University of Szeged
Basic Course in Biopharmacy
Edited by: István Zupkó Ph.D.
Authors: István Zupkó Ph.D. Eszter Ducza Ph.D. Árpád Márki Ph.D. Renáta Minorics Ph.D.
Reviewed by: Gábor Halmos Ph.D.
Szeged, 2015.
This work is supported by the European Union, co-financed by the European Social Fund, within the framework of "Coordinated, practice-oriented, student-friendly modernization of biomedical education in three Hungarian universities (Pécs, Debrecen, Szeged), with focus on the strengthening of international competitiveness" TÁMOP-4.1.1.C-13/1/KONV-2014-0001 project. The curriculum can not be sold in any form! Contents
1. Basic concepts in pharmacology and biopharmacy. Routes of drug administration 1 1.1. Basic concepts in pharmacology and biopharmacy 1 1.2. Classification of routes of drug administration 2 1.2.1. Enteral drug administration 2 1.2.2. Parenteral drug administration 5 2. Receptors, signal transduction mechanisms 9 2.1. Introduction to pharmacological receptors 9 2.2. Signal transduction 10 2.3. G protein -coupled receptors ( GPCRs) 11 2.4. Ligand -gated ion channels 14 2.5. Receptors as enzymes 16 2.6. Nuclear hormone receptors and transcription factors 18 3. Dose –response relationships 21 3.1. General remarks 21 3.2. Concentration vs. response relationships in in vitro systems 22 3.3. Dose vs. response relationships in in vivo systems 26 4. Absorption and distribution of drugs and factors influencing this 30 4.1. Absorption of drugs 30 4.1.1. Main features of drug absorption 30 4.1.2. Absorption of drugs by passive diffusion 31 4.1.3. Absorption of drugs by active transport 33 4.1.4. Absorption of drugs by additional transport mechanisms 34 4.1.5. Factors influencing drug absorption 34 4.2. Distribution of drugs 37 4.2.1. General remarks 37 4.2.2. Volume of distribution 38 4.2.3. Binding to plasma proteins 39 4.2.4. Special drug distributions: the blood brain –barrier (BBB) and the placental barrier 39 5. The drug metabolism 42 5.1. The main features of the drug metabolism 42 5.2. Phase I of the drug metabolism 43 5.3. Phase II of the drug metabolism 48 5.4. Factors influencing the drug metabolism 50 6. Elimination, continuous intravenous infusion and multiple dosing regimen 53 6.1. Elimination 53 6.1.1. Renal excretion 53 6.1.2. Excretion by the liver 55 6.1.3. Pulmonary excretion 55 6.1.4. Salivary excretion 56 6.1.5. Excretion through the skin 56 6.1.6. Excretion into the breast milk 57 6.1.7. Clearance 57 6.2. Continuous intravenous infusion 58 6.2.1. Concept of plateau 59 6.2.2. Rate of infusion 59 6.2.3. Plateau fraction 61 6.2.4. Loading dose of the infusion 63 6.3. Multiple dosing regimen 63 6.3.1. Dosing interval ( τ) 65 6.3.2. Concept of plateau and minimum and peak plasma concentrations 66 6.3.3. Considerations during the application of a multiple dosing regimen 67 7. Compartmental models 70 7.1. One -compartment open model 71 7.1.1. One -compartment intravascular model 72 7.1.2. One -compartment extravascular model 74 7.2. Two -compartment open model 78 7.2.1. Two -compartment intravascular model 78 7.2.2. Two -compartment extravascular model 82 7.3. Effects of the ratio ka/ke on tmax and cmax 84 8. AUC, model-independent pharmacokinetics 87 8.1. Trapezoid method 87 8.2. Determination of AUC based on clearance 90 8.3. Model -independent pharmacokinetics 91 8.4. Application of model -independent calculations 95 8.4.1. Calculation of apparent volume of distribution at steady -state ( Vss ) 95 8.4.2. Calculation of the clearance ( Cl ) 96 8.4.3. Calculation of dosing rate 96 8.4.4. Calculation of bioavailability 97 9. Physiological and biological availability of drugs; bioequivalence 99 9.1. Introduction 99 9.2. Physiological availability 99 9.3. Biological availability (bioavailability) 100 9.3.1. Absolute bioavailability 100 9.3.2. Relative bioavailability 101 9.4. Special cases 102 9.5. Equivalence 102 9.5.1. Therapeutic alternatives 103 9.5.2. Pharmaceutical alternatives 103 9.5.3. Pharmaceutical (chemical) equivalence 103 9.5.4. Bioequivalence 104 9.5.5. Therapeutic equivalence 104 9.5.6. Generic preparations 104 9.6 Biosimilarity 105 10. Drug interactions 108 10.1. Relevance of drug interactions 108 10.2. Classification of drug interactions 108 10.3. Synergisms 110 10.3.1. Additive synergism 110 10.3.2. Potentiating synergism 110 10.4. Antagonisms 111 10.4.1. Chemical antagonism 111 10.4.2. Biological antagonism 112 10.4.3. Functional antagonism 112 10.4.4. Competitive antagonism 112 10.4.5. Non -competitive antagonism 114 10.4.6. Additional types of interactions 115 11. Factors influencing drug action and drug administration 118 11.1. Effects of age – Older patients 118 11.2. Effects of age – Paediatric patients 119 11.3. Sex differences 121 11.4. Body weight 122 11.5. Pregnancy 123 11.6. Genetic factors 124 11.7. Pathological factors 124 12. Non-linear pharmacokinetics and therapeutic drug monitoring 127 12.1. Non -linear pharmacokinetics 127 12.1.1. Relevance of non -linear pharmacokinetics 127 12.1.2. Capacity -limited metabolism 129 12.1.3. Estimation of Michaelis –Menten parameters ( Vmax and KM) 130 12.1.4. Additional possibilities for non -linear pharmacokinetics 132 12.2. Therapeutic drug monitoring (TDM) 133 12.2.1. Individualization of drug therapy 133 12.2.2. Theory of TDM 134 12.2.3. Practice of TDM 136 13. Adverse drug reactions 139 13.1. Classification of adverse drug reactions 139 13.2. Pharmacodynamic variation of genetic polymorphism 144 13.3 Pharmacokinetic variation of genetic polymorphism 145 14. Practical considerations 149 14.1. Important considerations of pharmacokinetic study design 150 14.1.1. Subjects 150 14.1.2. Types of study 150 14.1.3. Dosage form, route of administration 151 14.1.4. Accuracy in administration of the dose 151 14.1.5. Blood samples 152 14.1.6. Sample handling and timing 153 14.1.7. Curve fitting and statistical considerations 154 14.2. Pharmacokinetics and clinical situations 155 15. Suggested readings 159
1. Basic concepts in pharmacology and biopharmacy. Routes of drug administration 1.1. Basic concepts in pharmacology and biopharmacy One of the most important concepts is the pharmacon or drug. This is a synthetic or natural compound or substance which has the capacity to induce a characteristic action on a living organism. The term pharmacon is not limited to substances currently used in medicinal practice. It also involves all biologically active substances with no medical use (e.g. natural and synthetic toxins), all the agents withdrawn from medical use, and agents still under development. A pharmacon is not necessarily a chemically pure substance; it may be an extract from a natural source. The term active pharmaceutical ingredient (API) has a narrower meaning: it is the component in a medicinal preparation from which the therapeutic action is expected. There is no clear definition for the term poison. All pharmacons, including medically used agents, may exert detrimental action after their inappropriate application (e.g. in excessive doses). In a general sense, a poison is a substance which in a low dose has the capacity to cause a serious deterioration of a living organism. A drug usually induces a change in more than one physiological parameter, and therefore exerts more than one action. The main effect is the action for which the drug is administered, and all of the others are side effects. Although the side effects are generally unwanted or inconvenient consequences of the therapeutic dose of the given drug, a side effect can sometimes be advantageous. For example, some of the agents used in psychiatry exert pronounced antihypertensive action, which can be utilized to maintain the optimum blood pressure. The relationship between the main and the side effects can be relative: it depends on the aim of the drug administration. Atropine has a wide range of pharmacological actions and it could be administered to relax the smooth muscles, to decrease secretions or to constrict sphincters. In any given case, one of these is the main effect and all the others are side effects. A toxic effect of a drug is always disadvantageous or harmful, and is exerted at a dose higher than the therapeutic dose. A toxic effect is therefore a consequence of an overdosage or intoxication. The site of action is that part of the living organism where the pharmacon exerts its actions. It can be an organ, a group of cells or a subcellular component (e.g. an organelle or even a molecule). Our current knowledge concerning the given drug usually determines the level at which the site of action is defined. For example, the site of action of digitalis glycosides is the
1 heart (as an organ), the cardiac muscle (a group of cells) or the Na/K ATPase (a subcellular component). The mechanism of action refers to the sequence of reactions leading to the final pharmacological effect. An effect of a pharmacon can be local or general. A local effect is one where that the drug exerts its action only at the site of its application (e.g. antacids in the stomach, or eye drops). A general occurs when the drug is present in the blood circulation and can reach and influence all the possible sites of action in the body. A general effect can develop in two cases: • The drug is administered directly into the circulation (intravascular administration), or • the drug is administered outside the circulation (extravascular administration), but it can move from the site of application into the bloodstream. This process is called absorption. 1.2. Classification of routes of drug administration The routes of drug administration can be classified on the basis of pharmacokinetic considerations: Is there any absorption before the drug reaches the circulation, or is it administered directly into the circulation? Intravascular administration involves an intravenous bolus and infusion, or the rarely used intra arterial injection, while all other types of drug administration are considered extravascular. A more practical classification of the routes of drug administration is based on the site of application. In the event of enteral drug administration, any part of the gastrointestinal tract may be utilized as a route for the drug, while all other cases involve parenteral administration. 1.2.1. Enteral drug administration The most common mode of drug administration is through the gastrointestinal tract. This route has many advantages, including non invasiveness and painlessness, and it is suitable for self administration. Since the wall of the small intestine is deeply folded and contains microvilli, the total surface area of the tract is approximately 120 m 2. The surface is therefore large enough and it usually does not limit the absorption of drugs administered enterally.
