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.
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