MOSCOW, March 4A mathematical model that allows one to predict the restoration of the skin after wounds of various origins was developed by scientists from the Tyumen State Medical University (TMU). According to them, the use of a mathematical expression from game theory helps to most accurately take into account the contribution of each substance participating in the regenerative process. The results of the study were published in the publication «University Medicine of the Urals».
Wound healing is a complex, multi-stage biochemical process, the development of which is difficult to predict due to the many substances involved. In case of serious damage to the skin, predicting their recovery is an important part of diagnosis, which allows doctors to adjust the patient’s treatment and carry it out as effectively as possible, TMU said.
It is customary to distinguish three layers in human skin: epidermis, dermis and hypodermis, TMU employees noted. In addition, the skin is “thick” and “thin” and differs in tissue composition, the presence of hair and glands. Therefore, the “starting position” of all cellular participants in regeneration, their order of involvement in the process, the time and duration of exposure to third-party substances that stimulate healing are quite individual for each patient.
TMU scientists set themselves the task of developing an optimal universal mathematical model that would allow “introducing,” “removing,” and “slowing down” “players” on the regenerative field.
Researchers proposed describing the process of healing a skin wound using the Shapley vector equation – an expression used in game theory to describe processes where several participants with different “starting positions” and capabilities combine their efforts to achieve the most favorable outcome.
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The Shapley vector is used in machine learning and for classifying objects according to various unequal characteristics. According to the authors of the work, restoration of the affected area of the skin is achievable if the conditions of the Shapley vector are met by various cellular structures in the epidermis and dermis, described through quantitative immunohistochemical characteristics.
These conditions include the idiot’s axiom, which allows one to take into account useless “players” in the process of healing damage to the skin, experts said.
«To explain, we can use the analogy of the Russian mathematician Alexey Savvateev. Imagine a group of musicians playing on the street and receiving money from passers-by. The money goes into a common “cash box”, at the end of the working day the musicians share the income. If it’s equal, then no questions arise. But what if musicians will ask the question, which of them makes a greater contribution to the “common cause”, then what method to use? How to compare a guitarist and a drummer, a violinist and a vocalist? — said Vita Sozonyuk, senior lecturer at the Department of Mobilization Training of Healthcare and Disaster Medicine at TMU.
She noted that one such method could be game theory, a mathematical approach for studying optimal strategies in games. A game is understood as a process in which two or more parties participate, fighting for the realization of their interests. Each side has its own goal and uses some strategy that can lead to winning or losing depending on the behavior of other players. Game theory helps to choose the best strategies, taking into account ideas about other participants, their resources and their possible actions.
TMU specialists mathematically modeled the healing process of skin wounds of various natures: chemical and thermal burns, cuts and punctures. Research has shown that it is the Shapley vector that most flexibly and at the same time accurately describes the changes in tissue observed during regeneration.
According to Vita Sozonyuk, ultimately the cycle of work on reparative regeneration, that is, tissue restoration, should bring the TMU team closer to the development of a prototype scaffold — “scaffolding” for the healing of full-thickness wounds, skin and other body systems.