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BME 210 Spring 2007 Homework 4 Solution Therapeutic Drug Development (200 Points) PART 1: COMPARTMENT MODEL SIMULATIONSection 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 equationsrepresenting 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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