- On 24 Nov 2001 at 19:49:17, "Mike Leibold" (m_leibold.at.hotmail.com) sent the message

Back to the Top

The following message was posted to: PharmPK

Dr.Whelan,

The Xo term in the pharmacokinetic bolus equations is simply

the dose. In the first order absorption model, the dose appears

as D (with F equal to fraction absorbed). In the zero order

absorption model, the dose appears as Ko, representing the dose

absorbed over time(usually represented as the dosage interval in

the case of sustained release forms such as oral theophylline).

The two compartment model can be adapted to oral absorption by

modifying the input function of the differential equation.

dX1/dt= -(k10+k12)X1 + (k21)X2 + KaFDe-Kat

dX2/dt= (k12)X1 - (k21)X2

In the above case, the oral absorption is modeled as a first-

order process KaFDe-Kat, with Ka= first oral absorption constant,

F= bioavailability, and D= the dose. Oral sustained release

medications can be modeled as above with a smaller Ka relative

to the immediate release form, or can be modeled as a zero order

process (or infusion model):

dX1/dt= -(k10+k12)X1 + (k21)X2 + Ko

dX2/dt= (k12)X1 - (k21)X2

As you can see, the difference in the two systems above is

the input function: KaFDe-kat or Ko.

The matrix respresentation of these systems of differential

equations is useful for solving the Laplace transformed systems

for the amount in the plasma compartment:

[SI-A][Xs]= [Us]

A) First order oral absorption:

[(s+k10+k12) -k21 ][X1s]= [KaFD/(s+Ka)]

[ -k12 (s+k21) ][X2s] [ 0 ]

B) Zero order oral absorption:

[(s+k12+k12) -k21 ][X1s]= [Ko(1-e-Ts)/s]

[ -k12 (s+k21)][X2s] [ 0 ]

Solving the above matrices for the amount in the central compartment

yields the following Lapace transforms:

A) First order oral absorption:

X1s= [(KaFD)(s+k21)]/[(s+a)(s+b)(s+Ka)]

B) Zero order absorption:

X1s= (Ko)(1-e-Ts)((s+k21)/[(s)(s+a)(s+b)]

Taing the inverse Laplace transforms of the above equations and

then dividing by Vc yields equations for the plasma concentration for

each oral absorption model:

A) First order absorption model:

Cp= (KaFD)(k21-a)e-at/[(Vc)(b-a)(Ka-a)] +

(KaFD)(K21-b)e-bt/[(Vc)(a-b)(Ka-b)] +

(KaFD)(k21-Ka)e-Kat/[(Vc)(a-Ka)(b-Ka)]

b) Zero order absorption model:

Cp= Ko(k21-a)(1-e-at)/[(Vc)(a)(b-a))] +

Ko(k21-b)(1-e-bt)/[(Vc)(b)(a-b)]

I hope this was what you were looking for!!

Mike Leibold, PharmD, RPh

ML11439.-a-.goodnet.com

References

1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker

1975

2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker

1982

3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug

Intelligence Publications 1975

4) Godfrey, Keith, Compartment Models and Their Application, New York,

Academic Press 1983

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Two Compartment Absorption Model 1st and 0 order Models" as the subject

PharmPK Discussion List Archive Index page

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)