Modelling Blood Flow Regulation by Nitric Oxide in Psoriatic Plaques

Abstract

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 cellsignalling molecule nitric oxide (NO) is actively synthesized within these plaques by the iNOS enzyme. In contrast, NO production from normal, healthy skin is a byproduct 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.

Topically applied S-nitrosothiol-containing hydrogels as experimental and pharmacological nitric oxide donors in human skin

“…This nonionic surfactant copolymer has a unique reverse-phase gelation property, which allows it to exist as a free-flowing liquid at room temperature and as a rigid semisolid gel at higher temperatures. [14][15][16] Synperonic F-127 is a well-studied biologically inert polymer and has been used in formulations for controlling drug release, for covering of burn wounds, in rectal, ophthalmic, parenteral and nasal administration, as well as in subcutaneous administrations. 17,18 Its use for pharmaceutical purposes is allowed by the Food and Drug Administration in the U.S.A. 19 Its attraction as a matrix for NO donor drugs such as RSNOs is that it allows easy application of the NO donor in the liquid vehicle to the desired site of action, where it transforms to the semisolid gel, ensuring continued localized action.…”

“…We have observed similar results when measuring NO concentrations at the skin surface of psoriatic plaques. 15 NO generated by inducible NO synthetase (iNOS) in the basal epidermis simultaneously diffused to the skin surface (where it was measured) and down to the dermis where it caused vasodilatation, and in so doing increased blood flow, and scavenging of NO by oxyhaemoglobin and serum thiols. At high blood flows, there was thus a paradoxical fall in NO measured at the skin surface.…”

Optimal Treatment Strategies for Control Model of Psoriasis

“…There has been research performed by mathematicians jointly with biologists to investigate the psoriasis pathogenesis dynamics and treatments effects. Some models of psoriasis are given in [11,14,16,17,18,20,22,24]. However, no optimal control problem has been stated and solved for those models.…”

Chattering and its approximation in control of psoriasis treatment

“…Now, we focus only on the mathematical models of the second group, which are described by systems of differential equations ( [6,10,18,26,28,31,32,35,36,39,40]). Among them we distinguish control mathematical models that are designed to find the best strategies for psoriasis treatment in one sense or another.…”

“…Here, the function w(m), which plays a key role in the analysis of the singular arc, is defined by formula (39). As a result, we obtain the equality:…”