Assessment of therapeutic potential by means of a probability model of antimicrobial action

The probability model of antimicrobial action is based on the definition of bactericidal activity as the probability, q, that any cell in the population will be killed during a division interval. Bacteriostatic activity is defined as a change in the division intervals (generation times) of the cells. A simplified, homogeneous model is used which assumes that, at a constant concentration of the drug, all cells have the same kill probability and the same generation times. Birth-death analysis techniques require that the combined bacteriostatic and bactericidal effects of the drug (they are not mutually exclusive) are accounted for. Moreover, to suitably reflect the combined effect, the rate of change of the viable population, i.e. the slope of a kill curve (activity), needs to be expressed not in terms of exposure time, but in units of drug-free generations (DFGs), obtained by dividing exposure time by a measured DFG time interval (growth rate). A Discrete MIC (DMIC) is defined as the zero slope kill curve, coinciding with the horizontal axis and dividing population change into a restrained (subinhibitory) growth region, below the DMIC, and population reduction above it. At the DMIC, the probability of a cell being killed is 0.5, resulting in no change from the initial inoculum concentration, since half the cells are killed but the remaining cells double. The DMIC is found to be a measure of bactericidal activity only, even though bacteriostatic activity may also be present. An antibiotic-organism activity profile includes measurement of the DMIC, rate of change of activity at the DMIC and normalized activity at a number of clinically relevant drug concentrations. An overall, quantitative efficacy value over a dosing interval can be obtained from the activity profile and expressed as the number of DFGs which are needed to achieve a 99.9% reduction of the viable population at the site of infection. These reference efficacy values can be used to derive interpretive standards (break-points) based upon a quantitative relationship between laboratory measurements and population reduction at the site of infection. Model-derived measures of efficacy also provide a basis for assessing drug combination activity, including quantitative criteria of synergy and antagonism.