Olar O.I., Biryukova T.V., Fediv V.I., Mykytiuk O.Yu, Ostafiychuk D.I.
Higher state educational establishment of Ukraine
Bukovinian State Medical University, Ukraine
MATHEMATICAL MODELING IN BIOLOGICAL
PROCESSES AND SYSTEMS STUDYING
Methods of mathematical modeling are widely applied in
medicine and biology due to the recent rapid progress of cybernetics and
informatics. Intensive development of modern cybernetics as interdisciplinary
research bringing management systems, theory of electrical circuits, logic
modeling, evolutionary biology, neurology together began in the 1940s of the
last century. It was found recently that the following issues rise on research
conducting in the field of medicine:
- intervention into biological systems is followed by
some changes and their causes cannot be established;
- insufficient level of experimental devices development
does not allow the implementation of some theoretically grounded research;
- experiments on humans are impossible due to a number
of moral, ethical and legal issues.
Abovementioned problems might be solved by means of mathematical
modeling that is a particular area of research in medicine allowing establishing
of various complex relationships between theory and experiment. Nowadays
mathematical models are widely used in biophysics, biochemistry, genetics,
immunology, epidemiology, physiology, pharmacology, medical equipment and other
new areas of science that are adjacent to medicine.
The emergence of new highly efficient methods of
diagnostics and treatment as well as invention of new medical devices is
closely linked with the development of mathematical models and methods. Implementation of mathematical modeling
in medicine, development of automated computer systems contributed to upgrading
of diagnostics and treatment of diseases. For example, generalized mathematical models based on
experimental data are used for studying of the nature of substance interactions
at the molecular level. Macromolecules functioning based on
electronic-conformational interactions are described successfully employing
mathematical equations in modern physical models. Thus, new methods of mathematical modeling in
biophysics are essential elements of nature cognition.
Students learn the basics of
mathematical modeling as a research tool in studying the following disciplines:
medical and biological physics, biophysics, higher mathematics, medical
informatics, information technology in pharmacy.
Medical students, students of Dentistry
and Pharmacy faculties are introduced to basic mathematical modeling stages as
part of classes on medical and biological physics, higher mathematics in
general medicine. They get acquainted to:
- the transformation of the investigated
task into mathematical language, e.g. construction of differential equation or
system of differential equations;
- the mathematical solution of the
problem;
- the results’ analysis.
Study plans of abovementioned
disciplines suggest studying of chemical reactions kinetics, processes of
tablet drugs formulations dissolution, modeling of changes in concentration of
drug in cells of the body depending on its administration ways, studying of
populations evolution, the epidemics theory, immunological processes essential
for pharmacokinetics and medical disciplines e.g., microbiology, virology,
immunology, infectious diseases etc, by
means of mathematical modeling.
For example, ways of various differential equations
solutions which are models of abovementioned processes are considered by
Pharmacy faculty students in classes on higher mathematics and statistics.
Students acquire understanding of the main advantages of analytical methods of
differential equations solving and functional relationship reception for the
process under investigation.
The second year medical students learn computer
modeling methods. The fact that some already established
mathematical models can detect side effects of certain medications prior to their
therapeutic application and that accuracy of mathematical prediction varies
depending on the type of a medication improves motivation for thorough study of
computer modeling.
Students are able to implement and investigate models
in the spreadsheet environment nowadays. Solving differential equations skills
acquired in the course of mathematics and statistics (Pharmacy students) or
medical and biological physics (general medicine students) are used for this
purpose.
Application of
spreadsheets in mathematical models allows young researchers to obtain and
analyze the dynamic results in case of change of the model parameters. Automatic rearrangement of charts in
Excel medium provides an overview of possible changes of the course
investigated process in case of changing of the initial data.
Mathematical modeling is a powerful tool for studying
physiological processes in living systems, biomechanical structures modeling in
dentistry. Hence, it is actual in study plans of relevant disciplines.