Skip to main content
NCBI home page
British Journal of Clinical Pharmacology logoLink to British Journal of Clinical Pharmacology
. 2011 Jun;71(6):815–823. doi: 10.1111/j.1365-2125.2011.03925.x

Understanding the time course of pharmacological effect: a PKPD approach

Daniel F B Wright 1, Helen R Winter 1,2, Stephen B Duffull 1
PMCID: PMC3099368  PMID: 21272054

Abstract

The key concepts that underpin the choice of drug and dosing regimen are an understanding of the drugs' effectiveness, the potential for adverse effects, and the expected time course over which both desired and adverse effects are likely to occur. Research in clinical pharmacology should therefore address three fundamental questions: (1) What is the magnitude of drug effects (beneficial or adverse) from a given dose? (2) How quickly will any given effects occur? (3) How long will these effects last? Under steady-state conditions, only the magnitude of drug effects can be examined. This requires researchers to consider non-steady-state conditions, which require more complex models and an understanding of the mechanisms that drive the time course of drug effect. The aim of this review is to provide a conceptual framework for understanding the time course of drug effects using pharmacokinetic–pharmacodynamic models. Key examples will illustrate how this can inform the optimal use of drugs in the clinic.

Keywords: population pharmacokinetic–pharmacodynamic models

Introduction

In 1961 Chauncey Leake outlined the fundamental research themes that define clinical pharmacology as a science. Notable among these are the study of pharmacokinetics (the time course of drug concentration in the body) and pharmacodynamics (the relationship between dose and drug effect) [1]. Fifty years on, these themes have become well-established research areas. More importantly, by framing clinical research questions around these topics clinical pharmacologists have been able to address one of the fundamental goals of the field which is to provide a theoretical foundation for the rational use of medicines [2].

The key concepts that underpin the choice of drug and dosing regimen are an understanding of the drugs' effectiveness, the potential for adverse effects, and the expected time course over which both desired and adverse effects are likely to occur. The observed variability in drug effects between patients must also be considered. Research in clinical pharmacology should therefore address three fundamental questions:

  1. What is the magnitude of drug effects (beneficial or adverse) from a given dose?

  2. How quickly will any given effects occur?

  3. How long will these effects last?

While these questions are of obvious importance in drug development, they apply equally to post-marketing research as well as research questions that may arise in the clinic.

Models are a useful framework for understanding the time course of drug effect [3]. They provide a means of characterizing the pharmacokinetic (PK) parameters of a drug and a conceptual framework for linking this to pharmacodynamic (PD) activity. Models that combine these effects into a single entity are termed PKPD models [4]. In this review, we distinguish ‘models’, i.e. constructs that represent the essential elements of biological and pharmacological systems, from ‘modelling’, i.e. the statistical and methodological techniques used to carry out population analyses. Population modelling techniques and their clinical interpretation are the focus of a companion paper [5].

The aim of this review is to provide a conceptual framework for understanding the time course of drug effects using PKPD models. A brief introduction to some general concepts concerning PKPD models will be followed by a discussion on steady-state and non-steady-state experiments, and how these can inform the selection of dose and dosing regimens. We refer readers seeking further details concerning PKPD models, not discussed in this paper, to several previous reviews [3, 6–15].

What is PKPD?

Historically, research in clinical pharmacology has focused on the study of drug concentrations. The assumption is that the drug concentration in the biophase (the hypothetical ‘effect compartment’ at the site of action [16]) provides the driving force for drug effect. At steady state the unbound concentration at the biophase will be in equilibrium with drug in the plasma, making unbound plasma drug concentration a useful surrogate. Clinically, the rationale for measuring drug concentration is that the relationship between concentration and effect should be less variable than the relationship between dose and effect [17]. Therefore, accurately measuring the concentration will allow for better predictions of drug effect than dose information alone.

