Homework_4_Solution

# Homework_4_Solution - BME210 Spring2009 Homework 4 Solution...

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BME210 Spring2009 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 4 (absorption compartment). The four differential equations representing the amount of the parent drug and its metabolite in their respective compartments are: () () ( ) () () () () () () () () () () t x k dt t dx t x k t x k dt t dx t x k t x k dt t dx t x k t x k k k t x k dt t dx 4 14 4 3 03 1 31 3 2 12 1 21 2 2 12 1 01 31 21 4 14 1 = = = + + + = ( 1 ) where, x 1 -x 3 are the amount of parent drug in compartment 1-3 respectively, and x 4 is the amount of metabolite in compartment 4, in unit of mg; the k 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 solve equations (1) 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 4, which produces a plasma concentration of the metabolite at 18 hours of 0.20 mg/L (within +/- 0.01mg/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. A brief discussion on more efficient approach, rather than just trying random numbers, for determining the dose is also presented.

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BME210 Spring2009 Section 2: The Program clc; clear; close all ; trange =[0 18]; % time interval % Solve using ODE45 x=[0 0 0 1000]; % initial condition options=odeset( 'RelTol' ,1e-5, 'AbsTol' ,1e-5); [t,x]=ode45( 'odecon' ,trange,x, options); % Determine the concentration in compartment 1 and 3 V1=25.0; V3=7.5; c1=x(:,1)/V1; % parent drug conc. in comp. 1 c3=x(:,3)/V3; % metabolite conc. in comp. 3 x(end,3)/V3 % Plots of the concentration in compartment 1 and 3 plotyy(t,c1,t,c3) xlabel( 'time (hr)' ); ylabel( 'concentrations (mg/L)' ); title( );
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## This note was uploaded on 07/15/2009 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.

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Homework_4_Solution - BME210 Spring2009 Homework 4 Solution...

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