2 The uppermost part of the tract is the oral cavity, which is frequently used for drug delivery. Within the oral cavity, there are three modes of oral drug application: sublingual, perlingual and buccal. • In sublingual administration, the medication is placed under the tongue. The sublingual area is highly vascularized and its venous drainage collects into the superior vena cava. Absorption is relatively fast and the given drug bypasses the metabolic activities of the small intestine and liver. This is the preferred mode of drug delivery when an immediate effect is needed without invasive intervention. Sublingually administered nitroglycerine can alleviate an angina attack, or captopril can result in a rapid decrease of blood pressure. • In perlingual application, the preparation is placed onto the tongue. Absorption after this kind of administration is limited; mostly local effects can be elicited. Typically antiseptic agents are used perlingually. • Buccal administration involves placement of the medication between the gums and the cheek. The absorption and the expected effect are similar to those of perlingual usage. Medications designed for sublingual, perlingual and buccal administrations can be solid forms (e.g. tablets) or sprays. The mode of drug usage involving the swallowing of the medication is strictly called administration per os . Frequently, however, no distinction is made between the terms oral and per os , and both cases are referred as to oral drug usage. After being swallowed the drug enters the oesophagus, where it spends only a limited period, and the stomach is the first place from which substantial absorption is possible. The venous drainage from the stomach to the rectum passes into the portal circulation, and the absorbed substances reach the systemic circulation only after crossing the liver. This phenomenon is called the first pass effect. During this process, a portion of the absorbed amount is metabolized, with a decrease in the overall drug exposure of the systemic circulation. Besides the liver, the gut wall can contribute substantially to the presystemic metabolism. The amount metabolized during the first pass effect is characteristic of the given drug. The presystemic metabolism may explain the huge differences between the oral and sublingual or parenteral doses of some agents. Most of the orally given pharmacons are weak bases or weak acids, which can be present in a liquid phase in ionized or non ionized forms, depending on the local pH value. The
3 ionization of a weak acid is promoted in an alkaline milieu, but suppressed in acidic fluid. The weak bases behave in the opposite way. Since the non ionized and therefore lipid soluble form of the agent is favoured during the absorption from the whole of the gastrointestinal tract, the role of the local pH in the absorption is obvious. The stomach has a capacity of 1–1.2 l when filled, while the empty stomach contains approximately 100 ml of gastric juice and the local pH may be 1–3.5 (Table 1.1). The ionization of drugs with an acidic character (e.g. non steroidal anti inflammatory drugs) may be suppressed and a majority of the administered amount may be present in a ready for absorption form. On the other hand, weak bases (e.g. alkaloids) are ionized, which excludes their fast absorption. Local irritation of the gastric mucosa (e.g. by carbon dioxide) may increase the rate of absorption, while a content with high viscosity usually decreases it. From the stomach, its content enters the small intestine, which is divided into three parts: the duodenum, the jejunum and the ileum. There is no crucial difference in the local pH values of these parts; the whole small intestine exhibits close to neutral acidity (pH 6.3–7.6). Although the surface of the duodenum is suitable for drug absorption, its length limits its role in pharmacokinetics. Most of the absorption of the orally administered agents takes place in the jejunum, and the ileum can be regarded as a reserve surface. As a result of the presence of the digestive juices, the whole gastrointestinal tract is unsuitable for the administration of chemically unstable agents, and especially proteins. The role of the colon in drug absorption is special: its microbiome has a high metabolic capacity, and unabsorbed substances can therefore be converted into lipid soluble metabolites which are readily absorbed into the portal circulation. Rectal drug administration is of great importance in paediatric practice, but it is also used in adult patients to elicit mostly local a effect. If the active ingredient is absorbed, roughly half of it undergoes the hepatic first pass effect, while the other half is absorbed directly into the systemic circulation.
4 Table 1.1. Most important parameters of the parts of the gastrointestinal tract that determine the absorption Organ or part of Average length Amount of Local pH Enzymes, juices the tract (cm) secretion (ml/day) Oral cavity 15 –20 6.4 amylase, saliva: 500 –1500 salivary lipase Oe sophagus 25 5.0 –6.0 – – Stomach 20 1.0 –3.5 pepsin, gastric juice: hydrochloric acid 2000–3000 Duodenum 25 6.5 –7.6 trypsin, bile: 250 –1100 chymotrypsin, amylase, maltase, pancreatic juice: lipase, nuclease, 300–1500 bile Jejunum 300 6.3 –7.3 erepsin, amylase, intestinal fluid: maltase, lactase, 3000 sucrase Ileum 300 7.6 lipase, nuclease Colon 150 7.9 –8.0 Rectum 15 –20 7.5 –8.0 1.2.2. Parenteral drug administration One route of parenteral drug administration is injection. The word injection has two basic meanings. An injection may be the dosage form, or it may be the mode of administration. An injection is considered to be a mode of administration if the site of the application is specified. Besides general requirements for injections (sterility, and freedom from pyrogens), intravascularly administered injections must be clear solutions that can be mixed with serum. An extravascularly given injection can be a suspension or an emulsion, and can contain oil as a vehicle. • An intradermal or intracutaneous injection is given into the dermal layer of the skin and its volume is strictly limited (0.05–0.1 ml). It is mostly used for diagnosis, e.g. for tuberculin or allergy testing. • A subcutaneous injection is administered into the fatty layer of tissue just under the skin. Since the blood flow in fatty tissue is limited, the absorption is slow. This mode of application is frequently used for self administration (e.g. heparin or insulin). The volume may be higher (at most 2 ml), and the sites usually used are the upper arm, the thigh and the abdominal area. If absorption should be inhibited or postponed, a vasoconstrictor (e.g.