In this framework, models for pharmacokinetics and pharmacodynamics are viewed as separate entities, linked by drug concentration (Figure 1). The PK model describes the relationship between dose and concentration which is normally depicted as the concentration vs. time profile for a given dose (see Figure 2A). The PD model describes the link between concentration and effect, independent of time (see Figure 2B). The PK model therefore helps to explain some of the variability between the administered dose and the observed effect by providing the driving intermediary of drug concentration.

Figure 1.

Figure 1

Open in a new tab

Schematic depicting pharmacokinetic (PK) and pharmacodynamic (PD) models used in clinical pharmacology

Figure 2.

Figure 2

Open in a new tab

Conceptual framework for pharmacokinetic–pharmacodynamic models. By combining the time element from pharmacokinetics (A) and the effect data from pharmacodynamic analysis (B) it is possible to explore the time course of drug effect (C)

A more generalized approach has been proposed where PK and PD are combined into a single entity termed a PKPD model [16]. This allows the observed drug effect to be related directly to the time after a given dose (see Figure 2C). Therefore, the combined PKPD model provides a means of understanding the time course of drug effect, namely the extent, onset and duration of drug action. By drug effect we refer to either a clinical response measure (e.g. diuresis) or the measurement of a biomarker of drug effect (e.g. prothrombin time). The two main methods used to explore the PKPD of drugs are steady-state and non-steady-state experiments.

Steady-state PKPD

The steady-state condition provides a powerful framework from which to describe the magnitude of drug effect. As a result, it is widely employed clinically (see examples [18–20]). An example of a typical steady-state PKPD model is given by:

graphic file with name bcp0071-0815-m1.jpg (1)
graphic file with name bcp0071-0815-m2.jpg (2)

In this setting, the assumption is made that the steady-state average concentration is sufficient to describe the important pharmacokinetic characteristics of the drug. Fluctuations in the concentration–time course are relatively unimportant and the experiment is independent of the chosen dosing regimen. This greatly reduces the complexity of the PK component (Equation 1) and provides a useful method to assess the magnitude of drug effects. If we substitute the PK model (Equation 1) into the PD model for Css,ave then we have the basis for a combined PKPD model (Equation 2). From a PKPD perspective, the potential benefits of characterizing PKPD models under steady-state conditions include:

  1. The binding kinetics of the drug and receptor are at equilibrium. In this setting, delays in response because of slow dissociation of drug from the receptor are inconsequential and therefore an Emax model can be used to describe competitive binding at equilibrium.

  2. The free concentration of drug is the same in all tissue water and proportional in all tissues, including at the biophase. Hence, the concentrations in the plasma water can be used as a surrogate. Slow distribution to the biophase is of no additional consequence.

  3. The influence of the drug on an intermediate and the subsequent time course of this intermediate are in equilibrium and therefore inconsequential. For instance, it is known that warfarin inhibits production of factors II, VII, IX and X. Factor II has a half-life of about 60 h and hence the influence of warfarin will be delayed while factor II reaches steady state. At steady state, the time required to achieve this condition can be ignored. Any potential delay associated with second messenger and intermediate biomarker kinetics does not need to be considered.

In all of these cases the steady-state model provided in Equations 1 and 2 are sufficient to characterize the magnitude of drug effects.

Non-steady-state PKPD

A limiting factor of experiments designed to study drug effects at steady state is the exclusion of time as a component of the analysis. This means that drug exposure can only be defined by the dose administered (or the steady-state average concentration) and the magnitude of the observed drug effect. The steady-state model cannot account for time-dependent factors, such as the onset and duration of drug effects.

The non-steady-state model can be considered a generalization of the steady-state model. This means that the non-steady-state model will collapse to the steady-state solution (provided in Equations 1 and 2) in circumstances when the experiment is conducted under steady-state conditions. It follows that non-steady-state models are necessarily more complex than those used under steady-state conditions. They also provide a framework for quantifying non-equilibrium conditions related to drug–receptor binding, drug concentrations at the biophase and the time course of any secondary (or later) messenger systems.

