PHAR 7632 Homework #6 1999

Numerical Integration, Optimization, One Compartment IV Bolus Urine Data, and another Laplace Transform

DUE 27th April 1999

Question 5. Given the PK model below, derive the integrated equation for Mu1.

The Model:

The Solution:

dX/dt = -ke*X - km1*X - km2*X = -kel*X

s*L(X) - Dose = -kel*L(X)

L(X) = Dose/(s+kel)

dM1/dt = km1*X - kmu1*M1

s*L(M1) = km1*L(X) - kmu1*L(M1)

L(M1) = km1*L(X)/(s+kmu1) = km1*Dose/(s+kel)*(s+kmu1)

dMu1/dt = kmu1*M1

s*L(Mu1) = kmu1*L(M1)

L(Mu1) = kmu1*L(M1)/s = kmu1*km1*Dose/(s*(s+kel)*(s+kmu1))

OK!!

Three roots: 0, -kel, and -kmu1

Mu1 = kmu1*km1*Dose/(kel*kmu1)
+ kmu1*km1*Dose*exp(-kel*t)/(-kel*(kmu1-kel))
+ kmu1*km1*Dose*exp(-kmu1*t)/(-kmu1*(kel-kmu1))