As discussed by Toutain ( 2002 ), this concentration–effect relationship is frequently
described by the sigmoidalEmaxmodel (also known as the Hill equation):
EðtÞ¼E 0 þEmaxCðtÞh
ECh 50 þCðtÞh; (1)
where,
E(t)is the effect observed for a given concentration (C) at timet
Emaxis the maximal effect attributable to the drug
EC 50 is the plasma concentration producing 50% ofEmax
his the Hill coefficient, which describes the steepness of the sigmoidal relationship
between log of the concentration and effect
E 0 is the rate of spontaneous cure.
Whenh= 1, the Hill model reduces to theEmaxmodel, which corresponds to a
hyperbolic function.
For drugs exhibiting time-dependent killing (e.g. theb-lactams), the duration of
exposure needed to achieve a targeted log-reduction in colony forming units
(CFUs) is a function of the magnitude of the PAE (Nicolau 2001 ). Mouton et al.
( 2005 ) defined the in vitro PAE as the period of suppression of bacterial growth
after the drug has been removed following a short duration of exposure to that
antimicrobial compound (unit = time). However, as discussed by Owens and
Ambrose ( 2007 ), although these predictions have often proven useful, the sudden
on–off modality of these in vitro tests may not adequately reflect in vivo conditions
where concentrations are constantly changing with time. Therefore, they defined an
in vivo PAE as the difference in the time needed for the number of bacteria in a
tissue of treated versus control animals to increase by tenfold once the drug
concentrations in serum or at the infection site have decreased below the MIC
(unit = time). Accordingly, the in vivo PAE includes any effect associated with drug
concentrations that are less than the MIC (sub-MIC effects).
For many compounds, the duration of the in vivo and in vitro PAEs is sub-
stantially greater for Gram-positive than for Gram-negative pathogens. As the
duration of the in vitro and the in vivo PAE ofb-lactams tends to be negligible
for Gram-negative species, it is often recommended that the concentrations of
drug remain above the MIC of those pathogens (T>MIC) for80% of the dosing
interval. In contrast, aT>MIC of about 40% is normally considered to be adequate
for Staphylococcal species. This difference in the duration of the in vitro and
in vivo PAE also appears to be a reason why the in vivo AUC/MIC for fluoro-
quinolones tends to be less for Gram-positive as compared to Gram-negative
organisms (Forrest et al. 1993 ; Ibrahim et al. 2002 ; Preston et al. 1998 ; Wright
et al. 2000 ).
A summary of the nature of the drug effect (killing versus stasis), the mechanism
through which the drug effect occurs, and the relationship of the drug effect to
duration versus extent of exposure, is provided in Table 1.
230 M. Martinez and P. Silley