This is how mathematics unlocks the secrets of skin lesions to enable personalised treatment

The skin? A veritable ‘shield’ of health, which protects the whole body. But even this organ – which can weigh between 2.7 and 4.5 kilos and, if laid flat, cover an area of nine metres by two – can become diseased or manifest conditions that can severely compromise quality of life.

Would you like an example? Consider chronic spontaneous urticaria (CSU), characterised by the appearance of skin rashes – specifically, the lesions we refer to as wheals. These, accompanied by itching, whilst being clearly visible (and certainly felt by those living with the condition), can take on various forms. Studying their characteristics and how they vary from person to person presents a challenge for science, not only in terms of our understanding of the pathophysiology of the condition but also in reassessing what happens in each patient within the ‘mix’ of mechanisms involved in the development of the condition, ranging from autoimmune responses to the presence of cellular infiltrates and the activation of the coagulation pathway by the complement system.

And it is in this area that there is a new development: thanks to a statistical approach known as hierarchical mathematical modelling, it is possible to gain a better understanding of the disease profile in individual patients, with a view to targeted treatments. The system has been proposed, backed by data, in a study published in Communications Medicine, coordinated by Sungrim Seirin-Lee, who works at the Institute for Advanced Study of Human Biology at Kyoto University.

Essentially, hierarchical modelling can be regarded as an approach that analyses different patients by creating uniform clusters. In this case, with regard to chronic spontaneous urticaria, the researchers focused on the shape of the skin rashes in order to link these morphological characteristics to the clinical profile of the condition in individual patients. The model, taking into account what occurs within and outside the blood vessels and integrating observations with experimental data, made it possible to identify five potential types of wheals. Subsequently, based on these characteristics, the Criteria for the Classification of Rash Geometry (EGe criteria) were established, based on their relationship with the dynamics of the tissue factor and histamine within mast cells, cells that act on blood vessels and induce the formation of the lesions themselves. Finally, this mathematical model was used to classify the condition in around a hundred patients, with a reliability of just under 90% (87.6%), compared with the observations made by dermatologists.

“This study was the first to use mathematical models to elucidate the pathophysiology of skin rashes based on their morphology, and may help pave the way for alternative treatment methods. – explained Seirin-Lee in a statement from the Japanese university. For example, patients could take photographs of their skin rashes to provide data useful for a definitive diagnosis of the underlying causes, or the effectiveness of treatment could be monitored over time. Furthermore, this study demonstrates the potential of mathematical models in understanding the mechanisms of diseases specific to humans, where animal models are not available.” In short: mathematical dermatology is a reality.