PNIPU: Mathematical model for selecting the most effective epithelial repair plan

The main articles are:

• Human skin
• Artificial skin in medicine

2022: Mathematical Model Development

The development of the Perm Polytechnic will help grow leather. The university announced this on November 11, 2022.

The human body is a complex system of a large number of cells that coordinate their vital activities within a single system. After receiving various deep, open injuries, a person may lack areas of such a vital organ as the skin. Perm Polytech scientists have developed a mathematical model that is designed to grow skin. Specialists in the field of tissue engineering will be able to use the developed technology to select the most effective epithelial restoration plan, taking into account the individual characteristics of the structure of the cells of the human body.

The mathematical model we developed solves problems in the development of scaffolds. Scaffolds are temporary "scaffolds" for the restoration of tissues, which are then absorbed. For example, there was a complex fracture that may not grow correctly or not recover at all. They turn to specialists in the field of tissue engineering with such a problem. These specialists prepare scaffold using 3D printing from a biodegradable material. The system is then filled with bone tissue cells and placed in a culture medium where the cells begin to grow intensively along the "scaffolds." It is worth noting that this system is being developed in the likeness of a broken area. Thus, bone tissue is grown and implanted at the fracture site, "said Ivan Krasnyakov, head of the laboratory at the PNIPU Department of Applied Physics.

According to the scientists, the model involves two important processes that mimic the properties of real cells: mitotic division and intercalation of cells.

Research was carried out by standard methods of mathematical modeling and numerical experiments. A discrete model of a deformable cell is taken as a basis. A motion equation based on elastic potential energy is written for each vertex of the cell. As it evolves, the tissue tends to occupy a position that meets the minimum potential energy, "said Dmitry Bratsun, Doctor of Physical and Mathematical Sciences, Head of the Department of Applied Physics at PNIPU.

According to scientists, this matmodel is universal and can be easily adapted to solve other problems. Thus, polytechnics have already performed a number of studies on the development of carcinoma (epithelial cancer). The technology can be useful for tissue engineering professionals as well as theoretical researchers.