HW4solution_1

HW4solution_1 - BME 210 Spring 2007 Homework 4 Solution...

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BME 210 Spring 2007 Homework 4 Solution Therapeutic Drug Development (200 Points) PART 1: COMPARTMENT MODEL SIMULATION Section 1: Problem Set-up The compartment model shown below describes the pharmacokinetics of a drug administered as an oral dose into compartment 5 (absorption compartment). The five differential equations representing the amount of the parent drug and its metabolite in their respective compartments are: 1. dX1/dt = X5*K15 – X1*(K21+K31+K01) + X2*K12 2. dX2/dt = X1*K21-X2*K12 3. dX3/dt = X1*K31 – X3*(K43+K03) + X4*K34 4. dX4/dt = X3*K43 – X4*K34 5. dX5/dt = -X5*K15 where, X1-3 are the amount of parent drug in compartment 1-3 respectively, and X4,5 are the amount of metabolite in compartment 4,5 respectively, in unit of mg; the Ks are the transport rates, in unit of 1/hr. Outline for the rest of the report of PART 1 : In section 2, the Matlab files (hw4a.m and func1.m) used to solve the above equations using ODE45, and the resulting concentration-time profile graph with both the parent drug and the metabolite are shown. In section 3, program in section 2 is used to determine the initial dose to compartment 5, which produces a plasma concentration of the metabolite at 18 hours of 0.25 mg/L (within +/- 0.05mg/L). The resulting plot, and the resulting values for the metabolite concentrations to three decimal places and the corresponding value of dose used to achieve this value are shown. 1
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Section 2: The Program %%%%%%%% % hw4a.m % clear all ; trange =[0 18]; % time interval % Solve using ODE45 x=[0 0 0 0 1000]; % initial condition options=odeset( 'RelTol' ,1e-5, 'AbsTol' ,1e-5); [t,x]=ode45( 'func1' ,trange, x, options); % Determine the concentration in compartment 1 and 3 V1=50.0; V3=15.0; c1=x(:,1)/V1; % parent drug conc. in comp. 1 c3=x(:,3)/V3; % metabolite conc. in comp. 3 x(:,3)/V3 % Plots of the concentration in compartment 1 and 3 plotyy(t,c1,t,c3) xlabel( 'time (hr)' ); ylabel( 'concentrations (mg/L)' ); title( 'Parent Drug in Comp.1 & Metabolite in Comp.3'
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HW4solution_1 - BME 210 Spring 2007 Homework 4 Solution...

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