BIOMECHANICS, BIOENGINEERING AND MATHEMATICAL BIOLOGY Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije: https://miteam.mi.sanu.ac.rs/asset/pkPCEADMcffpGhjaQ

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Plan rada Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije za JUN 2025.

Ponedeljak, 23.06.2025. u 16:00, sala 301f, MISANU, Kneza Mihaila 36 i Online
Isidora Rapajić, Mathematical Institute SANU
MATHEMATICAL MODEL OF HEMOLYMPH FLOW IN AN INSECT ANTENNA
Antennae in insects are important sensory organs that enable movement. Their shape varies in adults depending on the species and sex; however, the fundamental structure is common. The importance of formulating and analyzing a mathematical model lies in its generality and the potential for application to other biological systems (e.g., water transport in plant vascular tissue) or in the design of microfluidic devices.
The mathematical model of hemolymph (insect blood) flow in the antenna can be formulated as a system of parabolic differential equations. It can be derived from basic principles—the laws of conservation of mass and momentum. The geometry of the antenna is represented by two concentric cylinders, with the inner one modeling the blood vessel. If the blood vessel is assumed to be porous, fluid flow and pressure fields are related through Darcy’s law. Since it is difficult to experimentally determine permeability, it is assumed to be proportional to the square of the vessel's radius. Another key assumption is that the inertial term in the model can be neglected, i.e., the viscous term dominates. This conclusion is reached through appropriate scaling and analysis of the Reynolds number.
In the absence of time dependence, it is possible to determine an analytical solution. In this presentation, the pressure distribution will be shown for three cases—a permeable blood vessel, an impermeable blood vessel, and an antenna that is interrupted at one end.

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Ponedeljak, 30.06.2025. u 16:00, sala 301f, MISANU, Kneza Mihaila 36 i Online
Stevan Maćešić, Faculty of Physical Chemistry, University of Belgrade, Serbia
EXPLORING THE DYNAMICS OF COMPLEX REACTION NETWORKS VIA ADVANCED ANALYSIS METHODS
Nonlinear reaction systems that exhibit spontaneous self-organization are at the heart of many natural and engineered processes, from biochemical oscillators in cellular signalling to pattern formation in developmental biology and smart materials. Oscillatory dynamics, bistability, and Turing instabilities underpin phenomena such as circadian rhythms, memory storage in synthetic gene circuits, and spatial structuring in reaction–diffusion media. Modelling these phenomena in the systems mentioned above remains difficult. Feedback loops, nonlinear rate laws, and diffusive transport result in high-dimensional, stiff systems. Moreover, dynamics in these systems change significantly when parameters are altered. Traditional methods like linear stability and bifurcation analysis are key for understanding the dynamics of a proposed model. However, exact analytical solutions are usually impossible to find within large chemical networks; hence, the analysis is limited to systematic numerical exploration of parameters.
In contrast to traditional methods, stoichiometric network analysis (SNA) is a powerful method enabling efficient and systematic analysis of such complex models. SNA identifies all feasible steady-state pathways and elucidates how network architecture governs the stability of steady states. This approach reveals the structural origins of Andronov–Hopf and saddle-node bifurcations, as well as diffusion-driven instabilities such as Turing patterns. It determines the chemical species and reactions essential for the existence of instabilities and associated dynamical states, yielding analytical expressions describing the precise conditions for their emergence. Therefore, this lecture will explain how to apply SNA to analyse complex reaction networks and derive results that are valuable and applicable to both theoretical analysis and experimental work.

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