Mathematical modeling of the “inoculum effect”: six applicable models and the MIC advancement point concept

Antimicrobial treatment regimens against bacterial pathogens are designed using the drug's minimum inhibitory concentration (MIC) measured at the bacterial density of 5.7 log10(colony-forming units (CFU)/mL) in vitro. However, MIC changes with pathogen density, which varies among infectious diseases and during treatment. Incorporating this into treatment design requires realistic mathematical models of the relationships. We compared the MIC-density relationships for Gram-negative Escherichia coli and nontyphoidal Salmonella enterica subsp. enterica and Gram-positive Staphylococcus aureus and Streptococcus pneumonia (for n = 4 drug-susceptible strains per (sub)species and 1-8 log10(CFU/mL) densities), for antimicrobial classes with bactericidal activity against the (sub)species: beta-lactams (ceftriaxone and oxacillin), fluoroquinolones (ciprofloxacin), aminoglycosides (gentamicin), glycopeptides (vancomycin), and oxazolidinones (linezolid). Fitting six candidate mathematical models to the log2(MIC) vs. log10(CFU/mL) curves did not identify one model best capturing the relationships across the pathogen-antimicrobial combinations. Gompertz and logistic models (rather than a previously proposed Michaelis-Menten model) fitted best most often. Importantly, the bacterial density after which the MIC sharply increases (an MIC advancement-point density) and that density's intra-(sub)species range evidently depended on the antimicrobial mechanism of action. Capturing these dependencies for the disease-pathogen-antimicrobial combination could help determine the MICs for which bacterial densities are most informative for treatment regimen design.