Kinetics of drug action in disease states: towards physiology-based pharmacodynamic (PBPD) models

Abstract

Gerhard Levy started his investigations on the "Kinetics of Drug Action in Disease States" in the fall of 1980. The objective of his research was to study inter-individual variation in pharmacodynamics. To this end, theoretical concepts and experimental approaches were introduced, which enabled assessment of the changes in pharmacodynamics per se, while excluding or accounting for the cofounding effects of concomitant changes in pharmacokinetics. These concepts were applied in several studies. The results, which were published in 45 papers in the years 1984-1994, showed considerable variation in pharmacodynamics. These initial studies on kinetics of drug action in disease states triggered further experimental research on the relations between pharmacokinetics and pharmacodynamics. Together with the concepts in Levy's earlier publications "Kinetics of Pharmacologic Effects" (Clin Pharmacol Ther 7(3): 362-372, 1966) and "Kinetics of pharmacologic effects in man: the anticoagulant action of warfarin" (Clin Pharmacol Ther 10(1): 22-35, 1969), they form a significant impulse to the development of physiology-based pharmacodynamic (PBPD) modeling as novel discipline in the pharmaceutical sciences. This paper reviews Levy's research on the "Kinetics of Drug Action in Disease States". Next it addresses the significance of his research for the evolution of PBPD modeling as a scientific discipline. PBPD models contain specific expressions to characterize in a strictly quantitative manner processes on the causal path between exposure (in terms of concentration at the target site) and the drug effect (in terms of the change in biological function). Pertinent processes on the causal path are: (1) target site distribution, (2) target binding and activation and (3) transduction and homeostatic feedback.

Keywords: Biophase distribution; Disease systems analysis; Dynamical systems analysis; Receptor theory.

Fig. 1

a Schematic representation of drug concentration versus time profiles at three different infusion rates in the plasma (continuous lines) and at the site of action (dashed lines). The time of onset of a pharmacologic effect is indicated by arrows. The representation is a simulation of a two-compartment system with a drug clearance of 0.029 l/h, a terminal drug half-life of 24 h and infusion rates of 0.42, 2.5 and 4.2 mg/min. It should be noted that the drug concentration in plasma at onset of effect decreases with decreasing infusion rate. b Effect of infusion rate on the concentration of phenobarbital in serum (total and unbound drug, respectively), brain and CSF of female rats at the onset of loss of righting reflex. Results are the mean of five to nine animals per group, with the vertical line indicating 1 SD. Infusion rate had a significant effect (p < 0.001 by one-way analysis of variance) on drug concentrations in serum and brain but not on concentrations in CSF. The symbols above the vertical bars indicate significant differences from the results produced by the lowest infusion rate (*p < 0.002; ^‡p < 0.01; ⁺p < 0.05; Newman-Keuls test). Reproduced from Danhof and Levy 1984 [5]

Fig. 2

Schematic representation of physiology-based pharmacodynamic (PBPD) modeling. PBPD models connect pharmacokinetics to the drug effects on disease progression, and contain expressions to describe the processes on the causal path between drug administration and effect (target site distribution, target binding and activation, and transduction and homeostatic feedback)

Fig. 3

The relationship between drug concentration and the intensity of the biological response depends on drug- and biological system specific factors. Drug specific properties are the target binding affinity and the intrinsic efficacy, which govern the target activation. A biological system-specific transducer function describes the relation between the target activation and the effect. Reproduced from: van der Graaf and Danhof [67]

Fig. 4

PK–PD modeling of anti-lipolytic effects of Adenosine A1 receptor agonists in rats: prediction of tissue-dependent efficacy in vivo. a Relationship between intrinsic efficacy in an in vitro (GTP-shift) and in vivo (log τ) bioassay for the effect of a series of A1 receptor agonists on heart rate and lipolysis (as measured by nonesterified fatty acids, NEFAs), respectively. The difference in the intercept for the two effects is explained by the difference in receptor density between adipose tissue and cardiac tissue. b Relationship between intrinsic efficacy in an in vitro bioassay (GTP shift) and in vivo intrinsic activity (α) for the effects on heart rate and lipolysis, respectively. The graphs show that partial agonists with GTP shift values between 1 and 5 display the highest selectivity of action for the effect lipolysis versus heart rate. Reproduced from van der Graaf et al. [70]

Fig. 5

PK–PD analysis of the EEG effect of alfentanil in rats following in vivo μ-opioid receptor (MOP) knockdown with β-flunaltrexamine. Pretreatment with β-flunaltrexamine resulted in an approximately 60 % reduction of functional MOP receptors at 35 min and at 24 h post administration. A parallel shift in the concentration–effect relationship without a major change in maximum effect was observed. This reduction in functional receptors is consistent with the observation that the MOP receptor functions with a high receptor reserve. Reproduced from Garrido et al. [74]