An important limitation of all models that are based on a mixture of biology and empirical evidence is that the empirical data often lack detail on the underlying PK and PD mechanisms. For instance, we know that warfarin dosing will affect production of clotting factors and this will subsequently result in an increase in bleeding time. However, we seldom measure the clotting factors themselves. Based on biology and mechanism, we can propose a model for the effects of a drug in non-steady-state conditions, which can then be evaluated against real data. It should be noted that when analysing data where the drug effect is measured without measurement of intermediary steps it is only possible to model the rate-limiting step in the time course of drug effects. So, although drug–receptor binding, distribution to the biophase and the effect on an intermediate biomarker all play a role in the time course of drug effects, it is only the slowest of these phases that can be evaluated in any modelling-based analysis.

Drug–receptor binding under non-equilibrium conditions

A large portion of drug action (although not all) can be attributed to drug binding at a receptor site of some kind [21]. Whether this is a true receptor or a specific binding site on a protein or enzyme does not change our interpretation of the interaction. This is usually represented schematically by Equation 3, where D is the drug in molar concentration units and R the receptor in molar concentration units. Under a 1:1 stoichiometry, the constant for drug–receptor association rate is given by kon and the dissociation rate constant by koff. The ratio of koff to kon is given by a constant KD, which is inversely related to the affinity of the drug for the receptor.

graphic file with name bcp0071-0815-m3.jpg (3)

When the rate-limiting step for the time course of drug effects is the drug–receptor interaction, the time course of onset will be related to the koff value. If the value of koff is high, providing a short equilibration half-life [=ln(2)/koff], then the drug will be seen to behave as if it has an immediate effect (often termed a ‘direct action model’[22]). By strict definition, only drugs that are administered i.v. and act in the plasma could truly be described by this model. For example, the anticoagulant effects of heparin are the result of binding to antithrombin in the plasma which, in turn, neutralizes thrombin (factor IIa) and other clotting factors [23]. The koff value for dissociation of heparin from antithrombin is very high [24] and therefore it is reasonable to assume that equilibrium binding is reached almost immediately. Heparin can therefore be described by a direct action model, i.e. driven by the plasma drug concentration (Cp) at a given time t (Equation 4):

graphic file with name bcp0071-0815-m4.jpg (4)

Note that EC50 and KD have identical interpretations in this equation but may have different numerical values. We use EC50 to represent an estimate derived from in vivo data (e.g. using a PKPD model) and KD for the ‘true’ ratio of koff/kon available from an in vitro binding experiment.

Several drugs which distribute readily to the site of action and are not limited by the slow turnover of a biological intermediate can be described by a direct action model (e.g. theophylline [15], dabigatran [25], diclofanac [26], see Table 1). However, there are some drugs for which drug–receptor dissociation is indeed the rate-limiting step. An extreme example is where the drug binds irreversibly to receptors. In this instance, the apparent rate off for the drug will be the degradation of the DR complex (Equation 3) and dilution with newly formed receptors resulting in a fractional receptor occupancy that decreases at a rate associated with DR degradation and receptor production. The time course to maximum effect, assuming a 1:1 stoichiometry and an excess of receptors (compared with drug), will depend on the rate of drug input into the system. For example, the sulphenamide metabolite of omeprazole binds irreversibly to H+K+ATPase within the parietal cell canaliculus resulting in reduced gastric acid production. The recovery of gastric acid secretion can only occur with the production of new H+K+ATPase, which has a synthetic half-life of approximately 50 h [27].

Table 1.

Examples of studies where non-steady-state PKPD models have been applied

Model type Drug/model Receptor Biophase Secondary messengers Drug effect of interest Reference
Direct effects Theophylline Phosphodiesterase Lung cAMP Bronchodilation (increased FEV1) [15]
Dabigatran Excite 1 (thrombin) Plasma Bleeding time (aPTT) [25]
Diclofenac Cyclo-oxygenase Diverse Prostaglandins Analgesia [26]
Effects compartment Fentanyl µ (opioid) receptor Central nervous system G-protein, potassium Respiratory depression [28]
d-tubocurarine Nicotinic receptor Neuromuscular junction Sodium Muscle paralysis [16]
Sotalol β-adrenergic receptor Heart G-protein, cAMP, calcium Cardiac rhythm (QTc interval) [29]
Secondary messengers Warfarin VKOR Liver Vitamin K-dependent clotting factors Bleeding time (PT/INR) [36]
Simvastatin HMG-CoA reductase Liver Various (cholesterol synthetic pathway) Reduced LDL [34]
Pyridostigmine Acetylcholine esterase Neuromuscular junction Acetylcholine Improved muscle function [32]
Open in a new tab

