| Title:
|
A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation (English) |
| Author:
|
Mukhopadhyay, Banibrata |
| Author:
|
Bhattacharyya, Rakhi |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
6 |
| Year:
|
2006 |
| Pages:
|
549-564 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability and bifurcation behavior. Clinical treatment of periodic catatonic schizophrenia is discussed in presence of transportation delays. Numerical simulations are presented to support analytic results. (English) |
| Keyword:
|
feedback mechanism |
| Keyword:
|
distributed time delay |
| Keyword:
|
discrete time delay |
| Keyword:
|
asymptotic stability |
| Keyword:
|
catatonic schizophrenia |
| Keyword:
|
hormone therapy |
| MSC:
|
34K18 |
| MSC:
|
34K20 |
| MSC:
|
34K60 |
| MSC:
|
92C30 |
| MSC:
|
92C50 |
| idZBL:
|
Zbl 1164.34553 |
| idMR:
|
MR2291781 |
| DOI:
|
10.1007/s10492-006-0020-z |
| . |
| Date available:
|
2009-09-22T18:27:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134652 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Cronin: Mathematical aspects of periodic catatonic schizophrenia.Bull. Math. Biol. 39 (1977), 187–199. Zbl 0366.92007, MR 0484501 |
| Reference:
|
[3] L. Danziger, G. L. Elmergreen: Mathematical theory of periodic relapsing catatonia.Bull. Math. Biophys. 16 (1954), 15–21. 10.1007/BF02481809 |
| Reference:
|
[4] L. Danziger, G. L. Elmergreen: The thyroid-pituitary homeostatic mechanism.Bull. Math. Biophys. 18 (1956), 1–13. 10.1007/BF02477840 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[8] B. N. Ghosh, D. M. Woodbury, and G. Sayers: Quantitative effects of thyrotropic hormone on iodine 131 accumulation in thyroid and plasma proteins of hypophysectomised rats.Endocrin. 48 (1951), 631–642. 10.1210/endo-48-5-631 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[14] B. Mukhopadhyay, R. Bhattacharyya: A delayed mathematical model for testosterone secretion with feedback control mechanism.Int. J. Math. Math. Sci. 34 (2004), 105–115. MR 2038801, 10.1155/S0161171204307271 |
| Reference:
|
[15] C. P. Richter: Biological Clocks in Medicine and Psychiatry.C. C. Thomas, Springfield, 1965. |
| Reference:
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| Reference:
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| . |
