Pharma c i Kinetics

Biochemical Pharmacology 87 (2014) 93–120

Review – Part of the Special Issue – Pharmacology in 21st Century Biomedical Research

Pharmacokinetics

Jianghong Fan, Ines A.M. de Lannoy *

InterVivo Solutions Inc., 120 Carlton Street, Suite 203, Toronto, ON, Canada M5A 4K2

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

2. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3. Overview of basic PK processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.1. Determination of in vivo PK parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.1.1. Study design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.2. Data analysis and interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.2.1. Non-compartmental analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.2.2. Compartmental analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4. Pharmacokinetics scaling from animals to humans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.1. Allometric scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.2. Physiologically based PK (PBPK) modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5. Absorption and permeability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1. Intestinal absorption and permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.1. Role of intestinal permeability and transporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.2. Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.3. Log P and log D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.4. Caco-2 permeability assay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.2. Brain permeability and penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6. Distribution and protein binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.1. Volume of distribution (V or Vd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.2. Plasma protein binding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

A R T I C L E I N F O

Article history:

Received 16 May 2013

Accepted 9 September 2013

Available online 17 September 2013

Keywords:

Pharmacokinetics

Absorption

Distribution

Clearance

Metabolite kinetics

Pharmacodynamics

A B S T R A C T

Pharmacokinetics (PK) is the study of the time course of the absorption, distribution, metabolism and

excretion (ADME) of a drug, compound or new chemical entity (NCE) after its administration to the body.

Following a brief introduction as to why knowledge of the PK properties of an NCE is critical to its

selection as a lead candidate in a drug discovery program and/or its use as a functional research tool, the

present article presents an overview of PK principles, including practical guidelines for conducting PK

studies as well as the equations required for characterizing and understanding the PK of an NCE and its

metabolite(s). A review of the determination of in vivo PK parameters by non-compartmental and

compartmental methods is followed by a brief overview of allometric scaling. Compound absorption and

permeability are discussed in the context of intestinal absorption and brain penetration. The volume of

distribution and plasma protein and tissue binding are covered as is the clearance (systemic, hepatic,

renal, biliary) of both small and large molecules. A section on metabolite kinetics describes how to

estimate the PK parameters of a metabolite following administration of an NCE. Lastly, mathematical

models used to describe pharmacodynamics (PD), the relationship between the NCE/compound

concentration at the site of action and the resulting effect, are reviewed and linked to PK models in a

section on PK/PD.

� 2013 Published by Elsevier Inc.

Contents lists available at ScienceDirect

Biochemical Pharmacology

jo u rn al h om epag e: ww w.els evier .c o m/lo cat e/b io c hem p har m

* Corresponding author.

E-mail addresses: [email protected] (J. Fan), [email protected], [email protected] (Ines A.M. de Lannoy).

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J. Fan, I.A.M. de Lannoy / Biochemical Pharmacology 87 (2014) 93–12094

6.3. Tissue binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7. Clearance (metabolism and excretion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.1. Systemic clearance (CLs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.2. Organ clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.2.1. Hepatic clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.2.2. Renal clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.2.3. Biliary clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.3. Clearance of large molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.3.1. Nano-sized particles and molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.3.2. Antibody drugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.3.3. Peptides and proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8. Metabolite kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8.1. Intravenous compound administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8.1.1. Formation rate-limited metabolite kinetics (k � km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8.1.2. Elimination rate-limited metabolite kinetics (k � km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.1.3. Time to achieve the maximum metabolite concentration (tmax,m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.1.4. Area under the plasma concentration versus time curve (AUC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.1.5. Stead-state i.v. infusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.2. Extravascular compound administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.2.1. Area under the concentration versus time curve (AUC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.3. Metabolite excretion in the urine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.4. Issues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.4.1. Absorption rate-limited kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.4.2. Elimination rate-limited disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.4.3. First-pass metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.4.4. Preformed and formed metabolite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.4.5. Pro-drug and metabolite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.4.6. Species differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.4.7. Metabolite-parent compound interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9. Pharmacokinetics and pharmacodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9.1. Pharmacological effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9.1.1. Quantal effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

9.1.2. Graded effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

9.2. Drug–target residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

10. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

1. Introduction

While potency, efficacy and selectivity are key attributes of anew chemical entity (NCE) that drive its characterization as acompound of potential interest in the drug discovery process oras a research tool that can be used to interrogate biologicalsystems in vitro and in vivo, unless the pharmacokinetics (PK)properties of an NCE are known, its use in vivo becomes limitedby shortcomings in PK that can confuse data interpretation andresult in experimental outcomes that are invalid. For instance,when making species comparisons of plasma exposure of an NCEin vivo, without knowledge of the variations in plasma proteinbinding and metabolic liability across species, correlation of thepharmacological response with plasma exposure becomeschallenging. As Hodgson has cogently noted [1] – ‘‘A chemicalcannot be a drug, no matter how active nor how specific itsaction, unless it is also taken appropriately into the body(absorption), distributed to the right parts of the body,metabolized in a way that does not instantly remove its activity,and eliminated in a suitable manner – a compound must get in,move about, hang around, and then get out.’’ Thus, evaluatingthe properties of a compound, especially an NCE, in vivo withoutknowledge of its PK properties – even at a rudimentary level – isan exercise in futility. The present overview provides anintroduction to the principles of PK, including guidelines forconducting PK studies and the equations required for character-izing and understanding the PK of an NCE and its possiblemetabolite(s).

2. Background

Pharmacokinetics (PK) is the study of the movement ofxenobiotics (drugs/compounds/NCEs) within the body after theiradministration, whereas pharmacodynamics (PD) is the study ofthe relationship between the concentration of a compound/NCE atits site of action, where the therapeutic targets (e.g., receptors,transporters or enzymes) are located, and the magnitude of thepharmacological response. In the simplest of terms, whatdistinguishes PK from PD is that the former describes what thebody does to the compound, whereas PD describes what thecompound does to the body [2]. Both fields of study are importantfor investigating the disposition profiles and pharmacologicalefficacy of compounds/NCEs in the body [3], and may be influencedby experimental as well as clinical conditions (e.g., gender, species,age, disease state).

In the past, drug discovery programs often concentrated theirefforts solely on selecting the most potent or efficacious compoundin in vitro receptor binding or functional assays, respectively, thatwere designed to test hundreds to thousands of compounds, andfailed to generate data on whether a compound would have theability to reach its therapeutic target at a sufficient concentrationand for a sufficient amount of time to alter target function whenadministered in vivo. This strategy was noted as being detrimentalto developing a successful drug, with a retrospective analysis of 7U.K. owned pharmaceutical companies conducted up to 1985revealing that 39% of NCEs failed in the clinic due to poor PKproperties [4]. Careful assessment of the PK profile in selecting and

J. Fan, I.A.M. de Lannoy / Biochemical Pharmacology 87 (2014) 93–120 95

optimizing a lead NCE in the early stages of a drug discoveryproject can reduce compound attrition at later, more expensive,stages of compound development [5]. Similarly, knowledge of theproperties of a reference compound or drug can aid in theinterpretation of the data. Evaluating a peptide ligand with a half-life of less than a minute in a biological assay where the firstobservation is made at 30 min can lead to erroneous and irrelevantoutcomes.

3. Overview of basic PK processes

The four fundamental processes which influence the in vivo PKof a compound are absorption, distribution, metabolism andexcretion (ADME). These are distinct, although in many respects,interrelated processes which occur between the administrationand elimination of a compound from the body. Following an oral(p.o.) dose of a compound, it must be absorbed across the intestinallumen and not be susceptible to metabolism by intestinal enzymesbefore it appears in the portal vein circulation where it is deliveredto the liver and will likely undergo first pass hepatic metabolismand/or biliary excretion prior to reaching the systemic circulation.In contrast, an intravenous (i.v.) dose of a compound is introduceddirectly into the venous circulation and is, as a consequence, notsubject to first pass elimination. Once in the venous blood, thecompound can then be pumped by the heart through the lungs,where it may be eliminated in expired air or by metabolic enzymes,before it reaches the arterial circulation. The arterial circulationwill then distribute the compound to the various tissues andorgans, some of which (e.g., kidney) in addition to the liver, mayeliminate the compound by metabolism and/or excretion. Thus,access of the compound and/or its active metabolites to thetherapeutic target(s) at a sufficient concentration to achieve aneffect, whether therapeutic or toxic, largely depends on all of theseprocesses. For targets within a cell or in the brain, a compound hasto cross the cell membrane and the blood brain barrier,respectively, adding additional challenges in ensuring targetengagement.

The most important site of compound absorption is thegastrointestinal (GI) tract, since p.o. dosing is the most commonand preferred route of administration of drugs; however, absorp-tion through the skin, the cutaneous tissue, the nasal epithelium,the peritoneum or the respiratory tract would need to beconsidered for dermally, subcutaneously (s.c.), intranasally (i.n.)or intraperitoneally (i.p.) administered or inhaled drugs, respec-tively. Regardless of the site of absorption, compounds mustpermeate membranes in order to be absorbed. For compoundsdosed p.o. in a solid dosage form, disintegration of the dosage forminto small particles (a suspension) should occur prior to theirdissolution in the GI fluid, and this must occur prior to permeationof the intestinal membrane. Disintegration is, in general, muchfaster than dissolution. Either dissolution or membrane perme-ation can be rate-limiting, depending on the relative magnitude ofeach process. The dissolution rate is a function of the aqueoussolubility of a compound, the surface area (SA) of the particles andthe dissolution rate constant. To increase the dissolution rate of acompound from solid particles, one can increase: (1) the aqueoussolubility of the compound (e.g., by elevating the temperature orchanging the pH if the compound is ionizable), (2) the SA of theparticle by reducing particle size, or (3) the dissolution rateconstant (e.g., through agitation of the medium). The permeationrate of a compound across the intestinal membrane is a function ofthe intestinal membrane permeability, the effective SA ofmembrane available for permeation and the concentration ofthe compound in the GI fluid. The permeability of a compoundacross a membrane is further dependent on its lipophilicity,molecular size, and charge [6]. Owing to the lipoidal properties of

the cell membrane, compounds must have sufficient lipophilicityto partition into membranes from an aqueous (e.g., GI fluid)environment and thereby passively diffuse across the membrane.The size of the molecule is also important; paracellular transportvia tight junctions between enterocytes is possible for small(molecular weight (MW) < 200 g/mole), highly water-solublecompounds, whereas transcellular transport (passive diffusionor active transport) becomes more important as the MW increases.For ionizable compounds, the unionized form of the molecule isconsidered better able to partition into lipophilic membranes thanthe ionized form. These properties are reflected in the ‘‘Rule ofFive’’ (RoF) which was developed to assess the ‘drug-like’properties of NCEs in the early stages of the drug discoveryprocess [7]. The RoF is based on four properties of molecules,namely, MW, Log P (the log of the partition ratio or partitioncoefficient, the ratio of compound concentrations in a mixture oftwo immiscible phases at equilibrium, e.g., water and octanol – ameasure of lipophilicity), the number of hydrogen-bond donors(HBD -taken as equivalent to the number of –OH and –NH groups),and the number of hydrogen bond acceptors (HBA – taken asequivalent to the number of oxygen and nitrogen atoms). Amolecule can be predicted to have poor absorption or permeation ifit has a MW greater than 500, a calculated Log P greater than 5, thenumber of HBDs is more than 5 and the number of HBAs is morethan 10.

In addition, although small lipophilic compounds generallycross the cell membrane via passive diffusion along a concentra-tion gradient, they may also be substrates for efflux transportersthat can limit their net permeation across the membrane. Bycontrast, large, highly polar or charged compounds which arelimited in their ability to partition into the lipid bilayers of themembrane, are dependent on the presence of active influxtransporters [8].

Once in the systemic circulation, the blood or plasmaconcentrations of a compound will depend on how extensively acompound is distributed to extravascular sites. Compoundconcentrations in whole blood represent the total concentrationsof drug in the circulatory system while plasma concentrations donot account for compound that can be sequestered in red, and to alesser extent white, blood cells. Compound distribution will beinfluenced by organ/tissue blood flow, whether the compound isable to passively diffuse across cell membranes or is a substrate foractive uptake or efflux transporters, and its extent of plasmaprotein and tissue binding [9].

For the majority of drugs and NCEs, metabolism is the majorpathway of elimination. The major organ involved in themetabolism of xenobiotics is the liver, however, extrahepatictissues may also play a significant role. The intestine (enterocytesand microflora/microbiome), kidney, lung, plasma, red blood cells,placenta, skin and brain are metabolic entities. In general,metabolism occurs via enzymatic processes that transform alipophilic compound into more hydrophilic metabolites in order tofacilitate their excretion into bile or urine. Metabolic reactions canbe divided into two categories: Phase I and Phase II reactions [10].Phase I reactions (e.g., oxidation, reduction and hydrolysis) involvethe introduction into or unveiling of a functional group (e.g. –OH, –NH2, –SH, –COOH) to the molecule. In contrast, Phase II metabolism

(e.g., sulfation, glucuronidation, glutathione conjugation, N-acety-lation, methylation, amino acid conjugation) involves the conju-gation of functional groups of the molecule or its metabolites withhydrophilic endogenous substrates.

There are two major excretory routes for xenobiotics and theirmetabolites from the body: renal and biliary excretion. Renalexcretion usually involves one or more of three distinct processes:glomerular filtration, tubular secretion and reabsorption from therenal tubular lumen [10]. Biliary excretion, a process that is often


facilitated by active transport systems located in the canalicularmembrane of the hepatocyte, can be an important hepaticelimination pathway for many compounds. Both processes arecovered in more detail in the section on Clearance (Section 7).

3.1. Determination of in vivo PK parameters

The assessment of PK parameters from in vivo experimentsfollowing various routes of administration of a compound topreclinical animal species and humans can be a challenge for thosenot well versed in PK theory. As a result, many PK studies are notexecuted or interpreted in a scientifically reliable and/or usefulmanner. In addition, PK studies may be challenging due to limitedaccess to the relevant tissues/organs for assessing the relevanttherapeutic compound concentrations (e.g., brain). Developmentand validation of bioanalytical methods with sufficient sensitivityfor a compound and its putative metabolites may also present achallenge. The following section will, therefore, concentrate onbasic PK concepts, study design and data analysis.

There are four PK parameters which are the most useful incharacterizing the in vivo disposition of a compound [11]. Theseare: (i) clearance (CL, units of volume/time, e.g., L/min), a measureof the ability of the body to eliminate a compound, (ii) volume of

distribution (V or Vd, units of volume, e.g., L), a measure of theapparent volume/space in the body which contains the compound,(iii) half-life (t1/2, units of time, e.g., min), a measure of the time ittakes for a compound to decrease to half of its initial concentrationin the fluid or tissue in which it is measured in (e.g., plasma) and(iv) bioavailability (F, unitless, often expressed as %, e.g., %F), thefraction of a compound that reaches the systemic circulationfollowing non-parenteral (e.g., p.o.) administration. Estimation ofthese parameters from an in vivo PK experiment, usually involvesthe determination of the blood or plasma concentration of acompound over time following its administration. In general,plasma is more widely analyzed than blood because samplepreparation and analysis methods are easier for plasma than forblood. For drugs with a blood to plasma concentration ratio oflarger than 2, measuring concentrations in whole blood rather thanplasma can increase the sensitivity of the assay. Also, in instanceswhen there is significant temperature-dependent red blood cellpartitioning (e.g., cyclosporine A and tacrolimus), whole blood isused for bioanalysis in order to avoid having to isolate plasma at37 8C [12]. For the data to be reliable one must consider the validityof the study design and its execution, as well as the methodsutilized for sample collection, handling and bioanalysis (asdiscussed below).

