Modelling Organs, Tissues and Devices (BIOM9711) Assignment 3 Due date: 29-3-2010 The ID-fibre Hodgkin-Huxley PDE formulation for a propagating neural impulse (action potential) is given below: With initial values everywhere along the length of the fibre as: Variable 1 at ir at at c.120 ex am --a.(-)-2.7 dr dh ---- an -0,1-1)-2.1 dt Initial Value -20 mV at x = 0 -60 mV for all other 0.3177 for all 0.0529 for all 0.5961 for all h with 20 1-exp 100(T' + 35) a.- -(V+35) 10 2. - 4000 exp - (V-60) 13 [-(-60) a. - 70 exp 1000 P- 1+exp -(V+30) 10 10( 150) - (V+50) 1-exp 10 -(+60)7 8. - 125expl 80 Using the method of lines, implement a MATLAB program to solve for and plot the propagating action potential down an ason of length 1 cm over a total time span of 20 ms, subject to zero-flux boundary conditions at either end. Estimate the conduction velocity of the impulse in ms. Assume that a small dose of the drug tetrodotoxin (TTX) is now applied to the nerve, so that 60% of the ina channels are blocked. Using the same initial values and boundary conditions as above, plot the new propagating membrane potential and estimate the new conduction velocity. Finally, assume an even higher dose of TTX is administered, so that 80% of the ina channels are now blocked. Again, using the same initial values and boundary conditions plot the membrane potential as a function of x and t. Estimate the conduction velocity in this case also. Are these results as you expect? Hand-in a hardcopy printout of your MATLAB source codes as well as the plots. Leave your MATLAB code on your assignment submission folder on your S: share drive, so we can run your code directly. Model parameters are: Parameter 81 Description Maximum membrane sodium conductance Maximum membrane potassium conductance Maximum membrane leakage conductance Reversal potential for sodium channels Reversal potential for potassium channels Reversal potential for leakage channels Membrane capacitance Cytosolic (.e. intracellular) resistivity Axon radius Value 120000 36000 300 55 -72 -49.387 1 0.0006 0.0025 Units S/cm S/cm S/cm MV mV mV F/cm Mcm 1 c. P. Modelling Organs, Tissues and Devices (BIOM9711) Assignment 3 Due date: 29-3-2010 The ID-fibre Hodgkin-Huxley PDE formulation for a propagating neural impulse (action potential) is given below: With initial values everywhere along the length of the fibre as: Variable 1 at ir at at c.120 ex am --a.(-)-2.7 dr dh ---- an -0,1-1)-2.1 dt Initial Value -20 mV at x = 0 -60 mV for all other 0.3177 for all 0.0529 for all 0.5961 for all h with 20 1-exp 100(T' + 35) a.- -(V+35) 10 2. - 4000 exp - (V-60) 13 [-(-60) a. - 70 exp 1000 P- 1+exp -(V+30) 10 10( 150) - (V+50) 1-exp 10 -(+60)7 8. - 125expl 80 Using the method of lines, implement a MATLAB program to solve for and plot the propagating action potential down an ason of length 1 cm over a total time span of 20 ms, subject to zero-flux boundary conditions at either end. Estimate the conduction velocity of the impulse in ms. Assume that a small dose of the drug tetrodotoxin (TTX) is now applied to the nerve, so that 60% of the ina channels are blocked. Using the same initial values and boundary conditions as above, plot the new propagating membrane potential and estimate the new conduction velocity. Finally, assume an even higher dose of TTX is administered, so that 80% of the ina channels are now blocked. Again, using the same initial values and boundary conditions plot the membrane potential as a function of x and t. Estimate the conduction velocity in this case also. Are these results as you expect? Hand-in a hardcopy printout of your MATLAB source codes as well as the plots. Leave your MATLAB code on your assignment submission folder on your S: share drive, so we can run your code directly. Model parameters are: Parameter 81 Description Maximum membrane sodium conductance Maximum membrane potassium conductance Maximum membrane leakage conductance Reversal potential for sodium channels Reversal potential for potassium channels Reversal potential for leakage channels Membrane capacitance Cytosolic (.e. intracellular) resistivity Axon radius Value 120000 36000 300 55 -72 -49.387 1 0.0006 0.0025 Units S/cm S/cm S/cm MV mV mV F/cm Mcm 1 c. P