Models that account for drug distribution to the biophase

For most drugs, the site of action is distal to the venous compartment. In this setting, a more complex model is required that can account for the delay in drug distribution to the hypothetical effect compartment. The distinction between the biophase and effect compartment is one of semantics. The effect compartment is a theoretical concept that describes a compartment that appears to have the same distributional properties as the location where the drug causes its effects. The biophase is the supposed true site of action. The effect compartment is therefore not a model for the biophase but rather a model for the delay in effect because of drug distribution to the biophase. This distribution is essentially a pharmacokinetic phenomenon, but it is described entirely and empirically by the observed delay in pharmacodynamic behaviour. An effect compartment model involves the addition of a link connecting the PK model to the PD model (Figure 3) [8, 11, 16]. If the distribution to the biophase is a first-order process, the delay {e.g. time to maximum effect [tmax(PD)]} will be independent of dose and systemic clearance and dependent only on the rate constant of elimination from the effect compartment. Mechanistically, these models only apply when the rate-limiting step in the time course of drug effects is the distribution of drug to the biophase. After constructing a PK model for the distribution into the effect compartment, the model comprises a simple Emax model driven by the effect compartment concentration (Ce; Equation 5).

Figure 3.

Figure 3

Open in a new tab

Schematic of a biophase model. The hypothetical effect compartment Ce (or biophase) acts as a link between the pharmacokinetic and pharmacodynamic models

graphic file with name bcp0071-0815-m5.jpg (5)

Effect compartment models are intuitively appealing and, because of their simplicity, have been widely applied (e.g. fentanyl [28], d-tubocurarine [16], sotalol [29] and digoxin [30], see Table 1).

Models that account for secondary messengers

The mechanism of action for many drugs involves the activation or blockade of a receptor which, in turn, initiates a physiological response mediated by a series of secondary messengers or, in some cases, the turnover of biological intermediates [31–33]. These physiological components have a time course of their own and, as such, often constitute the rate-limiting step in the time course of drug effects. Like effect compartment models, these models are characterized by a delay in the observed effect with respect to the measured plasma concentration and are often referred to as turnover models (and sometimes ‘indirect response’) models [32]. This delay is easiest to characterize at the time of the maximum effect, such that tmax(PK) < tmax(PD). Models that account for secondary messengers must include a link model which describes the time course of the biological intermediate(s) and connects the PK model to the PD model (see [8]). Note that an important difference between models based on physiological intermediaries and those based on a supposed effect compartment is that the tmax (time of maximum effect) for the turnover model will depend on dose.

These models have been widely applied in clinical research (see, for example, [31–34]) and are inherently mechanistic in nature. It is not usually necessary to measure the intermediary directly as its time course can be determined from PK and PD data.

There are four proposed mechanisms for drugs acting on a single biological intermediary (see Figure 4) [31–33]:

Figure 4.

Figure 4

Open in a new tab

Schematic of a turnover model. The four proposed mechanisms are (A) reduced production of an intermediary/response function, (B) enhanced production of an intermediary/response function, (C) reduced degradation of an intermediary/response function and (D) enhanced degradation of an intermediary/response function (after Jusko & Ko [32])

  1. Inhibition of input (e.g. warfarin reducing production of clotting factors)

  2. Enhanced input (e.g. glucose stimulating insulin release)

  3. Inhibition of loss [e.g. GABA uptake inhibitors (e.g. tiagabine [35]) inhibits loss of GABA from the synaptic cleft]

  4. Enhanced loss (e.g. insulin stimulating glucose uptake)

A classic example is warfarin, which inhibits the natural production rate (Ratein– a presumed zero-order rate) of vitamin K-dependent clotting factors [36]. Equation 6 indicates that as the plasma warfarin concentration increases the production rate of the clotting factors decreases (here Emax must be ≤1).