Determination of the blood or plasma concentration versus timeprofile following i.v. administration of a compound is critical toaccurately determine all four of the PK parameters mentionedabove. A true estimate of the total body or systemic clearance (CLs)of a compound can only be obtained from its concentration versus

time profile after i.v. administration. This is because the systemicclearance of a compound is defined as its rate of elimination fromthe body normalized to the concentration of the compound in thebody fluid (plasma or blood) in which the compound is introduced(i.e. 100% of the compound administered is available). Thus, CLs canbe estimated following non-parenteral routes of administration aslong as the compound is completely bioavailable, that is, it must becompletely absorbed and not eliminated prior to reaching thesystemic circulation following dosing. The latter requirement isusually not met as most routes of administration (particularly p.o.)result in a significant loss of parent compound due to poorabsorption, metabolism or excretion. It should be noted thatsystemic blood clearance (i.e. CLs calculated from blood concen-trations), can be viewed as the actual volume of blood cleared of acompound per unit time from the entire blood pool in the body,

whereas the systemic plasma clearance does not represent theactual volume of plasma cleared of a compound, but rather theapparent volume of plasma cleared per unit time. The volume ofdistribution at steady-state (Vss) must also be determinedfollowing i.v. administration and not following other routes ofadministration. Vss is defined as a proportionality constantbetween the total amount of compound present in the body andthe concentration of the compound, at steady-state, in the bodyfluid in which the compound is being measured (i.e. plasma). Thevolume of distribution is a direct measure of the extent ofdistribution of a drug from the plasma to tissues, although it doesnot represent a real physiological volume (Section 6.1). Theterminal half-life (t1/2) of a compound following i.v. administrationis determined by its distribution and elimination. Generally, sincedistribution is much faster than elimination, the terminal half-lifeis governed by its elimination. As a result, t1/2 values may differsignificantly between species, with smaller species, e.g., mice,which generally have a higher metabolic rate, exhibiting shorter t1/

2 values for compounds than larger species (such as human). Incontrast, the terminal half-life determined following other routesof administration may be governed by the absorption of thecompound from the site of administration, in addition to itselimination and distribution. The latter occurs if the absorptionprocess is rate-limiting, and to determine whether this is the case,the t1/2 value estimated from i.v. administration is compared tothat following the non-parenteral route of administration (e.g.,p.o.). Equal values for t1/2 would suggest that absorption is not rate-limiting. And lastly, total body exposure to the compound, asdetermined by the area under the blood/plasma concentrationversus time curve (AUC) from time zero extrapolated to timeinfinity (AUC0–inf), following i.v. dosing is used as the reference(100% is available) for estimating the bioavailability (%F) of acompound following non-parenteral routes of administration.

3.1.1. Study design

There are several practical considerations for conducting in vivo

dosing studies in preclinical species such as rodents. These includethe: (i) duration of the i.v. injection, e.g., bolus or short infusion, (ii)composition of the dosing solution, (iii) dosing volume adminis-tered, (iv) dose level, (v) food intake, (vi) blood/plasma samplingtime points and (vii) blood sample volume.

3.1.1.1. Duration of the i.v. injection. Intravenous (or intra-arterial)injection of a compound is generally assumed to be a bolusinjection (i.e. it is delivered within a few seconds); if it takes morethan 1 min, it should be treated as a short infusion for PK dataanalysis. Intravenous infusion over longer time periods may beused for the evaluation of steady-state kinetics, and are analyzeddifferently than the administration of a bolus dose or short i.v.

infusion.

3.1.1.2. Composition of the dosing solution. The composition of thedosing solution may be a consideration if it does not consist of anaqueous solution at neutral pH. Many compounds have limitedsolubility or are unstable in aqueous solution and thus require a co-solvent for dissolution. Several guidelines for the incorporation ofacceptable co-solvents are available [13,14], since solubility hasbeen a challenge for more recent drug discovery programs. For i.v.dosing, non-aqueous co-solvents such as ethanol, propylene glycol(PG), polyethylene glycol (PEG) 300, PEG 400, Cremophor1 EL,Solutol1, dimethyl sulfoxide (DMSO), N-methyl-2-pyrolidone,Tween 20 and solubilizing agents, e.g., various cyclodextrins (suchas b-cyclodextrin), are often used in preclinical studies. Cyclodex-trins should be used with caution, as they can form very tightcomplexes with some compounds, resulting in the ineffectiverelease of the compound particularly following i.v. administration


[15]. In general, the co-solvent(s) should not exceed 20% of thetotal injection volume, since hemolysis of red blood cells andinhibition of drug metabolizing enzymes and transporters mayaffect the PK profile of a compound as well as its pharmacologicaland toxicological activity. With the exception of ethanol, several ofthe co-solvents have been used in higher percentages [13,14] whenthe aqueous solubility of the compound is very poor. The pH of theformulation may also be adjusted (pH 2–9) in order to optimize thesolubility of a molecule, however, extreme pH values may causetissue irritation and compound precipitation once the formulationis administered. The proportion of a co-solvent should alsoconsider the viscosity of the resulting formulation, since the easeof injection of a high viscosity solution may be affected. For p.o.

administration, a solution, suspension or gelatin capsule (Size 9 forrats) filled with the test material may be administered. Forsolutions, the co-solvents used are usually the same as those usedfor i.v. administration. Suspensions for oral dosing are usuallyformulated in carboxymethylcellulose. In general, obtaining auniform and accurate dose of a suspension is more difficult thandosing a solution due to sedimentation of the suspended particles.

3.1.1.3. Dose volume. For i.v. dosing, if the volume is too large itmay be difficult to inject as a bolus and, in addition, may dilute thecirculating blood volume. The injection of too small a volume maymake injection of an accurate dose difficult. The recommendedvolume for i.v. bolus injection is �1 mL/kg body weight for themajority of laboratory animals, however, for mice and rats, largervolumes (e.g., 5 mL/kg) are tolerated [16]. For the estimation ofsteady-state PK parameters, the rate of continuous i.v. infusion inrodents should generally not exceed 4 mL/kg/h. For the oraladministration of solutions or suspensions, up to 10 mL/kg can beadministered to fasted rodents, whereas 5 mL/kg is generallyrecommended for fed animals.

3.1.1.4. Dose level. For estimating p.o. bioavailability (F), the doseused for oral administration should equal that used for i.v.administration, in case the compound exhibits nonlinear PK. Inearly drug discovery, however, a higher p.o. than i.v. dose iscommonly administered if oral bioavailability is suspected to bepoor. This allows the compound to be adequately quantified in theblood/plasma samples when the latter is the case. However, if acompound exhibits nonlinear (i.e. saturable) PK characteristics andis sufficiently orally bioavailable, using a higher oral than i.v. dosecan result in an overestimation of F. This may be detected onlywhen estimates of %F are greater than 100%.

3.1.1.5. Food intake. The presence of food in the stomach andintestine can alter the rate and extent of absorption of some orallyadministered compounds. Similarly, restrictions on water intakemay be required to reduce the variability in the extent of absorption(due to compound precipitation) for compounds which have a pooraqueous solubility. Rodents may also feed on their own feces(coprophagy), which can significantly alter oral absorption and/orwill re-introduce compound which has been excreted in the feces.Conducting experiments in metabolism cages can avoid this issue,since urine and feces are separated from the animal for collection.

3.1.1.6. Blood/plasma sampling time points. In order to accuratelycharacterize the blood/plasma concentration versus time profile ofa compound, one needs to sample blood/plasma over seven ormore (at the very minimum, five) time points. For i.v. administra-tion, this is because most compounds have an early distributionphase prior to a terminal elimination phase. As a result, at least 2points in the initial phase (usually within the first 15 min afterinjection) are recommended for a reliable estimation of the initialblood/plasma concentration extrapolated to time zero (C0).

Although this concentration after i.v. dosing is imaginary, sinceno compound is in the plasma at the time of injection, C0 is usefulfor calculating the AUC from time zero to the first sampling timepoint (for non-compartmental analysis methods, the first 2 timepoints are extrapolated back to time zero on a semi-logarithmicscale). At least 3 time points during the terminal phase are requiredfor a reliable estimation of the terminal half-life. In addition, the 3or more time points chosen for estimation of the terminal half-lifeshould span at least 2 half-lives. Important PK parametersestimated from plasma concentration versus time curves followingoral (and other extravascular routes of) administration include: (i)Cmax, which is the highest compound concentration observed aftera non-parenteral route of administration, and tmax, which is thetime at which Cmax is observed, (ii) terminal half-life (t1/2), whichcan be affected by the rate of compound absorption and disposition(distribution and elimination), and (iii) bioavailability (F), that is,the fraction of an extravascularly administered dose that reachesthe systemic circulation. Thus, as with i.v. administration, seven (atleast 5) time points are recommended after oral or other non-parenteral routes of administration in order to adequately capturethe entire concentration versus time profile. At least one time pointprior to and 3 time points after tmax during the terminalelimination phase is recommended for the estimation of the t1/2.The data point at tmax should not be included in an estimation ofthe terminal half-life.

3.1.1.7. Blood sample volume. As a general rule of thumb, no morethan 10% of the total circulating blood volume should be sampledover a 1–2 week period [16], in the absence of blood samplevolume replacement. Up to 15% of the circulating blood volumemay be sampled when the sample volume is replaced (followingeach sampling time point) with blank blood (blood freshlycollected from drug naıve animals) or saline. Higher samplingvolumes (e.g., 20%) result in significant hemodynamic changes andtissue anoxia and may also affect the PK of the compoundadministered.

3.2. Data analysis and interpretation

To estimate PK parameters from plasma concentration versus

time profiles, compartmental and non-compartmental approachesmay be used [17,18]. The compartmental approach represents thebody as a system of one or more compartments that usually haveno physiological or anatomical meaning. Rate constants describethe transfer of molecules between the compartments and out ofcompartments (elimination). The approach relies on nonlinearregression analysis to fit an exponential equation to the data. Bycontrast, the non-compartmental method (using statistical mo-ment analysis) is based on the area under the compoundconcentration versus time curve (AUC0–1) and the mean residencetime (MRT) and can be applied practically to any PK data [19]. Non-compartmental analysis (NCA) requires that fewer assumptions bemade than for compartmental analysis in modeling concentrationversus time data. However, the limitation of NCA, unlikecompartmental analysis, is that it lacks the ability to predict PKprofiles when there are alterations in a dosing regimen, since itcannot predict a compound concentration at any time. Thus, themost appropriate method to use will depend on the purpose of theanalysis and the nature of the data. The fundamental PKparameters reviewed below can be calculated by the compart-mental as well as non-compartmental approach.

3.2.1. Non-compartmental analysis

The AUC estimated for compound plasma concentrations (oralternatively blood or serum concentrations; while plasma andserum are derived from whole blood, serum is obtained from


coagulated blood such that it differs from plasma in not havingfibrin and related coagulation factors) is the primary measure ofoverall compound exposure following i.v. or extravascularadministration. The units of AUC are concentration � time (e.g.ng/min/mL). The AUC is commonly estimated by the linear or logtrapezoidal methods or a combination thereof. The lineartrapezoidal method for estimating AUC over 2 adjacent timepoints, t1 and t2 (AUCt1�t2

, the area of a trapezoid between t1 andt2), should be performed on a linear scale as follows:

AUCt1�t2 ¼ðt2 � t1Þ � ðC2 þ C1Þ

2(1)

The log trapezoidal method uses the following equation:

AUCt1�t2¼ ðt2 � t1Þ � ðC2 � C1Þ

lnðC2=C1Þ(2)

The linear trapezoidal rule is most reliable for slowly ascendingand declining curves, but is error prone if there is a sharp bendingin the curve. The log trapezoidal rule is usually more reliable for anexponentially declining curve and is error prone in an ascendingcurve or near a peak. As a result, the choice of a combination oflinear and log trapezoidal methods is available in commerciallyavailable software (e.g., Phoenix1 WinNonlin1, Certera). The lattersoftware uses the log trapezoidal rule after Cmax or after C0 for i.v.bolus administration (if C0 > Cmax); otherwise the linear trapezoi-dal rule is used. Following a single i.v. dose, the AUC from time zeroto the first sampling time point (AUC0�t1

) uses C0 as theconcentration at time zero, whereas following a single non-parenteral (e.g., p.o.) dose, the concentration at time zero isgenerally zero. To estimate the AUC over an extended time period,the areas of the individual trapezoids are added. To estimate theAUC from the last sampling time point (tlast), assuming that theconcentration (Ctlast

) is not zero, to infinity the following equationis used:

AUCtlast�1 ¼Ctlast

lZ(3)

where lZ is the terminal rate constant, usually obtained fromnonlinear regression analysis of at least the last 3 data points on thecompound concentration versus time curve plotted on a semi-logarithmic scale. The value used for Ctlast

is either the measuredconcentration at tlast or that predicted from the regression line fittedto the last 3 data points. The latter is more reliable in cases where thecompound concentration determined at tlast is near the lower limit ofquantification of the bioanalytical assay and/or the correlationcoefficient (r) for the regression analysis is poor. The AUC from thetime of dosing and extrapolated to infinity (AUC0–1) is equal to thesum of the AUC0�tlast

and AUCtlast�1 . For the estimate of the AUC0–1to be reliable, the percentage of the AUC0–1 that is extrapolated fromtlast to infinity should not, as a rule, exceed 15%.

The mean residence time (MRT) is the arithmetic mean of theduration that a compound resides in the body before beingeliminated and can be calculated as AUC0–1/AUMC0–1, whereAUMC0–1 is the area under the first moment curve (the AUC of aplot of the product of concentration (C) � time (t) versus t). The unitof MRT is time (min or h). AUMC0�tlast

can also be estimated withthe trapezoidal rule as described above. To extrapolate the AUMCfrom the last time point to infinity:

AUMCtlast�1 ¼Ctlast

� tlZ

þ Ctlast

l2Z

(4)

AUMC0–1 is equal to the sum of AUMC0�tlastand AUMCtlast�1 . The

units for AUMC are concentration � time2 (e.g. ng/min2/mL).The systemic clearance of a compound (CLs, also referred to as

the total body clearance, CLT) can be calculated from the plasma

concentration versus time curve determined following i.v. dosing(AUCiv

0�1):

CLs ¼Doseiv

AUCiv0�1

(5)

where Doseiv is the i.v. dose administered. The units of CL areexpressed as volume/time (e.g. mL/min or L/min (or h)) and areusually normalized to kg of body weight (e.g. mL/min/kg).

The simplest method to estimate the volume of distribution at

steady-state (Vss) is to use moment analysis; Vss equals the productof CLs and MRT, determined following i.v. administration [20]:

Vss ¼ CLs � MRTiv (6)

The units of V are usually expressed as mL/kg or L/kg, whennormalized to kg body weight. As mentioned previously, CLs andVss can only be estimated from i.v. administration data and notfrom concentrations determined following non-parenteral admin-istration. As discussed in Section 6, Vss is used to assess the extentof distribution of a compound from the plasma to the tissues.

The bioavailability (F) of a compound is the fraction of anextravascularly administered dose that reaches the systemiccirculation. Absolute bioavailability (F) is determined by calculat-ing the ratio of the dose-normalized AUCs following extravascularand i.v. administration. Oral bioavailability (Fpo) is given as anexample below:

Fpo ¼AUCpo

0�1 � Doseiv

AUCiv0�1 � Dosepo

(7)

Relative bioavailability (Frel) between 2 routes of administration,dosage forms or formulations is similarly calculated as the ratio ofthe dose-normalized AUC of the test form or formulation to thedose-normalized AUC of the reference form or formulation. Since F

is a fraction (between 0 and 1), it has no units and is oftenexpressed as a percentage (%F = F � 100%).

The mean absorption time (MAT) following oral administrationof a compound (MATpo) can be estimated from the MRT since theMRT of a compound after p.o. administration (MRTpo) includes thetime required for absorption and the MRT after i.v. administration(MRTiv):

MATpo ¼ MRTpo � MRTiv (8)

The half-life (t1/2) of a compound is the time (units in min or h) ittakes for the plasma concentration or the amount of compound inthe body to decrease by 50%. For compounds with plasmaconcentration versus time profiles that decline in a mono-phasicmanner (1 compartment model), half-life is readily determinedand the relationship between t1/2, CLs and V is represented as:

t1=2 ¼ 0:693 � ðV=CLsÞ (9)

As CLs increases, t1/2 decreases; as V increases, t1/2 increases.Thus, t1/2 is a secondary parameter that is a function of the CL and V

of the drug. For compounds which exhibit multi-exponential (e.g.,bi- or tri-phasic) patterns of decline (2- and 3-compartmentmodels, respectively), two or more half-lives may be calculated.The terminal or elimination t1/2 of a compound refers to the time ittakes for its concentration in plasma to decrease by half during theterminal log-linear phase (represented as a straight line on a semi-logarithmic plot) of the plasma concentration versus time profile.This may be estimated by curve-fitting, in which at least 3 datapoints during the terminal phase are used (over which the timeinterval is greater than at least twice the estimated t1/2). The slope(�lZ/2.303) of the terminal phase of the Log plasma concentration


versus time curve is used to determine the terminal t1/2:

t1=2 ¼0:693

lZ(10)

It should be noted that the terminal t1/2 of a compound,determined using a protocol in which the blood sampling period istoo short and which neglects to consider the appropriate timepoints can lead to a significant underestimate of the true t1/2. Assaysensitivity may also make it difficult to accurately estimate t1/2,especially when the dose administered is relatively low or thecompound is poorly bioavailable. The latter is a commonoccurrence in early drug discovery programs, where bloodsampling protocols are arbitrarily determined in order to facilitaterapid PK screening.

