A single reaction-diffusion equation for the multifarious eruptions of urticaria

Abstract

Urticaria is a common skin disorder characterized by the rapid appearance and disappearance of local skin edema and flares with itching. It is characterized by various macroscopic skin eruptions unique to patients and/or subtypes of urticaria with respect to shape, size, color, and/or duration of eruptions. Nevertheless, the mechanism underlying multifarious eruptions in urticaria is largely unknown. The eruptions are believed to be evoked by histamine release from mast cells in the skin. However, the majority of visible characteristics of urticaria cannot be explained by a simple injection of histamine to the skin. To explain the multifarious eruptions of urticaria, we developed a single reaction-diffusion model suggesting the self-activation and self-inhibition regulation of histamine release from mast cells. Using the model, we found that various geometrical shapes of eruptions typically observed in patients can be explained by the model parameters and randomness or strength of the initial stimuli to mast cells. Furthermore, we verified that the wheal-expanding speed of urticaria, which is shown to be much smaller than that of the intradermal injection experimental system may be explained by our model and a simple diffusion equation. Our study suggests that the simple reaction-diffusion dynamics, including the independent self-activating and-inhibitory regulation of histamine release, may account for the essential mechanism underlying the formation of multifarious eruptions in urticaria.

Traveling wave of inflammatory response to regulate the expansion or shrinkage of skin erythema

“…In pathological skin showing expansion, inflammatory response persists and the concentration of mediators fails to return to the original level [ 10 – 13 ]. Recent theoretical studies have shown two independent mechanisms of how the pathological inflammatory response causes expansion [ 14 , 15 ]. One is the diffusion of inflammatory mediators and the other is positive feedback, which can generate bistability.…”

“…Expansion occurs when S T is closer to S NI than to S I , whereas shrinkage occurs when S T is closer to S I than to S NI in a wide range of parameters controlling the inflammatory response, including positive feedback, basal secretion, and degradation ( Fig 4 ; S3 Fig in S1 Appendix ). An interesting future study would be the analysis of whether the balance captures such inflammatory wave dynamics in other bistable systems, with more complex biochemical reactions [ 12 , 14 , 15 ]. Therefore, the balance of bistable states could provide an experimentally testable framework for the normal and pathological inflammatory responses ( Fig 5 ).…”

“…This type of model incorporates the reaction and diffusion of molecules, referred to as the reaction–diffusion model [ 20 , 21 ]. Another reaction–diffusion model incorporating self-activation, that is, positive feedback of histamine, has also shown expansion [ 15 ]. These models show that the diffusion of mediators could cause erythema expansion.…”

Prevalencia de urticaria crónica en una unidad médica

“…7 Las señales que activan a los mastocitos aún no están definidas del todo, pero se cree que estos no solo responden a alérgenos que entran en contacto con las moléculas de IgE de su superficie, sino que también responden a estímulos como superantígenos, neuropéptidos, anticuerpos, agentes físicos, adenosín trifosfato (ATP), anafilotoxinas y agentes químicos. 10,11,12 La histamina y otros mediadores como el factor activador de plaquetas (PAF), factor de necrosis tumoral alfa (TNF-α), interleucinas (IL) 3, 4, 5, 6, 8, 13 determinan el desarrollo temprano de la inflamación, induciendo la activación de neuropéptidos (sustancia P, endorfinas, encefalinas) por las terminaciones nerviosas, vasodilatación, extravasación de plasma y reclutamiento de células inflamatorias; causando prurito, ardor y las lesiones clásicas de urticaria, ronchas. 9,10 Las células inflamatorias recién involucradas en este proceso secretan mediadores inflamatorios, intensificándose y prolongando la respuesta inflamatoria.…”

Moxibustion therapy for chronic spontaneous urticaria

“…Urticaria is a localized edema response caused by the expansion of cutaneous small blood vessels and mucous membranes and increased permeability with the activation of mast cells as the core. [ 1 – 3 ] It is often accompanied by wind masses of varying sizes, itching, and angioedema. According to the statistics of the World Allergy Organization, about 20% of people have had urticaria during their lifetime.…”