{"title":"Stability Analysis for an Extended Model of the Hypothalamus-Pituitary-Thyroid Axis","authors":"Beata Jackowska-Zduniak","volume":118,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":521,"pagesEnd":527,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10005762","abstract":"We formulate and analyze a mathematical model
\r\ndescribing dynamics of the hypothalamus-pituitary-thyroid
\r\nhomoeostatic mechanism in endocrine system. We introduce
\r\nto this system two types of couplings and delay. In our model,
\r\nfeedback controls the secretion of thyroid hormones and delay
\r\nreflects time lags required for transportation of the hormones. The
\r\ninfluence of delayed feedback on the stability behaviour of the
\r\nsystem is discussed. Analytical results are illustrated by numerical
\r\nexamples of the model dynamics. This system of equations describes
\r\nnormal activity of the thyroid and also a couple of types of
\r\nmalfunctions (e.g. hyperthyroidism).","references":"[1] F. M. Atay, Van der Pol\u2019s Oscillator under Delayed Feedback, J. Sound\r\nand Vibration, 218, 1998, 333\u2013339.\r\n[2] Z. Baloch and P. Carayon, Laboratory medicine practice guidelines:\r\nLaboratory support for the diagnosis and monitoring of thyroid disease,\r\nThyroid, 13, 2003, 57\u201367.\r\n[3] L. Danziger and G.L. Elmergreen , Mechanism of periodic catatonia,\r\nConfinia Neurol., 18, 1958, 159\u2013166.\r\n[4] M. Degon, S.R. Chipkin and C.V. Hollot, A computational model of the\r\nhuman thyroid, Mathematical Biosciences, 212, 2008, 22\u201353.\r\n[5] J.V. Dietrich, G. Landgrafe and E. Fotiadou, TSH and Thyrotropic\r\nAgonists: Key Actors in Thyroid Homeostasis, Journal of Thyroid\r\nResearch, 2012.\r\n[6] U. Fory\u00b4s, Matematyka w biologii, WNT Warsaw, 2005.\r\n[7] B.Mukhopadhyay and R. Bhattacharyya, A mathematical model\r\ndescribing the thyroid-pituitary axis with time delays in hormone\r\ntransportation, Applications of Mathematics,51, 2006, 549\u2013564. [8] B. Pandiyan, A patient specific model of the negative feedback control\r\nof the hypothalamus-pituitary-thyroid axis in autoimmune thyroidits,\r\nMathematical Medicine and Biology, 2013, 1\u201333.\r\n[9] B. Pandiyan, Modeling the hypothalamuspituitaryadrenal axis: A review\r\nand extension, Mathematical biosciences, 268, 2015, 52\u201365.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 118, 2016"}