BENG449 Problem 9 3

# BENG449 Problem 9 3 - 1:51 AM C\Documents and Settings\Alex...

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Unformatted text preview: 4/23/08 1:51 AM C:\Documents and Settings\Alex Lemon\My ...\BENG449 Problem 9 3.m 1 of 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Alex Lemon % % BENG 449 -- Biomedical Data Analysis % % Problem Set 9, Question 3 % % Due April 22, 2008 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Consider the one tissue compartment model in PET with: % % K1 = 0.5 % % k2 = 0.1 % % Assume the input function: % % CP(t) = exp(- beta * t) % % Using Matlab, for beta taking values form 0.00, 0.01, 0.02, 0.03, 0.04 % % and 0.05, solve for the tissue concentration, CT(t), for in the range % % [0, 120]. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % First, initialize the problem parameters % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% colors = {'r', 'g', 'b', 'm', 'c', 'k'}; K1 = 0.5; k2 = 0.1; beta = [0.00, 0.01, 0.02, 0.03, 0.04, 0.05]; clear CTN CTA; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Solve for CT(t) numerically using ode45 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tspan = [0 120]; CT0 = 0; for(i = 1:length(beta)) params = [K1 k2 beta(i)]; [t, CT] = ode45(@dCTdT, tspan, CT0, , params); CTN{2 * i - 1} = t; CTN{2 * i} = CT; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Solve for CT(t) using the analytical solution % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% t = 0:0.1:120; for(i = 1:length(beta)) b = beta(i); CT = K1 / (k2 - b) * (exp(- b * t) - exp(- k2 * t)); CTA{i} = CT; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % A.) Graph the simulated tissue curves one graph, CT(t) vs. t % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 4/23/08 1:51 AM C:\Documents and Settings\Alex Lemon\My ...\BENG449 Problem 9 3.mC:\Documents and Settings\Alex Lemon\My ....
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BENG449 Problem 9 3 - 1:51 AM C\Documents and Settings\Alex...

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