graphic file with name bcp0071-0815-m6.jpg (6)

The clotting factors can be measured in plasma, but the anticoagulant effect is usually determined using either a composite of factor activity, called prothrombin complex activity (PCA) [37], or the blood-clotting time [prothrombin time or international normalized ratio (INR)]. A plot depicting the published PCA and warfarin plasma concentration data from O'Reilly et al. [37], and O'Reilly and Aggeler [38] (expressed at the population mean values) is shown in Figure 5. Plasma warfarin concentrations were described by a one-compartment pharmacokinetic model with first-order absorption and elimination. The PCA data were best described by a ‘turnover’ model (inhibition of input, option A in Figure 4). A delay is evident between the appearance of warfarin in the plasma [tmax(PK) about 1–2 h] and the peak coagulation effect on PCA [tmax(PD) about 35 h; see Figure 5]. Other examples, including simvastatin [34] and pyridostigmine [32], are summarized in Table 1.

Figure 5.

Figure 5

Open in a new tab

Warfarin plasma concentrations (A) appear in the plasma within an hour or two of dosing, yet the peak drug effect on PCA (B) is significantly delayed. PCA = prothrombin complex activity, [warfarin]= plasma total (R- and S-) warfarin concentration, normalized to dose. Data from O'Reilly et al. [37], and O'Reilly and Aggeler [38]

Factors affecting duration of effect

Once the time course of drug action has been appropriately accounted for, the duration of drug effect can be assessed based on dose, EC50 and half-life. Because of the non-linear relationship between dose and effect (see Equation 2), it is possible to predict that doubling the dose will not double the effect [11]. However, doubling the dose has a predictable impact on the duration of drug effects. Based on first principles, doubling the dose will double the drug concentration for those drugs that demonstrate first-order elimination. As concentration drives the PD effect, we can predict that after doubling the dose it will take one half-life for the concentration to return to the value had the dose not been doubled [11]. Therefore, the duration of drug effect will increase by one half-life. This useful rule of thumb (although approximately true) does not necessarily hold for turnover models.

A special note on schedule dependence

Schedule dependence is a dose–response phenomenon that can be predicted with PKPD models and observed in clinical practice. Essentially, for any drug dose that is given over a defined period of time, the total drug effect will depend on the dosing schedule. Schedule dependence is the result of the non-linear relationship of effect to concentration and occurs for drugs that demonstrate reversible binding properties at the site of action. Schedule dependence is therefore an important determinant of the dosing regimen for most drugs. An example is highlighted in Figure 6 using the diuretic furosemide. The PK of furosemide are adequately described by a one-compartment first-order input and output model (Equation 7) and the PD (natriuresis) by an immediate-effect model (Equation 8). Two dosing regimens are depicted, a single dose of 120 mg and three doses of 40 mg given every 4 h. Each provides the same total dose over a 12-h period. If the total natriuresis (drug effect) is summed over the 12-h interval, the area under the natriuresis curve is 430 and 600 mmol Na+ 12 h−1 for the single dose of 120 mg and the three doses 40 mg every 4 h respectively. It is seen that the single 120-mg dose causes less total diuresis over 12 h than three equally spaced 40-mg doses. In short, the drug effect in this case is dependent on the dosing schedule.

Figure 6.

Figure 6

Open in a new tab

Furosemide and schedule dependence. AUCe = the area under the effect curve which in this case is Na+ excretion. A single 120-mg dose of furosemide results in less total diuresis over 12 h than three 40-mg doses. 40 mg × 3. AUCe = 600 mmol Na+ 12 h−1 (Inline graphic); 120 mg × 1. AUCe = 430 mmol Na+ 12 h−1 (Inline graphic)

graphic file with name bcp0071-0815-m7.jpg (7)
graphic file with name bcp0071-0815-m9.jpg
graphic file with name bcp0071-0815-m8.jpg (8)
graphic file with name bcp0071-0815-m10.jpg

Conclusions

Understanding of the onset, magnitude and duration of drug effects that results from a given dose or dosing regimen is a central tenet of both clinical pharmacology and PKPD modelling. PKPD models provide an important framework by which we can learn about the time course of drug effects and best optimize the use of drugs in the clinic.

