Geodesic
Mathematical models of thyroid follicle functioning
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 20-31

Voir la notice de l'article provenant de la source Math-Net.Ru

Four mathematical models of thyroid follicle functioning are suggested. Two models view the follicle as a point system, and the other two – as a system with distributed parameters. The main biochemical reactions — iodine intake in the follicle and the formation of thyroglobulin and hormone thyroxine — are taken into consideration. The models are formed on the principle of pair interactions and represent a Cauchy problem for a system of ordinary differential equations or a boundary value problem for a system of nonlinear differential equations in partial derivatives. The stability analysis of stationary points is performed in the point models, and in the diffusion models — the robustness of the trivial solution. A numerical algorithm for solving a nonlinear boundary value problems is suggested. Based on the numerical experiments, the effect of the rates of different reactions on the hormonal secretion rate is evaluated. Bibliogr. 21. Il. 7.
Keywords: mathematical modeling, differential equations, numerical methods, thyroid gland. 
@article{VSPUI_2013_3_a2,
     author = {Yu. E. Balykina and E. P. Kolpak},
     title = {Mathematical models of thyroid follicle functioning},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {20--31},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a2/}
}
TY  - JOUR
AU  - Yu. E. Balykina
AU  - E. P. Kolpak
TI  - Mathematical models of thyroid follicle functioning
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2013
SP  - 20
EP  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a2/
LA  - ru
ID  - VSPUI_2013_3_a2
ER  - 
%0 Journal Article
%A Yu. E. Balykina
%A E. P. Kolpak
%T Mathematical models of thyroid follicle functioning
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2013
%P 20-31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a2/
%G ru
%F VSPUI_2013_3_a2
Yu. E. Balykina; E. P. Kolpak. Mathematical models of thyroid follicle functioning. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 20-31. http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a2/