Simulation of Biological Systems

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Synopsis:

In Simulation of Biological Systems course, students will gain notions of basic terms, principles, and approaches to modeling of biological systems behavior. Students will become familiar with important phenomena observed in real biological systems and will gain insights into their mathematical bases for expressing them analytically including possible utilization of artificial intelligence tools. The discussed phenomena are for example the deterministic chaos or synchronization of coupled bio(systems). The notion of uncertainty in real systems and the modeling tools handling uncertainty will be discussed. Among others, students will become familiar with the simplified model of cardiovascular system focusing fast beat-by-beat control influences of autonomous nervous system to heart-rate variability. During the labs, the model-design utilization of MS Excel, Maple, Matlab (Simulink, NN toolbox, ANFIS) and Dataplore will be demonstrated.

Requirements:

The regular attendance of lectures and labs, individual activity during labs, and a more detailed study on a particular topic elaborated into a report is required. It is recommended students should be familiar with basic terms taught in undergraduate mathematic courses (integration, differential equation, ?) There are no specific requirements for skills with any particular modeling software.

Syllabus of lectures:

1.The difference between the concepts of modeling technical and biological systems. Introduction into the theory of catastrophes; Zeeman?s catastrophic machine.

2.Properties of nonlinear models of dynamic systems; periodic, quaziperiodic, and chaotic behavior of systems; deterministic chaos. Synchronization phenomenon of coupled biological systems.

3.Design principles of basic models of biological systems and their properties: population models, models of simple chemical reactions, cell regulation models, epidemiological model.

4.Design of dynamical model from measured data recordings (state-space reconstruction). Optimization of parameters of deterministic models: mathematical analysis, adaptation, genetic algorithms,...

5.Conventional and nonconventional models of a biological neuron. Possible utilization of artificial neural networks for modeling; advantages and disadvantages. Artificial neural network as predictor of heart beat rhythm.

6.Approaches to the design of biological models featuring uncertainty; uncertainty in biological systems. Fuzzy model of the effect of combination of anesthetics with uncertainty in measured data.

7.The model of the fast control influences of autonomous neural system affecting the heart-rate variability; monitoring of the dynamics of cardiovascular system.

Syllabus of tutorials:

1 - 2 Simulation of simple catastrophic models. Simulation of bifurcations in models of beetle population. Simulation of continuous chaotic model (MS Excel, demonstration of program Maple).

3Determining parameters for state space reconstruction (False Neighbors Method, Mutual Information). Automated design of an artificial neural network model predicting heart-beat rhythm; designing a model from measured data (R-R recordings) (MS Excel, Dataplore, Matlab/Simulink).

4 Simulation of monitoring the actual changes in the dynamics of cardiovascular system with higher-order nonlinear neural units (HONNU) (Matlab/Simulink)

5Automated design of adaptive neuro-fuzzy model of combined anesthetics effects with uncertainty in measured data (MS Excel, Matlab/Simulink ANFIS).

6The model of the fast control influences of autonomous neural system affecting the heart-rate variability (Matlab/Simulink).

Study Objective:

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: