Indirect-response models may be successfully applied for tolerance modeling of drugs after multiple dosing.
Aims Understanding the impact of drug input rate on its pharmacokineticpharmacodynamic relationship may lead to a more optimal drug therapy. The aim of the present study was to investigate the influence of the rate of administration on tolerance development to frusemide, by giving the drug at four different infusion rates. Methods Eight healthy volunteers were given 10 mg of frusemide on four different occasions, as a constant-rate intravenous infusion during 10, 30, 100 and 300 min, respectively. Urinary volume and contents of frusemide and sodium were measured in samples collected over 8 h. Results The four different infusion rates systematically influenced the frusemide excretion rate versus diuretic and natriuretic response relationship. Counter-clockwise hysteresis occurred for the most rapid infusion rate, whereas a progressive clockwise hysteresis was observed for the slower infusions, indicating development of tolerance. For each subject, diuresis and natriuresis were modeled for all four treatments simultaneously, using a feedback tolerance model. It was not possible to describe the data using a model without tolerance. The time course of tolerance development showed remarkable differences between the infusion rates. The intensity of maximum tolerance development was significantly less for the slowest infusion rate compared with the more rapid infusions and it appeared significantly later. However, no differences in diuretic or natriuretic response were found between the treatments. Conclusions The direction of the hysteresis loop is dependent on the input rate of frusemide. After the administration of a single low dose of frusemide, the time course of tolerance, rather than the integrated time course of tolerance, is influenced by the drug input rate.
The classic approach to describe the pharmacological response to a drug is to analyse its concentration-effect relationship, using a variety of possible models such as maximum effect (Emax) models or sigmoid Emax models. The aim of this review is to discuss an alternative way of describing the pharmacological effect in terms of effect per unit of drug concentration, instead of simple effect. This variable is called efficiency, analogous with concepts used in other fields. The pharmacodynamic model for efficiency is derived from the sigmoid Emax model and is dependent on the same parameters. Since the sigmoid Emax model incorporates 'the law of diminishing returns', requiring ever higher concentrations to increase the effect by a given percentage, efficiency is bound to decrease with increasing concentrations. However, as a mathematical consequence of its derivation from the sigmoid Emax model, efficiency also has a maximum value, which can be expressed as a function of the slope factor (s) and drug concentration associated with half the maximum effect (C50), provided that the slope factor is greater than 1. The efficiency concept is potentially applicable to all drugs and particularly useful for those that follow concentration-effect relationships according to Emax or sigmoid Emax models. Most experience has been obtained with loop diuretics, especially with furosemide (frusemide). Slow administration of furosemide, leading to slow excretion of the drug, has been shown, in many studies, to significantly increase the total diuretic effect per amount of drug recovered in urine. In this review, some examples of the applicability of the efficiency concept to other drugs, such as antibacterials, opioids and antineoplastics, are discussed. In addition to pharmacodynamically varying efficiency, other saturable processes, such as the formation of active metabolites and saturable transport, may form a basis for the application of the efficiency concept. The efficiency of a drug dosage may also be influenced by tolerance and counter-regulation produced by the drug. All these factors contribute to schedule dependency. It is concluded that the shape of the time course of drug presentation to its site of action is an independent determinant of overall response. The possibility of adjusting the drug input profile to maximise therapeutic effect per dose and to separate cumulated therapeutic from cumulated adverse effects should be considered in designing administration schedules and in drug development.
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