3.2.2. Compartmental analysis

3.2.2.1. Intravenous administration. The compartmental approachviews the body as a series of pharmacokinetically distinctcompartments, each of which represents a combination of varioustissues and organs which are in rapid equilibrium with each otherwith respect to concentrations of the compound. Compounds mayexhibit 1-compartment (e.g., mono-exponential) or multi-com-partment (e.g., bi- or tri-exponential) plasma concentration versus

time profiles. All concentration versus time profiles will appearcurvilinear when plotted on a linear scale. Thus, in order todetermine whether a compound exhibits mono- or multi-exponential decay, a semi-logarithmic plot of plasma concentra-tion versus time will appear as a single straight line (1-compartment or mono-exponential decay) or as a bi- or triphasicdecline with a straight line during the terminal phase (Fig. 1). Forcompounds which exhibit a mono-exponential decline on a semi-logarithmic scale, the body appears to behave as one pharmaco-kinetically homogeneous compartment for the compound. Afteri.v. administration, the blood/plasma concentrations of thecompound (C(t)) at time t may be represented as:

CðtÞ ¼ Doseiv

V� e�k�t (11)

where V is the volume of distribution, k is the first orderelimination rate constant (units of time�1, e.g., min�1), andDoseiv/V is equal to C0. Eq. (11) may be converted to the commonlogarithm (base 10) as follows (Fig. 1A):

log CðtÞ ¼ log C0 �k

2:303� t (12)

The systemic clearance (CLs) and t1/2 can be estimated for acompound exhibiting mono-exponential decay as:

CLs ¼ k � V (13)

t1=2 ¼0:693

k(14)

For an i.v. administered compound with 1-compartmental PKbehavior, tissue concentrations will decline in parallel with plasmaconcentrations (same t1/2), with the difference in concentrationsreflecting the differences in the magnitude of accumulation in eachtissue.

Most compounds exhibit a multi-exponential decline in theirplasma concentration versus time profile on a semi-logarithmicscale, as long as samples are collected during the distributionphase(s) in addition to the elimination phase. There are 3 differenttypes of 2-compartment models and 7 types of 3-compartmentmodels, depending on the compartment responsible for compoundelimination. However, unless experimental evidence indicatesotherwise, it is generally assumed that compound elimination

takes place from the central compartment, since most compoundsare eliminated by the liver and/or kidneys and both of these organsare highly perfused with blood. Without specifically describing the2-compartmenal model and the associated rate constants, plasmaconcentrations of a compound exhibiting bi-exponential decayunder linear conditions on a semi-logarithmic scale following i.v.administration, can be described as follows [18,21]:

CðtÞ ¼ A � e�a�t þ B � e�b:t (15)

where A, B, a and b are obtained from the intercepts and slopes ofthe plasma concentration versus time curve by curve fitting withthe method of residuals or by nonlinear regression analysis usingcomputer software (Fig. 1B). Thus, A is the Y-intercept of thedistribution phase (with a slope, a) and B is the Y-intercept ofthe elimination phase (with a slope, b). C0 in this case is equal tothe sum of A + B and the volume of distribution of the centralcompartment, Vc, is equal to Doseiv/(C0). The steeply decliningphase immediately after administration is primarily due to rapiddistribution of the compound from plasma to well perfused organs,whereas the terminal straight line, which is shallower, is primarilydue to elimination of the compound from the body.

Similarly, for compounds which display a tri-exponentialdecline profile following i.v. administration:

CðtÞ ¼ A � e�a�t þ B � e�b�t þ C � e�g�t (16)

where A + B + C = C0, a and b represent the rate constants for twodistribution phases (b is smaller than a) or alternatively onedistribution and one faster elimination phase and g represents therate constant for the terminal elimination phase (g is the smallestof the rate constants).

3.2.2.2. Extravascular administration. Following extravascular ad-ministration of a compound, compartmental models become morecomplicated because now the compound absorption rate constant(ka) needs to be included in the model. In the simplest of cases (a 1-compartment model or a compound exhibiting mono-exponentialdecay), ka can be estimated by the method of residuals or curve-fitting. The equation most often used is based on a 2-compartmentmodel (in the case of oral dosing the intestine is the firstcompartment and the rest of the body is the second compartment),with elimination occurring from the second compartment:

CðtÞ ¼ ka � F � Dosepo

V � ðka � kÞ � ðe�k�t � e�ka �tÞ (17)

where Dosepo represents the oral dose and F, V and k (thebioavailability, volume of distribution and elimination rateconstant, respectively) must be estimated from an i.v. dose(assuming the compound exhibits mono-exponential decay). Forthe latter model, the assumptions are that absorption andelimination follow first order kinetics, and absorption occurs ina homogeneous manner.

The maximum concentration (Cmax) after extravascular admin-istration which occurs at the time at which it is observed (tmax), canalso be derived from Eq. (18):

Cmax ¼F � Dosepo

V� e�k�tmax (18)

and

tmax ¼lnðka=kÞka � k

(19)

It should be evident from Eqs. (18) and (19) that both Cmax and tmax

can be affected by ka (compound absorption) as well as by k

(compound elimination). This also indicates that either step

Fig. 1. Plasma concentration versus time profiles following i.v. administration on a semi-logarithmic scale for a compound which exhibits (A) a one compartment model and

(B) a two compartment model.


(absorption or elimination) of a compound can be rate-limiting inthe overall elimination process.

3.2.2.3. Flip-flop kinetics. In general, the elimination rate of acompound after oral administration is rate-limiting in thedisposition of the compound (ka� k, i.e. absorption is a fasterprocess than elimination). In the latter case where absorption maybe much faster (ka� 3 � k), the terminal elimination t1/2 will besimilar to that after i.v. administration and the true elimination t1/2

can be estimated following non-parenteral administration. How-ever, in some instances, absorption may be the rate-limiting step inthe overall disposition of a compound (k � 3 � ka), and thuscompound absorption becomes the rate-limiting step in the overallelimination of the compound. As a result, the t1/2 value followingoral administration is longer than that following i.v. administra-tion. This occurrence is called ‘‘flip-flop kinetics’’ [22].

3.2.2.4. Hepatobiliary disposition and bioavailability. CytochromeP450 (CYP) enzymes and transporters expressed in the liver playimportant roles in compound clearance and oral bioavailability.Lipophilic molecules are usually biotransformed into more polar orwater-soluble metabolite(s) by Phase I enzymes followed by PhaseII conjugation. Transport of substrates through the hepatobiliarysystem is facilitated by the polarized nature of hepatocytes, whichhave distinct sinusoidal (basolateral) and canalicular (apical)membranes. The basolateral transport proteins include Na+-taurocholate co-transporting polypeptide (NTCP), organic aniontransporting polypeptides (OATPs), multidrug resistance associat-ed proteins (MRPs), and organic anion and cation transporters(OATs and OCTs) [23]. Canalicular transport is mediated predomi-nantly via P-glycoprotein (P-gp), multidrug resistance protein 2(MRP2), the bile salt export pump (BSEP), and the breast cancerresistance protein (BCRP) [23]. Basolateral transporters areresponsible for translocating substrates across the sinusoidalmembrane into hepatocytes, whereas active canalicular transpor-ters are responsible for the biliary excretion of compounds andmetabolites [24].

Functional changes in these enzymes and the uptake and effluxtransporters will greatly affect the clearance and hepaticavailability of compounds and thereafter their oral bioavailability.Oral bioavailability is a function of FH (hepatic availability), FG (gutavailability), FL (lung availability) and Fabs (fraction absorbed), asgiven in Eq. (20):

F ¼ Fabs � FG � FL � FH (20)

where FH is defined as:

FH ¼ 1 � CLH

Q(21)

where Q represents the hepatic blood flow rate (units of volume/time, e.g., mL/min) and CLH is the hepatic clearance. CLH and theoverall hepatic intrinsic clearance (CLint,all) can be expressed withthe following expressions (see Section 7):

CLH ¼ Q �f u;b � CLint;all

Q þ f u;b � CLint;all(22)

CLint;all ¼ PSinf �CLint

PSeff þ CLint(23)

where PSinf and PSeff represent the basolateral uptake intrinsicclearance and the sinusoidal efflux intrinsic clearance, respective-ly, CLint is the sum of the metabolic intrinsic clearance (CLmet) andthe biliary efflux intrinsic clearance and fu,b is the fraction ofunbound compound in blood.

Based on Eqs. (21)–(23), hepatic availability is determined by Q,PSinf, PSeff, CLint and fu,b. Uptake clearance, metabolic clearance andblood flow rate can each be rate-limiting steps in the overallhepatic elimination and thus are major parameters influencing thehepatic clearance of a compound and furthermore its oralbioavailability.

4. Pharmacokinetics scaling from animals to humans

4.1. Allometric scaling

PK scaling is the discipline of predicting human PK based onpreclinical data obtained from one or more animal species.Allometric scaling is based solely upon differences in body size[25], without necessarily examining the underlying mechanism(s).Empirical observations indicate that many physiological param-eters change as a function of size and the relationship can bedescribed as [26]:

Y ¼ a � Wb (24)

where Y is the physiological parameter that is being measured (e.g.,clearance or volume of distribution), W is the weight of the animal(or another measure of size such as body surface area) and a and b

are constants. When a PK parameter is available from one species,the allometric equation can be used to predict the value of theparameter in humans:

Yhuman ¼ Yanimal �Whuman

Wanimal

� �b

(25)

The value of b has been observed to often be related to the type ofparameter that is being measured: (1) biological time (t1/2 orMRT) = 0.25, (2) distribution volume = 1.0, and biological rate(blood flow, renal and hepatic CL) = 0.75 [27].


If PK data in multiple species is available, a plot of log Y versus

log W results in an intercept of log (a) and a slope of b, as shown inthe equation below:

log Y ¼ logðaÞ þ b � logðWÞ (26)

In this case, the value of b is derived from compound specific dataas opposed to the predefined values of b when scaling is based ondata from a single species. Not surprisingly, multiple speciesscaling is far more reliable than single species scaling. However,allometric scaling sometimes fails in the prediction of PKparameters, due to species differences in factors such asmetabolism and plasma protein binding. An improvement in theprediction of PK in humans can be obtained by using in vitro

metabolism data from different species to adjust the PKparameters obtained from allometry [28].

4.2. Physiologically based PK (PBPK) modeling

Another method for PK prediction in humans is the physiologi-

cally based PK (PBPK) modeling approach, which is based on actualphysiological, anatomical and biochemical factors important incompound disposition [29]. These include organ blood flow ratesand size, tissue and fluid volumes, blood to plasma and tissue toplasma compound concentration ratios, protein binding andmetabolizing enzyme and transporter activities. The applicationof PBPK models has been somewhat limited due to theirmathematical complexity and the requirement for large amountsof preclinical (in vitro and in vivo) data [30]. Commercial PBPKpackages have become available and strategies for the applicationof PBPK have been published [31–33], making these models moreattractive.

5. Absorption and permeability

5.1. Intestinal absorption and permeability

The key factors controlling oral compound absorption are thesolubility/dissolution of the compound in the GI tract and thepermeability of the compound across the intestinal membrane.The physicochemical properties of the compound (e.g., solubility,hydrophobicity, ionization, MW) and the physicochemical andbiological properties of the GI tract jointly determine the rate andextent of compound absorption and ultimately affect compoundbioavailability following oral administration.

5.1.1. Role of intestinal permeability and transporters

Intestinal epithelial cells, the major cell type governing theabsorption of orally administered compounds, constitute aphysical as well as functional barrier. Compounds may traversethe barrier through paracellular or transcellular pathways. Theparacellular pathway is regulated by apical intercellular tightjunctions [34]. Small pores in the tight junctions allow thepermeation of small and hydrophilic molecules that are not able topermeate through the transcellular pathway. The transcellularpathway is predominantly mediated by the ability of highlylipophilic compounds to diffuse across the apical (luminal) andbasolateral (blood side) membranes, as well as by the presence ofspecific transporters or channels located on these membranes. Formost lipophilic compounds, the transcellular pathway is thepredominant pathway of absorption. The intestinal luminalmembrane contains several uptake transporters, such as the OATPfamily, the peptide transporter 1 (PEPT1), the apical sodiumdependent bile acid transporter (ASBT), the monocarboxylic acidtransporter 1 (MCT1), and the ATP-dependent efflux transporters,e.g., MRP2, BCRP and P-gp. The basolateral membrane of intestinal

epithelia contains OCT1, the organic solute transporter (OST), andthe multidrug resistance protein 3 (MRP3) [35].

Permeability assessments help to identify potential drugcandidates that are likely to pose challenges during preclinicaland clinical development. Poor intestinal permeability leads tolimited absorption. Generally, if a compound achieves 90% orgreater oral absorption, it is considered highly permeable (e.g.,propranolol or metoprolol). Compounds that display 50% or lessoral absorption are considered poorly permeable (e.g., ranitidineand atenolol) although this does not preclude their ability tobecome drugs. Compounds with extremely poor permeability arelikely to have limited in vivo absorption.

There are several in vitro assays that are available for apreliminary assessment of intestinal absorption (as well aspermeability across other membrane barriers) and which helpinform the conduct and interpretation of in vivo experiments. Themost commonly used assays include solubility, log P and log D andCaco-2 permeability assays [10].

5.1.2. Solubility

Solubility is a key parameter for the dissolution of compoundsfollowing oral administration, but it may also complicate otherroutes of administration (e.g., i.v.) if the compound comes out ofsolution once it is administered. For oral absorption, thecompound must be present in the aqueous solution of the GItract, except when absorption occurs through pinocytosis orlymphatic pathways. Poor aqueous solubility can also causeproblems in many in vitro assays, leading to high variability and/orpoor reproducibility. As a result, knowing the solubility limita-tions of a compound is important when characterizing its PKproperties. In addition, screening assays to determine thesolubility of novel compounds have been developed. The standardshake-flask method for determining the solubility of a compoundinvolves adding an excess quantity of solid material to a volume ofbuffer at a set pH [36]. The saturated solution is agitated untilshake-flask equilibrium is attained. Following separation byfiltration or centrifugation, the compound in solution is analyzedand quantified by UV spectroscopy or HPLC. However, rapidmethods reliant on turbidity or filtration for the removal of theinsoluble solids prior to spectroscopy have been developed tomeasure solubility. Since ionization can also govern solubility,measurement of the pKa values of sparingly soluble compoundsmay also be useful [10].

5.1.3. Log P and log DAs a measure of compound-membrane interaction, lipophilicity

is one of the most important physicochemical parameters inpredicting and interpreting membrane permeability. As a measureof the lipophilicity, the partition coefficient (P or log P as it isgenerally expressed) of a compound is defined as the ratio of theconcentrations of the un-ionized compound in the phases of 2immiscible solvents: organic (1-octanol) and aqueous (water) atequilibrium. c log P is a mathematically calculated estimate of log P

[10]. The distribution coefficient (D or log D) is defined as the ratioof ionized and unionized compound in organic (1-octanol) andaqueous (buffer, pH 7.4) phases at equilibrium. Since log P refersonly to the equilibrium of un-ionized compound between phases,it is pH-independent, whereas log D is pH-dependent because thepH and the pKa of the compound will affect its ionization inthe aqueous phase. Thus log D is the appropriate descriptor for thelipophilicity of ionizable compounds, whereas log P describeslipophilicity for neutral compounds only. In general, a value oflog D7.4 between �0.5 and 2 is considered to be optimal for the oralabsorption of compounds. Compounds with log D7.4 below �0.5suffer from poor permeability and those with values above 2 sufferfrom poor aqueous solubility [37].


5.1.4. Caco-2 permeability assay

The Caco-2 cell permeability assay has been widely adopted forunderstanding the GI compound absorption process as well as forutilizing as a relatively rapid in vitro screening tool in support ofdrug discovery within the pharmaceutical industry [38]. Caco-2cells are derived from a human colon adenocarcinoma andspontaneously differentiate after reaching confluency, forming apolarized monolayer with a well-defined brush border on theapical surface and tight junctions between cells, and this usuallyoccurs over three weeks of culture. Caco-2 cell monolayersmorphologically resemble small intestinal epithelial cells andexpress typical small intestinal microvillar hydrolases and some ofthe drug transporters such as P-glycoprotein (P-gp), which isresponsible for the efflux of substrates. Caco-2 cell monolayers areusually cultured on semi-permeable plastic supports that are fittedinto the well of multi-well culture plates and provide a vectorialtransport system. Transport studies may be performed in the apical(A, luminal) to basolateral (B, blood side) direction (the direction ofabsorption) by placing a compound solution in the apical side andcollecting samples from the basolateral side at different incubationtime points. Studies may also be conducted in the B to A direction(the direction of intestinal excretion). The side of the epithelial cellwhere the compound is added is referred to as the donor side,whereas that on the opposing side of the monolayer is referred toas the acceptor or receiver side. The apparent membranepermeability coefficient (Papp, expressed as cm/s) of a compoundin a Caco-2 cell assay, determined in either direction, is calculatedas:

Papp ¼dA=dt

SA � C0;donor(27)

where dA/dt (ng/s) is the initial slope of the cumulative amount (A)of compound in the acceptor compartment (volume of acceptorcompartment � compound concentration in acceptor compart-ment) over time (Dt), C0 is the initial concentration (at t = 0) in thedonor compartment (ng/mL which is equivalent to ng/cm3), and SAis the surface area of the filter (cm2). It is important to maintain‘‘sink conditions’’ over the sampling interval and the recovery ofthe compound measured at the end of the experiment should besufficiently high. If the transport of the compound is mediated bynet passive diffusion, Papp estimates in the A to B and B to Adirections should be equal (Papp,A!B/Papp,B!A � 1). If a compound issubject to net active influx or efflux, then the Papp values measuredfrom A to B will be larger (Papp,A!B/Papp,B!A > 1) or smaller(Papp,A!B/Papp,B!A < 1) than those measured from B to A,respectively.

