of two and three-dimensional ultrasound measurements.Materials and Methods: Mathematical modeling was done with the methods of interpolation. Ultrasound measurements of internal organs were made with common methods of standard planes and results were analyzed. The basis of mathematical modeling to convert reference values of organs to values of organs in live conditions (in vitro) was elaborated. For example Heart was modeled with double cylindrical volume with convex surface. Liver was modeled with triangle pyramid (tetrahedron) with concave and convex surface. Kidney was modeled with the shape of rotating ellipse with convex and hollow surface. Spleen was modeled with the shape of cutting pyramid with concave and convex surface. Pancreas was modeled with the shape of cylinder with convex surface. Gallbladder was modeled with the shape of cutting cone with spherical bottom. Following formulas were defined and used for modelingWhere V-volume, r-modelled average value of 3 dimensions radius of rotation, k-coefficient for converting volume of mathematical models to original volume, P-perimeter, S-calculated bottom square with formula Guron, ϱ- density of tissue, h - height, a - length, b - width, c -thickness, r 1; r2 ;r3 – average value of radius, m - mass, I- total length. Results: Comparative analysis of the volume of internal organs of adult Mongolians determined with the help of mathematical modeling with the volume established with 2D ultrasound linear measurements revealed no statistically significant difference between parenchymal organs and revealed statistically significant difference between other organs (P<0.001).