Modelling blood flow regulation by nitric oxide in psoriatic plaques

Psoriasis is a common skin disease, with a clinical appearance of red, scaly lesions, known as plaques. Recent experimental research has shown that the ubiquitous cell-signalling molecule nitric oxide (NO) is actively synthesized within these plaques by the iNOS enzyme. In contrast, NO production from normal, healthy skin is a by-product of the reduction of nitrite in sweat. Measurement of NO release rates at the skin surface are 100 times greater from psoriatic lesions than normal skin. We propose a mathematical model for the dynamics of NO within psoriatic plaques, that incorporates diffusion, production in the basal epidermis, decay within the plaque, and active scavenging by red blood cell haemoglobin; this last effect introduces a key nonlinearity into the model. We present numerical simulations of the model in two space dimensions, and then describe an approximation that reduces the model to two coupled ordinary differential equations. This reduced system can be solved exactly, giving an approximation for the NO release rate as an explicit function of model parameters. We use this approximation to explain some recent, surprising experimental results.