Acknowledgments

Dan Wright was supported by a University of Otago Postgraduate Scholarship.

Competing Interests

There are no competing interests to declare.

REFERENCES

  • 1.Leake CD. The scientific status of pharmacology. Science. 1961;134:2069–79. doi: 10.1126/science.134.3496.2069. [DOI] [PubMed] [Google Scholar]
  • 2.Reidenberg MM. Clinical pharmacology: the scientific basis of therapeutics. Clin Pharmacol Ther. 1999;66:2–8. doi: 10.1016/S0009-9236(99)70047-0. [DOI] [PubMed] [Google Scholar]
  • 3.Danhof M, de Jongh J, De Lange ECM, Della Pasqua O, Ploeger BA, Voskuyl RA. Mechanism-based pharmacokinetic-pharmacodynamic modeling: biophase distribution, receptor theory, and dynamical systems analysis. Annu Rev Pharmacol Toxicol. 2007;47:357–400. doi: 10.1146/annurev.pharmtox.47.120505.105154. [DOI] [PubMed] [Google Scholar]
  • 4.Sheiner LB, Steimer JL. Pharmacokinetic/pharmacodynamic modeling in drug development. Annu Rev Pharmacol Toxicol. 2000;40:67–95. doi: 10.1146/annurev.pharmtox.40.1.67. [DOI] [PubMed] [Google Scholar]
  • 5.Duffull SB, Wright DFB, Winter HR. Interpreting population pharmacokinetic-pharmacodynamic analyses – a clinical viewpoint. Br J Clin Pharmacol. 2011 doi: 10.1111/j.1365-2125.2010.03891.x. DOI: 10.1111/j.1365-2125.2010.03891.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 6.Bonate PL. Recommended reading in population pharmacokinetic pharmacodynamics. AAPS J. 2005;7:E363–73. doi: 10.1208/aapsj070237. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 7.Brendel K, Dartois C, Comets E, Lemenuel-Diot A, Laveille C, Tranchand B, Girard P, Laffont CM, Mentre F. Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004. Clin Pharmacokinet. 2007;46:221–34. doi: 10.2165/00003088-200746030-00003. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 8.Al-Sallami HS, Pavan Kumar VV, Landersdorfer CB, Bulitta JB, Duffull SB. The time course of drug effects. Pharm Stat. 2009;8:176–85. doi: 10.1002/pst.393. [DOI] [PubMed] [Google Scholar]
  • 9.Minto C, Schnider T. Expanding clinical applications of population pharmacodynamic modelling. Br J Clin Pharmacol. 1998;46:321–33. doi: 10.1046/j.1365-2125.1998.00792.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 10.Ette EI, Williams PJ. Population pharmacokinetics I: background, concepts, and models. Ann Pharmacother. 2004;38:1702–6. doi: 10.1345/aph.1D374. [DOI] [PubMed] [Google Scholar]
  • 11.Holford NH, Sheiner LB. Understanding the dose-effect relationship: clinical application of pharmacokinetic-pharmacodynamic models. Clin Pharmacokinet. 1981;6:429–53. doi: 10.2165/00003088-198106060-00002. [DOI] [PubMed] [Google Scholar]
  • 12.Jacqmin P, Snoeck E, van Schaick E, Gieschke R, Pillai P, Steimer J, Girard P. Modellling response time profile in the absence of drug concentrations: definition and performance evaluation of the PK-PD model. J Pharmacokinet Pharmacodyn. 2007;34:57–85. doi: 10.1007/s10928-006-9035-z. [DOI] [PubMed] [Google Scholar]
  • 13.Mandema JW, Verotta D, Sheiner LB. Building population pharmacokinetic – pharmacodynamic models. I. Models for covariate effects. J Pharmacokinet Biopharm. 1992;20:511–28. doi: 10.1007/BF01061469. [DOI] [PubMed] [Google Scholar]