5 adrenaline) is added to the liquid. Added hyaluronidase elicits the opposite action: it decomposes a crucial constituent of the extracellular matrix, making the absorption much faster. • Hypodermoclysis is a continuous subcutaneous infusion through which typically saline or glucose solutions are administered. • Solutions can be administered by a sophisticated device fitted with a continuous subcutaneous catheter (e.g. an insulin pump), which can calculate the needed amount. • A higher volume (5–10 ml) can be injected intramuscularly, most frequently into the gluteal muscles, from which absorption can be rather rapid. When long durations are needed, oils or suspensions can be injected in this way. • Intravenous administration involves a bolus and continuous infusion. There is no absorption in this case, and the onset of the action is fast. • Intra arterial injections are rarely used; typically, contrast media are administered for diagnostic purposes. • There are two possibilities for eliciting local actions on the spinal cord. A solution can be administered into the cerebrospinal fluid at lumbar height. In order to prevent an increase of the pressure of the cerebrospinal fluid the same amount of fluid should be withdrawn just before the injection. This kind of injection is called subdural or intrathecal. A simpler procedure is an injection around the dura mater, when the pharmacon reaches the neurons by diffusion (peridural injection). Mostly local anaesthetics are used in these ways in obstetrical or surgical practice. • An intra articular injection involves an administration into a joint. Mostly anti inflammatory agents are used in this way to treat inflammatory conditions of the large joints. • Rarely used modes of injection are intracardial (into the heart muscle), intraocular (into the eye) and intracavernous (into the base of the penis). • An intraperitoneal injection (solution into the abdominal cavity) is suitable to elicit a very rapid onset of action. It is routinely used in animal experimentation, but practically never in human practice. Medicinal implants are special solid dosage forms for subcutaneous application. Since such an implant can release the pharmacon for years, it is a convenient way to achieve a sustained
6 effect. Most medicinal implants contain hormones for contraceptive purposes. The most highly developed medicinal implants are composed of biodegradable vehicle systems and there is no need for removal of the preparation. Transdermal administration is drug delivery through the skin. The upper layer of the skin (epidermis) is composed of stratified squamous epithelial cells, which can be regarded as a lipid barrier. Highly lipid soluble substances (e.g. nicotine, oestradiol and nitroglycerine) are sufficiently absorbed when incorporated into a patch. In the cases of ionized, water soluble drugs, direct current is used to facilitate the absorption. This procedure is called iontophoresis. A reservoir containing the drug solution is placed on the skin and an electrode charged identically with the active ion is coupled to it. The identical charge of the electrode repels the active ion, facilitating its penetration into the deeper layers. The electrode connected to the drug reservoir is called the different electrode, and another reservoir containing saline is placed nearby and connected to the indifferent electrode in order to close the electric circuit. The positive and the negative electrodes are called the anode and the cathode, respectively. Typically non steroidal anti inflammatory drugs (e.g. diclofenac) are applied in this way; these agents should be placed beneath the anode. The direct current used is 1–4 mA and the voltage is a few V. The respiratory tract is also a suitable route for drug administration. The surface area of the nasal mucosa is limited (approximately 150 cm 2) and its proteolytic enzymes further restrict the applicable agents. Most of the nasal drug applications therefore target local action (e.g. decongestants). Some peptides (e.g. vasopressin analogues) are well absorbed from the nasal mucosa and such sprays are used to elicit systemic effects. The surface area of the alveoli is substantially larger (about 140 m 2) and is well vascularized. Inhalational drug administration is not painful, but may require well coordinated movements, which are difficult for children and elderly patients. During absorption from the bronchial and alveolar surfaces, the pharmacon is transported into the pulmonary circulation, which is a special feature of this mode of drug application. The drug is therefore present in the general circulation earlier than with any other mode of administration. Gases, vapours or disperse systems can be inhaled; in the latter case, the size of the particles is crucial. The optimum size is 2–5 m; larger particles are deposited in the upper part of the respiratory tract and do not reach the site of action, while smaller particles are exhaled without deposition at the proper site. Gases and vapours are used to induce general effects such as inhalational anaesthesia. Disperse inhalations are mostly intended to elicit local
7 action (e.g. antiasthmatic inhalations). It is important to know that, even in the case of proper usage, some of the inhaled aerosol or powder is deposited in the oral cavity and the patient swallows it. This fraction can therefore be regarded as orally administered. The most frequently used devices are the vaporizer, the metered dose inhaler and the powder inhaler. Vaporizers are electric devices that vaporize a high volume of solutions, from which the patient continuously inhales. A metered dose inhaler is a reservoir under pressure, from which defined doses can be released and inhaled. The pressure of the propellent may be uncomfortable for some patients. In powder inhalation, there is no propellent, but the patient generates the airflow which carries a dose of fine powder into the airways. Besides anti asthmatics, other agents can be administered through the airways, including insulin and analgesics. Used abbreviation: API active pharmaceutical ingredient Questions 1. Which of the following statements are true? A. After inhalation, the elicited effects are always local. B. After intravenous infusion, the elicited effects are always general. C. Only lipid soluble agents are used on the skin surface. D. Drugs with a basic character are absorbed well from the stomach. 2. What is the meaning of first pass effects? A. Absorption from the first part of the oral cavity. B. The first pass of a drug through the pulmonary circulation. C. The first pass of an orally administered drug through the liver. D. This is the first metabolic reaction in the liver, independently of the mode of administration.
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2. Receptors, signal transduction mechanisms 2.1. Introduction to pharmacological receptors As a result of the development of pharmacological knowledge, it is now possible to specify the site of action of most drugs at a molecular level, i.e. the endogenous molecule (typically a protein) to which the drug is bound as a precondition of the initiation of its action. The basic importance of drug binding was recognized by the German scientist Paul Ehrlich (1854–1915): “Corpora non agunt nisi fixata”, which means that agents only function when they are bound. The binding of a drug or a ligand to a receptor is usually reversible, and it can initiate a reversible change in the conformation of the macromolecule, which will elicit a well defined change in a physiological function. The currently administered drugs alter the rate or magnitude of an intrinsic activity of the living organism rather than create new responses. Drugs can also interact with acceptors, which are proteins in the organism that do not directly cause any change in biochemical or physiological response. However, the interactions of drugs with acceptors (e.g. serum albumin) can modify the pharmacokinetic profile of a drug and may therefore influence its action. A distinction must be made between a site of action and a receptor. Both are macromolecules functioning as molecular targets for drugs. Receptors are proteins that have the physiological function of accepting endogenous substances carrying information within the organism (e.g. hormones, growth factors, neurotransmitters or transcription factors). Pharmacological receptors therefore play a crucial role in the communication between the cells of the organs of the body. Most non receptor drug targets are also proteins, including enzymes (e.g. acetylcholinesterase or dihydrofolate reductase), proteins involved in any kind of transport processes (e.g. the glucose transporter or ion pumps) and structural proteins (e.g. tubulin). Other macromolecules, such as DNA, are also exploited for therapeutic purposes. Many antiviral and chemotherapeutic agents act by binding to DNA. While receptors located either intracellularly or on the cell surface have the special functions of recognizing and responding to endogenous ligands, exogenous compounds (xenobiotics) can also bind to them, mimicking or inhibiting the actions of their natural ligands. These agents are called agonists or antagonists, respectively.
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The natural ligands of the receptors, the agonists, can bind reversibly. Most currently utilized drugs bind reversibly too, but there are a few examples of irreversible binding leading to inhibition of the function of the given receptor. The driving force of the binding is the affinity of the ligand for the receptor, which can be expressed by the dissociation constant ( KD; Chapter 3). One of the most crucial features of the ligand–receptor interaction is the specificity. Specificity is the situation that a receptor exhibits high affinity only for its natural ligand, and lower affinities for a limited number of exogenous ligands. 2.2. Signal transduction Receptors have at least two basic functions: ligand binding and initiation of the response, implying that there must be at least two functional units or domains within the receptor: a ligand binding domain and an effector domain. The action of a ligand bound to a receptor may be exerted directly on its cellular target or it may be conveyed by intermediary molecules called transducers carrying an intracellular response. The mechanism of the action of a ligand that is elicited by binding to a receptor involving any intermediary molecules and effector proteins is referred to as a signal transduction pathway. The first effector protein of a receptor is frequently not the molecule that is directly responsible for the cellular response. The first effector is typically an enzyme that synthesizes or degrades a small molecule (such as cyclic nucleotide or nitric oxide) called a second messenger. Second messengers can diffuse within the cell and carry information to a variety of intracellular targets, which may integrate multiple signals. The final effector protein which is directly responsible for the detectable pharmacological action may receive signals from several receptors. A further common property of receptors is their capacity to amplify a physiological signal significantly. Natural ligands are typically present in low concentrations at the ligand binding domain of a receptor. During the signal transduction pathway, the signal can be amplified by a complex enzyme cascade. For example, when a single agonist molecule binds to a ligand operated ion channel receptor, thousands of ions are transported during the signal transduction procedure. In the case of steroid receptors, a single agonist molecule is able to initiate the transcription of many copies of specific mRNAs, which in turn can induce the synthesis of
10 multiple copies of the corresponding protein molecule. This feature of signal transduction may explain the outstanding efficacy of receptor targeted pharmacological interventions. Receptors can be classified into families on the basis of their molecular structures and the mechanism of their signal transduction procedure. Four main receptor families are described: G protein coupled receptors (GPCRs), ligand gated , enzymatic receptors and transcriptional factors (Fig. 2.1). The most important features of the main families of receptors are presented below.
