CC BY
9solving biomedical problems [1], to the analysis of three-dimensional images of computed tomography of pa-
tients.
This work is supported by the Russian Science Foundation grant 21-15-00091.
References
1. Ronneberger O., Fischer P., Brox T. U-net: Convolutional networks for biomedical image segmentation // Intern.
Conf. on Medical image computing and computer-assisted intervention. Springer, Cham, 2015. P. 234-241.
Three-dimensional shape reconstruction of abdominal aortic aneurysm for hemodynamic modeling
Y. V. Fedotova, R. I. Mullyadzhanov
Novosibirsk State University
Email: i.antonevich@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-03-02
Abdominal aortic aneurysm (AAA) is a degenerative disease that significantly increases the rupture risk of
arterial wall. It�s a localized enlargement of the abdominal aorta such that the diameter is greater than 3 cm or
more than 50 % larger than normal. So an accurate prediction of AAA rupture is critical.
In this study, algorithm for automatic 3D reconstruction of AAA, obtained from tomographic images, was
developed and implemented. Accurate reconstruction of the geometry is necessary for automatic mesh pro-
cessing with a high quality in hemodynamic simulations. Moreover, the developed program can be applied to
measure important volume geometric characteristics of AAA [1]. The results of the work will be included in the
software package for predicting the rupture risk.
This work was supported by the Russian Science Foundation, project 21-15-00091.
References
1. Martufi, G., Di Martino, E. S., Amon, C. H., Muluk, S. C., & Finol, E. A. (2009). Three-dimensional geometrical char-
acterization of abdominal aortic aneurysms: image-based wall thickness distribution.
Formalization of target invariants of the system of anaerobic biological wastewater treatment
A. A. Fomenkova, A. A. Klyucharev, S. I. Kolesnikova
Saint-Petersburg State University of Aerospace Instrumentation
Email: skolesnikova@yandex.ru
DOI 10.24412/cl-35065-2021-1-02-40
A model of a two-stage process of anaerobic fermentation in a bioreactor-mixer is considered, the math-
ematical description of which is a system of nonlinear differential equations [1].
The aim of the study is to apply a new approach to organizing energy-saving control based on the princi-
ples of nonlinear adaptation on target manifolds with an attractive property [2], called invariants or laws of
behavior of the target system of the object under study.
In this regard, a necessary preliminary study is the formalization of these target invariants as given (de-
sired) laws of the control object's behavior.
Further, on their basis, an algorithm is proposed for the analytical synthesis of a vector controller with
compensation for systematic and random disturbances along the control channel ofthe system of anaerobic
biological wastewater treatment [3].
This work was supported by the Russian Foundation for Basic Research (grant 20-08-00747).
References
1. Klyucharyov A.A., Fomenkova A.A. Mathematical model of an anaerobic bioreactor with fixed biomass as a control
object. Information control systems. 2019. No. 2. P. 44-51. (in Russian).
2. Kolesnikov A.A. Synergetics and problems of control theory. Moscow: Fismatlit. 2004. (in Russian).
3. Kolesnikova S. I. Synthesis of the Control System for a Second Order Non-Linear Object with an Incomplete
Description. Autom. and Remote Control. V. 79. P. 1556�1566.
Mathematical models for dynamics of HIV infection acute phase
I. A. Gainova
Sobolev Institute of Mathematics SB RAS
Email: gajnova@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-41
There are considered mathematical models for dynamics of HIV infection acute phase. The first mathe-
matical models describing the dynamics of HIV infection appeared as early as 1986 [1], three years after the
discovery of HIV. The basic mathematical model of the dynamics of HIV infection includes three key cell popu-
lations: uninfected target cells, infected target cells, and free virus particles. This basic model allowed to obtain
such important quantitative characteristics of the infectious disease as the virus replication rate and an aver-
age half-life of a virus particle, the rate of decrease of the viral load, a life span of infected T-lymphocytes and
the rate of virus production by a single infected cell (basic reproduction number, R0). The next generation of
dynamic models is an extension of the basic model by considering various types of cells in the immune system,
types of infection (acute, latent), localization in the compartments (blood, lymphatic system), mutated strains
of the virus, etc. [2, 3].
This work was supported by the Russian Foundation for Basic Research (grant 20-01-00352) and the state contract of
the Sobolev Institute of Mathematics (Project No. 0314-2019-0013).
References
1. Covert D.L., Kirschner D. Revisiting early models of the host-pathogen interactions in HIV infection // Comm.
Theor. Biol. 2000. V. 5(6), P. 383-411.
2. Bocharov G., Chereshnev V., Gainova I., Bazhan S., Bachmetyev B., Argilaguet J., Martinez J., Meyerhans A. Human
Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling // Mathematical
Modelling of Natural Phenomena. 2012. V. 7 (5), P. 78�104.
3. Chereshnev V. A., Bocharov G. A., Kim A. V., Bazhan S. I., Gainova I. A., Krasovskii A.N., Shmagel N. G., Ivanov A. V.,
Safronov M. A., Tretyakova R. M. Introduction to modeling and control of HIV infection dynamics. Institute for Computer
Research, Moscow � Izhevsk, 2016.
Random graphs as structural models of biological networks
D. A. Gavrilov1, N. L. Podkolodnyy2,3
1Novosibirsk State University
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
3The Federal Research Center Institute of Cytology and Genetics SB RAS
Email: dgavrilov14@gmail.com
DOI 10.24412/cl-35065-2021-1-02-42
Modern methods of experimental research allow reconstruction of biological networks of various types,
including gene, metabolic, interatomic networks, gene co-expression networks, disease networks, etc.
