Rob MacLeod and Quan Ni
The goal of this assignment is to experiment with a numerical simulation of the cardiac action potential. The form of this simulation is just as described in class, using the Hodgkin-Huxley formalism and differential equations to reproduce the currents responsible for the action potential. As we saw in class, To simulate the cardiac action potential, it is necessary to expand the number of channels from the simple squid giant axon case, and also to alter the dynamic behavior of these currents compared with the original work of Hodgkin and Huxley.
The background for the simulations you will find in your notes from class on the Luo-Rudy model, implemented according to the first edition (i.e., based on the 1991 and 1994 papers[1,2]. Below is a description first of how to obtain and use the code and then of what I would like you to investigate with it.
Additional background is in the accompanying pdf document called background.pdf so please make sure to read it first.
The programs to perform the simulation are all written in MATLAB--they are m-files and thus completely readable and editable by each of you. Feel free to experiment with your copy of the files and investigate the structure of the code and numerical methods employed. For details or questions about MATLAB, contact me (macleod@cvrti.utah.edu) or see the associated references from my web site.
To make the code work, perform the following steps:
Note: the report from this assignment must be typeset and include graphs of your results. See the homework tips site for details. I appreciate people who can write sentences and prepare decent looking reports. So please take the time to organize the report clearly, and integrate the output from the simulations into the document. I anticipate reports in the range of 3-6 pages in length (including figures) but there are no restrictions or requirements (in either direction) so please write concisely and answer the questions directly.
Set up at least twenty combinations of stimulus strength and duration and observe the resulting action potential amplitudes and durations. The Map_demo.m file provides a template that can be the starting point for this set of simulations. Create an overlay plot showing the set of action potentials. Make sure to include in the series of simulations, some combinations of stimulus duration and amplitude that do not elicit an action potentials and also some that just barely result in an action potential. Be aware that you a probing a highly nonlinear behavior (all-or-nothing) so select values of stimulus pulses thoughtfully.
Now greate a a plot of stimulus intensity vs. stimulus duration for all the combinations that just barely generated a more or less normal action potential.
What do these results tell you about how the (simulated) cell responds to stimulation? Do your results validate the all-or-nothing behavior you expected? Can you explain a method or mechanism for determining whether a specific intensity/duration combination is likely to be enough to stimulate an action potential?
Why does the action potential not disappear completely even when the sodium concentration gradient approaches zero? What is providing the inward current in this case?
Try and discuss the results in terms of your qualitative knowledge of cellular electrophysiology.
Submit the assignmemt in paper or electronic form by Friday, February 13, 2009.
This document was generated using the LaTeX2HTML translator Version 2002-2-1 (1.71)
Copyright © 1993, 1994, 1995, 1996,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
Copyright © 1997, 1998, 1999,
Ross Moore,
Mathematics Department, Macquarie University, Sydney.
The command line arguments were:
latex2html -split 3 -no_white -link 3 -no_navigation -no_math -html_version 3.2,math -show_section_numbers -local_icons homework
The translation was initiated by Rob Macleod on 2009-02-10