The utility of this model to rank order a large number ofcompounds for their potential for absorption has been demon-strated [39,40], however, comparison of the absolute permeabilitycoefficients of compounds between laboratories has been difficult.This may be attributed to differences in culture conditions, passagenumber and the composition of the cell subpopulation. As a result,it is important to include in each assay at least two referencecompounds, one of which is poorly permeable and is absorbed bythe paracellular route (e.g., mannitol) and one which is highlypermeable and is absorbed by the transcellular route (e.g.,propranolol). The absorption potential of a compound should beassessed by comparison to the low and high permeability referencecompounds included in each assay. In addition, if the goal is also toidentify potential P-gp substrates, a known P-gp substrate e.g.,digoxin, should be included as a reference. The efflux ratio (ER), i.e.the ratio of the B–A and A–B permeability coefficients, should begreater than 2 in order for a compound to be considered as being apotential substrate of this transporter. Both the Papp values and theER values can differ considerably between laboratories. For

example, the ER of digoxin varied between 8 and 102 among 11laboratories participating in a P-glycoprotein Inhibitory PotencyWorking Group [41]. The ER may be used to determine possibleactive transport in other cell lines, especially in some of thetransporter gene knockin or knockout cell models. Single- ordouble-transfected cell models, such as the MDCK-MDR1, MDCK-OCT1, MDCK-BCRP, MDCK-OCT1-MATE1 cells, and single- ordouble-knockout Caco-2 cell models have been developed toidentify substrates of transporters [42–44]. The concentration oforganic solvent used in permeability studies may also affect thevalues of Papp. In general, less than 1% (v/v) acetonitrile, methanol,or DMSO can be tolerated. Sufficient agitation is also necessary inorder to minimize the un-stirred water layer. The Caco-2 cell lineexpresses the CYP3A4 enzyme to a very low extent, but the enzymecan be induced by incubation with Vitamin D3 [45].

Other animal tissue-based methods, such as the everted gut,intestinal segment, and isolated membrane vesicles, are also usedfor permeability studies [46]. However, these methods are laborintensive and the viability of the excised tissues has been an issue.The extrapolation of in vitro data to the animal or human in vivo

should be performed with caution because the effect of physio-logical factors such as gastric emptying time, gastrointestinaltransit rate, and gastrointestinal pH, are not reflected in most of thein vitro systems.

5.2. Brain permeability and penetration

The brain is separated from the systemic circulation by twomain barriers, the blood–brain barrier (BBB) and the blood–cerebrospinal-fluid barrier (BCSFB) [47]. The BBB is composed ofcerebral endothelial cells that differ from those in the rest of thebody by the presence of extensive tight junctions, an absence offenestrations and sparse pinocytotic vesicular transport. TheBCSFB is formed by a continuous layer of polarized epithelialcells that line the choroid plexus. The BBB and BCSFB expresstransport proteins that actively restrict entry of substances fromblood and/or remove those molecules from the brain. Thetransporters at the luminal side of the BBB include effluxtransporters, such as P-gp, MRP1, MRP2, MRP4, and BCRP, andinflux transporters, such as OATP and MCT1 [48,49]. Transporterswhich mediate intracellular uptake at the abluminal membrane ofthe BBB, such as Oatp and Oat, are thought to act in concert withefflux transporters at the luminal membrane, thereby enhancingthe extrusion of drugs from the brain. There are large dissim-ilarities between the BBB and the BCSFB regarding the expressionof transporters. At the BCSFB, MRP1, MRP4, OAT and OATP2 arelocated at the basolateral side, and OATP1 and OAT1 are situated atthe apical side [50] while the localization of P-gp in the BCSFB iscontroversial.

Two parameters, the brain to plasma concentration ratio (Kp)and BBB permeability (quantified as the permeability surface areaproduct (PS) or the influx clearance (CLin with units of volume/time/g brain, e.g., mL/min/g)) had been typically used to describebrain penetration. However, Kp for the prediction of brainpenetration has little value, since it does not take into consider-ation the differences between the unbound concentrations of thecompound in the plasma and brain which occur as a result of theBBB [51]. PS and CLin indicate the rate of transport of a compoundinto the BBB. In situ or in vivo methods, such as the brain uptakeindex (BUI; also called the in vivo carotid artery injectiontechnique), the in situ brain perfusion method and quantitativemicrodialysis can be used to measure the CLin. However, unlikeintestinal permeability, the rate of BBB transport (which isdependent on the BBB permeability of the compound) is a lessimportant parameter for prediction of brain penetration than theextent of compound penetration. A low BBB permeability indicates


slow transport into the brain, but it may also indicate slow removalfrom the brain for a compound that has a relatively high brainpenetration. An example of compound with low BBB permeabilityand good brain penetration, morphine-6-glucuronide (M6G), isdiscussed below.

The partition coefficient between unbound compound in brainextracellular fluid (ECF) and unbound compound in plasma atsteady-state (Kp,uu) can be used to describe the extent of brainpenetration and also can demonstrate whether net diffusion or netactive efflux or influx is present or not. An accurate in vivo methodfor determining Kp,uu is quantitative microdialysis [52]. Since thelatter method is labor intensive and difficult for lipophiliccompounds, the unbound brain concentration of a compoundbased on the total brain concentration and unbound fractiondetermined in brain homogenate or from the brain slice uptakemethod is often used to calculate Kp,uu. The unbound brainconcentration determined in this manner, however, does notalways accurately represent the unbound compound concentra-tion in the ECF, and thus may result in erroneous estimates of Kp,uu.

An example which illustrates the importance of Kp,uu for theprediction of brain penetration is M6G, which has a very low brainpermeability clearance of 0.11 mL/min/g brain, and would beconsidered to be unable to penetrate the BBB. However, its Kp,uu is0.29 and M6G is pharmacologically active in the CNS [53].

6. Distribution and protein binding

6.1. Volume of distribution (V or Vd)

The extent of compound distribution and the amount ofcompound in the body necessarily affect the compound concen-tration in plasma. The extent of distribution of a compound isassessed by its volume of distribution (V), although V does notrepresent a real physiological volume. The real distributionvolume of a compound is related to body water and cannot exceedthe total body water (�58% of body weight in humans or 600 mL/kg in an average adult of 70 kg, 167 mL/rat depending in the strain[54]). Some compounds such as Evans blue, indocyanine greenand dextran which are essentially confined to the circulatingplasma after i.v. administration, can be used to estimate plasmavolume (47.9 mL/kg in human, 31.3 mL/kg in rat), whereas lowMW water soluble substances such as ethanol and a few of thesulfonamides, distribute uniformly throughout the body waterand can be used to estimate the volume of body water. V is definedas a proportionality constant between the amount of compoundpresent in the body (A) and the concentration (C) of compound inthe body fluid where it is being measured (e.g., plasma) at anygiven time (t):

VðtÞ ¼ AðtÞCðtÞ (28)

As already indicated, if a compound is confined to the plasma, itsV(t) will approximate the actual plasma volume and may notchange significantly with time. If a compound diffuses from plasmato other tissues, the V(t) of the compound changes over time afterdosing and can be significantly greater than the total plasmavolume.

There are three different volume of distribution terms that maybe determined following i.v. bolus administration of a compound.The simplest is the volume of distribution of the centralcompartment (Vc). This is estimated by dividing the i.v. dose(Doseiv) by C0, the estimated plasma concentration at time zero,under the assumption that the compound administered into thesystemic circulation is instantaneously distributed into plasmaand into highly perfused organs before distributing (equilibrating)

into other organs/tissues.

Vc ¼Doseiv

C0(29)

The volume of distribution at steady-state (Vss), whichrepresents the volume in which a compound would appear tobe distributed during steady-state if the compound existedthroughout that volume at the same concentration as that inthe measured fluid (plasma), was introduced in Eq. (6). The termsteady-state implies that the rate of change in the amount ofcompound in the body is zero, which is achieved, for example,when the rate of a continuous infusion of a compound is equal to itsrate of elimination (i.e. the plasma compound concentration isconstant over time).

The third V is that at pseudo-distribution equilibrium (VlZ or Vb

if the compound exhibits bi-exponential decay), and it is estimatedby dividing the CLs by the rate constant determined from theterminal elimination phase (lZ or b) after i.v. dosing:

VlZ¼ CLs

lZ¼ Doseiv

lZ � AUCiv(30)

There are, not surprisingly, differences between the 3 volumeterms, and one should be cognisant of which term is used to makepredictions of the PK properties of a compound. Following an i.v.administration, compounds, in principle, instantaneously dispersewithin plasma, red blood cells and rapidly distributing organs,thus, the Vc cannot be smaller than the volume of plasma withinthe body. Vc is useful as a parameter when the compound exhibits amono-exponential decline in plasma concentrations (1-compart-ment model). However, the majority of compounds will furtherdistribute into more slowly equilibrating organs/tissues and will asa result exhibit a bi- or multi-exponential profile. At a certain timepoint (tss), the rate of change of the amount of the compound in thetissues becomes zero, and the apparent volume of distribution ofthe compound equals Vss. Vss is important as it describes onlydistribution, i.e. it reflects the extent of compound distributionfrom the plasma pool into organs/tissues which has physiologicalrelevance. At equilibrium, the distribution of a compound withinthe body depends on binding to blood cells, plasma protein andtissue components. Only unbound compound is capable ofentering and leaving the plasma and tissue compartments. Thus,Vss can be expressed as follows:

Vss ¼ Vp þ V t �f u;p

f u;t

(31)

where Vp and Vt are the physiological volumes of plasma and thetissue (the extravascular volume, including the erythrocytevolume) and fu,p and fu,t are the fractions unbound in plasma andtissue (including erythrocytes), respectively. A compound that ishighly plasma protein bound (i.e. low fu,p) will generally exhibit asmall volume of distribution (e.g., the weakly acidic drug,tolbutamide, which has a V of 0.112 L/kg and a fu,p of 0.093 inhuman [55]), whereas one that is extensively bound to tissuecomponents (low fu,t) will exhibit a Vss that can be much greaterthan the physiological volume of the body (e.g., the lipophilic,weakly basic drug, chloroquine, which exhibits a V of 200–800 L/kg in human [56]). After tss, V(t) continues to increase over timeuntil the terminal exponential phase is achieved. The V termwhich is derived from this phase is VlZ

. Unlike Vss, however, VlZ

varies when the rate constant for compound eliminationchanges, even when there has been no change in the distributionspace [57].


6.2. Plasma protein binding

The plasma proteins that bind a compound (and its metabolites)include albumin, a1-acid glycoprotein (AAG), lipoproteins and a-, b-and g-globulins, however, albumin and AAG are the two majorproteins in plasma and are responsible for the binding of mostcompounds [58]. Albumin is the most abundant (�4% w/v) plasmaprotein, has multiple hydrophobic binding sites and appears to havea higher binding affinity for acidic compounds. In contrast, AAG ismuch less abundant in plasma (<0.1% w/v) and it has one bindingsite per molecule. AAG binds drugs primarily by nonspecifichydrophobic interactions and in general the binding affinity forAAG is much higher than that for albumin. It primarily binds basiccompounds, although the latter also bind to albumin to a significantextent. The extent of protein binding of a compound can becompound- or protein-concentration dependent, based on theaffinity and capacity of the plasma protein. The extent of compoundbinding to plasma proteins can also vary considerably amongdifferent species, whereas, a similar extent of tissue binding has beenreported among different species [54,59,60]. The effects of speciesdifferences in plasma protein binding can be demonstrated forzamifenacin. Based on its total plasma concentration, oral clearanceof this compound in human (0.6 mL/min/kg) was determined to besubstantially lower than that in rat (61 mL/min/kg) and dog (26 mL/min/kg) [61,62]. As a result, the dose normalized Cmax in human was,respectively, 74 and 40 times that in rat and dog. The unboundfraction in plasma (fu,p), however, was 20-fold lower in human(0.01%) than in rat (0.2%) and 10-fold lower than in dog (0.1%), andthus unbound Cmax values in human were only 8 and 4-fold higherthan rat and dog, respectively. Since the correlation betweenpharmacological response in animals and humans was consistentwith exposure of the unbound compound, without consideringdifferences in plasma protein binding between species, the PD of thecompound could not have been rationalized.

The fraction unbound in plasma (fu,p) is calculated as the ratio ofthe unbound plasma concentration (Cp,u) to the total plasmaconcentration (Cp, total):

f u;p ¼Cp;u

Cp;total(32)

There are several in vitro methods for measuring the unboundfraction in plasma including equilibrium dialysis, ultrafiltration,ultracentrifugation, microdialysis, solid phase microextraction andhigh performance frontal analysis [63]. Equilibrium dialysis(considered the standard method for binding measurements)and ultrafiltration are the two most commonly used methods.

6.3. Tissue binding

The need to determine unbound tissue concentrations ofcompounds, especially at the site of clearance and/or action isincreasingly being recognized. Compared to plasma protein binding,much less is known about tissue binding or the sequestration ofcompounds, since reliable methods for estimating binding to tissuecomponents in vivo are experimentally more difficult to perform.Generally, the term ‘‘non-specific binding’’ is used which includeshydrophobic interactions of neutral compounds with neutral lipidsand phospholipids and the interaction of basic compounds withacidic phospholipids (such as phosphatidylserine) present in cellularmembranes, however, binding components such as ligandin andDNA have been reported [64–66]. Furthermore, the lysosomalsequestration of basic lipophilic compounds (e.g., thioridazine,perazine and propranolol) has been recognized as important fortheir tissue distribution in addition to non-specific binding tocellular membranes [67–69], especially when the lysosomes can act

as a depot for compound release over time. To predict the impact of acompound on an extracellular or intracellular target, the unboundcompound concentration in the extracellular or intracellular fluid,respectively, must be estimated. Obtaining unbound extracellularfluid (ECF) concentrations of a compound for therapeutic targetswhich reside in organs which have leaky capillary membranes (e.g.,hepatic sinusoids) is easier than in an organ such as the brain whichis protected by the BBB. Obtaining unbound intracellular concen-trations of a compound is even more challenging. Microdialysis isthe gold standard in vivo technique for measurement of unboundECF concentrations of a compound within a localized region of tissue(e.g., striatum of the brain), however, it is relatively labor intensiveand problematic for lipophilic compounds due to their poor recoveryas a result of binding to the dialysis membrane and/or tubing [52]. Insome instances, compound concentrations in cerebrospinal fluid(CSF) have been utilized as a surrogate for unbound brain ECFconcentrations. To date, the validity of such measurements remainscontroversial [70,71]. The most commonly used in vitro methods forassessing non-specific tissue binding are equilibrium dialysis andultrafiltration of homogenized tissue. Homogenization disrupts thetissue and is problematic for basic drugs which are sequestered intolysosomes and other organelles. A superior method may be thetissue slice uptake method due to the preservation of cellularstructures [72]. Regardless, the fraction unbound in tissue (fu,t)estimated from an in vitro method is used to correct the totalconcentration of compound measured in whole tissue followingdosing of the drug. Blood and whole tissue samples are commonlycollected at designated time points from a group of animalsfollowing euthanasia. It should be noted that the use of CO2

inhalation for euthanizing animals can significantly affect thedistribution of lipophilic basic drugs [73]. CO2 euthanasia resulted inan increase in plasma concentrations and a slight decrease in brainconcentrations of basic compounds, e.g., raloxifene, in mice, relativeto two other methods of euthansia. This suggests that as a result ofacidification of the blood by CO2, rapid redistribution of the basiccompounds from lysosomes may have occurred. No speciesdifferences in non-specific tissue binding have been reported [59].

7. Clearance (metabolism and excretion)

Elimination generally refers to the irreversible removal of acompound or its metabolite(s) from the body, primarily by tworoutes: metabolism and excretion. As already mentioned, com-pound metabolism generally involves a chemical or enzymaticconversion of the parent compound into one or more metabolites,which are readily excreted and excretion is mainly facilitated byrenal or biliary clearance. Again, clearance reflects the ability of thebody to eliminate the compound (CLs) or a single organ to eliminatethe compound (organ clearance), without identifying the individualelimination process involved. Estimation of CLs is essential fordetermining the efficacious duration of action and concentration ofthe compound in the body, and for the avoidance of toxic effects.

