The pharmacodynamic inoculum effect from the perspective of bacterial population modeling

The quantitative determination of the effects of antimicrobials is essential for our understanding of pharmacodynamics and for their rational clinical application. Common pharmacodynamic measures of antimicrobial efficacy, such as the MIC and the pharmacodynamic function, fail to capture the observed dependence of efficacy on the bacterial population size -- a phenomenon called inoculum effect. We assessed the relationship between bacterial inoculum size and pharmacodynamic relationship and determined the consequences of the inoculum effect on bacterial population dynamics with a mathematical multi-hit model that explicitly describes the interaction between antimicrobial molecules with their targets on the bacterial cells. Our model showed that the inoculum effect can arise from the binding dynamics of antimicrobial molecules to bacterial targets alone. A pharmacodynamic function extended by the inoculum effect on its parameters was able to predict the long-term population dynamics of simple scenrios well. More complex scenarios, however, were only captured with by the mechanistically more explicit multi-hit model. In simulations with competing antimicrobial-susceptible and -resistant bacteria, neglecting the inoculum effect led to an overestimation of the competitive ability of the resistant strain. Our work underpins the importance of including the inoculum effect into quantitative pharmacodynamic frameworks, and provides approaches to accomplish that.