# Simulation of Biological Systems

Class Schedule

Lectures +  Labs:       Wednesdays    9:00-12:15       room 308

## Credit and Exam Conditions

There are 2 versions of SBS class as follows:

Non-Exam version:

E376012          2+2                  credit ,   (4 credits, no official marking!!!, just pass or F)

Exam version:

E374013          2+2                  credit + exam . (5 credits, official marking (A-F )

To qualify for the credit (zápoèet), you are supposed to attend labs (minum 80% ) and accomplish two assignments and submit their reports, min. 10 pages each, with proper formalities and briefly present your work and results in the class.

If you will not attend 50%-80% of labs, you may get more assignments to compensate your absence and to still get the credit.

If you missed more than 50% of the labs, you will not qualify to get the credit.

For those, who have subscribed for the exam-version class (E374013 is in your student book (index)), the credit will qualify you for an exam, and the exam will consist of two parts:

1 – Solving a simulation lab – a problem selected from the topics we were doing during the semester.

2 – Theoretical part of the exam – test of your knowledge about the topics we were dealing in the class.

# Assignment 1 (for both SBS versions):

(the requirement details have been explained in the class, or contact me for more clarification)

Your task is to find a published research paper related to the modeling of a biomedical system where differential equations or discrete-time equations are involved. (you do not need to look for space-distributed problems).

You should become familiar of what is the purpose of the model in the paper, and what is the meaning of its variables and parameters, and analyze it in your report.

T1.  Implement the model on a PC and present the model and your results

T1.1.       You may simplify the model if it is too complicated or vice versa (continuous-time models should be at least 3-D (3rd order of dynamics), you might need to add one more state variable to make it 3rd order  – as z(t) bellow

$$\begin{matrix} \dot{x}(t)=f_x(x,y,z,t) \\ \dot{y}(t)=f_y(x,y,z,t) \\ \dot{z}(t)=f_z(x,y,z,t) \end{matrix}$$

T1.2.       Discrete-time model has to be nonlinear, or you can make it nonlinear and study the effect.

T2.  Considering  Poincaré-Bendixson theorem for continuous-time dynamic systems, analyze briefly the model regarding its potentials for developing deterministic chaos (linear vs. nonlinear, order of dynamics, continuous  vs. discrete systems).

T3.  Theoretically, how many equilibrium points we can find for the model by a simple analysis? (analyze and calculate them)

T4.  Try to modify the model parameters to achieve oscillations, quasiperiodic, or even chaotic behavior and conclude your results.

Reports containing copy and paste texts will not be accepted!

Exceptionally, you may adopt or modify some original figures (only for our class), but you must provide your report with proper references to the adopted figure and its resource.

Look on the end of the journal paper, how they write references and you may use the same style (it should be systematic and unified).

The resources for looking for a paper might be as follows:

Open-Access:

[1]   Theoretical Biology and Medical Modelling (TBioMed), BioMed Central , (http://www.tbiomed.com/)

[2]   Computational and Mathematical Methods in Medicine, Hindawi Publishing Corp. (http://www.hindawi.com/journals/cmmm/contents/), ISSN: 1748-6718 (Online), doi:10.1155/CMMM

Available for campus network (or let me know):

If you are unable to download a paper outside of campus, you might need log in to https://dialog.cvut.cz/ and than to try find a paper using electronic resources

Also, http://scholar.google.com/  will do a great job for you to find a paper.

# Assignment 2 (for both SBS versions):

(the requirement details will be explained in the class)

Analyze real biomedical data and implement a simple predictive model for the data.

You will be provided with one or two signals to analyze and study.

The points are:

a)      Calculate and plot auto-correlation function of each signal, and analyze results

b)      (two signals) Calculate and plot cross-correlation function of each signal, and analyze results

c)      Calculate and plot the Fourier transform of each signal and analyze results

d)     Calculate and plot the Fourier transform of autocorrelation function and analyze results

e)      Calculate difference signals and repeat the above analysis.

f)       Estimate a configuration of a simple predictive model and adapt its parameters by gradient descent or Levenberg-Marquardt algorithm.

g)      Test the model how it predicts on new data and analyze the result.

o   e.g. calculate coefficient of determination (r2) between real data and the model output and also between the differences of the signals.

Do not hesitate to contact me if you feel you need more details or clarification.

References

Neural Network

[4]   Brain power” Special Report: 1998: 05/98: The Human Body , http://news.bbc.co.uk/2/hi/special_report/1998/05/98/the_human_body/114977.stm, accessed 07/10/20113.

[5]   “BBC Human Body 05 Brain Power”, also available on You Tube on 07/10/2013.