Studying the geometry of a common skin disease

January 28, 2020

Hives afflict 1 in 5 people, but the exact mechanisms behind the itchy red rashes are not well known.

The research team studied the patterns of hives in patients and reproduced the hive patterns using a mathematical model called a reaction-diffusion model, a common prototype for understanding how patterns develop. The researchers' model is a single equation type which had never before been used to generate complex patterns.

In response to injury, allergens, or stress, hives can form when cells called mast cells in the skin release a compound called histamine. The red swollen mark (also known as wheals) can range from a few millimeters to the size of a hand or even larger.

While research has shown that histamine itself helps mast cells release histamine, this study considers for the first time that certain mechanisms might also inhibit histamine release and that there may be more going on behind the disease than previously thought.

"Our model succeeded in creating complex pattern of urticaria (hives), which is a very surprising result from both mathematical and biological points of views," said lead author and Associate Professor Sungrim Seirin-Lee.

To create the equation, the researchers gave rashes to eight healthy volunteers and measured the time it took for the rash to form and determined the velocity of formation. The team then looked at 14 patients with urticaria and measured them using the same model as the healthy patients.

Rather than relying solely on biological studies to investigate hives, which often requires inducing hives in patients, the mathematical focus provides a new avenue for skin disease research. In the future, the mathematical model could possibly be used as a tool to find the molecules which play a role in the inhibition process, as well.

"Finding the mechanism of urticaria is difficult only by biological methods," said Seirin-Lee. "Thus, we tried a completely different approach, mathematics. The approach using mathematical model for urticaria is the first trial in the world."

Ultimately, the findings from the study will help put together a more detailed picture of how the common skin disease develops and how to effectively deliver treatments.

S. Seirin-Lee
Department of Mathematical and Life Sciences, Graduate School of Integrated Science for Life,
Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
Tel: +81-82-424-7394 Fax: +81-82-424-7394

Michihiro Hide
Division of Molecular Medical Science,
Department of Dermatology,
Graduate School of Biomedical Sciences,
Hiroshima University, 1-2-3 Kasumi, Minami-ku, Hiroshima 734-8551, Japan
Tel: +81-82-257-5235 Fax: +81-82-257-5239

Hiroshima University

Related Mathematical Model Articles from Brightsurf:

A mathematical model facilitates inventory management in the food supply chain
A research study in the Diverfarming project integrates transport resources and inventory management in a model that seeks economic efficiency and to avoid shortages

Mathematical modelling to prevent fistulas
It is better to invest in measures that make it easier for women to visit a doctor during pregnancy than measures to repair birth injuries.

Predicting heat death in species more reliable with new mathematical model
An international research with the involvement of the Universitat Autònoma de Barcelona (UAB), published in Science, has developed a new dynamic mathematical model which represents a change in paradigm in predicting the probability of heat-related mortality in small species.

Using a Gaussian mathematical model to define eruptive stages of young volcanic rocks
Precise dating of young samples since the Quaternary has been a difficult problem in the study of volcanoes and surface environment.

Moffitt mathematical model predicts patient outcomes to adaptive therapy
In an article published in Nature Communications, Moffitt Cancer Center researchers provide a closer look at a mathematical model and data showing that individual patient alterations in the prostate-specific antigen (PSA) biomarker early in cancer treatment can predict outcomes to later treatment cycles of adaptive therapy.

New mathematical model can more effectively track epidemics
As COVID-19 spreads worldwide, leaders are relying on mathematical models to make public health and economic decisions.

Mathematical model could lead to better treatment for diabetes
MIT researchers have developed a mathematical model that can predict the behavior of glucose-responsive insulin in humans and in rodents.

New mathematical model reveals how major groups arise in evolution
Researchers at Uppsala University and the University of Leeds presents a new mathematical model of patterns of diversity in the fossil record, which offers a solution to Darwin's ''abominable mystery'' and strengthens our understanding of how modern groups originate.

Mathematical model reveals behavior of cellular enzymes
Mathematical modeling helps researchers to understand how enzymes in the body work to ensure normal functioning.

New mathematical model for amyloid formation
Scientists report on a mathematical model for the formation of amyloid fibrils.

Read More: Mathematical Model News and Mathematical Model Current Events is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to