Kinetics of Antimicrobial Action

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Abstract
To better quantify the relative antibacterial activity of β-lactam antibiotics in vitro, mathematical descriptions of bacterial growth were developed. Growth curves for the initial 2- to 4-hr period of exposure to antibiotic can be expressed as quadratic functions of time. Moreover, the rate of change of growth (a) shows a linear dependence on the logarithm of the antibiotic concentration. For some drug-organism interactions, the initial growth rate (ko) is also a concentration-dependent variable. This mathematical quantitation of the antibacterial action of a drug in vitro covers a range of concentrations above and below its minimal inhibitory concentration. The slope of the regression line of a on log concentration may vary for different microorganisms and antibiotics. However, several analogues yield parallel concentration-effect slopes, a circumstance allowing for the calculation of potency ratios. Two murine models were used to determine if these in vitro studies could predict activity in vivo. The relative efficacy in vivo also was expressed as a potency ratio, which was measured in terms of the number of bacteria in either homogenized kidney after intravenous challenge or an infected thigh muscle. For drugs with similar pharmacokinetics, the potency in vivo could be predicted from the value in vitro. However, for drugs with concentration curves in serum of different shapes, the potency in vivo varied from the value in vitro. A more prolonged course of drug in serum, which yielded a flatter concentration curve, appeared to be associated with greater activity in vivo.

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