Simulation of Biological Systems
- Department of Instrumentation and Control Engineering
Biological dynamic systems can be modeled by analytical approaches or by computer supported optimization techniques. Analytical approaches may result in models of population dynamics, bioreactor, epidemiological models, artificial neurons, arterial CO2, or the model explaining chaos in heart rate. The computational intelligence based approaches will be like the prediction of real lung motion during respiration or adaptive monitoring of ECG.
Attending students should have accomplished basic course of mathematics on differential equations.
- Syllabus of lectures:
1-2.Introduction. The difference between the concepts of modeling technical and biological systems. Historical background- theory of catastrophes; Zeemans catastrophic machine.
3-4.Properties of nonlinear models of dynamic systems; periodic, quaziperiodic, and chaotic behavior of systems; deterministic chaos. Synchronization phenomenon of coupled biological systems.
5-6.Design principles of basic models of biological systems and their properties: population models, models of simple chemical reactions, cell regulation models, epidemiological model.
7-8.Design of dynamical model from measured data recordings (state-space reconstruction). Optimization of parameters of deterministic models: mathematical analysis, adaptation, genetic algorithms,...
9-10.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.
11-12.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.
13-14.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 Useful programming techniques, worksheet calculators, introduction to Matlab,Maple, Simulink, efficency of matrix and vector operations in Matlab.
3-4 Fundamentals on modelling dynamical systems, linear s
3-4 Simulation of simple catastrophic models. Simulation of bifurcations in models of beetle population. Simulation of continuous chaotic model (MS Excel, demonstration of program Maple).
5-6Determining 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).
7-8Simulation of monitoring the actual changes in the dynamics of cardiovascular system with higher-order nonlinear neural units (HONNU) (Matlab/Simulink)
9-10Automated design of adaptive neuro-fuzzy model of combined anesthetics effects with uncertainty in measured data (MS Excel, Matlab/Simulink ANFIS).
11-12The model of the fast control influences of autonomous neural system affecting the heart-rate variability (Matlab/Simulink).
13-14Accomplishing projects, consulting, credits
- Study Objective:
Students will practice modeling techniques related to the deterministic chaos, quasiperiodic behavior, synchronization, uncertainty, neural networks, model optimization, adaptation, and will become familiar with related terms.
- Study materials:
See the subject web page ( www.fs.cvut.cz/~bukovsky/SBS/ ) for links to the on-line sources.
(SW: Matlab, MS Excel)
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: