Mathematical modelling of cell proliferation dynamics
in psoriatic epidermis
sensitized by the furocoumarins under UVA-radiation
M.M. Stolnitz
Department of Optics, Saratov State University, Russia
Efficiency of photochemotherapy with ultraviolet A-band radiation sources, including laser, for treatment of psoriasis and other skin diseases, depends on many factors, the effects of which must be considered for both increasing the therapeutic effect and decreasing the risk degree because of the UV-radiation inducing mutagenic injuries. From the other hand, the cell population dynamics in the normal and psoriatic epidermis is an interesting example of nonlinear, stochastic dynamics.
In the work, the mathematical model is presented, which describes the processes in the epidermis sensitized by the furocoumarins, under UVA-radiation. The model describes processes on three levels: molecular (photochemical transformations of the psoralen molecules and their reactions with the DNA-molecules), cellular (proliferation, differentiation and injuries repairing), and tissue (humoral regulation, space-time cell dynamics in the epidermis).
As it is known, psoriasis, from point of view of cellular biology, is a consequence of abnormal
rapid proliferation (i.e., deviation of dynamical parameters of the system) of some cells of the
epidermis [1]. One of the methods of the treatment is the using of long wavelength ultraviolet
light (UV-A, 
) and epidermis sensibilization by compounds from furocoumarin
group [2]. Furocoumarin molecules penetrate into cells, reach nuclear DNA, and then form under
UV-A irradiation various types of cycloadducts with pyrimidine bases. Hence, the mitotic block
appears and is on, while injuries are not repaired, that leads to reduce of the effective cell
proliferation rate. Since the laser PUVA-therapy supposes the using of the eximer ( 
) or
nitrogen ( 
) lasers, which emit high power pulses, we have to take into account the
multiphoton processes [3].
The DNA-psoralen-UV-photons interaction is described by system of nonlinear ordinary differential equations for population densities of energy levels of furocoumarin and DNA- molecules, numbers of cycloadducts and one- and double-strand breaks in DNA chains. On cellular level, we take into account two subpopulations of proliferating cells: intact cells and the cells with block of mitosis caused by injuries. Solving correspondent system of differential equations, we find cells distribution by number of injuries of each type. Moreover, assuming independence of repairing of injuries of each type, we find mitotic block time distribution and rate of return of cells into intact subpopulation. The spatial-temporal dynamics of tissue cells is described by the system of nonlinear partial differential equations (continual and improved variant of system from [4]).
The described system of equations is used for investigation of the difference in dynamical properties of normal and psoriatic epidermis and for analysis of UV-radiation correcting effect.