1. Two Compartment IV Administration.

For many drugs a one compartment model is not a completely satisfactory description of the plasma concentration versus time data. For these drugs a second compartment is often added to the pharmacokinetic model. This compartment helps to explain distribution within the body which is not 'instantaneous', that is slow enough to see in the plasma concentration versus time curve. This shows up as a rapid drop at first with elimination and distribution, followed by a slower phase. As I'll explain later this curve can be described by the sum of two exponential terms. Is it biexponential (similar to the earlier oral curve which is calculated as the DIFFERENCE between two exponential terms)?

Differential equation (using microconstants - kel, ktp, kpt)

Integrated equation

where A, B, , and are combined parameters derived from Vc, kel, ktp, and kpt. NOTE, the integrated equation is biexponential.

Later we will talk about using the method of residuals to separate values for the fast and slow exponential just as we have with oral data.

Select parameter values to produce a definite two compartment

(biexponential) curve on a semi-log graph. Note that the transfer rate constants ktp and kpt will be lower to produce a two-compartment model. Change the parameter values to produce a one-compartment type curve using the two-compartment model. This will involve using much faster distribution rate constants. The assumption for a one compartment model is that distribution is too rapid to see, thus try increasing the magnitude of the distribution constants (ktp and kpt).

Try Vc = 20 liter, ktp = 0.5 hr^{-1},
kpt = 0.5 hr^{-1},
kel = 0.2 hr^{-1}
as a start, or A = 25 mg/L, B = 15 mg/L, = 2 hr^{-1},
= 0.5 hr^{-1}.

If you use Vc, ktp, kpt, and kel you should enter 0 to and . Otherwise the program will use the A, B, , and values from the previous run.

2. Two compartment IV Infusion Administration

Enter suitable parameters to give a two-compartment
curve. What shape is the curve on the linear or semi-log
graph? Calculate an infusion rate to achieve a steady state level of 25 mg/L.
Use Cpss = k0/clearance with clearance = kel * Vc, where kel is the overall
elimination rate constant from central compartment and Vc is the apparent
volume of distribution of the central compartment. Use kel = 0.2 hr^{-1}
and Vc = 20 L. It doesn't matter what kpt and ktp are but try something like
0.5 hr^{-1}
for each. How long does it take to get to 50% (12.5 mg/L), 75% (18.75 mg/L),
and 87.5% (21.9 mg/L) of steady state? You will need to experiment with the x
and y scale to get a good estimate of these times. Change kpt and ktp to 5
hr^{-1},
that is, more like a one compartment model. Now how long does it take to get to
50, 75, and 87.5% of steady state? Is it still aiming for the same steady state
value? You will need to use a fairly long maximum time scale, for example 24 or
better 48 hours.

3. Two compartment Oral Administration.

Now we have three exponential terms to describe the plasma concentration versus
time curve. Start with kel, kpt, ktp = 0.25 hr^{-1}
and ka = 3 hr^{-1}.
What shape is the curve on linear and semi-log
graph? Can you see the two-compartment
(bi/triexponential) nature of this curve. That is, do you see a rapid then slow
fall after the peak plasma concentration? If you do, change the ktp and kpt to
hide this extra exponential. If you don't see three exponentials, try changing
the kpt and ktp values.

4. Two compartment IV Bolus and Infusion Administration.

a) What shape does the curve have with 30 minute infusions every 4 hours (no bolus doses)?

b) Develop a dosing regimen of one bolus and one infusion rate to rapidly
achieve a plasma concentration of 25 mg/L. [kel = 0.15 hr^{-1},
ktp = 0.5 hr^{-1},
kpt = 0.5 hr^{-1},
and Vc = 12 L]. Note Cp(0) = Bolus dose/Vc and Cp(ss) = k0/(kel*Vc) = k0/TBC.
Try to keep the plasma concentration above 16 mg/L at all times but also below
30 mg/L.

c) Develop another dosing regimen with two infusion rates (one fast [maximum duration 2 hours] and the other slower - maintenance). Use the same parameter values as b) above. Again try to keep the plasma concentrations between 20 and 30 mg/L throughout the dosing regimen.

WRITE-UP

The programs can produce printer output of the plot you have on the screen. You can have more than one line on each graph. You might try to get two or three lines on a graph so that you can illustrate a point with one graph. You can photocopy the printer output for each member of the group however each person should write up their own comments. Briefly describe each graph that you produce, answering the questions as appropriate.

Section 2 and 4b. Show your working when calculating the doses that you use.

This page was last modified: 12 February 2001

Copyright 2001 David W.A. Bourne