Population Dynamics of Antibiotic Treatment: a Mathematical Model and Hypotheses for Time-Kill and Continuous-Culture Experiments

Abstract

ABSTRACT The objectives of the study were to develop a quantitative framework for generating hypotheses for and interpreting the results of time-kill and continuous-culture experiments designed to evaluate the efficacy of antibiotics and to relate the results of these experiments to MIC data. A mathematical model combining the pharmacodynamics (PD) of antibiotics with the population dynamics of bacteria exposed to these drugs in batch and continuous cultures was developed, and its properties were analyzed numerically (using computer simulations). These models incorporate details of (i) the functional form of the relationship between the concentrations of the antibiotics and rates of kill, (ii) the density of the target population of bacteria, (iii) the growth rate of the bacteria, (iv) byproduct resources generated from dead bacteria, (v) antibiotic-refractory subpopulations, persistence, and wall growth (biofilms), and (vi) density-independent and -dependent decay in antibiotic concentrations. Each of the factors noted above can profoundly affect the efficacy of antibiotics. Consequently, if the traditional (CLSI) MICs represent the sole pharmacodynamic parameter, PK/PD indices can fail to predict the efficacy of antibiotic treatment protocols. More comprehensive pharmacodynamic data obtained with time-kill and continuous-culture experiments would improve the predictive value of these indices. The mathematical model developed here can facilitate the design and interpretation of these experiments. The validity of the assumptions behind the construction of these models and the predictions (hypotheses) generated from the analysis of their properties can be tested experimentally. These hypotheses are presented, suggestions are made about how they can be tested, and the existing statuses of these tests are briefly discussed.