7.1. Systemic clearance (CLs)

Systemic clearance (CLs) is defined as the volume of blood orplasma cleared of compound from the body per unit of time. CLs

can be estimated from the area under the blood or plasmacompound concentration versus time curve extrapolated to infinity(AUC0–1) following i.v. bolus administration of a compound:

CLs ¼Doseiv

AUCiv0�1

(33)

where Doseiv is the dose administered. CLs can also be estimatedfollowing administration via routes other than i.v. injection (e.g.,


p.o.) as long as the systemic bioavailability (F) following that routeof administration is known:

CLs

Fpo ¼Dosepo

AUCpo0�1

(34)

where Dosepo, Fpo and AUCpo0�1 are the dose, F and AUC0–1

following an oral dose. The value of CLs/F is reported if the systemicbioavailability of the compound is not known. CLs may also bedetermined following a continuous i.v. infusion of the compoundfrom the infusion rate (k0) and steady-state compound plasmaconcentration (Css):

CLs ¼k0

Css(35)

For repetitive oral administration, CLs is also expressed as afunction of F (i.e. CLs/F

po).Clearance may be calculated as the product of k and V for a

compound which exhibits a mono-exponential plasma concentra-tion versus time curve (assuming a 1-compartment model), wherek and V are the elimination rate constant and volume ofdistribution, respectively. In contrast, the clearance estimatedfrom the area under the plasma or blood compound concentrationversus time curve is predominantly model independent.

7.2. Organ clearance

Organ clearance reflects the ability of an organ to remove thecompound from the blood and is defined as:

CLorgan ¼ Q � Cin;ss � Cout;ss

Cin;ss

� �(36)

Cin,ss and Cout,ss are the compound concentrations in the bloodentering and leaving the organ at steady-state, and Q is the bloodflow rate to that organ. The organ clearance is often expressed asthe blood flow rate multiplied by the extraction ratio (E) (Eqs. (37)and (38)), the latter of which represents the fraction of the amountof compound entering the organ that is extracted by the organduring perfusion. The availability of a compound after it passesthrough the elimination organ can be expressed as Forgan, whichequals 1 � E (Eq. (39)) and represents the fraction of the amount ofcompound entering the organ that is not extracted by the organduring perfusion.

CLorgan ¼ Q � E (37)

E ¼ Cin;ss � Cout;ss

Cin;ss(38)

Forgan ¼ 1 � E (39)

These three terms (CLorgan, E and Forgan) are very useful for theevaluation of the ability of an organ to clear a compound. Eq. (37)describes the effect of Q on the organ clearance, and indicates thatorgan clearance cannot be greater than the blood flow rateperfusing through the organ, since E ranges between 0 and 1. Thisapproach (Eq. (37)) has been used in physiologically-based

pharmacokinetics (PBPK) models, which are based on individualorgan or tissue clearances. The kidney and liver are the mostcommon organs involved in compound excretion and metabolism.The effect of enzymes, transporters and the fraction of unbounddrug, in addition to blood flow rate, must be considered for theestimation of hepatic or renal clearance. This enables anunderstanding of the impact of a DDI (drug–drug interaction) ordisease state on clearance.

7.2.1. Hepatic clearance

7.2.1.1. Intrinsic hepatic clearance. Enzyme kinetics and membranetransport follow Michaelis–Menten kinetics, a combination offirst- and zero-order kinetics [74]. The rate of the reaction (v) isdefined as:

v ¼ Vmax � ½SKm þ ½S (40)

where Vmax is the maximum velocity and [S] is the substrateconcentration. Km, the Michaelis constant, is defined as thesubstrate concentration when the velocity of the reaction is equalto one-half (50%) of the Vmax. The intrinsic hepatic clearance (CLint)can be calculated by the following expression:

CLint ¼Vmax

Km þ ½S (41)

CLint reflects the inherent ability of the liver to eliminateunbound compound by the activities of metabolizing enzymes andbiliary excretion in the absence of a blood flow rate limitation. Vmax

and Km represent the maximum rate and the apparent Michaelis–Menten constant of all metabolizing enzymes and transportersinvolved in biliary excretion. Eq. (41) may be used in PBPK modelsto describe the non-linear kinetics of a drug, that is, when CLint

does not equal Vmax/Km (Km� [S]).

7.2.1.2. Hepatic clearance (CLH). Hepatic clearance characterizescompound elimination based on the blood flow rate, the unboundfraction in blood (fu,b) and the CLint, as evident in the followingequation (well-stirred liver model):

CLH ¼ Q �f u;b � CLint

Q þ f u;b � CLint(42)

7.2.1.2.1. High hepatic clearance. If the CLint of a compound isgreater than 70% of the Q to the liver, the compound is generallyconsidered as having a high hepatic clearance. In this case, achange in fu,b and CLint does not affect CLH to a significant extent,whereas an alteration in Q can have a substantial effect on CLH. IfCLint is very large in comparison to Q, then Eq. (42) reduces toEq. (43):

CLH ¼ Q (43)

In this case, CLH is only dependent on Q, and independent of fu,b

and CLint. The elimination of such compounds is considered to beblood flow limited. For compounds with a high hepatic clearance,the elimination half-life and AUC are not markedly affected by achange in CLint and fu,b following i.v. or p.o. administration. Q is themain factor influencing CLH, AUC and elimination half-life. Highhepatic clearance is also responsible for high first-pass eliminationand low oral bioavailability.7.2.1.2.2. Low hepatic clearance. If CLint of a compound is lower than30% of Q, a compound is generally considered as having a lowhepatic clearance. In this case, CLH of a compound is not affected tomajor extent by changes in Q, whereas alterations in fu,b and CLint

can have a significant effect on CLH. If CLint is very small incomparison to Q, then Eq. (42) reduces to Eq. (44):

CLH ¼ f u;b � CLint (44)

In this instance, a change in CLint and fu,b will cause a proportionalchange in CLH. The elimination half-life and AUC will also changesignificantly with a change in CLint and fu,b following i.v. or p.o.

administration. The rate-limiting step is, therefore, the activity ofthe enzymes and transporters involved in compound eliminationin the liver.


7.2.1.2.3. Transporter-mediated hepatic clearance. The well-stirredmodel mentioned in Section 7.2.1.2 assumes the absence of amembrane transport barrier. By considering transporter effects onthe hepatic intrinsic clearance, the overall hepatic intrinsicclearance (CLint,all) can be expressed as follows (same equationas Eq. (23)):

CLint;all ¼ PSinf �CLint

PSeff þ CLint(45)

where again PSinf and PSeff represent the basolateral uptakeintrinsic clearance and the sinusoidal efflux intrinsic clearance,respectively and CLint is the sum of the metabolic intrinsicclearance and biliary efflux intrinsic clearance.

For highly lipophilic compounds that are not transportersubstrates, PSinf and PSeff are much larger than CLint andPSinf � PSeff, and as a result CLint,all is approximated by CLint. Thisis the case when there is no membrane transport barrier.

For substrates of transporters (especially for less lipophilicdrugs), when PSeff� CLint, CLint,all can be approximated by PSinf:

CLint;all ¼ PSinf (46)

When this is the case, the hepatic uptake becomes the rate-limiting(membrane limited) step in the overall hepatic elimination. Thetransport activity of a hepatic uptake transporter(s) is a criticalfactor in determining systemic exposure of a compound, whereasCLint does not directly reflect systemic exposure. However, it isCLint and not PSinf that determines the intrahepatic compoundconcentration. This is very important for compounds targetinghepatocytes, since in this instance, the systemic compoundconcentration does not completely reflect a change in the hepaticcompound concentration. As a result, the in vitro metabolicclearance obtained from experiments with liver microsomescannot be used to predict the hepatic intrinsic clearance, eventhough metabolism may be the predominant elimination pathway.Drugs such as pravastatin [75], atorvastatin [76] and methotrexate[77] show uptake limited hepatic elimination.7.2.1.2.4. Species differences in hepatic biotransformation enzy-

mes. The successful prediction of the PK properties of compoundsin human depends on the similarity in metabolic activitiesbetween humans and experimental animals. A difference inenzyme activities and gene expression patterns leads to speciesdifferences in hepatic metabolic activities. CLint values in rat liverfor most human CYP1A2, CYP2C, CYP2J2 and CYP3A substrates arecomparable to those in human liver (within 10-fold). Six Cyp2D6isoforms have been identified in rats, whereas only CYP2D6 occursin humans. Cyp2D15 is the major Cyp2d in dog liver, withenzymatic activities similar to human CYP2D6. Thus, for mostCYP2D6 substrates, CLint values are higher in rats (2–459-fold) andsimilar in dogs (within 10-fold) compared to those in humans. Forcompounds that are metabolized by different enzymes in differentspecies, e.g., lidocaine, which is metabolized by CYP1A2 in human[78,79] and Cyp2b1 and Cyp3a2 in rats [80], the metabolicactivities exhibit species differences. CLint values determined indog liver for human CYP1A2, CYP2J2 and CYP3A substrates werecomparable to those in human liver (within 10-fold), whereasmetabolic activities for CYP2C substrates exhibited a differencebetween human and dog [81]. Aldehyde oxidases (AOXs) oxidizearomatic aldehydes into the corresponding carboxylic acids, andheterocycles into hydroxylated derivatives. Humans and higherprimates have a single functional AOX1 gene, while rodents havefour AOXs [82]. Hence, large differences in the metabolism and PKof compounds has been found between human and rat [83].Rabbits are characterized by the presence of the same complementof AOX genes (AOX1 and AOX3) as mice and rats. Otherexperimental animals, like dogs, cats and pigs do not recapitulate

the human complement of AOX genes. Therefore, they are unlikelyto be adequate predictors of human metabolism. In contrast,current studies have demonstrated that guinea pigs and Rhesusmonkeys are more likely to be used as models to predict humanmetabolism when compounds are systemically administrated.However, when the compound is administered topically via theintra-ocular or the intra-nasal route, data extrapolation fromguinea pigs or Rhesus monkeys to human must be used withcaution [82]. Phase II enzymes also exhibit species differences. Inaddition, the rates of metabolism may differ among differentanimal species even though the biotransformation pathways arethe same [81]. The recently developed chimeric mouse with ahumanized liver may become a valuable animal model for theprediction of human compound metabolism and DDIs [84–86].7.2.1.2.5. Genetic polymorphisms. A genetic polymorphism occursif, within a population, a single gene responsible for producing ametabolizing enzyme has a variant allele with the arbitraryfrequency of 1%, which affects patient therapeutic response or themetabolism of a given compound [87]. Based on the metaboliccapacity, four groups of metabolizers can be defined: (i) poor

metabolizers (PMs, deficiencies in or no metabolism of drugs due tomutations), (ii) intermediate metabolizers (IMs, reduced enzymeactivity), (iii) extensive metabolizers (EMs, efficiently metabolizecompounds), and (iv) ultra-rapid metabolizers (UMs, increasedcompound metabolism as a result of gene amplification or overexpression). Different populations have different frequencies of thevarious metabolizers. Metabolic enzymes that exhibit clinicallyimportant genetic polymorphisms include CYP2C9, CYP2D6,CYP2C19, UDP-glucuronosyl transferase and N-acetyltransferase[88]. PMs are associated with increased plasma drug concentra-tions and corresponding adverse effects, whereas UMs have sub-therapeutic plasma drug concentrations and patients in the UMgroup are prone to therapeutic failure, when given recommendeddrug doses. Individualized drug therapy may thus be required forthose drugs which are metabolized by enzymes exhibiting geneticpolymorphism in order to minimize the potential side effects andmaximize the clinical benefits.

7.2.2. Renal clearance

Renal excretion is a major route of elimination of compoundsand metabolites from the body. Compounds eliminated by renalexcretion are water-soluble, have a low molecular weight (MW), orare slowly biotransformed in the liver. Renal elimination isdetermined by glomerular filtration, active tubular secretion,tubular reabsorption and renal metabolism:

CLR ¼ ð f u; p � GFR þ CLR;secÞ � ð1 � FRÞ þ CLR;m (47)

where CLR is the renal clearance, GFR is the glomerular filtrationrate, CLR,sec represents the tubular secretion clearance, FR is thefraction of filtered and secreted compound that is reabsorbed, andCLR,m is the renal metabolic clearance. Glomerular filtration is aunidirectional and size-selective process. Only small (MW < 500)and unbound compounds in the blood undergo glomerularfiltration. The GFR is the rate at which blood is filtered throughthe glomerulus to form urine, and this can be used to test kidneyfunction. The GFR is often measured by determining the renalclearance of a compound that is not significantly bound to plasmaproteins and is renally eliminated by filtration only, such ascreatinine or inulin. The normal GFR for humans is 125–130 mL/min and in rats is 1.3–2.3 mL/min.

Tubular secretion is an active carrier-mediated transportprocess, which occurs in the proximal tubules that are formedby epithelial cells. Organic anion uptake transporters (OAT1 andOAT3), ABC efflux transporters (P-gp, MRP4 and MRP2) and organiccation uptake and efflux transporters (OCT2, OCTN and MATE) are


all involved in the active tubular secretion process [77]. Thisprocess is capacity limited and may become saturated. Sincemembrane transport also follows Michaelis-Menten kinetics,active tubular secretion clearance is affected by renal blood flowrate, unbound fraction in plasma and intrinsic renal tubularsecretion clearance.

Tubular reabsorption occurs mainly at the distal tubulesthrough a passive diffusion process. The extent of FR depends onthe lipophilicity and ionizability of a compound and also theurinary pH. The more lipophilic and the more un-ionized acompound is, the greater its reabsorption. Uptake and effluxtransporters in the proximal tubules may also contribute to thereabsorption process [89].

Renal metabolism is a minor elimination pathway for mostcompounds; however, glucuronidation and amino acid conjuga-tion appear to play an important role in the renal clearance ofseveral drugs, e.g., zidovudine [54]. In human, renal clearancevalues can range from 0 mL/min, the normal value for glucosewhich is usually completely reabsorbed, to a value equal to therenal plasma flow rate of about 650 mL/min for compounds such asp-aminohippuric acid. Eq. (47) can be used in PBPK models fordetermining the physiological mechanisms of renal compoundelimination. After comparing the data of CLR and fu,p � GFR, onemay characterize the mechanism of CLR as net renal reabsorption(CLR < fu,p � GFR), net renal secretion (CLR > fu,p � GFR), or no netreabsorption or secretion (CLR � fu,p � GFR). If renal secretion isknown to be involved in renal elimination, especially forcompounds with a renal clearance higher than 50% of CLs, thepossibility of clinical DDIs needs to be considered, since thesecretion process is saturable and may be inhibited by co-administrated drugs.

Renal clearance may also be estimated using Eqs. (48) and (49)regardless of the route of administration:

CLR ¼DAe;urine=Dt

Cp;mid(48)

CLR ¼Ae;urine

AUC(49)

where DAe,urine refers to the amount of unchanged compoundexcreted in the urine over a designated time interval and Cp,mid isthe plasma compound concentration at the midpoint of the urinecollection interval. A plot of DAe,urine/Dt versus Cp,mid should give astraight line with a slope equal to CLR. The accuracy of estimates ofCLR using Eq. (48) depends upon the urine collection interval. It isimportant to avoid collecting urine during the distribution phasefollowing compound administration. For Eq. (49), Ae,urine is theaccumulated amount of unchanged compound excreted in theurine and AUC is the area under the plasma compoundconcentration versus time curve. For the latter equation, urinecan be collected for a finite period of time (t0 � t or t1 � t2) or fromt0 to infinity.

The accumulated amount of unchanged compound excreted inthe urine following oral and i.v. administration can be used toestimate bioavailability:

F ¼Apo

urine;0�1

Aivurine;0�1

(50)

f e ¼Aurine;0�1

Dose(51)

The conditions which have to be met for this method are that atleast 20% of a dose is excreted unchanged in the urine following i.v.administration and that the fraction of compound excretedunchanged in the urine (fe) (Eq. (51)) is constant (i.e., the

compound exhibits linear PK). Urine samples should be collectedup to 5–7 � t1/2 [90].

The accuracy of an estimate of CLR also depends upon thestability of a compound and its metabolite(s). For compounds likeketoprofen, naproxen and probenecid, the ester glucuronidemetabolites are unstable and quickly revert back to the parentcompound once excreted into the urine [91]. Therefore, if the urinesamples are not assayed immediately, the renal clearance of theparent compound will be appreciably overestimated.