  • 14.Atkinson AJ, Jr, Lalonde RL. Introduction of quantitative methods in pharmacology and clinical pharmacology: a historical overview. Clin Pharmacol Ther. 2007;82:3–6. doi: 10.1038/sj.clpt.6100248. [DOI] [PubMed] [Google Scholar]
  • 15.Holford NH, Sheiner LB. Kinetics of pharmacologic response. Pharmacol Ther. 1982;16:143–66. doi: 10.1016/0163-7258(82)90051-1. [DOI] [PubMed] [Google Scholar]
  • 16.Sheiner LB, Stanski DR, Vozeh S, Miller RD, Ham J. Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharmacol Ther. 1979;25:358–71. doi: 10.1002/cpt1979253358. [DOI] [PubMed] [Google Scholar]
  • 17.Atkinson AJ. Clinical Pharmacokinetics. In: Atkinson A, Abernethy D, Daniels C, Dedrick R, Markey S, editors. Principles of Clinical Pharmacology. 2nd edn. New York, NY: Academic Press; 2007. pp. 11–23. [Google Scholar]
  • 18.Wright DFB, Begg EJ. The ‘apparent clearance’ of free phenytoin in elderly vs. younger adults. Br J Clin Pharmacol. 2010;70:132–38. doi: 10.1111/j.1365-2125.2010.03673.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 19.Sharp CF, Gardiner SJ, Jensen BP, Roberts RL, Troughton RW, Lainchbury JG, Begg EJ. CYP2D6 genotype and its relationship with metoprolol dose, concentrations and effect in patients with systolic heart failure. Pharmacogenomics J. 2009;9:175–84. doi: 10.1038/tpj.2009.9. [DOI] [PubMed] [Google Scholar]
  • 20.Brooks AJ, Begg EJ, Zhang M, Frampton CM, Barclay ML. Red blood cell methotrexate polyglutamate concentrations in inflammatory bowel disease. Ther Drug Monit. 2007;29:619–25. doi: 10.1097/FTD.0b013e31811f39bb. [DOI] [PubMed] [Google Scholar]
  • 21.Bourne HR, von Zastrow M. Drug Receptors and Pharmacodynamics. In: Katzung BG, editor. Basic and Clinical Pharmacology. 8th edn. New York, NY: McGraw-Hill; 2001. pp. 9–34. [Google Scholar]
  • 22.Csajka C, Verotta D. Pharmacokinetic-pharmacodynamic modelling: history and perspectives. J Pharmacokinet Pharmacodyn. 2006;33:227–79. doi: 10.1007/s10928-005-9002-0. [DOI] [PubMed] [Google Scholar]
  • 23.Gray E, Mulloy B, Barrowcliffe TW. Heparin and low-molecular-weight heparin. Thromb Haemost. 2008;99:807–18. doi: 10.1160/TH08-01-0032. [DOI] [PubMed] [Google Scholar]
  • 24.Beeler D, Rosenberg R, Jordan R. Fractionation of low molecular weight heparin species and their interaction with antithrombin. J Biol Chem. 1979;254:2902–13. [PubMed] [Google Scholar]
  • 25.Liesenfeld KH, Schäfer HG, Trocóniz IF, Tillmann C, Eriksson BI, Stangier J. Effects of the direct thrombin inhibitor dabigatran on ex vivo coagulation time in orthopaedic surgery patients: a population model analysis. Br J Clin Pharmacol. 2006;62:527–37. doi: 10.1111/j.1365-2125.2006.02667.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 26.Auler Júnior JO, Espada EB, Crivelli E, Quintavalle TB, Kurata A, Stolf NA, Issy AM, Paschoa OE, Danhof M, Breimer DD, Chamone DA, Santos SR. Diclofenac plasma protein binding: PK-PD modelling in cardiac patients submitted to cardiopulmonary bypass. Braz J Med Biol Res. 1997;30:369–74. doi: 10.1590/s0100-879x1997000300010. [DOI] [PubMed] [Google Scholar]
