[Mathematical model of proliferative activity in epidermis of the normal skin and of the skin afflicted by psoriasis].
A mathematical model of the mitotic activity of epidermis in norm and psoriasis is presented, which consists of a system of two autonomous nonlinear differential equations. A qualitative analysis of the model was done, and numerical solutions at the parameter values corresponding to these state were obtained. It was shown that, in norm, the system can exist only in one stationary equilibrium state of the "focus" type, and in psoriasis, due to an increase in the growing fraction, hyperproliferation, and enhanced migration of keratinocytes, a stable limiting cycle arises from the state of an unstable focus. The existence of two stable states (focus and the limiting cycle) is regulated by a parameter that describes the inhibition of division of maturing cells of suprabasal epidermal layers by the intrinsic tissue-specific transmitters of mitosis of G1-keilon type. The model is consistent with experimental data on the kinetics of cell proliferation in the epidermis in norm and psoriasis and the clinical course of the disease.
Laptev
M V
MV
Nizhegorodskii Research Dermatovenerologic Institute, Ministry of Health, of the Russian Federation, Nizhnii Novgorod, Russia.
Nikulin
N K
NK
D000465:Algorithms; D002455:Cell Division; D004817:Epidermis / Q000473:pathology*; D015603:Keratinocytes / Q000473:pathology; D007700:Kinetics; D008954:Models, Biological; D011565:Psoriasis / Q000473:pathology*