7.2.3. Biliary clearance

Once a compound enters hepatocytes, it is subject to bothmetabolism and biliary excretion. Excretion of a compound intothe bile occurs through canalicular membranes surrounding thebile canaliculi of the hepatocytes. Compounds that have a MW inexcess of 500, such as glucuronide-conjugated metabolites, aremainly excreted in the bile. Biliary clearance (CLBiliary) can bedefined as:

CLBilliary ¼DAe;bile=Dt

Cp;mid(52)

CLBilliary ¼Ae;bile;0�t

AUC0�t(53)

where DAe,bile refers to the amount of unchanged compoundexcreted in the bile over a designated time interval and Cp,mid is theplasma compound concentration at the midpoint of the bilecollection interval. A plot of DAe,bile/Dt vs Cp,mid should give astraight line with a slope equal to biliary clearance. For Eq. (53),Ae,bile,0-t is the accumulated amount of unchanged compoundexcreted in bile up to time t (or infinity) and AUC0t is the area underthe plasma compound concentration vs. time curve from time zeroto time t (or infinity) following an i.v. dose.

As the bile flow is relatively slow (0.06 and 0.008 mL/min/kg inrats and humans, respectively), biliary excretion is generally not amajor route of compound elimination. Compounds that areextensively excreted in the bile include cromoglycate (unchangeddrug), morphine, and chloramphenicol (as a glucuronide conju-gate) [54]. Compounds excreted into the GI tract via the biliarypathway may be reabsorbed and returned to the systemiccirculation. For conjugated metabolites excreted into the bile,intestinal de-conjugation and reabsorption as intact compoundmay occur. This cycling is referred to as enterohepatic recirculation(EHC) which is often associated with multiple peaks in the plasmaconcentration versus time profile and a longer apparent half-life[92]. Of particular importance is that the EHC may account for largeinter- and intra-individual variability [93].

7.3. Clearance of large molecules

Larger molecules, e.g., nanoparticles, therapeutic antibodies andproteins, have different PK profiles compared to conventionalsmall molecules. Knowledge of the clearance mechanisms of largemolecules is important when selecting dose levels and doseregimens.

7.3.1. Nano-sized particles and molecules

Factors currently known to affect clearance of nanoparticles(NPs) and nano-sized molecules (NMs) (1–100 nm) includeparticle material, size, shape, surface chemistry and charge [94].Once entering into the systemic circulation, NPs and NMs mayundergo adsorption or opsonization by serum proteins and theeffective in vivo size of the particle is subsequently altered. The in

vivo diameter of the nanoparticle is referred to as the hydrody-namic diameter (HD).

Fig. 2. A general model of compound metabolism (to a primary metabolite) and

excretion, and metabolite formation and elimination.


7.3.1.1. Renal clearance. Molecules with a HD of less than 6 nm aretypically cleared through glomerular filtration, whereas those withgreater than 8 nm are not capable of being cleared via glomerularfiltration. The clearance of molecules with 6–8 nm in HD, dependsupon both size and charge of the particles. For similar sizedparticles, renal filtration is greatest for cationic compoundsfollowed by neutral compounds, while anionic molecules arethe least readily filtered [94].

7.3.1.2. Hepatic clearance. The hepatobiliary system represents theprimary route of excretion for blood–borne particles that do notundergo renal clearance. Particles enter hepatocytes via endocy-tosis and undergo enzymatic degradation and subsequently areexcreted in the bile. Independent cellular removal of particles inthe liver is through the reticuloendothelial system (RES) in Kupffercells, in which the particles are degraded and intracellularlyremoved [94].

7.3.2. Antibody drugs

IgG antibodies, e.g., belimuma, alefacep and vedolizuma [95],are cleared slowly from the body, and thereby have longelimination half-lives (7–23 days). The extended systemic expo-sure is the result of salvage recycling by the neonatal Fc receptor(FcRn) and exclusion from renal filtration due to the largemolecular size [96].

7.3.3. Peptides and proteins

Generally, proteins are broken down into amino acid fragmentsthat can be re-utilized in the synthesis of endogenous proteins. Themechanisms for elimination of peptides and proteins include:hepatic metabolism, biliary excretion and renal excretion andmetabolism. Most proteins are catabolized by proteolysis via

cellular enzymes called proteases. Based on their size andlipophilicity, peptides may enter into hepatocytes either throughpassive diffusion or carrier-mediated transport. These are subse-quently metabolized by CYP enzymes or intracellular peptidases oractively excreted into the bile. Large peptides or proteins may alsoenter into hepatocytes via receptor-mediated endocytosis. Thekidney appears to be the dominant organ for small proteincatabolism. Peptides or proteins with an appropriate size andcharge may be cleared through renal filtration. After filtration,some peptides or proteins can be actively reabsorbed by theproximal tubules and then hydrolyzed by peptidases [97].

8. Metabolite kinetics

The process of compound metabolism is, on occasion, a double-edged sword as it does not always lead to compound inactivationand detoxification. Some compounds may be converted to

Fig. 3. Consequences of a rate limitation on compound and metabolite plasma concentrat

is smaller than that of the metabolite, the metabolite declines in parallel with the parent

smaller than that of the parent compound, the metabolite declines more slowly than t

pharmacologically active metabolites, e.g., the metabolites oftricyclic antidepressants [98] and imatinib [99], and/or to toxicmetabolites, such as the metabolites of carbamazepine [100],methotrexate [101] and acetaminophen [102]. In these instances,understanding the PK of the relevant metabolite(s) is important forcharacterizing pharmacological effects and drug safety and forassessing risk.

8.1. Intravenous compound administration

In order to understand the principles relevant to metabolitekinetics, a simple metabolic scheme is depicted in Fig. 2. where ani.v. administered compound is converted to a primary metabolite,which is eliminated in urine without further metabolism, and theunchanged parent compound is also eliminated in urine. Linearkinetics and unidirectional metabolism are assumed. The metabo-lite plasma concentration (Cm) versus time (t) curve after i.v.

administration of the compound exhibits biphasic kinetics(Eq. (54)), where the two exponents are the elimination rateconstants for parent compound and metabolite [103] as follows:

Cm ¼FHðmÞ � kf � f m � Doseiv

Vm � ðkm � kÞ � ðe�k�t � e�km �tÞ (54)

where kf and km are the formation and elimination rate constantsfor the metabolite, Vm is the volume of distribution of themetabolite, k is the elimination rate constant for the parent drugand fm is the fraction of the dose converted to the metabolite.. If themetabolite formed undergoes sequential metabolism to a second-ary metabolite in the liver or undergoes biliary secretion followedby fecal excretion, the equation must include another term, thesystemic availability of the metabolite, FH(m), which is the ratio ofthe amount of metabolite leaving the liver to the amount ofmetabolite formed.

8.1.1. Formation rate-limited metabolite kinetics (k � km)

If the elimination rate constant of the parent compound (k) ismuch smaller than that of the metabolite (km), then the semi-logarithmic plot of the metabolite plasma concentration versus

time curve declines in parallel with that of the parent compound

ion versus time profiles. When the elimination rate constant of the parent compound

compound (A). Conversely, when the elimination rate constant of the metabolite is

he parent compound (B).


during the terminal phase, and compound and metabolite willhave similar half-lives (Fig. 3A). The slope of the terminal linearportion of the metabolite plasma concentration versus time profilereflects the elimination rate constant for the parent compound, andusing the feathering technique, the elimination rate constant of themetabolite can also be obtained (Fig. 3A). The higher the value of k,the faster the terminal slopes of the metabolite and parentcompound will decline in parallel. In this case, the formation of themetabolite becomes the rate-determining step in the overallchanges in metabolite concentrations in the body. It should benoted that if the metabolite itself is administered i.v., its terminalhalf-life will be shorter than that of the parent compound after i.v.administration. The relative plasma concentrations of the parentcompound (Cp) and its metabolite (Cm) during the terminal phase isproportional to the ratio of the metabolic clearance of the parentcompound and the systemic clearance of the metabolite. As aresult, changes in renal function, metabolic induction or inhibition,or capacity-limited metabolism could alter Cm/Cp.

8.1.2. Elimination rate-limited metabolite kinetics (k � km)

If the elimination rate constant of the parent compound (k) ismuch greater than that of the metabolite (km), then the metabolitewill have a longer terminal half-life than the parent compound andthe metabolite plasma concentration versus time profile will nolonger be parallel to that of the parent compound (Fig. 3B). Theslope of the terminal linear portion of the metabolite plasmaconcentration versus time profile on a semi-logarithmic scale willreflect the true elimination rate constant for the metabolite,whereas the elimination rate constant obtained from the feather-ing technique is the elimination rate constant of the compound(Fig. 3B). This situation is termed flip-flop kinetics (also mentionedin Section 3.2.2.3).

8.1.3. Time to achieve the maximum metabolite concentration

(tmax,m)

When the metabolite formation rate becomes equal to themetabolite elimination rate, the plasma metabolite concentrationreaches a maximum value. The time to reach the maximummetabolite concentration (tmax,m) is a function of the two rateconstants [103]:

tmax;m ¼lnðkm=kÞkm � k

(55)

The value of tmax,m is increased with a decrease in km or k. Both theregular and flip-flop metabolite curves will have the same tmax,m

(e.g., case 1: km = 4 and k = 1 versus case 2: km = 1 and k = 4). Insituations of DDIs, auto-induction or end product inhibition, theeffect of a change in km or k on tmax,m needs to be considered,especially when the metabolite contributes significantly to acompounds pharmacological or adverse effects.

8.1.4. Area under the plasma concentration versus time curve (AUC)

The ratio of the area under the metabolite concentration versus

time curve to that of the parent compound is related to thesystemic clearance of the parent compound and metabolite [104]:

AUCp;ivm

AUCp;ivp

¼ f m � FHðmÞ � CLs

CLðmÞ (56)

f m ¼AUCp;iv

m

Dosep;iv=

AUCm;ivm

Dosem;iv(57)

where fm is the fraction of the compound converted to themetabolite (Eq. (57)), CLs is the systemic clearance of the parentcompound, CL(m) is the systemic clearance of the metabolite andAUCp;iv

m and AUCp;ivp are the area under the metabolite and parent

compound concentration versus time curves, respectively, after i.v.administration of the parent compound. AUCm;iv

m is the AUC of themetabolite after i.v. administration of the preformed metabolite.Since the terms fm and FH(m) are invariably less than one, if theratio AUC(m)/AUC is greater than 1, then CL(m) must be slowerthan CLs. This has been observed for the metabolism of prodrugs,like valine-valine-acyclovir, a dipeptide ester prodrug of acyclovir[105]. CL(m) is often greater than CLs due to the increasedhydrophilicity of the metabolites as compared to the parent drug.

8.1.5. Stead-state i.v. infusion

The ratio of the metabolite concentration (Cm,ss) to the parentcompound concentration (Cp,ss) during steady-state after multipleadministration or continuous infusion of the parent compound canbe predicted from the ratio of metabolite AUC to the parentcompound AUC following a single i.v. bolus dose of the parentcompound as long as clearance is constant (linear kinetics):

Cm;ss

Cp;ss¼ AUCp;iv

m

Dosep;ivp

(58)

If the metabolite displays elimination rate-limited kinetics, parentcompound concentrations will reach steady-state before those ofthe metabolite. It is impossible to know whether a metabolite hasreached steady-state or not before the metabolite is identified andcharacterized. Therefore, caution should be utilized when the AUCratio from a single dose study is used to predict the concentrationratio at steady-state for a compound having elimination rate-limited metabolite kinetics.

8.2. Extravascular compound administration

Compound administration by an extravascular route mayproduce quite a different primary metabolite concentration versus

time profile compared to that observed following i.v. administra-tion of the compound. The rate and extent of absorption of theparent compound, together with its disposition characteristics,will determine the compound concentration versus time course,which in turn will influence the metabolite concentration versus

time course. The metabolite plasma concentration (Cm) versus time(t) curve after extravascular compound administration will exhibittri-exponential kinetics (Eq. (59)) [103], which incorporates theexponents describing compound absorption and disposition, andmetabolite disposition, as follows:

CðmÞ ¼ A � e�k�t þ B � e�km �t � C � e�ka �t (59)

where the coefficients, A, B and C are functions of the various rateconstants and ka is the absorption rate constant for the parentcompound.

8.2.1. Area under the concentration versus time curve (AUC)

If metabolism occurs only in the liver and CL approximates theapparent oral clearance of the parent drug, the ratio of AUCm to theAUCp following oral administration is [103]:

AUCp;pom

AUCp;pop

¼ f m � FHðmÞ � CLs

FH � CLðmÞ (60)

The FDA guidance on metabolite in safety testing (MIST)suggests that any metabolite with exposure greater than 10% of theparent compound at steady-state in humans warrants separatenon-clinical toxicological and PK studies [106]. The fraction ofparent compound absorbed (fa) may be calculated from themetabolite AUC ratio following i.v. and p.o. administration of the


parent compound [103]:

f a ¼AUCp;po

m

AUCp;ivm

(61)

Based on the value of fa, it is possible to determine whether first-pass metabolism or incomplete absorption results in the low oralbioavailability of the compound.

8.3. Metabolite excretion in the urine

If plasma concentrations of the parent compound or metaboliteare not available, the analysis of urinary metabolite profiles mayprovide an alternative method for determining overall compoundelimination. There are two useful equations: (i) the amountremaining to be excreted (ARE) equation (Eq. (62)) and (ii) the rateof excretion equation (Eq. (63)).

M1e � Me ¼M1e

k � kmðk � e�km �t � km � e�k�tÞ (62)

dMe

dt¼ kme � kf � Dose

k � kmðe�km �t � e�k�tÞ (63)

The ARE profile and rate of excretion profile both exhibit bi-phasickinetics with two exponents: k and km. These two graphs may beused to estimate k or km (Fig. 4). When metabolite displaysformation rate-limited kinetics, the estimated rate constant basedon these two graphs will be k, whereas km will be obtained if themetabolite exhibits elimination rate-limited kinetics. However,without prior knowledge of the compound and metabolite kinetics,it is impossible to determine whether the estimated rate constantis k or km. In this case, the metabolite would need to beadministered. The ARE method requires total urine collection upto �7 half-lives. The method is not accurate if some urine is lostand difficult to use if the compound has a long half-life. Total urinecollection is not needed for the rate of excretion method. Thecollection of all the urine within a time interval (Dt, e.g., 2–4 h) isrequired and the urine only needs to be collected up to 3–4 � t1/2.The accuracy of the method depends on the chosen Dt. The smallerof Dt relative to t1/2, the more accurate the estimation.

8.4. Issues

8.4.1. Absorption rate-limited kinetics

Flip-flop kinetics often occur when the rate of absorption isslower than the rate of elimination with extravascularly adminis-tered drugs. If it is not recognized, it can create errors in theacquisition and interpretation of the PK parameters of themetabolite, such as terminal elimination half-life, volume ofdistribution, clearance, time to reach steady-state and mean

Fig. 4. Semi-logarithmic plot of amount of metabolite remaining to be excreted

(ARE) versus time and semi-logarithmic plot of metabolite excretion rate (DMe/Dt)

versus time.

residence time. When flip-flop kinetics are anticipated, a longerduration of sampling may be required in order to avoid overestima-tion of the AUC and the fraction of dose absorbed. Determining ka

and k is often even more complicated when ka and k are close invalue. It is recommended that the calculation of ka and k should notonly be based on p.o. data, but that i.v. data are also necessary.

8.4.2. Elimination rate-limited disposition

When an active metabolite displays elimination rate-limiteddisposition, dosing based upon the PK of the parent compound maylead to accumulation of the metabolite. The time to achieve steady-state for the metabolite will be longer than that of the parentcompound and the metabolite concentration will not immediatelydecline if compound infusion ceases before reaching the steady-state concentration of the metabolite (Fig. 5A, panel b) [103]. Hence,dosing based upon the disposition of the parent will result inmetabolite accumulation and may result in toxicity. When an activeor toxic metabolite exhibits elimination rate-limited disposition, thedosing regimen needs to consider metabolite kinetics. In contrast,when the metabolite exhibits formation rate-limited disposition,metabolite accumulation is not a concern (Fig. 5A, panel a).

8.4.3. First-pass metabolism

Formation of the metabolite during the first-pass elimination ofthe compound can alter the appearance of the concentration versus

time curve of a metabolite that displays formation rate-limiteddisposition. In order to characterize the metabolites kinetics, a fulltime course of the metabolite concentration profile needs to beobtained. An example is the 4-hydroxylation of propranolol(Fig. 5B), which exhibits an apparent bi-exponential decline afteroral administration. The initial decay in the concentration of the 4-hydroxylated metabolite is faster than the decay in the parent,

Fig. 5. (A) Parent compound and metabolite concentration versus time profiles

during and after parent compound infusion. Curve 1 refers to parent compound and

Curve 2 to metabolite for formation rate-limited metabolite disposition (panel a)

and parent compound elimination rate-limited metabolite disposition (panel b).

