Slope of the Concentration-Effect Relationship
Although clinicians have traditionally relied on pharmacokinetic
parameters in predicting the time course of drug effect, the temporal profile of
drug effect is a function of both pharmacokinetic and pharmacodynamic parameters.
For opioids, the concentration-effect relationship is usually
described graphically by a sigmoidal maximum-effect curve in which drug concentration
in the site of action is plotted against drug effect. This sigmoidal curve is presented
mathematically by the following equation.
Figure 11-17
Time to reach brain concentration after simultaneous
bolus applications of fentanyl, sufentanil, and alfentanil. The fraction of peak
brain concentration results from the amount of drug extracted from arterial blood
(arterial-jugular bulb concentration difference, integrated over time) plotted as
a fraction of the cumulative absorption. Data are presented as the median (solid
lines) and 50th and 95th percentiles (dotted lines)
from individual patients. (From Metz C, Gobel L, Gruber M, et al: Pharmacokinetics
of human cerebral opioid extraction: A comparative study on sufentanil, fentanyl,
and alfentanil in a patient after severe head injury. Anesthesiology 92:1559–1567,
2000.)
Where E is the predicted effect, E0
is the baseline effect, Emax
is the maximal effect, Ce
is the effect site concentration and γ
is a measure of curve steepness. EC50
is the effect site concentration
that produces 50% of maximal effect and can be compared with other drugs as a comparative
measure of drug potency. For drugs such as opioids that have a steep concentration-effect
relationship (high γ), the correlation of effect with concentration is often
observed to be binary.
Pharmacokinetic parameters cannot be interpreted alone in predicting
the duration of drug effect. Although knowledge of the predicted decline in drug
concentration based on pharmacokinetic parameters is helpful, it must be interpreted
with knowledge about the drug's potency and the steepness of the concentration-effect
relationship.[330]
The implications of context-sensitive
half-time (or 50% decrement time) must thus be interpreted in concert with knowledge
of the concentration-effect relationship. The duration of drug effect as predicted
by the context-sensitive half-time closely parallels that predicted by the mean effect
time when the concentration-effect relationship is shallow. When the concentration-effect
relationship is less steep, the context-sensitive half-time may be less useful in
predicting the time course of drug effect.
The clinical application of these concepts with regard to opioid
pharmacology relates to the steepness of the concentration-effect relationship of
opioids. Very small changes in opioid concentration can produce large changes in
drug effects. This means that for patients in whom a typical analgesic regimen fails,
sometimes very small increases in dosage can result in adequate analgesia.
