Search

This paper represents the results of research of mutual synchronization of self-oscillations of epidermal cellular density in skin lesions caused by psoriasis under strong limited noise conditions by the method of computing experiment. As an initial model the system of three ordinary nonlinear differential equations, presumably describing principles of paracrine regulation of epidermal proliferation with participation of populations functionally activated by CD4+/CD8+ T-lymphocytes is used. The results of research have shown, that if epidermal proliferation is considered as an attribute determining pathomorphologic features of dermatoses, synchronization can appear to be responsible for development of linear, annular, arcuate, geographical, and also the limited and common forms of disease. It is shown, that strong noise is capable of providing different duration for clinical manifestation of ensembles of synchronously connected lesions of psoriatic skin within several days, as to phase slip - it is up to several tens of days, and distinction of physical parameters - it is from several hours up to about several days.

A mathematical model of paracrine regulation of the proliferative activity of epidermis in the foci of skin lesions in psoriatic patients is presented. The model simulates the participation of skin-infiltrating activated T-lymphocytes as cellular regulators of apoptosis of proliferating keratinocytes. It allows one to describe all basic phases of the development of the focus of psoriatic lesion: the beginning of formation, a long stable or periodic manifestation, and the resolution of lesion and its involution to clinically uninvolved and normal skin. The model shows also the possibility of a spasmodic (triggering) transition of a pathological focus of lesion from the condition of remission to a new exacerbation and vice versa, which is a characteristic feature of the disease.

The results of numerical modeling of mutual synchronization of self-oscillations of epidermal hyperproliferation in foci of lesions in psoriasis are presented. It is shown that this phenomenon enables one to explain some facts of development of the disease such as: (1) figured arrangement of pathological elements; (2) unexpected exacerbation of the process a short time after the treatment; (3) persistence of lesions in a limited region of the skin or, vice versa, their fast distribution throughout the surface of the body of a patient.

On the basis of the modern conceptions postulating that the growing layer of normal epidermis contains two populations of keratinocytes differing greatly in the rate of mitotic division (stem and transient cells), a hypothesis was proposed that explains the reason for the establishment of the portion of the proliferating fraction close to 60%. A relationship between this value and the distribution of keratinocytes of the basal layer in space was demonstrated, and formulae for its calculation were derived. Possible pathways of the transition from the normal spatial configuration to the distribution typical for the focal lesion in psoriasis were analyzed when all stem cells begin to divide vigorously, and the size of the population of transient cells is 100%.

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.