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 a 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 non-typhoidal 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: β-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.