GPCR
ion channel
enzymatic receptor transcriptional factor Fig. 2.1. The basic structures of receptor classes. S, P and G indicate substrate, product and G proten, respectively. 2.3. G protein coupled receptors (GPCRs) GPCRs are integral membrane proteins with seven transmembrane alpha helices. Humans express over 800 GPCRs, many of which are involved in sensory perception (smell, taste and vision). Others participate in the regulation of a wide range of physiological functions, including the contractility of the smooth muscles, the secretion of the glands or the metabolism. Most of the receptors that are targeted by currently available drugs belong in this family. The endogenous ligands for GPCRs include acetylcholine, noradrenaline, serotonin, histamine, eicosanoids and peptide hormones. After interacting with the agonist, the receptor transmits signals from extracellular ligands to the intracellular G proteins, which are associated with the receptor itself. A G protein is a heterotrimer that consists of Gα, Gβ and Gγ subunits. In the inactive resting state, the Gα subunit binds a guanosine diphosphate (GDP) molecule, but upon activation the receptor and G protein subunit undergo a conformational change, leading to the release of GDP, and guanosine triphosphate (GTP) is bound instead. GTP binding activates the G protein (hence
11 the name). The trimer then separates from the receptor and dissociates into Gα GTP and dimeric Gβγ units. These units usually remain attached to the plasma membrane through their lipid anchors. It is generally accepted that Gα GTP plays the most crucial role in the signal transduction, though the Gβγ dimer elicits some actions too. Since the family is comprised of 23 Gα, 7 Gβ and 12 Gγ subunits, a considerable variability of the heterotrimer is possible. The Gα subunits are responsible for the initiation of the next step of the signal transduction, which is typically the induction or inhibition of the synthesis of an intracellular molecule called the second messenger. The Gα proteins are classified into four classes: Gs, G i, G q and G 12/13 . The Gs subunit activated by GTP binding can activate the membrane bound enzyme adenylyl cyclase, which then catalyses the synthesis of cyclic adenosine monophosphate (cAMP) from adenosine triphosphate (ATP). As a typical second messenger, cAMP has several intracellular targets, of which cAMP dependent protein kinase A (PKA) is the most important. PKA is a heterotetramer complex consisting of two catalytic (C) subunits reversibly bound to a regulatory (R) subunit dimer to form R2C2. When its intracellular concentration is elevated, four cAMP molecules bind to the complex, two to each R subunit, leading to the liberation of the C subunits. The active C subunits phosphorylate serine and threonine residues on a wide range of specific protein substrates, and this is responsible for the final response of the affected cell. The targets of PKA include metabolic enzymes, transport proteins and regulatory proteins, including other protein kinases, ion channels and transcription factors. The stimulation of a given Gs coupled receptor may therefore lead to very different responses, depending on the enzyme pattern of the given cell.
For example, all of the β adrenergic receptors are coupled to G protein containing Gs. The stimulation of the receptor may result in smooth muscle relaxation (e.g. in the bronchi) and in secretion (e.g. in the pancreatic β cells). These target tissues contain the same signal transduction machinery up to PKA, but the downstream machineries are different (Fig. 2.2). The active states of all types of Gα proteins are terminated by GTP hydrolysis, catalysed by the G subunit itself, yielding the inactive form, Gα GDP. Activated Gα proteins therefore have an intrinsic self limiting function that terminates the activity. Gα GDP in turn recruits free Gβγ dimmers, reforming the inactive heterotrimer, which then becomes attached to the receptor. Since the activity of PKA is regulated via cAMP, the concentration of this second messenger is a crucial point in the signalling procedure. Phosphodiesterases (PDEs) are a superfamily of more than 50 enzymes that can hydrolyse the phosphodiester bond in cyclic nucleotides. Gi is another
12 well characterized Gα protein. After activation by receptorial stimulation, it can inhibit adenylyl cyclase, leading to a decrease of the intracellular cAMP concentration. The final effect of the stimulation of a receptor coupled to Gi protein is the opposite of that of receptor signalling via a
Gs containing heterotrimer.
Fig. 2.2 . Mechanism of receptors coupled to G s and G i proteins.
A further type of Gα protein is Gq, which functions similarly to G s, but its target enzyme is different. Upon activation by GTP binding, the released Gq activates phospholipase C (PLC), which in turn hydrolyses a membrane phospholipid, phosphatidylinositol 4,5 bisphosphate, to generate two intracellular signals, inositol 1,4,5 trisphosphate (IP 3) and the lipid diacylglycerol (DAG). PLCs are cytosolic enzymes that translocate to the membrane upon receptor stimulation. Both of these products are second messengers. IP3 has its own receptor on the intracellular calcium (Ca 2+ ) store, the endoplasmatic reticulum (ER), causing the release of stored Ca 2+ . A rapid rise in the cytosolic Ca 2+ level activates Ca 2+ dependent proteins, including calmodulin. The resultant calmodulin–Ca 2+ complex activates calmodulin sensitive enzymes such as myosin light chain kinase (Fig. 2.3). The stimulation of receptors coupled to G the protein with G q typically leads to smooth muscle contraction (e.g. α 1 adrenergic receptor mediated vasoconstriction). The receptor of IP3 is a ligand gated Ca 2+ channel that is highly expressed in the membrane of the ER. The channel can be phosphorylated by a set of kinases, including PKA, and this phosphorylation may enhance Ca 2+ release. The intracellular elevation of Ca 2+ is terminated by a membrane Ca 2+ pump that extrudes Ca 2+ to the extracellular space, where it accumulates in its storage site in the ER. Meanwhile, DAG can directly activate members of the protein kinase C
13
(PKC) family, which modulates the functions of further proteins, including ion channels, by phosphorylation.
Fig. 2.3. Mechanism of receptor coupled to G q protein.
The mechanism of signal transduction mediated through G 12/13 has been less well described. G12 and G13 are separate G proteins with considerable homology; upon receptorial activation by an agonist, they may participate in a wide range of cellular responses, including cytoskeletal changes, cell growth and oncogenesis. G 12/13 transmits its signals to a set of small intracellular GTPases, including Rho protein. They can also interact with several members of the cadherin family of cell surface adhesion proteins, resulting in changes in the adhesion behaviour of the cell. Additionally, some transcriptional factors may dissociate from cadherins, and therefore the expressional pattern of the cell may change. While Gα proteins play the most important role in the heterotrimer in signal transduction, the Gβγ dimer makes its own contribution to the overall procedure. It can directly modulate some ion channels, including K+ and Ca 2+ channels. 2.4. Ligand gated ion channels Since the plasma membrane is impermeable to water soluble substances, including ions, the transmembrane flux of ions requires specialized structures called ion channels or ion pumps. These proteins are essential for maintaining the physiological ion composition in the cytoplasm.