Adapted from Ref. [107] with permission. (B) Plasma concentration versus time

profiles for propranolol (*) and its metabolite, 4-hydroxy propranolol (*),

following oral administration of propranolol in man.

Adapted from Ref. [103] with permission.


propranolol [107]. It was erroneously reported that the half-life of4-hydroxylated propranolol was shorter than the parent com-pound half-life and AUC(m) was also underestimated [103]. Afterextending the study duration and increasing the analyticalsensitivity, the second phase of the plasma concentration versus

time profile with a half-life of the metabolite similar to that of theparent compound was revealed.

8.4.4. Preformed and formed metabolite

The synthesis and administration of preformed metabolites toanimals and humans for the assessment of formed metabolitetoxicity and pharmacological activity has been suggested in FDAguidelines [106]. However, it has been observed that the kineticbehavior of a preformed and formed metabolite may be different,and sometimes different secondary metabolites are generated dueto the effect of membrane barriers and transporters, competingpathways, sequential metabolism or the zonal distribution ofenzymes in the liver [108–111]. Therefore, safety and toxicitystudies conducted with preformed metabolites are useful onlywhen the compound and metabolite are highly permeable andhave independent transport systems, and when enzymes involvedin metabolite formation are readily accessible. Clearly, theseassumptions are easily violated, therefore, the assumption that thepreformed metabolite behaves in the same manner as the formedmetabolite should be used with caution.

8.4.5. Pro-drug and metabolite

Pro-drugs are bio-reversible derivatives of a compound thatmust undergo an enzymatic and/or chemical transformation in

vivo to release the active parent compound [112]. Basically, the PKrequirement of an effective pro-drug is to achieve adequatecompound plasma or tissue exposure relative to the administeredcompound in order to obtain the desired pharmacological effect.

The systemic (FS) (Eq. (64)) and tissue (FT) (Eq. (65)) availabili-ties of the compound following oral or i.v. administration of thepro-drug relative to i.v. compound administration, can be definedas [113]:

FS ¼AUCdrug;prodrug

plasma � Dosedrug

AUCdrug;drugplasma � Doseprodrug

(64)

FT ¼AUCdrug;prodrug

tissue � Dosedrug

AUCdrug;drugtissue � Doseprodrug

(65)

The selective advantage value [113] in tissue for potential pro-drugs is calculated using Eq. (66):

Selective advatage ¼AUCdrug;prodrug

tissue

AUCdrug;drugtissue

=AUCdrug;prodrug

plasma

AUCdrug;drugplasma

(66)

Since the pro-drug is usually inactive, there is no need to calculatethe bioavailability for the pro-drug. If the plasma concentration forthe inactive pro-drug is available, a bioequivalence study for thepro-drug can be conducted.

8.4.6. Species differences

Animal models are commonly used in the preclinical develop-ment of NCEs to predict their metabolic behavior in human.However, human can differ from animals with regard to isoformcomposition, expression and catalytic activities of enzymes [114].Some metabolites are formed only in human or are formed atdisproportionately higher levels in humans than in animals, suchas famciclovir [115], zaliplon [116] and zoniporide [117]. Hence,their risk assessment cannot be addressed by animal testing.Experiments with human liver microsomes, liver slices or

hepatocytes in vitro or in vivo using the recently developedchimeric mouse with a humanized liver, have allowed human-specific metabolites to be identified in the preclinical setting.

8.4.7. Metabolite-parent compound interactions

8.4.7.1. Auto-induction. Some compounds which are the substratesof metabolic enzymes are also capable of inducing enzymeexpression and activity. Repeated administration of such compoundsmay lead to a decreased plasma exposure of the parent compoundand increased plasma exposure of its metabolites, reducing thetherapeutic response of the compound or increasing the toxicity ofthe metabolite(s). Tolerance may gradually be developed with adiminished responsiveness upon repeated exposure to the samecompound. Dosage adjustment over time is required for suchcompounds, including carbamazepine [118], phenobarbital [119]and rifampicin [120]. At the same time, in order to avoid metabolite-related toxicity, the metabolite plasma concentration profile needsto be monitored and evaluated. Some compounds with long half-lives and/or those given at high doses also require an awareness ofauto-induction-related toxicity. For compounds which are chroni-cally administered, a withdrawal effect needs to be considered uponcessation of treatment, since it will usually take several days for theinduced enzyme activity to return to the basal level. A simple methodthat has been employed to evaluate the induction of enzyme activityis to measure the ratio of the amount of compound and metaboliteexcreted in urine over time [121]. In vitro methods, using humanhepatocytes or recombinant CYP enzyme systems, are also useful forassessing the auto-induction potential of a drug candidate beforestarting clinical trials [122].

8.4.7.2. End product inhibition. When a metabolite resembles theparent compound in terms of structure, it may compete with theparent compound for the same catalytic site on an enzyme,potentially resulting in inhibition of parent compound metabo-lism, a phenomenon known as end product inhibition. Although endproduct inhibition has been reported for some drugs, e.g.,phenytoin, [123] and diazepam [124], end product inhibition isconsidered to be of minor importance in vivo. However, whenperforming in vitro–in vivo extrapolations of CLint with microsomaldata using the substrate depletion approach, this phenomenonmust be carefully considered [125]. The lack of functioning Phase IIconjugation enzymes and transporters in the microsomal systemresults in the accumulation of metabolites, and subsequently maylead to end product inhibition. This is responsible for theunderestimation of the in vivo CLint and CLH [126]. Therefore,careful selection of the substrate depletion experimental incuba-tion conditions, such as enzyme concentration and incubationtime, will reduce the likelihood of biphasic depletion profiles andimprove the prediction of in vivo clearance.

9. Pharmacokinetics and pharmacodynamics

Pharmacodynamics (PD) describes the relationship betweenthe compound concentration at the site of action and the effectproduced by the compound, including its time course and theintensity of therapeutic and adverse effects [2]. The interaction of acompound with its target initiates a sequence of events whichresults in the pharmacological response. PD aims to quantify thecompound effects through linking the compound effect andcompound concentration at the site of action [127].

9.1. Pharmacological effects

The pharmacological effects of a compound can be character-ized as either quantal or graded. A quantal effect is an all-or-none


effect, with no intermediate response, e.g., alive or dead, asleep orawake, pain-free or in pain. For compounds that produce a quantaleffect, the PD model is used to identify the relationship betweenthe dose and the frequency of the effect. A graded effect occurswhen the effect of the compound is proportional to the fraction ofreceptors/drug target occupied by the compound and the maximaleffect is obtained when all receptors are occupied. The gradedeffect, thus, is a continuous function of dose, concentration or time.The PD model for drugs producing a graded effect can thereby beused to identify the relationship between dose and the intensity ofthe effect [128].

9.1.1. Quantal effect

The fixed-effect model (logistic model) relates compoundconcentration to a pharmacological effect that is either presentor is absent or is a defined cutoff for a continuous effect (fixedeffect). The magnitude of the effect is not important, but rather,whether it occurs or not is important [129]. The PD modelquantifies the likelihood or probability that a given concentrationwill produce an effect (Eq. (67)). The underlying statisticaldistribution of the probability of the effect resembles the sigmoidalEmax model (described in Section 9.2.1.1.2 below):

PðY ¼ 1Þ ¼Cg

P

CgP þ ECg

50

(67)

where P(Y = 1) is the probability that the response will occur, EC50

is the compound concentration that produces a 50% probability ofresponse and g expresses the steepness of the effect-concentrationrelationship, which reflects the inter-individual variability of themeasured effect and CP is the plasma compound concentration.

9.1.2. Graded effect

9.1.2.1. Reversible effect. The characteristic of a reversible effect isthat the increased or decreased effect levels will return towardbaseline levels over time after stopping the administration of thecompound. Reversible effects can be classified as direct andindirect responses. Direct responses are effects produced by drugsthat act immediately and directly and are related to the compoundconcentrations at the site of action. Indirect responses are effectsthat require time to develop and are not apparently related tocompound concentrations at the site of action [54].9.1.2.1.1. Simple direct effect. If a direct and immediate link existsbetween compound concentrations at the site of action and theintensity of an effect, a PD model such as a linear model, a log-linear model, an Emax model and a sigmoid Emax model can beutilized to characterize the relationship between the compoundconcentrations and effect.

9.1.2.1.1.1. Linear and log-linear models. If the pharmacologicaleffect is within 20–80% (log-linear) or less than 20% (linear) of the

Fig. 6. (A) Linear (B) log-linear an

maximum effect (Emax), the linear or log-linear model can beapplied, respectively (Eqs. (68) and (69), Fig. 6A and B,respectively).

E ¼ E0 S � C (68)

E ¼ E0 m � log C (69)

where E is the intensity of the effect, E0 is the baseline effect and Crepresents the compound concentration at the site of action. S andm are the slopes of the respective relationships, which may beeasily calculated by simple linear regression analysis.

The linear and log-linear models are often used for thedescription of effect–concentration relationships in human studieswhen the range of doses or compound concentrations apparentlylimits the approach to Emax. These two models are useful forinterpolation but not for extrapolation, and as such, Emax cannot beestimated [130]. Furthermore, both models include a thresholdconcentration (E0), below which no effect occurs (E = E0) [131].

9.1.2.1.1.2. Emax and sigmoid Emax model. The nonlinear responseversus concentration profiles occurs due to either the limitedconcentration or capacity of receptors or the limitation inphysiological systems. The Emax model (Eq. (70), Fig. 6C) is derivedfrom the Hill equation and depicts that an increase in compoundconcentration near the maximum pharmacological responseproduces a disproportionately smaller increase in the pharmaco-logic response. The typical effect versus log concentration curvefrom the Emax model is curvilinear and avoids the disadvantages ofthe previous models (linear or log-linear models). The parameters,Emax and EC50, can be obtained by least-square regression analysis.

E ¼ Emax � CEC50 þ C

(70)

where Emax represents the maximum effect, EC50 is the compoundconcentration which produces 50% of Emax and C is the compoundconcentration at the site of action.

If the effect–concentration relationship cannot be fitted to theEmax model, an additional parameter, g, can be added into themodel, which is then called sigmoid Emax model (Fig. 6C).

E ¼ Emax � Cg

ECg50 þ Cg (71)

The slope of E versus ln C plot at the inflection point (Sfp) isEmax � g/4 (Fig. 6C). The parameter g is a slope that reflects thesteepness of the effect versus concentration curve and g representsthe sensitivity of the effect-concentration relationship. When gequals to 1, the sigmoidal Emax model reduces to the Emax model.When g is greater than 1, the slope becomes sigmoidal and verysteep and rapid changes in responses occur with small changes incompound concentration. A value of g > 5 indicates an all-or-noneresponse (Fig. 6C). When g is less than 1, a shallow hyperbolic

d (C) sigmoidal Emax models.

Fig. 7. (A) Plasma compound concentration versus time profile, (B) effect versus ln concentration profile and (C) effect versus time profile for compounds following mono-

exponential disposition after i.v. administration. When the effect is between 20 and 80% of maximum response, the effect is directly proportional to the log of compound

concentrations (Eq. (75)) and the effect declines linearly with time, whereas the plasma concentration declines exponentially with time (Eq. (76)).


concentration-effect relationship is displayed, with changes ineffects occurring over a wide range of compound concentrations[132].

For compounds following mono-exponential disposition afteri.v. administration, the slope of the E versus time plot at theinflection point (SI) is �k � Emax � g/4 (Fig. 7C), which indicateshow fast the response curve is receding. Identical slopes areobtained for a wide range of doses providing C0 > EC50, since theinflections of the curves occur at the EC50 value for compoundsfollowing mono-exponential disposition. There will be no inflec-tion on the response curve if C0 < EC50 (Fig. 7B) [132].

For the excitatory and inhibitory sigmoid Emax models, thebaseline effect (E0, measured in the absence of drug) needs to beeither added or subtracted from the model (Eqs. (72) and (73),respectively).

E ¼ E0 þEmax � Cg

ECg50 þ Cg (72)

E ¼ E0 �Emax � Cg

ECg50 þ Cg (73)

9.1.2.1.1.3. Pharmacokinetics and pharmacodynamics for simple

direct compound effects. For compounds that are rapidly distribut-ed in the body and eliminated by apparent first-order kinetics, afteri.v. administration, plasma compound concentration falls expo-nentially, (Fig. 7A) then:

C ¼ Dose

V� e�kt (74)

(a) If the pharmacological effect and log compound concentrationfollowing i.v. administration exhibits a linear relationship(Fig. 7B) then:

E ¼ E0 þ m � log C (75)

The decline of the pharmacological effect with timefollowing i.v. administration (Fig. 7C) can be described as

follows:

E ¼ E0 � k � m � t (76)

The time course of the effect (Eq. (76)) includes theinformation about kinetic (k) and dynamic (m) processescontrolling the compound effect. In the absence of the rapiddevelopment of functional tolerance or the occurrence of otherrelevant time-dependent physiological changes, the durationof the compound effect (td) can be described as:

td ¼1

k� ðln Dose � ln AminÞ (77)

where k is the elimination rate constant and Amin is the

minimum effective amount of compound in the body [133].

Doubling the dose usually does not lead to the doubling of the

effect, but will increase the duration of the effect by one t1/2

[134]. If the compound exhibits an essentially linear relation-

ship between the intensity of effect and ln Dose over the

clinically relevant intensity of the effect range, then the rate of

decline of the effect (rR) in that range is:

rR ¼ k � m (78)

Substitution of Eq. (78) into Eq. (77) and rearrangementyields:

td � rR ¼ m � ðln Dose � ln AminÞ (79)

Thus, the product of duration (td) and rate of decline of effect(rR) reflect changes in the PD parameters, m or Amin, and areindependent of the PK parameter, k, even though these may bealtered concurrently. As a result, in instances when the value of td

is changed while tdrR remains the same, it may be concluded thatthe PD of the compound is unaltered and the observed change inthe time course of the effect is due to the change in k. However, iftdrR is changed, one must conclude that the PD parameters, m orAmin, and also the PK parameters are all altered [135].

If the pharmacological effect and Log compound concentra-tion relationship follows the Emax model (Eq. (70)), then the


total net compound effect can be expressed as the area underthe effect curve (AUCE) (Eq. (80)).

AUCE ¼Emax

k� ln 1 þ Dose=V

EC50

� �(80)

AUCE

AUC¼ Emax

C0� ln 1 þ C0

EC50

� �(81)

where AUCE describes the overall effect which is related to theexposure of the system to the compound and therefore can beconsidered as a measure of effectiveness of different dosingregimens [136]. As evident in Eq. (80), the PK (V and k) and PD (Emax

and EC50) factors control the net effect of the compound. Thetrapezoidal rule is generally used to calculate AUCE. The ratio ofAUCE/AUC indicates the sensitivity of patients to the action of thecompound [137].9.1.2.1.2. Indirect effect. For compounds exhibiting an indirecteffect, e.g., warfarin [138], nizatidine [139] and tolrestat [140],there is a lag time for the development of a response due tomechanistic or equilibration delays. A mechanistic delay resultsfrom the occurrence of serial biological events that occur after theinitial interaction of a compound with its target, whereas theequilibration delay results from the delay in the equilibrationbetween the plasma compartment and the biophase. The latterdelay is primarily dependent upon the physicochemical propertiesof the compound and of the site of action. Many compoundsproduce responses with a lag time, e.g., those targeting synthesis,secretion, and cell trafficking processes or enzyme induction [141].Warfarin is a classic example of a drug with an indirect mechanismof action; it rapidly inhibits the synthesis of the prothrombincomplex activity P, but it takes several days before an anticoagu-lant effect is produced [138]. PD models have been applied todescribe the effects of compounds/drugs produced by indirectmechanisms and establish the relationship between the dose andthe response profiles of compounds.

9.1.2.1.2.1. Hysteresis of the pharmacological response. For somecompounds, the plot of therapeutic effect versus plasma concen-tration exhibits a hysteresis loop. As shown in Fig. 8, the sameplasma compound concentration causes different effect levels atdifferent time points after compound administration. Dependingon the different mechanisms involved in the temporal dissocia-tion between plasma concentration and effect, two types of

Fig. 8. Clockwise hysteresis (A) and counter clockwise hysteresis (B) relationships betwee

at the earlier time point (t3) is more pronounced than that at the later time point (t5) desp

The effect at the earlier time point (t2) is lower than that at the later time point (t4) d

pharmacologic response are identified: clockwise hysteresis

(Fig. 8A) and counter clockwise hysteresis (Fig. 8B). Causes ofclockwise hysteresis include: (i) tolerance; (ii) target down-regulation, (iii) target translocation; (iv) enzyme deactivation or(v) formation of a metabolite with an effect opposite to that of theparent, e.g., an agonist metabolite formed from an antagonistparent compound [54]. Counter clockwise hysteresis may resultfrom: (i) a distributional delay of the compound to the target, (ii) amechanistic response delay; (iii) sensitization of compoundtarget, e.g., receptor sensitization; (iv) enzyme induction; (v)target up-regulation or (vi) formation of a metabolite with agonistproperties.

