Ilya Starodumov: "The Highest Value for Scientists Is Knowledge of the World"

12:31, November 24, 2021

How math helps cure heart disease and predict ice melt, scientist says

It's My City, together with the Brusnika company, continues to talk about Ural scientists in the "Science in the City" series. This time the journal's correspondent prepared a text about the work of Ilya Starodumov from the laboratory of multiscale mathematical modeling at UrFU. Ilya told how higher mathematics helps people to treat heart disease and influence climate change, and also explained what scientists and detectives from the TV series "The X-Files" have in common.

Conditionality solves everything

In mathematics, I learned that many of the definitions that were presented at school as postulates are scientific assumptions: you can do it this way, and you can do it another way. In my freshman year, my instructor wrote an example on the board: "X + 5 = 15" and seriously suggested finding "X." Everyone was embarrassed because the answer was obvious, but it turned out to be not so simple. Without further explanation, what is "X", what is "+" and "=" written on the blackboard are just "squiggles", and the answer to the question posed depends on what meaning they contain and what conventions they imply.

In the usual sense, we would decide that the root of the equation is ten. But if, for example, we preliminarily assume that "X" is only odd numbers, we can't find a solution. Or it may turn out that "+" is not our usual addition, but the designation of the operation with numbers, then the solution of "X + 5 = 15" can be "X = 1". That is, you need to clearly define what "X" is, what "5" is, what "+" is, and so on. Otherwise, the answer can turn out to be anything.

When you start to understand that some symbols are more suitable for a certain task, and others less so, this carries over to more complex representations in working not only with numbers, but also with functions, and with generalizations of functions. With the accumulated arsenal, it becomes possible to formulate theories, and within the framework of the theory, to formulate applied mathematical models. If one initially selects the basic system of conventions correctly, one can come to very interesting conclusions.

When working with information, it is necessary to lay it out

Mathematical modeling, which I am passionate about, is a very broad scientific field. Any person, when he is trying to make a decision, is also engaged in modeling. At that moment, he models the situation from his life experience. Mathematical modeling differs from worldly modeling in that its toolkit is based on a mathematical apparatus, not on feelings or habits.

The rigor of the apparatus dictates its requirements: thus, when working with information, it is necessary to lay it out on the shelves. That is, after getting acquainted with the problem, one must determine the appropriate basic equations and regularities, then evaluate quantitative values, find limitations, and potential errors. And only after that, formulate a mathematical problem: derive a single equation or system of equations and look for a solution.

For example, if we consider the question "buy an apartment or wait" in terms of mathematical modeling, first we have to define the criteria for decision-making, research all market data, their dynamics, then formulate a mathematical problem, turning the collected information into a system of equations, and then look for the desired answer in the solution of this system.For complex mathematical calculations I have a 64-core computer. It looks like an ordinary personal computer, but it has a very powerful processor, more RAM and a special cooling system. The same setup is used maybe by computer graphics professionals. But the computer is not a prerequisite for creating models. Einstein's famous equation E=mc² is also a simulation, and all that was needed was a pen and paper.

Mathematics and heart disease

Today, mathematical models can also help in the treatment of diseases. For example, heart disease caused by stenosis (narrowing of a coronary artery), most often caused by a buildup of cholesterol plaques. When an artery is narrowed, its flow capacity decreases and less blood than needed enters the heart. To treat this condition, either special medications are used or a complex operation is performed: a special stent, a small mesh that widens the vessel, is placed in the artery. The procedure is very expensive and risky.

To do the operation or not - the doctor decides, and for this, as a rule, first conducts another procedure: placing sensors inside the vessel, which measures how stenosis interferes with blood flow. This test also has its risks, so about ten years ago they started to develop a system of mathematical modeling of blood flow in coronary vessels based on the data of noninvasive diagnostics (without surgical intervention. - Ed.) instead.

To model the blood flow, the patient first undergoes an ordinary cardiac CT scan, and then the data are transferred to a special program that builds a geometric model of all major coronary vessels and simulates blood flow in them. With such a solution, it is possible to assess quite accurately, quickly, and safely for the patient whether surgical intervention is necessary.

We are currently investigating such models in collaboration with colleagues from the Ural Medical University. However, many questions related to cardiac physiology and vascular mechanics have no unequivocal answers, either from doctors or biologists. Therefore, modeling becomes also a way to confirm or refute theoretical hypotheses. We discuss the results of modeling with practicing physicians: we show the calculated values and regularities, and they tell us whether our conclusions are similar to the truth.

Mathematical models that predict climate change

Mathematical models are also used to solve global problems. Today, for example, many people are concerned about climate change in the Arctic zone, a place on which much of the world's life depends. Usually prognoses are based on the analysis of multiyear observations. We used multiscale modeling for this task, which allows using not average statistical indicators, but full-fledged physical theory both at the micro level (for example, when studying ice structure and its thermodynamic characteristics), and at the macro scale of ice cover (for example, if we are talking about absorption/reflection of solar radiation). It is clear that ice structure affects macro-processes and macro-processes affect changes in this structure. But this is the essence of modeling, when multilevel entities are linked through common variables.

Multiscale modeling is a resource-intensive approach. But it has an important advantage over statistical methods: greater detail and validity of the results. Climatic changes can go almost unnoticed for several decades or even centuries, and then manifest themselves sharply and intensely. Statistics over several years may not catch them.

What do scientists and characters from The X-Files have in common?

I can say with confidence that mathematicians are made, not born. All children have their own predispositions, but it is very difficult to say what they have and don't have. Instead, it's wise to help your child develop and encourage his or her diligence. It's dangerous to tell someone as a child, "That's not yours." If you don't have a predisposition for math at some age, it doesn't mean it will never happen. It will definitely not appear only in one case: if you discourage a child from taking an interest in this science, and therefore in the very essence of all things.The highest value for scientists is knowledge of the world. But with this task in mind, do most people on earth wake up every day? Of course not, for the average person, a scientist is a freak out of this world, like Agent Mulder in the famous TV series "The X-Files". For this character, discovering the truth is the main goal and meaning of life. At the same time, the people around him consider him abnormal for his unconventional thoughts and actions.

The system of scientists' values helps them avoid conjunctural conclusions, which are sometimes easier and more convenient to draw. It also makes it possible not to dwell on the familiar and to find true explanations for what is happening around us, to offer the most effective, rather than profitable, solutions to pressing problems. Because of this, research romance almost always conflicts with making money. On the other hand, research itself has become increasingly ambitious and requires considerable financial resources.

What should be the compromise? How to avoid professional burnout and the emergence of pseudo-researchers who are only interested in the financial side of their work? These questions are faced by the whole world science, and the more technological our life becomes, the more important it is to get an answer to them.