Direct Effect Models
Just as shown for plasma pharmacokinetics earlier, the biophase
concentration is the convolution of an input function (in this case, the plasma drug
concentration over time) and the disposition function of the biophase. This relationship
can be expressed as
Cbiophase
(t) = Cplasma
(t) *
Dbiophase
(t) (6)
The disposition function of the biophase is typically modeled as a single exponential
decay:
Dbiophase
(t)
= ke0
e−ke0
t
(7)
The monoexponential disposition function implies that the effect
site is simply an additional compartment in the standard compartmental model that
is connected to the plasma compartment (see Fig.
12-5
). The effect site is the hypothetical compartment that relates the
time course of plasma drug concentration to the time course of drug effect, and ke0
is the rate constant of drug elimination from the effect site. By definition, the
effect compartment receives such tiny amounts of drug from the central compartment
that it has no influence on plasma pharmacokinetics.
We cannot directly measure either Cbiophase
(t) or Dbiophase
(t),
but we can measure drug effect. Knowing that the observed drug effect is a function
of the drug concentration in the biophase, we can predict the drug effect as
Effect = fPD
[Cplasma
(t) * Dbiophase
(t),
PPD
, ke0
] (8)
where fPD
is a pharmacodynamic model (typically
sigmoidal in shape), PPD
is the parameters
of the pharmacodynamic model, and ke0
is the rate constant for equilibration between plasma and the biophase. Nonlinear
regression programs are used to find values of PPD
and ke0
that best predict the time course
of drug effect. Knowledge of these parameters can then be incorporated into dosing
regimens that produce the desired time course of drug effect.[30]
[31]
If a constant plasma concentration is maintained, the time required
for the biophase concentration to reach 50% of the plasma concentration (t½
ke0
) can be calculated as 0.693/ke0
.
After a bolus dose, the time to peak biophase concentration is a function of both
plasma pharmacokinetics and ke0
. For
drugs with a very rapid decline in plasma concentration after a bolus (e.g., adenosine,
which has a half-life of several seconds), the effect-site concentration peaks within
several seconds of the bolus, regardless of the ke0
value. For drugs with a rapid ke0
and
a slow decrease in concentration after a bolus injection (e.g., pancuronium), the
peak effect-site concentration is determined more by ke0
than by plasma pharmacokinetics. The time to peak effect and the t½ ke0
for several intravenous anesthetics are listed in Table
12-1
.