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Humans express more than 200 distinct ion channels, which can be classified according to the regulation of their gating mechanism. From a pharmacological point of view, two families of ion channels are especially relevant: voltage activated and ligand activated ion channels. Although only ligand activated channels may be regarded as receptors, both of these groups are targets for currently used drugs. Since ligand binding elicits changes in ionic currents, these receptors are frequently called ionotropic receptors. The most relevant ligand gated channels in the nervous system are those that bind excitatory neurotransmitters [acetylcholine (ACh) or glutamate] and inhibitory neurotransmitters [glycine or γ aminobutyric acid (GABA)]. The nicotinic ACh receptor, expressed in the central nervous system (CNS), in the autonomic ganglia and at the neuromuscular junction, is the best characterized ligand gated ion channel. Its pentameric structure consists of four different subunits in the neuromuscular junction (β, γ, δ and two copies of α), while only α and β subunits are present in the nicotinic ACh receptors in the CNS and in the autonomic ganglia. Each α subunit has a binding site for ACh, and this binding induces the opening of the pore, allowing a fast inward flow of Na + and therefore depolarization of the membrane (Fig. 2.4).
Fig. 2.4. Mechanism of nicotinic ACh receptor.
15
Glutamate is the major excitatory neurotransmitter in the CNS. The structure and the function of the glutamate receptors are similar to those of the nicotinic ACh receptors; their activation leads to an increased inward flow of cation current, mostly Na + current, initiating depolarization.
One type of GABA receptors (GABA A) is a pore formed by five subunits. Agonist mediated activation of these receptors increases Cl– conductance, which hyperpolarizes the cell membrane and inhibits the propagation of action potentials. 2.5. Receptors as enzymes The membrane of mammalian cells contains a diverse group of receptors with enzymatic activity in the cytoplasmic domain. These enzyme receptors can be classified into two main types depending on the signal transduction they mediate. One type possesses intrinsic enzymatic activity for the synthesis of a second messenger (e.g. receptors of natriuretic peptides). The other type has kinase activity, through which the intracellular domain becomes autophosphorylated, initiating a diverse chain reaction (e.g. insulin receptors). Membrane receptors of natriuretic peptides [atrial natriuretic peptide (ANP), brain natriuretic peptide (BNP) and C type natriuretic peptide (CNP)] contain an extracellular ligand binding domain, a transmembrane linker and an intracellular domain with intrinsic guanylate cyclase activity. This intracellular unit synthesizes cyclic GMP (cGMP) from GTP when the ligand binds to the extracellular unit and induces a conformational change of the whole protein. The downstream effects of cGMP are carried out by a set of cGMP regulated protein kinases [protein kinases G (PKGs)] which, similarly to PKA, activate a wide array of intracellular targets, depending on the given cell. cGMP gated ion channels and cGMP modulated PDEs are additional executors in the signal transduction mediated by cGMP. The other type of enzyme linked receptors is the tyrosine kinase receptors, including receptors for insulin and a set of growth factors [e.g. epidermal growth factor (EGF), platelet derived growth factor (PDGF), fibroblast growth factor (FGF) and vascular endothelial growth factor (VEGF)]. These receptors have an extracellular ligand binding domain, a short transmembrane domain and an intracellular domain with tyrosine kinase activity. The stimulation
16 of growth factor receptors leads to cell proliferation and differentiation. The insulin receptor has an exceptional structure in the class: it is composed of two α and two β chains, independently of its ligand binding state. Other receptors belonging in this class are monomeric in the inactive state, but binding of the appropriate ligand induces dimerization of the receptor and cross phosphorylation of the kinase domains on intracellular tyrosine residues. The phosphorylation of these tyrosines forms docking sites for the SH2 (Src homology 2) domains contained in a large number of signalling proteins. Large, multiprotein signalling complexes are formed on the receptors and initiate a cascade like chain reaction involving the activation of intracellular enzymes, including γ isoforms of PLC (PLCγ) and phosphatidylinositol 3 kinase (PI3K). These enzymes can increase the intracellular levels of Ca2+ and phosphatidylinositol 3,4,5 trisphosphate (PIP3), respectively. PIP3 participates in the formation of further docking sites at the plasma membrane for signalling molecules such as protein kinase B (PKB, also known as Akt). The final effects of these signal transduction pathways typically modulate the growth and differentiation of the cells as well as their apoptosis survival balance (Fig. 2.5). Similarly, the agonist induced activation of intracellular GDP binding proteins of the Ras family leads in turn to activation of a protein kinase cascade termed the mitogen activated protein kinase (MAP kinase or MAPK) pathway. Activation of this pathway is one of the most prominent routes for growth factor receptors to signal to the nucleus and stimulate cell proliferation. A disturbance of these pathways can lead to uncontrolled cell division, and many recently approved antiproliferative agents, called tyrosine kinase inhibitors, exert their actions through interactions with the proteins of these signal pathways (e.g. imatinib and lapatinib).
Fig. 2.5. Mechanism of tyrosine kinase receptors. Tyr and P inducate tyrosine residues and phosphate, respectively. 17
2.6. Nuclear hormone receptors and transcription factors In contrast with the previously discussed classes of receptors found in the plasma membrane, nuclear hormone receptors and related transcription factors are expressed intracellularly, predominantly in the nucleus. In humans, these receptors comprise a superfamily of 48 receptors that respond to a diverse set of ligands. Nuclear hormone receptors function as ligand dependent transcriptional factors and thus provide a direct link between signalling molecules and the expression of proteins. Some nuclear receptors have been identified through sequence similarity to known receptors, but have no identified natural agonists. These proteins are referred to as nuclear orphan receptors. Well known members of the family include receptors for steroid hormones (e.g. androgens, oestrogens and glucocorticoids), thyroid hormone and vitamin D. Additional members of the family are receptors for a variety of lipids, bile acids and vitamin A. Nuclear receptors share a common structural organization, including a DNA binding domain, a ligand binding domain and additional domains with regulatory functions. This class of receptors can be classified into two main types, depending on the mechanism of signal transduction. Type I nuclear receptors without an agonist are located in the cytosol, forming complexes with heat shock proteins (HSPs). Binding of an agonist results in the release of the receptors from HSPs, and the formation of homodimers containing two receptors and two ligands. Such complexes can be translocated into the nucleus and bind to specific DNA sequences called hormone responsive elements (HREs). The final result of the procedure is the initiation of transcription, and the expression of a specific protein is therefore increased. The signals elicited by classical steroid hormones (e.g. oestrogens, androgens, gestagens and gluco and mineralocorticoids) are conveyed to the nucleus through this mechanism. The measurable action of the agonist can be attributed to the function of the induced protein (Fig. 2.6). In contrast, type II receptors are located in the nucleus, regardless of the ligand binding status. In the absence of an agonist, these receptors are typically complexed with corepressor proteins. Upon the binding of an agonist, this corepressor is released and another protein, a coactivator, is recruited. A ligand–receptor complex forms a heterodimer with an orphan receptor known as RXR. The actions of thyroid hormone and vitamin D are mediated through this signal transduction.
