Mathematical corrections for bacterial loss in pharmacodynamic in vitro dilution models

Abstract

In vitro dilution models are used to simulate in vivo drug concentration-time profiles and thus to study the effects of various antibiotic concentrations on the bacteria investigated. The major disadvantage of these models is permanent dilution of the bacterial culture, which falsifies the resulting kill curves. Known equations, which usually correct bacterial loss by simple first-order kinetics, do not take into account special test conditions, such as variable elimination rate constants, exceptionally long periods of investigation, or formation of biofilms. In the present investigation, we examined the validity of these equations with regard to the test conditions mentioned. We simulated the concentration-time curves resulting from continuous infusion of 1,000 mg of meropenem with steady-state levels of 2.5, 5.0, and 7.5 g/ml in an in vitro dilution model. The resulting kill curves were compared with the kill curves obtained from incubation of bacteria in an undiluted system with meropenem at constant concentrations corresponding to the above-mentioned steady-state levels. Comparison of the matching kill curves showed that the common corrections, which do not consider the formation of biofilms in the compartments, partly overestimated the effect of bacterial dilution. We defined a factor, f, as an extension to the known equations which compensates for the effect of biofilms. Another extension was developed to allow the investigation of variable elimination rate constants. With the help of these extended mathematical corrections, we were able to fit the kill curves resulting from the in vitro dilution model exactly to the kill curves given by an undiluted system. Several in vitro kinetic models which simulate in vivo drug concentration-time profiles use continuous dilution to fit drug concentrations to the corresponding serum pharmacokinetics (4). The major disadvantage of these models is inevitable dilution of the bacterial culture, which falsifies the resulting kill curves. Several attempts have been made to compensate for this effect. (i) The antimicrobial activity of constant concentrations of antibiotics may be examined in a static system in which the bacterial culture is not diluted during the investigation (12). (ii) Dynamic in vitro models which do not allow bacteria to be washed out have been developed (1, 2). (iii) The loss of bacteria in an in vitro dilution model may be compensated for by mathematical correction.In the present report, we have summarized the previously existing equations (5,8,11) and investigated their validity with regard to different test conditions by simulating continuous infusion of meropenem with steady-state levels of 2.5, 5.0, and 7.5 g/ml in an in vitro dilution model. The resulting time-kill curves were compared with the kill curves resulting from incubation of test bacteria with meropenem at constant concentrations of 2.5 to 7.5 g/ml in a static system (batch culture). We assumed that bacterial growth in the batch culture is not limited by the supply of nutrients as long a...

Issues in Pharmacokinetics and Pharmacodynamics of Anti-Infective Agents: Kill Curves versus MIC

“…This effect is particularly important when the dilution rate is higher than the bacterial growth rate, and the resulting increased bacterial clearance needs to be accounted for. Some equations to correct this effect for exponentially changing cultures have been proposed (117,64). Löwdin et al employed a 0.45-m filter membrane in the culture flask to prevent bacterial outflow.…”

Comparative Bactericidal Activities of Ciprofloxacin, Clinafloxacin, Grepafloxacin, Levofloxacin, Moxifloxacin, and Trovafloxacin against Streptococcus pneumoniae in a Dynamic In Vitro Model

“…If the rate of reduction was less than that which would have been predicted by flow rate alone, the reduction was attributed to the effect of the drug. However, if the reduction in the numbers of CFU was greater than or equal to that predicted by the flow rate, a mathematical model that allowed correction for this dilutional effect was used (11). The changes in the log number of CFU per milliliter from the starting inocula at times of 24 and 48 h were determined for each regimen and isolate.…”

Beneficial Influence of Platelets on Antibiotic Efficacy in an In Vitro Model ofStaphylococcus aureus-Induced Endocarditis

“…Moreover, prior studies demonstrated that this inoculum reproducibly infects sterile SEVs in this model (12). A peristaltic pump supplied fresh MEM and removed exhausted medium from the model at a half-life equal to 6 h. At this flow rate, loss of S. aureus from the model is negligible, since the doubling time (ϳ20 min) far exceeds the loss attributed to model effluent (10). A magnetic stir bar continuously circulated the fluid within the chamber compartment of the model.…”

“…Furthermore, tPMP-1-resistant S. aureus or C. albicans strains cause significantly more severe forms of experimental IE than do tPMP-1-susceptible counterpart strains (3,11,29). In addition, the enhancement of the antimicrobial activities of conventional antibiotics by tPMPs in vitro was previously demonstrated (8)(9)(10).…”