Heriot-Watt Mathematics Report Series
HWM01-59, 25 Jan 2002
Modelling blood flow regulation by nitric oxide in psoriatic plaques
J A Sherratt, R Weller and N J Savill
Abstract
Psoriasis is a common skin disease, with a clinical appearence of red,
scaly lesions, known as plaques. Recent experimental research has
shown that the ubiquitous cell-signalling molecule nitric oxide is
actively synthesised 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 nitric oxide
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 nitric oxide release rate as an explicit function of model
parameters. We use this approximation to explain some recent,
surprising experimental results.
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