18
ligand
HSP dimer receptor
Fig. 2.6. Mechanism of type I nuclear receptors. Used abbreviations: ACh acetylcholine ANP atrial natriuretic peptide BNP brain natriuretic peptide cAMP cyclic ade nosine monophosphate cGMP cyclic guanosine monophosphate CNP C type natriuretic peptide CNS central nervous system DAG diacylglycerol EGF epidermal growth factor ER endoplasmatic reticulum FGF fibroblast growth factor GABA γ aminobutyric acid GDP guanosine diphosphate
19
GPCR G protein coupled receptor GTP guanosine triphosphate HRE hormone responsive element HSP heat shock protein IP3 inositol 1,4,5 trisphosphate
KD dissociation constant MAPK mitogen activated protein kinase PDE phosphodiesterases PDGF platelet derived growth factor PI3K phosphatidylinositol 3 kinase PIP3 phosphatidylinositol 3,4,5 trisphosphate PKA protein kinase A PKB protein kinase B PKC protein kinase C PKGs protein kinases G PLC phospholipase C SH2 Src homology 2 VEGF vascular endothelial growth factor Questions 1. Which of the following receptors are found intracellularly? A. G protein coupled receptors B. Ligand gated ion channels C. Transcription factors D. Enzyme receptors 2. Which of the following receptors generate second messengers? A. G protein coupled receptors B. Ligand gated ion channels C. Transcription factors D. Enzyme receptors
20 3. Dose–response relationships 3.1. General remarks
The word dose is a frequently used term in pharmacology and therapy. Its exact meaning seems obvious, but confusion sometimes arises in connection with dose-related expressions. A dose is always an amount of a given drug, but a dose can be specified in many ways. In an in vivo experiment or in clinical practice, a dose may be given as a weight, expressed in mg or g. In many cases it is given for a unit of body weight (e.g. in mg/kg) or rarely for a unit of body surface (e.g. in mg/m2). The dose of an inhalational anaesthetic (e.g. isoflurane) is given as its percentage concentration in the inhaled air. In in vitro investigations, concentrations are used instead of doses, e.g. mg/ml, μg/ml, mM or μM. There are some special doses. The minimally effective dose (MED) is the lowest dose that elicits a detectable degree of the main effect of the drug. In a clinical situation, this is the lowest useful dose. The maximum tolerated dose (MTD) is the upper limit of the clinically usable dose; at higher doses the drug is not tolerated. In a clinical setting, the range between these two special doses is the therapeutic range. The wider the therapeutic range, the easier it is to find the optimum dose which elicits the desired action without unacceptable side-effects. Basically two kinds of systems can be utilized in pharmacological experiments, including dose vs. response studies: in vitro (“in glass”) and in vivo (“in the living organism”) systems. Both systems have advantages and limitations and therefore a well-established place in pharmacology. A typical in vitro system contains animal tissue (e.g. smooth muscle) maintained in buffered physiological saline containing everything needed for survival of the preparation (i.e. ions and glucose in oxygenized solution at a controlled temperature). A tested agent can be added to the solution containing the tissue, and the possible response is a change in the contractility of the smooth muscle, which can be recorded. Since the force of contraction is dependent on the size of the dissected muscle, the response is usually given in relative units (e.g. a percentage of the maximum contraction). In a setting of this kind, the pharmacological response is determined exclusively by the interaction of the tested agent and the targeted receptor. Since the drug concentration in the buffer is constant, its elimination does not have to be considered. This kind of simple preparation can tolerate even extreme conditions, including high concentrations of the
21 tested agent. In vitro systems are therefore used whenever simplification of the complexity of a living organism is required, especially for mechanistic studies. In in vivo studies, a living animal is treated, and effects are evaluated through the determination of some physiological parameter (e.g. the blood pressure or heart rate). In vivo systems have limitations: the pharmacokinetic profile of the tested agent must be considered, because some organs may not be exposed to the drug, and the elimination can limit the duration of its action. The sensitivity of the animal may also be a limiting factor, and extreme doses can disturb the recorded function or even kill the animal. On the other hand, the results obtained from an in vivo experiment are more conclusive when they are extrapolated to a clinical situation.
3.2. Concentration vs. response relationships in in vitro systems
In an ideal in vitro system, the action of a tested agent (usually contractions) is determined exclusively by the interaction of the receptor (R) and the ligand (L). They can form a complex, RL, in a reversible interaction: R + L ↔ RL 3.1 At equilibrium, the rates of dissociation and association are equal. The driving force for the formation of the complex RL is the affinity between R and L, which can be described by the dissociation constant: [L] ∙ [R] = 3.2 [RL] where KD is the dissociation constant of RL; [L], [R] and [RL] are the concentrations of L, R and
RL, respectively. It is not simple to determine these concentrations, apart from [L], and KD cannot be calculated directly. R is present either in free form (R) or complexed with the ligand (RL), and therefore
[R ] = [R] + [RL] 3.3 and
[R] = [R ] − [RL] 3.4 where [Rtot] is the total concentration of R. If Eq. 3.4 is substituted into Eq. 3.2, we obtain [L]{[R ] − [RL]} = 3.5 [RL] On rearrangement:
22
[RL] [L] = 3.6 [R ] + [L]
The left-hand side of Eq. 3.6 still seems problematic. [Rtot] cannot be easily measured. On the other hand, if we suppose that the saturation of each receptor contributes to the overall action, it seems reasonable that the ratio [RL]/[Rtot] corresponds to the ratio of the effect elicited by [L] and the maximum effect that can be elicited in the experimental system: ∆ [L] = 3.7 ∆ + [L] where Δ and Δmax refer to the actual effect and the maximum effect, respectively. The actual effect can therefore be described as a function of [L] as follows: ∆ ∙ [L] ∆= 3.8 + [L] When the actual effect is plotted against the [L], a typical saturation curve is obtained (Fig. 3.1). During the generation of the experimental data, [L] is increased exponentially for practical reasons (e.g. threefold or tenfold). A linear concentration scale is therefore not suitable, and concentration vs. response curves are typically presented as semilogarithmic plots (Fig. 3.1). The saturation curve is also called a sigmoid curve.
23
Fig. 3.1. The same set of concentration vs. response data in linear (panel A), semilogarithmic (panel B) and double reciprocal plots (panel C). Panel D exhibits a part of panel C.
Before the computer era, curve fitting to the experimentally determined points was a great challenge and linearization of the curve was attempted. Equation 3.8 can be rearranged into the following form: 1 1 1 = + 3.9 ∆ [L] ∆ ∆ Equation 3.8 describes a linear function of 1/Δ and 1/[L], and its graphical presentation is called a double reciprocal or Lineweaver–Burk plot (Fig. 3.1). One of the most important aims of in vitro concentration vs. response studies is the determination of the affinity of a tested ligand towards its receptor. For this, KD should be expressed. If Eq. 3.7 is solved for the concentration when exactly half of the maximum action is obtained, we obtain KD = [L]. The ligand concentration that elicits exactly half the maximum effect is therefore identical with the KD of the drug. This means that concentration vs. response curves are suitable for determination of the affinity of the agent in question. The higher the
24 affinity of the drug, the lower the value of KD, which is usually expressed as molar concentration. In order to avoid numbers containing exponential components, its negative logarithm is used –7 instead (e.g. 6.26 instead of 5.43 x 10 M), this being called the pD2 value. Thus, pD2 is the negative logarithm of the agonist concentration that elicits 50% of its maximum effect in the given in vitro system. The higher the affinity of the tested agent, the higher its pD2 value (Fig. 3.2). Agonists may differ not only in their affinities, but also in their abilities to initiate signal transduction through the receptor. As a consequence, some agonists cannot induce the maximum effect in the given system, even at high concentrations. This character of the receptor–ligand interaction is expressed in a further parameter, the specific activity. The specific activity, α, is the ratio of the maximum effect of the given drug and the maximum effect that can be elicited in the given experimental system:
∆ / ∝= 3.10 ∆ / The maximum value of α is 1 (or 100%), indicating that the tested agonist is able to elicit the maximum effect in the given system. This kind of ligand is called a full agonist. If α is <1, but >0, the ligand can elicit an effect, but its maximum effect is less than that possible in the experimental system. This kind of ligand is referred to as a partial agonist (Fig. 3.2). When α=0, the tested drug has no capacity to initiate the signal transduction which is characteristic of antagonists.
Fig. 3.2. In vitro concentration vs. response curves of agents with different properties. The order of affinity is A > C > B. The specific activity of A and B are identical while that of C is lower. 25
In some special cases, α<0. This is possible when the targeted receptor has continuous intrinsic signalling activity without ligand binding. The intrinsic activities of these receptors can be decreased by this kind of drugs, called inverse agonists.
3.3. Dose vs. response relationships in in vivo systems
A living animal or a human volunteer is obviously a much more complex pharmacological system than an in vitro preparation. Since the drugs may exert off-target toxicities the covered dose ranges are typically less wide than concentrations ranges tested in vitro. The effects in in vivo situations are usually measured, in the units of the physiological parameter (e.g. blood pressure in mmHg, or blood clotting time in seconds). Besides the interaction of the drug and its receptor, the determined effect can be modified by a wide range of factors, including the pharmacokinetic behaviour of the pharmacon. The parameters used to describe the concentration vs. response curves, i.e. affinity and specific activity, are therefore not suitable for characterization of the results obtained in an in vivo system. On the other hand, the shape of the plot is similar. The dose eliciting 50% of the maximum effect is called the ED50 (effective dose 50%) and is a measure of the potency of the drug. The higher the potency, the lower the value of ED50 value. The maximum height of the curve reflects the efficacy of the drug (Fig. 3.3).