9.1.2.1.2.1.1. Biophase distribution model. If the response delay is

clearly due to the distribution of the compound from plasma to thetarget site, the biophase distribution model with a hypotheticaleffect compartment is useful in describing the plasma concentra-tion and response relationship (Fig. 9). In this model, compounddistribution to the site of action represents a rate-limiting step inthe onset of the biological effect [130]. The effect compartment isnot part of the PK model but is a hypothetical PD compartment thatprovides a mathematical link between the plasma compoundconcentration and its response. The assumptions required for thismodel are: (i) the amount of compound entering the effectcompartment is considered to be negligible relative to the plasmaconcentration and, therefore, will not affect the plasma compoundconcentration profile, (ii) only free compound can transfer into theeffect compartment and; (iii) the transfer rate constant is a firstorder process (Fig. 9). The rate of change of the compoundconcentration in the effect compartment (the site of action) can bedefined as follows:

dCe

dt¼ k1e � Cp � ke0 � Ce (82)

where k1e and ke0 are first order distribution rate constants, andwhich are assumed to be equal since they are unidentifiable. Cp andCe are the compound concentrations in plasma and the hypotheti-cal effect compartment, respectively. A smaller keo will producelater effect peaks and a prolongation of the response. The peakeffect will be delayed relative to the plasma concentration,whereas the time for peak effects is dose-independent. Thecompound concentration in the central compartment (assumingthat the compound follows a one-compartment model after bolus

n plasma compound concentration and effect from time t1 to t6. Panel (A): The effect

ite that the compound concentrations are same at these two time points. Panel (B):

espite that the compound concentrations are same at these two time points.

Fig. 9. Biophase distribution model.

Adapted from Ref. [130] with permission.


i.v. administration) is:

Cp ¼Dose

Vc� e�kt (83)

The corresponding expression for the concentration of com-pound in the effect compartment is:

Ce ¼k1e � Dose

Vcðke0 � kÞ � ðe�kt � e�ke0tÞ (84)

where Vc and Ve are the volume of distribution in centralcompartment and effect compartment, respectively.

9.1.2.1.2.1.1.1. Full parametric models. Eqs. (83) and (84) and anappropriate PD model (linear, log-linear or sigmoid Emax model)can be sequentially or simultaneously fitted to experimental data ,in order to estimate parameter values using nonlinear regressionmethods.

9.1.2.1.2.1.1.2. Semi-parametric models. An appropriate PKmodel is fitted to the plasma concentration data to estimate PKparameter values. Then, the PK parameter values are used as inputsfor the effect compartment model. The keo can be estimated by anapproach termed ‘‘collapsing the hysteresis loop’’ (Fig. 10). Thetheoretical time course of the effect site concentrations isestimated by convolving the plasma concentration with keo. Ifthe value of keo is chosen as too large or too small, the plot of theeffect site concentration versus the effect will produce a counterclockwise or a clockwise hysteresis loop. Once the keo isappropriately chosen, the hysteresis loop collapses and then theapparent effect site concentration and effect relationship can bedefined using a PD model [142]. The limitation for the effect link

Fig. 10. The fundamental basis of nonparametric PK-PD. The theoretical time course

of effect-site concentration is estimated by convolving the plasma concentration

with a first order constant (keo). The left panels depict plasma concentration (solid

line) and effect-site concentration (dashed line or circles) versus time profiles,

whereas the right panels depict effect versus time profiles. The effect-site

concentration is linked to the plasma concentration by keo. The resulting effect-

site concentration is translated into a pharmacological effect. If keo is too large, the

predicted effect-site concentrations (dashed lines) are shifted to the left of the

actual effect-site concentration (circles; top left panel). Thus, the effect versus time

plot shows a counterclockwise hysteresis loop (top right panel). If keo is too small,

the predicted effect-site concentrations (dashed lines) are lower than the actual

effect-site concentrations (circles; middle left panel). Thus, the effect versus time

plot exhibits a clockwise hysteresis loop (middle right panel). When keo is chosen

appropriately, the hysteresis loop uniquely collapses and the apparent

concentration-effect is defined (bottom panels).

model is that it is not truly mechanistic. It assumes that thedistribution of compound between plasma and tissue is by passivediffusion and that only the free compound concentration drives theintensity of the response. In fact, compound distribution to thetarget tissue may be regulated by transporters and the freecompound hypothesis may be invalid. For compounds with a highaffinity for their biological target and those which are transportedby active influx transporters, the biophase distribution might benonrestrictive [143].

9.1.2.1.2.2. Indirect response models. A fundamental physiologi-cal model for drugs that produce pharmacological effects byindirect mechanisms is shown in Fig. 11A. In this model, theprecursor may synthesize or secrete the response variable.Compounds can act on either of these processes to produce aneffect through producing a precursor, acting on a precursor,inhibiting or stimulating the synthesis or secretion of the responsevariable or acting on the process of the response variable’s removal[141]. Depending on the direction of the pharmacologicalresponses and the factors affected, four basic indirect PD responsemodels (described below) have been proposed and characterizedwhich may be used to describe the PD responses of drugs withindirect mechanisms of action [141].

Assumptions in these proposed models are: (i) the response tocompound is independent of the amount of the precursor present(i.e., k0

in is an apparent zero-order rate constant), (ii) the baseline ofthe system is stationary, and k0

in and kout fully account forproduction and loss of response, (iii) the compound responsebegins at a baseline value, changes with time following compoundadministration, and after dissipation of the response variable,returns to Ro (the initial value) and (iv) compound effects correlatedirectly with the compound concentrations at the site of action.The rate of change of the response over time with no compoundpresent can be described by:

dR

dt¼ kin � kout � R (85)

As mentioned above, it is assumed that the response variablebegins at a pre-determined baseline value (R0), changes with timefollowing compound administration, and eventually returns to R0.Therefore, at baseline or at steady-state, dR/dt = 0, and thus:

kin ¼ kout � R or kin ¼ kout � Rss (86)

Model I describes the compound response resulting from theinhibition of the factors regulating the production of the responsevariable (k0

in), whereas Model II describes the compound responseresulting from the inhibition of the factors governing thedissipation of the response variable (kout) (Fig. 11B). The rate ofchange of the response over time can be described as:

Model I :dR

dt¼ k0

inIðtÞ � koutR (87)

Model II :dR

dt¼ k0

in � koutIðtÞR (88)

where k0in is the apparent zero-order rate constant for the

production of the response, kout is the first-order rate constantfor the loss of the response, and R is the response variable with an

Fig. 11. (A) Basic scheme for indirect PD responses. The response variable is affected by compounds which can alter the formation of a precursor, or the production or

dissipation of the response variable. Compounds can inhibit or stimulate any of these processes. Red arrows indicate stimulation, while blue arrows indicate inhibition of a

process. Arrows intercepted with a double line indicate that process inhibition or stimulation results in an inhibitory compound response, whereas arrows without a double

line indicate that process inhibition or stimulation results in an excitatory compound response. (B) Four basic indirect response models representing processes that inhibit or

stimulate the factors controlling compound responses. Model I describes the compound response resulting from the inhibition of the factors regulating the production of the

response variable (koin), whereas Model II describes the compound response resulting from the inhibition of the factors governing the dissipation of the response variable

(kout). Model III describes compound response resulting from the stimulation of the factors regulating the production of the response variable (koin), whereas Model IV

describes compound response resulting from the stimulation of the factors governing the dissipation of the response variable (kout).


initial value of R0 (k0in=kout). The response variable can be a directly

measured variable or it may be an observed response, which isdirectly and immediately proportional to the concentration of amediator.

The inhibition function I(t) can be defined as:

IðtÞ ¼ 1 � ImaxCp

IC50 þ Cp(89)

where Imax is the maximum fractional ability of the compound toaffect the kin or kout processes and is always less than or equal tounity (0 < Imax � 1), the IC50 value is the concentration of acompound that produces 50% of maximum inhibition achieved atthe effect site and Cp represents plasma compound concentration.

Model III describes compound response resulting from thestimulation of the factors regulating the production of the responsevariable (k0

in), whereas Model IV describes compound responseresulting from the stimulation of the factors governing thedissipation of the response variable (kout). The rate of change ofthe response over time can be described as:

Model III :dR

dt¼ k0

inSðtÞ � koutR (90)

Model IV :dR

dt¼ k0

in � koutSðtÞR (91)

The stimulation function S(t) is defined as:

SðtÞ ¼ 1 þ SmaxCp

SC50 þ Cp(92)

where Smax can be any number greater than zero (Smax > 0), SC50 isthe concentration that produces 50% of maximum stimulationachieved at the effect site and Cp represents the plasma compoundconcentration. An example of a drug which has a response that canbe characterized with indirect response Model I is nizatidine, anH2-receptor antagonist that blocks the gastric acid secretion (theresponse variable) stimulated by histamine [139]. The indirectresponse Model III can be applied to characterize the PD ofinterferon a-2a. This protein is used for the treatment of chronichepatitis C, hairy cell leukemia, AIDS-related Kaposi’s sarcoma, andchronic myelogenous leukemia (CML) and induces the synthesis of

MX protein, a dynamin superfamily member that interferes withviral replication [144]. Examples of drugs which have PD responsescan be characterized with Models II and IV are pyridostigmine andterbutaline. Pyridostigmine is a cholinesterase inhibitor which canincrease muscle response [145]. Terbutaline, a b2-adrenergicagonist, causes hypokalemia and an increase of plasma glucose andserum insulin concentrations [145].

In each of these models, the presence of inhibitory orstimulatory compound concentrations for a sufficient period oftime contributes to the initial fall or rise in the response variable.The initial response of the compound reflects kout. After theoccurrence of the maximum achievable response (Rmax), the returnto baseline is a function of both k0

in and compound elimination (k)as compound concentrations decline below IC50 or EC50 values.

9.1.2.1.2.2.1.1. Area between the baseline and the effect curve

(ABEC). The parameter used to characterize the overall effect of acompound is the area between the baseline and the effect curve(ABEC). ABEC summarizes the influences of all the determinants ofcompound pharmacological response: PK variables (V and k fordrugs following mono-exponential disposition) and dynamicvariables (R0, IC50 or SC50 and Imax or Smax). At high doses, ABECis simply proportional to the natural log (ln) of the dose. For ModelsI and III, the ABEC is (for drugs following mono-exponentialdisposition) [141]:

Model I : ABEC ¼ R0 � Imax

k� ln 1 þ Dose=V

IC50

� �(93)

Model III : ABEC ¼ R0 � Smax

k� ln 1 þ Dose=V

SC50

� �(94)

If the Hill coefficient g is not equal to 1, then the ABEC is:

Model I : ABEC ¼ R0 � Imax

g � k � ln 1 þ Dose=V

IC50

� �g� �(95)

Model III : ABEC ¼ R0 � Smax

g � k � ln 1 þ Dose=V

SC50

� �g� �(96)

ABEC equations are complicated for Models II and IV. For Models Iand III, ABEC values at two or more dose levels can be used to


estimate Imax or Smax and IC50 or SC50 values by regression analysis.An altered ABEC value indicates a change in response in studies ofdisease effects and DDIs.

9.1.2.1.2.2.1.2. Initial parameter estimate. The Imax or Smax and k0in

can be estimated according to the following equations [141]:

Model I : Imax ¼R0 � Rmax

R0k0

in ¼ �SI=Imax (97)

Model II : Imax ¼Rmax � R0

Rmaxk0

in ¼ SI=Imax (98)

Model III : Smax ¼Rmax � R0

R0k0

in ¼ SI=Imax (99)

Model IV : Smax ¼R0 � Rmax

Rmaxk0

in ¼ �SI=Imax (100)

where R0 (baseline), Rmax (maximum drug response) and SI (initialslope) can be obtained from experimental data following a largedose which should be sufficiently high to produce either fullinhibition or stimulation of the system.

9.1.2.1.2.2.1.3. Pharmacokinetics and pharmacodynamics for

indirect responses. The indirect models operate via differentialequations with PK, mechanism (Hill equations) and systemcomponents (production or loss). Modeling indirect responsesdata should be a two-stage process. The plasma compoundconcentration data are first fitted to estimate PK parameters andthen the dynamic data are fitted with one of the indirect responsemodels to obtain PD parameter estimates (k0

in, kout, IC50 or SC50, andImax or Smax). Data from baseline and several dose levels should befitted simultaneously [141].

9.1.2.2. Irreversible effects. Some chemotherapeutics, e.g., antican-cer and antimicrobial drugs, and enzyme inhibitors exert theirbiological effects through irreversible interactions with cells orproteins. A general equation for describing irreversible effects is,

dR

dt¼ gðRÞ � f ðCÞ � R (101)

where R represents the cell number, C is either the plasmacompound concentration or the compound concentration at thesite of effect, g(R) is a function to describe the natural proliferationof cells and f(C) is a function to describe the irreversible interactionwith the cells. In a simple model, g(R) and f(C) can be defined asfollows:

gðRÞ ¼ kg � R (102)

f ðCÞ ¼ k � C (103)

where kg is the first-order cell growth rate constant and k is thesecond-order cell-kill rate constant. Due to the joint effect of cell-killing and cell natural growth, the effect versus time curve isbiphasic, with an initial phase of cell-killing followed by regrowthafter compound concentrations decline below a minimumeffective value [130]. Mechanistic models provide uniqueadvantages in understanding compound efficacy and safety bymathematically describing the underlying biological and phar-macological processes.

9.2. Drug–target residence time

Once a compound binds to its target to form a binary complex,its efficacy becomes a function of its target residence time, t, andthe rate constant for the dissociation of the compound–target

complex, (koff) (Eq. (104)):

t ¼ 1

koff(104)

This can be directly related to the half-life of dissociation(Eq. (105)):

t1=2 ¼0:693

koff(105)

which can be rearranged to:

t ¼t1=2

0:693

The relationships between these terms are a function of the precisemechanism of the compound–target interaction and any confor-mational changes that occur as the result of the compoundengaging the target. For a number of compounds, efficacy asmeasured by a cellular or tissue PD response is better predicted bytarget residence time, t, than the equilibrium dissociationconstant, Kd [3,146–149].

Examination of three ATP-competitive inhibitors of the EGRF(Epidermal Growth Factor Receptor) tyrosine kinase, lapatinib,gefitinib and erlotinib, that had similar in vitro potency (Ki = 0.4–3 nM) showed differences in enzyme inhibition as measured as afunction of EGRF autophosphorylation. For gefitinib and erlotinib,enzyme activity recovered in less than 10 min, while recovery forlapatinib was approximately 7 h, an indication of a prolongedresidence time, and as a result, an enhanced PD effect [150].

9.3. Summary

This section introduced fundamental mechanism-based con-cepts and provides important model features and operableequations. A number of mechanistic processes can be incorporatedinto PD models to successfully describe the compound-target/system interactions, such as signal transduction, tolerance andslow receptor-binding models. With an understanding of mecha-nisms of compound interactions [2] with their targets (receptors,enzymes, transporters, etc.), mechanism-based PD models areessential in prospectively predicting compound efficacy and safety.

10. Conclusions

Using a compound – whether a known drug or an NCE – as a toolto aid in defining the role of a protein in cellular and tissuehomeostasis and its potential as a drug target requires that thecompound be hierarchically evaluated in vitro and in vivo

[151,152]. While the potency, efficacy and selectivity of acompound can be facilely determined in vitro, its use in vivo

and/or potential as a drug candidate requires an understanding ofits PK and ADME properties [153]. To test a compound, especiallyan NCE, in vivo without knowledge of its PK properties – even at arudimentary level – can be an exercise in futility.

The lack of a sufficient emphasis on assessing PK/ADME in NCEshas been shown to be a primary factor in compound attrition in theclinic [4,5] such that PK is assessed very early in a drug discoveryprogram to ensure medicinal chemistry efforts are focused oncompound series that have acceptable PK properties that can beoptimized to provide the most promising drug-like clinicalcandidate. Many NCEs and legacy compounds do not, however,have this level of assessment and are used indiscriminately in in

vivo experiments based on previous findings to define the role oftargets and systems. Given the cost and ethical aspects of animaltesting [153], especially in non-human primates, it can be a


foolhardy use of resources to initiate in vivo testing in the absenceof any knowledge of the PK/ADME properties of a compound anduse the results to draw definitive conclusions for the target beinginterrogated especially when the metabolites may have significantefficacy/side effect properties that may confound outcomes.

In the present overview, the basic elements of PK have beenoutlined in detail allowing the reader to assess the benefits andrisks in proceeding from in vitro to in vivo studies.

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Pharma c i Kinetics

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