  • 27.Stedman CA, Barclay ML. Review article: comparison of the pharmacokinetics, acid suppression and efficacy of proton pump inhibitors. Aliment Pharmacol Ther. 2000;14:963–78. doi: 10.1046/j.1365-2036.2000.00788.x. [DOI] [PubMed] [Google Scholar]
  • 28.Yassen A, Olofsen E, Romberg R, Sarton E, Teppema L, Danhof M, Dahan A. Mechanism-based PK/PD modeling of the respiratory depressant effect of buprenorphine and fentanyl in healthy volunteers. Clin Pharmacol Ther. 2007;81:50–8. doi: 10.1038/sj.clpt.6100025. [DOI] [PubMed] [Google Scholar]
  • 29.Salazar DE, Much DR, Nichola PS, Seibold JR, Shindler D, Slugg PH. A pharmacokinetic-pharmacodynamic model of d-sotalol Q-Tc prolongation during intravenous administration to healthy subjects. J Clin Pharmacol. 1997;37:799–809. doi: 10.1002/j.1552-4604.1997.tb05627.x. [DOI] [PubMed] [Google Scholar]
  • 30.Hornestam B, Jerling M, Karlsson MO, Held P, Group DAT. Intravenously administered digoxin in patients with acute atrial fibrillation: a population pharmacokinetic/pharmacodynamic analysis based on the Digitalis in Acute Atrial Fibrillation trial. Eur J Clin Pharmacol. 2003;58:747–55. doi: 10.1007/s00228-002-0553-3. [DOI] [PubMed] [Google Scholar]
  • 31.Sharma A, Jusko WJ. Characteristics of indirect pharmacodynamic models and applications to clinical drug responses. Br J Clin Pharmacol. 1998;45:229–39. doi: 10.1046/j.1365-2125.1998.00676.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 32.Jusko WJ, Ko HC. Physiologic indirect response models characterize diverse types of pharmacodynamic effects. Clin Pharmacol Ther. 1994;56:406–19. doi: 10.1038/clpt.1994.155. [DOI] [PubMed] [Google Scholar]
  • 33.Dayneka NL, Garg V, Jusko WJ. Comparison of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm. 1993;21:457–78. doi: 10.1007/BF01061691. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 34.Faltaos DW, Urien S, Carreau V, Chauvenet M, Hulot JS, Giral P, Bruckert E, Lechat P. Use of an indirect effect model to describe the LDL cholesterol-lowering effect by statins in hypercholesterolaemic patients. Fundam Clin Pharmacol. 2006;20:321–30. doi: 10.1111/j.1472-8206.2006.00404.x. [DOI] [PubMed] [Google Scholar]
  • 35.Cleton A, de Greef HJ, Edelbroek PM, Voskuyl RA, Danhof M. Application of a combined ‘effect compartment/indirect response model’ to the central nervous system effects of tiagabine in the rat. J Pharmacokinet Biopharm. 1999;27:301–23. doi: 10.1023/a:1020999114109. [DOI] [PubMed] [Google Scholar]
  • 36.Holford NH. Rational warfarin dosing: a pharmacokinetic-pharmacodynamic analysis. Clin Pharmacol Ther. 1986;39:199. [Google Scholar]
  • 37.O'Reilly RA, Aggeler PM, Leong LS. Studies on the coumadin anticoagulant drugs: the pharmacodynamics of warfarin in man. J Clin Invest. 1963;42:1542–51. doi: 10.1172/JCI104839. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 38.O'Reilly RA, Aggeler PM. Studies on coumarin anticoagulant drugs. Initiation of warfarin therapy without a loading dose. Circulation. 1968;38:169–77. doi: 10.1161/01.cir.38.1.169. [DOI] [PubMed] [Google Scholar]

Articles from British Journal of Clinical Pharmacology are provided here courtesy of British Pharmacological Society

RESOURCES