The mathematical discoveries of recent decades help to systematize personifying signs of any living creature, claims surgeon Alexey Kirichenko

“When you need to solve a difficult task from chemistry, physics or biology, take any, absolutely any, beautiful mathematical theory. Summing it, you will find a solution sooner or later”
Paul Dirac

Alexey Kirichenko – Doctor-traumatologist, surgeon. He graduated from the faculty of training doctors for the Navy in the Military Medical Academy of S. M. Kirov in St Petersburg, in 2001. He entered the clinical residency of the Military Medical Academy specializing in military traumatology and orthopedics, in 2004. He participated in “The basics of cardiovascular and microvascular surgery” enhancement study as part of the training program at the Department of Surgery Faculty of St. Petersburg State Medical University named after academician I.P. Pavlov.

At the end of the clinical residency he served in hospitals of the Moscow district from 2007 to 2009, leading the specialized ward. He studied the “Surgery with the Course of Plastic and Reconstructive Microsurgery” at the State Institute of Advanced Medical Studies of the Ministry of Defense of the Russian Federation in 2008.

Today we talk to Alexey Kirichenko on the topics of the future of medical engineering and the relationship between mathematics and medicine:

Which questions will the medical engineering of the future?

First of all, it will disclose “living patents”: how, for what purpose and under which evolutionary circumstances were some engineering solutions achieve in nature? The answers to these questions provide great opportunities: technical devices, be it mechanisms or system of artificial intelligence. Being “biologically similar” they promises to provide significant savings in materials and energy, increase the tasks accuracy and durability, because the development of these properties is the main thoroughfare of evolution.

Our work is focused on revealing the physical essence of processes occurring in living systems. Self-similarity in biological organization, the universality of the laws of physics in the animate and inanimate nature, a high degree of integration of living systems often give us surprises. We studied the articular cartilage friction dynamics, and discovered the muscular contraction law, we studied the biological frames elasticity, and detected the multidimensional surface without edges, and so on.

You are a practicing surgeon who came to Riemannian geometry and differential equations systems. How?

Once I accumulated the doctor orthopedist clinical experience, and medical experience is the main array of information for prediction and decision-making, there was a need to formalize it. The fact was that in the pathogenesis of diseases and injuries small deviations of bones, not described in classical works on orthopaedics and biomechanics, had a clear relevance. I began to study biomechanics, but was unable to find a convincing answer to my question. There was something missing from books, there was the lack of something important, that I was unable to formulate. It became obvious that I need a teacher and mentor, since the front of emerging issues started to disappear rapidly away over the horizon.

Then you met with Professor Sergey Valentinovich Petoukhov?

You are absolutely right. I have asked for help the Biomechanical Systems Studies Laboratory of the Institute of Mechanical Engineering named after A. A. Blagonravov of RAS. Sergey Valentinovich then presented me one of his books. As I read, my disparate interests were firmly connected to a new holistic system of knowledge, which harmoniously merged information from anatomy and physics, genetics and mechanics, evolutionary biology and clinical disciplines. Mathematics linked them surprisingly accurately and consistently.

For example, it became clear that when describing the geometry of the living systems the traditional Euclidean geometry “steals” many parameters, converting helical complex path to a flat type and straightening the important “irregularity” of living surfaces, or chaotic processes and structures in Living Nature. A chaos means disorder in the everyday understanding, but chaos in the world of large dimensions is “disordered hyperhomogeneity”, and it is quite meaningful and orderly phenomenon.

Medicine gets closer to the implementation of controlled tissue regeneration and biofabrication (bioprinting). What benefits of axiomatic theories do you see here?

Indeed, there are still tasks in the reconstructive surgery, including Traumatology and Orthopaedics, that do not have a full-fledged solutions — these are tasks on the reimbursement of complex defects — conditions in which it is necessary to recover bones, muscles, and nerves with blood vessels, and there is a need to replace the affected internal organs in some cases.

Bioprinting is a method for tissue construction from poorly differentiated cells. It became clear very quickly that the stem cells do not have enough information for the “self-identification” and further differentiation. Cells receive this information during embryonic development and the ontogenesis, on the basis of the information contained in the genetic code. The genetic information can be used to quickly pass through the embrional phase and achieve the status of a mature unit of “printed” tissues.

To do this it is necessary to identify the system parameters, consider the interaction of each and every one of them in time, discover the patterns of change and create a draft of the biological object under construction. The Geometry and topology, combinatorics, the theory of groups, control theory and nonlinear dynamical systems theory are perhaps the beginning of the approach to the strict understanding of morphology.

Although we are not yet close to the full solutions, formalizing such a task mathematically is already a serious step forward. This demonstrates, for example, the “mechanical environment of morphogenesis” concept. The point is, of course, not only in the mechanical effect, but in the oscillatory processes in general, for the description of which there are orderly mathematical and physical theories.

For example, blood vessels grow along the lines of force of alternating electromagnetic field generated by the first leiomyocytuses. Blood cells predecessors migrate in the embryonic blood vessels under the influence of ultrasonic range oscillations, the muscle cells differentiate in the conditions of mechanical vibrations of 100-150 Hz frequency. The oscillations in the concentrations of biologically active substances and metabolites, the phase states of biological fluids and others are also important.

You spoke about the fluctuations in living matter as physical phenomena, and what role do geometry and united numbers theory have in the biomedicine?

Academician Konstantin Vasiljevich Frolov comprehensively formulated the relationship of algebra and medicine in 1969. Mathematics is a tool for identification of living systems, i.e., it allows you to understand the essence of living matter and the evolutionary concept, which has given birth to it.

The Geometry and topology are of great interest from the point of view of biomorphic energy-saving technologies and materials processing technologies. The mathematical discoveries of recent decades, for example, some topologically related multidimensional space, lift the veil of secrecy of biological diversity and help to organize personifying signs of any living creature. We also know about the influence of biological frames geometry on the cells which inhabit them.

The properties of numbers on the number line, their density, distribution, divisibility miraculously reproduce the properties of biological processes and structures. For example, the cells distribution and size in the tissues, the cells action potentials form, the nature of the order observed in living systems, and so on.

What are the prospects of medicine “algebraization”?

In reconstructive surgery it is the automated systems for the cultivation of the complex tissue sets for the replacement of defects, artificial organs “cultivation”. For example, the anthropomorphous robot concept, as the bioreactor, has already been developed. The authors believe, quite rightly, that the conditions of cultivation will be most appropriate in this case.

Briefly summarizing, we can say that it is well known in surgery, what would happen if there is a damage or destruction of any part of the body. However, so far no one knows the “technical conditions of design and construction” of more or less complex element of living organism.

Interview: Ivan Stepanyan

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