BME 301A Fall 2020 Computational Lab Project Released: December 9, 2020 Due: December 11, 2020 11:59 pm This project takes the place of an in-person CLab Practical Examination. It is intended to be completable in the ordinary lab period, that is, in four hours or less. It’s recommended that you work on this project only during your regularly scheduled lab period, and turn in what you have at the end. Really, just turn it in. You may: use any course materials and the internet (citing all sources). You may not: discuss this project with any person other than the course instructors, or use someone else’s work as your own. In addition to a report document, all code and models must be submitted. Your report can be simply numbered answers with your labeled plots and typed answers to the questions; no introduction, connecting text, or conclusion is required. There is no page limit. Problem 1. Please copy and paste, and then sign (typed signature or other signature) the following statement into your submission: By continuing with this assignment, I affirm that I will not give and I will not receive any unauthorized assistance on this assignment. The work I submit represents my work and my work alone. I will abide by the academic integrity policy and I am aware of the consequences associated with engaging in academic misconduct. Signature: ________________________ Problem 2. List all sources, official and unofficial, used to complete this examination. BME 301A Fall 2020 Computational Lab Project Released: December 9, 2020 Due: December 11, 2020 11:59 pm Problem 3. The Belousov-Zhabotinsky reaction is an important example of a nonphysiological excitable system. We observed the physical system in PLab 5; now we will model its dynamics. The reaction describes the oxidation of malonic acid by bromate in an acidic solution, catalyzed by a metal; we used ferroin (an iron-based indicator). The kinetic equations that describe this reaction are (from Tyson and Fife, 1980, equation 17a/b): = − − + + − 2 = − where denotes the concentration of bromous acid and denotes the concentration of the oxidized catalyst metal. (a) Calculate (show the equations) and then plot the nullclines of Equations 17, as in Fig 4. Note that the x-axis limits in the paper are a and 1.0, and the y-axis limits are 0 and approximately (1/4)*b. (Choose values for a and b based on information in Section III as needed to achieve similar-looking nullclines. Note that the system changes rapidly for small . ) (b) Based on the nullcline plot, in what region(s) would you expect the system to be globally stable, and in what region(s) would you expect the system to act as a stable oscillator? Give a brief justification. You can give values or simply indicate on your plot. (Hint: the discussion associated with Fig 5 in the paper may provide insights for this.) Problem 4. (a) Model the two equations of 17a/b in Simulink or MATLAB, as you wish. (Hint: remembering that this system models a chemical reaction environment with no external/stimulus inputs, where must the driving force of the system originate (ie, what makes it go?).) Using = 0.01 and = 0.005, explore the effect of on the system. Illustrate your findings by creating an overlaid phase plane plot of vs showing the system as a stable spiral and as a stable oscillator. Indicate the value of b that produced each trace. (b) Create a plot of vs time using a value of that generates a stable oscillator. (c) Discuss the suitability of this model as it applies to cardiac action potentials. What aspects of cardiac action potentials does it model well, and what aspects less well? Turn in a simple report document and all models and/or code generated for this project.
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