14. Compartment Models

Question 1

What is meant by the terms one-, two- and three-compartment models?

Answer 1

Compartment models are used to
design mathematical models that will
predict the drug-handling characteristics of the body.

They help us calculate the doses and frequency
of drug administration,

and form the basis of anaesthetic infusion regimes

used in target-controlled infusions.

Question 2

One-compartment model

Body viewed

Drug adminstration - rate constants

how does it distribute

Curve
Semi Log plot

Can we use this in practice?

Answer 2

> The body is viewed as

a single central compartment (C1)

with a defined volume of distribution.

> When a drug is administered
(rate constant k01)

it is assumed to disperse instantaneously

and

uniformly throughout C1.

> It is also assumed that the

drug is then completely cleared from C1

by elimination alone (rate constant k10).

> This model produces a
mono-exponential decay curve.

> Semi-logarithmic plot produces a straight line.

> In reality, this model is
far too simplistic because plasma drug
concentrations decline due to a
multitude of factors including

distribution from plasma into different tissues
(which can occur at different rates
due to differences in tissue perfusion),

drug metabolism

and

excretion.

Therefore a less simplistic model with two or three compartments is required.

Fig. 14.1 Semi-logarithmic plot of plasma concentration of drug over time

Question 3

Two-compartment model

Answer 3

> The body is now viewed as a
central compartment
(C1 – representing plasma)

in conjunction with a
peripheral compartment
(C2 – representing tissues).

> Additional rate constants apply to this model
and
plasma drug concentrations

now decline due to drug distribution

from plasma to tissues (k12)

and

drug elimination from the central compartment (k10).

> This produces a bi-phasic exponential decay curve.

Fig. 14.2 Semi-logarithmic plot showing bi-exponential decay of plasma concentration of
drug over time in a two-compartment model

Alpha-phase - slower elimination from C1

Beta-phase - initial rapid distribution
from C1 to C2

Question 4

Three-compartment model

Answer 4

> The body is viewed as a

central compartment
(C1 – representing plasma),

an intermediately well-perfused
peripheral compartment
(C2 – representing tissues like muscle)

and a poorly perfused peripheral compartment
(C3 – representing tissues like fat).

> Additional rate constants apply 
to this model and 
plasma drug concentrations 
now decline due to 
drug distribution into the peripheral
compartments of C2 (k12) and C3 (k13) 
and drug elimination from the
central compartment (k10).

> This produces

a tri-phasic exponential decay curve

where the distribution part of the curve

can be divided into
a fast (α)
and
slow (β) phase

followed by an elimination phase.

> The distribution to
and redistribution from
the peripheral compartments

along with drug elimination
from the central compartment occurs

simultaneously and down concentration gradients.

> Peripheral compartments can
act as stores for the drug,

keeping the central compartment full
even after drug administration
into it has ceased and
drug elimination from it continues.

> This redistribution of drug into
the central explains why the

effect of a drug can continue long after
its administration has ended and this is

an integral concept
in target-controlled infusions

and
context-sensitive half-lives