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BME 210 Spring 2007
Homework 4 Solution
Therapeutic Drug Development
(200 Points)
PART 1: COMPARTMENT MODEL SIMULATION
Section 1:
Problem Setup
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*K21X2*K12
3.
dX3/dt = X1*K31 – X3*(K43+K03) + X4*K34
4.
dX4/dt = X3*K43 – X4*K34
5.
dX5/dt = X5*K15
where, X13 are the amount of parent drug in compartment 13 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 concentrationtime 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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View Full DocumentSection 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'
,1e5,
'AbsTol'
,1e5);
[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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 Spring '07
 D'Argenio

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