Geodesic
Mathematical models of thyroid follicle functioning
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 20-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Khizhnyak O. O., “Old Problems in New Millenium: Iodine Deficiency Disorders”, Zdorovie Ukrainy, 2010, no. 1, 12–14

[2] Distefano J. J., Mak P. H., “Optimal control policies for the prescription of thyroid hormones”, Math. Biosci., 42 (1978), 159–186 | DOI | Zbl

[3] Yamada H., Distefano J. J., Yen Y.-M., Nguyen T. T., “Steady-state regulation of whole-body thyroid hormone pool sizes and interconversion rates in hypothyroid and moderately T3-stimulated rates”, Endocrinology, 137:12 (1996), 5624–5633 | DOI

[4] Shumakov V. I., Novoseltsev V. N., Sakharov M. P., Shtengold E. Sh., Modeling of Physiological Systems, Medicina, M., 1971, 352 pp.

[5] Riggs D. S., “Quantitative aspects of iodine metabolism in man”, Pharmacol. Rev., 4:3 (1952), 284

[6] Degon M., Chait Y., Hollot C. V., Chipkin S., Zoeller T., “A Quantitative model of the human thyroid: development and observations”, Proc. Amer. Control Conference, v. 2, 2005, 961–966

[7] Hoermann R., Midgley J. E. M., Larisch R., Dietrich J. W., Is Pituitary Thyrotropin an Adequate Measure of Thyroid Hormone-Controlled Homeostasis During Thyroxine Treatment?, European Journal of Endocrinology, 168:2 (2012), 271–280 | DOI

[8] Bilich G. L., Universal atlas. Biology, v. 1, Oniks 21 vek, M., 2005, 1008 pp.

[9] Kettyle W. M., Arky R. A., Endocrine Pathophysiology, Lippincott-Raven, 1998

[10] Zaichik A. Sh., Churilov L. P., Pathochimie (Endocrine and Metabolic Disorders), 3d ed., Elbi-SPb, S.-Petersburg, 2007, 768 pp.

[11] A. I. Kubarko, S. Yamashita, Thyroid. Fundamental Aspects, Min. med. in-t, Minsk; Med. shkola Un-ta g. Nagasaki, Nagasaki, 1998, 355 pp.

[12] Romanovskiy B. V., Fundamentals of Chemical Kinetics, Ekzamen, M., 2006, 415 pp.

[13] Degon M., Chipkin S. R., Hollot C. V., Zoeller R. T., Chait Y., “A computational model of the human thyroid”, Math. Biosci., 212:1 (2008), 22–53 | DOI | MR | Zbl

[14] Merrill E. A., Clewell R. A., Robinson P. J., Jarabek A. M., Gearhart J. M., Sterner T. R., Fisher J. W., “PBPK model for radioactive iodide and perchlorate kinetics and perchlorate-induced inhibition of iodide uptake in humans”, Toxicol. Sci., 83:1 (2005), 25–43 | DOI

[15] Lüllmann H., Mohr K., Hein L., Taschenatlas Pharmakologie, George Thieme Verlag, Stuttgart–New York–Thieme, 2008, 420 pp.

[16] Miot F., Dupuy C., Dumont J. E., Rousset B. A., Thyroid hormone synthesis and secretion, (Retrieved 10.03.2010) http://www.thyroidmanager.org/chapter/thyroid-hormone-synthesis-and-secretion/

[17] Samura B. A., Dralkin A. V., Pharmacokinetics: a textbook for pharmaceutical universities and faculties, Osnova, Kharkov, 1996, 288 pp.

[18] Samarskiy A. A., Tikhonov A. N., Mathematical Physics Equations, Nauka, M., 1977, 735 pp. | MR

[19] Khmelnitskiy O. K., Cytological and histological diagnosis of thyroid diseases, Sotis, S.-Petersburg, 2002, 288 pp.

[20] Kolbin A. S., Sidorenko S. V., Balykina Yu. E., Trials of new antibacterial agents — any prospects?, Pediatric pharmacology, 7:5 (2010), 12–16

[21] Churilov L. P., Stroev Yu. I., Smirnov V. V., “Hashimoto's thyroiditis — an urgent problem of modern endocrinology”, Vestnik S.-Peterb. un-ta, ser. 11: medicina, 2006, no. 2, 3–25