Synchronization of oscillations of proliferation of keratinocytes in psoriatic skin by external periodic force: A mathematical model
A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to...
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| Published in: | Journal of theoretical biology Vol. 235; no. 4; pp. 485 - 494 |
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| Format: | Journal Article |
| Language: | English |
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21-08-2005
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| Abstract | A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to these states. It was shown that in the norm, a single stable equilibrium of a “focus” type exists in the system; whereas in psoriasis, owing to an increase in the growing fraction, hyperproliferation, and enhanced migration of interacting keratinocytes, a stable limit cycle arises from the state of unstable focus. In this paper we also report on the results of computer modeling of synchronization of self-excited oscillations of keratinocyte population density in psoriatic lesions by an external periodic force. This synchronization is viewed as a possible mechanism of the clinically observed dependence of psoriasis course on some natural factors of cyclic nature. |
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| AbstractList | A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to these states. It was shown that in the norm, a single stable equilibrium of a "focus" type exists in the system; whereas in psoriasis, owing to an increase in the growing fraction, hyperproliferation, and enhanced migration of interacting keratinocytes, a stable limit cycle arises from the state of unstable focus. In this paper we also report on the results of computer modeling of synchronization of self-excited oscillations of keratinocyte population density in psoriatic lesions by an external periodic force. This synchronization is viewed as a possible mechanism of the clinically observed dependence of psoriasis course on some natural factors of cyclic nature. |
| Author | Laptev, M.V. Nikulin, N.K. |
| Author_xml | – sequence: 1 givenname: M.V. surname: Laptev fullname: Laptev, M.V. email: nnikvi@mail.ru – sequence: 2 givenname: N.K. surname: Nikulin fullname: Nikulin, N.K. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/15935167$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1001/archderm.1963.01590220005001 10.1159/000254096 10.1046/j.1365-4362.1997.00251.x 10.1016/S0190-9622(84)80103-6 10.1016/S0733-8635(18)30144-X 10.1111/j.1346-8138.1998.tb02357.x 10.1111/j.1365-2133.1978.tb07337.x 10.1111/j.1365-2133.1993.tb03177.x |
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Venerol. contributor: fullname: Antonyev – start-page: 23 year: 1982 ident: 10.1016/j.jtbi.2005.02.002_bib16 article-title: Structure of skin contributor: fullname: Michaylov – volume: 26 start-page: 563 issue: 11 year: 1975 ident: 10.1016/j.jtbi.2005.02.002_bib4 article-title: The geographic distribution of psoriasis publication-title: Hautarzt contributor: fullname: Eckes – year: 2003 ident: 10.1016/j.jtbi.2005.02.002_bib21 contributor: fullname: Pikovsky – year: 1991 ident: 10.1016/j.jtbi.2005.02.002_bib17 contributor: fullname: Mordovtsev – volume: 11 start-page: 42 year: 1985 ident: 10.1016/j.jtbi.2005.02.002_bib25 article-title: Seasonality, incidence and prevalence of psoriasis publication-title: Vestn. Dermatol. Venerol. contributor: fullname: Shchadei – volume: 12 start-page: 805 issue: 4 year: 1994 ident: 10.1016/j.jtbi.2005.02.002_bib7 article-title: Psoriasis in the tropics. Epidemiologic, genetic, clinical, and therapeutic aspects publication-title: Dermatol. Clin. doi: 10.1016/S0733-8635(18)30144-X contributor: fullname: Farber – volume: 54 start-page: 284 issue: 4 year: 1971 ident: 10.1016/j.jtbi.2005.02.002_bib11 article-title: Pustulosis palmaris et plantaris. Prevalence, clinical observations and prognosis publication-title: Acta Derm.-Venereol. contributor: fullname: Hellgren – year: 1999 ident: 10.1016/j.jtbi.2005.02.002_bib22 contributor: fullname: Plis – volume: 4 start-page: 20 year: 1974 ident: 10.1016/j.jtbi.2005.02.002_bib24 article-title: Effect of climatic factors on the course of psoriasis publication-title: Vestn. Dermatol. Venerol. contributor: fullname: Shchadei – volume: 5 start-page: 56 year: 1984 ident: 10.1016/j.jtbi.2005.02.002_bib30 article-title: Eczema, neurodermatitis and psoriasis in children in Tajikistan publication-title: Vestn. Dermatol. Venerol. contributor: fullname: Zoirov – volume: 25 start-page: 97 issue: 2 year: 1998 ident: 10.1016/j.jtbi.2005.02.002_bib20 article-title: Factors influencing psoriasis: an analysis based upon the extent of involvement and clinical type publication-title: J. Dermatol. doi: 10.1111/j.1346-8138.1998.tb02357.x contributor: fullname: Park – volume: 1 start-page: 53 year: 1984 ident: 10.1016/j.jtbi.2005.02.002_bib8 article-title: Features of the clinical picture of psoriasis in the extremely continental climate of central Iakutia publication-title: Vestn. Dermatol. Venerol. contributor: fullname: Grebennikov – volume: 100 start-page: 1167 issue: 11 year: 1990 ident: 10.1016/j.jtbi.2005.02.002_bib29 article-title: A survey of the social and psychological effects of psoriasis publication-title: Nippon Hifuka Gakkai Zasshi contributor: fullname: Yasuda – volume: 98 start-page: 85 issue: 1 year: 1978 ident: 10.1016/j.jtbi.2005.02.002_bib9 article-title: Psoriasis in Sri-Lanka—a computer analysis of 1366 cases publication-title: Br. J. Dermatol. doi: 10.1111/j.1365-2133.1978.tb07337.x contributor: fullname: Gunawardena – start-page: 327 year: 1990 ident: 10.1016/j.jtbi.2005.02.002_bib28 article-title: Cell proliferation kinetics contributor: fullname: Weinstein – volume: 175 start-page: 242 issue: 4 year: 1989 ident: 10.1016/j.jtbi.2005.02.002_bib12 article-title: The effect of endogenous and exogenous factors on psoriasis vulgaris. A clinical study publication-title: Dermatol. Monatsschr. contributor: fullname: Knopf – volume: 129 start-page: 458 issue: 4 year: 1993 ident: 10.1016/j.jtbi.2005.02.002_bib26 article-title: Cyclical psoriatic arthritis responding to anti-oestrogen therapy publication-title: Br. J. Dermatol. doi: 10.1111/j.1365-2133.1993.tb03177.x contributor: fullname: Stevens |
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| Snippet | A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear... |
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| SubjectTerms | Cell Proliferation Computer Simulation Epidermis Humans Keratinocytes - pathology Kinetics Mathematical modeling Models, Biological Nonlinear Dynamics Periodicity Proliferation Psoriasis Psoriasis - pathology Synchronization |
| Title | Synchronization of oscillations of proliferation of keratinocytes in psoriatic skin by external periodic force: A mathematical model |
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