26
Fig. 3.3. In vivo dose vs. response curves of agents with different properties. The order of potency is A > C > B. The efficacy of A and B are identical while that of C is lower.
Instead of determining the effect in the units of a physiological function, there is another approach for the study of dose vs. response relationships. In this case, the effect is defined as a bimodal variable: it either develops or it does not. A typical example is lethality, determined during acute toxicity studies. Groups of animals are treated with increasing single doses and the proportions of those that die within a defined time are recorded. The higher the dose, the higher the proportion of animals that die. The final plot is similar, but the interpretation is slightly different. The LD50 (lethal dose 50%) is the dose which causes half of the treated animals die. This approach is called qualitative dose vs. response interpretation, in contrast with the previously detailed quantitative mode of investigation. In a qualitative approach, ED50 generally indicates the dose at which half of the subjects display the effect in question. In clinical situations, qualitative interpretation of the dose vs. response relationship is quite common, e.g. the dose of an antihypertensive agent at which the blood pressure of half of the patients lie below a previously defined value could be important. All of the concentration or dose vs. response relationships discussed so far followed the trend of the saturation curve. In pharmacological practice, however, many examples are to be found of atypical relationships both in vitro and in vivo. Most of these atypical dose vs. response relationships exhibit a biphasic character: the recorded parameter (e.g. the blood pressure) can decrease or increase, depending on the dose applied. This phenomenon can generally be explained by the superposition of two opposite actions elicited by the same drug, with different 27 mechanisms. Adrenergic agonists may cause the relaxation of smooth muscles at low concentrations by acting on β-adrenergic receptors. At higher concentrations, the relaxation can be decreased and the same agent results in increased contractility, mediated through the α- adrenergic receptors. The overall action is the sum of the two separate effects. If these effects were measured separately, in the presence of selective α- and β-adrenergic antagonists, two sigmoid curves would be obtained (Fig. 3.4). All atypical or non-sigmoid dose vs. response curves can be broken down into two or more regular curves.
Fig. 3.4. An atypical concentration vs. response curve of an agent (black line) is the sum of contraction (red line) and relaxation (blue line).
Used abbreviations: Δ the actual effect elicited by the ligand
Δmax maximum effect elicited in the given system α specific activity
ED50 effective dose 50%
KD dissociation constant [L] concentrations of the ligand L,
LD50 lethal dose 50% MED minimally effective dose MTD maximum tolerated dose [R] concentrations of the free receptor, R [RL] concentrations of the receptor–ligand complex, RL
[Rtot] total concentration of the receptor, R
28
Questions
1. Which of the following parameters can describe the binding force between the ligand and the receptor? A. the specific activity
B. the ED50 C. the dissociation constant D. the maximum effect
2. What is the meaning of pD2? A. the logarithm of the specific activity
B. the reciprocal of KD
C. the logarithm of KD
D. the ratio of the specific activity and KD
29
4. Absorption and distribution of drugs and factors influencing this 4.1. Absorption of drugs 4.1.1. Main features of drug absorption
The absorption of a drug is the process of uptake of the pharmacon from the site of administration into the bloodstream. This definition implies that there is no absorption after intravascular (intravenous or intra-arterial) administration. The predominant route of drug administration is extravascular (enteral, intramuscular, subcutaneous or transdermal) and a systemic effect is often expected. In these cases, therefore, absorption is a prerequisite of the therapeutic action. Absorption is a special pharmacokinetic procedure that starts with the administration of a formulated preparation containing the active pharmaceutical ingredient (API). All of the subsequent steps (distribution, metabolism and excretion) describe the fate of the pharmacon, and the vehicle does not have a relevant role. The API in the dosage form can be interpreted as an extravascular depot from which the pharmacon enters the circulation. A prerequisite of the absorption is the liberation of the API from the dosage form and the formation of a water-phase solution at the appropriate site. As the initial step, most of the solid dosage form (e.g. a tablet, capsule or suppository) should disintegrate, followed by dissolution of the API in some body fluid outside the circulation. After enteral administration, this solvent could be the gastric juice or the intestinal fluid. The procedure is similar for other routes of administration. In the cases of an intramuscular injection or a drug-containing patch, the API is dissolved in the tissue fluid or in the sweat, respectively. There are dosage forms which release the API without disintegration (e.g. patches and some matrix tablets), while in other cases the application of disintegration is problematic (e.g. an intramuscular oil injection). Dissolution is a necessary step in all of these cases. The slowest of these three consecutive steps (i.e. disintegration, dissolution and absorption) determines the overall rate of absorption; it is the rate-limiting step. The disintegration of orally administered solid dosage forms is usually more rapid than the dissolution and drug absorption, except in the case of controlled-release preparations. For APIs with relatively poor aqueous solubility, the dissolution determines the rate of the drug eaching the systemic circulation. In contrast, for pharmacons with comparatively good aqueous solubility, the
30 dissolution is faster and the rate-limiting process is the permeation through the cell membranes, i.e. the absorption itself. The liberation of the API from a dosage form (i.e. the disintegration and the dissolution) can be influenced by technological means, and absorption is the only pharmacokinetic procedure that can be directly modified or optimized by appropriate formulation design. When the API enters the circulation, the molecules must cross at least one cell layer (the endothelia of the capillaries). This implies that, before it reaches the circulation, it must cross cell membranes. The cell membrane allows the absorption of lipid-soluble substances. Substances with low molecular weight that have limited lipid solubility may also be readily absorbed through the pores of the membrane. Transcellular absorption means that the API moves across the cells, while paracellular absorption is the process of intravasation though tight junctions (i.e. between the cells). The two procedures do not exclude each other; an API can be absorbed through a mixed mechanism. There are basically two possibilities by which an API molecule can cross a cell membrane: passive diffusion and carrier-mediated transport. The latter category includes active transport and diffusion.
4.1.2. Absorption of drugs by passive diffusion
During passive diffusion, molecules spontaneously move from a region of higher concentration to a region of lower concentration. The driving force of the movement is the concentration gradient and there is no energy utilization. Passive diffusion can be the mechanism of absorption when a cell layer or a membrane separates the intravascular fluid and a drug solution at the site of application. The concentration at the site of application is obviously higher, and the molecules therefore cross the membrane and enter the circulation. The procedure ends when the concentrations become equilibrated. Absorption driven by passive diffusion can be described by Fick’s law: = − 4.1 ℎ where dQ/dt is the rate of absorption (i.e. the amount of drug absorbed in unit time); A is the surface area of the membrane; K is the lipid–water partition coefficient of the drug; h is the thickness of the membrane; D is the diffusion coefficient (the factor determining the rate of
31 absorption when all other factors are unity); C0 and Cp are the concentrations of the drug at the site of application and in the circulation, respectively. Although diffusion is generally a directional process, Cp cannot be higher than C0, and the overall direction of the movement of the API is therefore always unidirectional (i.e. from the depot into the circulation). Since no structural element is involved in the procedure (except for the membrane itself), diffusion cannot lead to saturation even at high concentrations. Equation 4.1 explains the importance of solubility in absorption. A higher aqueous solubility leads to a higher concentration gradient (i.e. C0 – Cp), which can make the whole procedure faster. The partition coefficient (K) reflects the lipid–water distribution of the pharmacon. A drug with a higher lipid solubility has a higher K value and reaches a higher concentration in the cell membrane. From a practical point of view, Eq. 4.1 is far from ideal; most of its constituents are difficult to determine experimentally. Since D, A, K and h are constant for a given drug and a given mode of administration, a combined constant (ka, the absorption constant) can be introduced. As concerns the concentration gradient, C0 is obviously substantially higher than Cp, partly because the intravascular volume is much less than the volume of the depot at the site of application, and partly because elimination starts immediately after the API enters the circulation. Cp can therefore be omitted without causing a substantial error: = 4.2 Equation 4.2 describes a typical first-order process. Integration leads to an equation describing the amount of API absorbed as a function of time:
= 4.3 where M is the amount of API absorbed up to time t; M0 is the total amount of API. Thus, if M0 and ka are known, the amount absorbed can be calculated. In terms of the time at t½a at which the half of the given amount is absorbed, i.e. the absorption half-life; 1 ½ = 4.4 2 i.e. 1 − = ln == −0.693 4.5 ½ 2 ka and t½a are therefore inversely proportional parameters; the one can be calculated from the other one. The meaning of ka is the proportion of the dose that is absorbed in unit time. Its units are 1/time (e.g. 1/h).
32
4.1.3. Absorption of drugs by active transport
The importance of active transport, and especially the role of ABC (the ATP-binding cassette) transporters, was recognized recently. The API is transported unidirectionally a carrier under the expenditure of energy (the hydrolysis of ATP); the direction of the transport is independent of the concentration gradient. The carrier is an integrant membrane protein that has affinity for the API, and the binding of the API follows the API–receptor interaction. An API with higher affinity for the transporter can displace agents with lower affinity. Since ATP is needed for the procedure, cell metabolic poisons (e.g. cyanide) inhibit the active transport non- competitively. The number of transporter proteins is finite and the process can be saturated with a high concentration of the API (Fig. 4.1).
Fig. 4.1. The rate of transporter-mediated absorption as a function of C0.
The transporter itself can be regarded as an enzyme with a special function, and the transport can be described by a special application of Michaelis–Menten kinetics: = 4.6 + where dQ/dtmax is the maximum rate of transport; KM is the API concentration at which the rate of transport is 50% of the maximum rate. The equation can be evaluated as a function of C0. At high concentrations, when C0 > KM, KM can be neglected and the rate of transport becomes equal to the maximum rate of absorption. At lower concentrations, when C0 < KM, C0 can be neglected and Eq. 4.7 is obtained:
33
4.7 =
The constants (dQ/dtmax and KM) can be combined as ka, giving Eq. 4.2.
4.1.4. Absorption of drugs by additional transport mechanisms
Facilitated diffusion combines the features of passive diffusion and active transport. It is carrier-mediated transport without energy utilization, driven by the concentration gradient. Since a membrane protein facilitates the movement of the API, the process can be saturated and the API can be displaced by another agent. In terms of API absorption, facilitated diffusion plays only a marginal role. Vitamin B12 forms a complex with the intrinsic factor produced by the stomach, and at low doses (up to 1.5 mg) this complex is absorbed by facilitated diffusion. At higher doses, passive diffusion can predominate. Vesicular transport is the only possibility for the absorption of undissolved substances. During this kind of transport, the cell membrane surrounds the material to be transported and forms a vesicle which crosses the cell. The content of this vesicle is then released into the circulation by exocytosis. Pinocytosis and phagocytosis are forms of vesicular transport. In pinocytosis, small fluid droplets are engulfed and transported, while phagocytosis involves the engulfment of larger particles. Vesicular transport is not crucial from a pharmacokinetic aspect, though lipid droplets containing lipid-soluble vitamins can be absorbed by pinocytosis. Convective transport is a mode of absorption that explains the paracellular movement of APIs from the site of application into the bloodstream. The intercellular gaps may be interpreted as pores in the endothelial cell layer which are suitable for the absorption of smaller (molecular weights up to 400) dissolved molecules. Energy is utilized in this kind of transport and the driving force is the concentration gradient.
4.1.5. Factors influencing drug absorption
Since many processes are involved between the application of a drug preparation and the end of the absorption of its API, the overall process can be influenced by a large number of factors. These can be classified into the following groups:
34
factors characteristic of the API (solubility and pharmacological profile); factors characteristic of the preparation (properties of the vehicle system, and the technology of the preparation); factors characteristic of the physiology of the site of application (vascularization and pH). As discussed earlier, aqueous solubility is required for absorption. Their lipid solubility determines the rate at which agents cross biological membranes, including the walls of capillaries. Higher lipid solubility is associated with faster absorption. Many drugs exhibit polymorphism and the polymorphic forms may differ in their biologically relevant properties. An amorphous form generally has a higher solubility and is therefore absorbed faster. Many drugs are absorbed by means of active transport and the affinities of the molecules for the transporter proteins are extremely important. Additionally, a drug can affect the physiological functions at the site of absorption (e.g. changing the gastrointestinal motility or the blood flow at the injection site). The size of the particles may be crucial when an agent has only low solubility in the body fluids. Reduction of the particle size increases the surface area of the API, and as a consequence the dissolution is more rapid. Agents that are poorly soluble in water are frequently formulated in a micronized or microcrystalline form containing particles measuring 2–10 μm. A further approach through which to increase the rate of absorption of such pharmacons is to add surface- active agents to the dosage form. The active agent is then solubilized by the tenside. The properties of the preparation are obviously determined by the technology utilized during the manufacturing (e.g. increase of the mechanical resistance of a tablet prolongs the disintegration and the dissolution time, and the overall adsorption therefore becomes slower). As concers the physiological conditions at the site of application, the local blood flow is obviously a critical factor. The choice of different sites for the subcutaneous administration of insulin can result in different onsets of action. Modification of the blood flow (e.g. through the addition of a vasoconstrictor to an intramuscular injection) may likewise have an impact on the absorption. The acidity at the site of application is another highly significant factor; numerous drugs are weak acids or weak bases, which may be present in either ionized or non-ionized form as a function of the local pH. Non-ionized forms are lipid-soluble and can readily cross cell membranes, whereas ionization delays absorption. Weak acids and weak ionize as follows: HA ↔ A + H 4.8
35
BH ↔ B + H 4.9 where HA and A– are the non-ionized and ionized forms, respectively, of a weak acid; B and BH+ are the non-ionized and ionized forms, respectively, of a weak base. The extents to which these agents dissociate can be described by Ka (the dissociation constant and the concentrations of the components): [H ][A ] = 4.10 _ [HA] [H ][B] = 4.11 _ [BH ] where Ka_acid and Ka_base are the dissociation constant of the weak acid and base, respectively, and the square brackets denote concentrations. Since acids and bases behave very similarly, the further description will be limited to weak acids. Rearrangement of Eq. 4.10 and the introduction of negative logarithms leads to the Henderson–Hasselbalch equation: [A ] pH = pK + log 4.12 [HA] where pKa is the negative logarithm of Ka. The stronger the acidity of a substance, the lower its pKa value. Rearrangement of Eq. 4.12 leads to [A ] = 10( ) 4.13 [HA] The ratio [A–]/[HA] can be regarded as the ratio of the concentrations of the ionized and non- ionized forms, or I/N, at the given pH. A new parameter may be introduced, the percentage ionization (PI), which expresses the percentage of the amount of the ionized form: 100 ∙ I PI = 4.14 I + N Substitution of Eq. 4.13 into 4.14 gives 100 PI = 4.15 1 + 10( ) and 100 PI = 4.16 1 + 10( )
Equations 4.15 and 4.16 indicate that the extent of ionization of acids and bases (PIacid and PIbase, respectively) are determined by the local pH. This explains why the ionization of acidic drugs (e.g. aspirin) is depressed in the stomach, whereas drugs with a basic character undergo extensive ionization in the same place.
36
The local pH determines the distribution of weak acids and bases between two fluid compartments that differ substantially in acidity (e.g. the gastric juice and the plasma). Thus, distributions between the plasma and any other body fluid can be described by the following equations:
1 + 10( ) 4.17 = = ( ) 1 + 10
1 + 10( ) 4.18 = = ( ) 1 + 10 where Racid and Rbase are the concentration ratios between the plasma and the other body fluid for an acid and a base, respectively; Cp and Cx are the concentrations in the plasma and the other fluid, respectively; and pHp and pHx are the pH of the plasma and the other fluid, respectively.
4.2. Distribution of drugs 4.2.1. General remarks
Distribution is the process in which a proportion of the API passes from the intravascular fluid to other body fluids or compartments. The distribution is finished when equilibrium is established between these body fluids and no further net API movement occurs. The water content in the human organism accounts for approximately 60% of the body weight. Let us consider a 70 kg person with a total body water content of 42 l. This water is distributed between various compartments (Table 4.1).
Table 4.1. The approximate volumes of the water compartments of the body
Compartment Volume (l) Plasma ~3 Interstitial water ~15 Intracellular water ~23 Transcellular water ~1
The transcellular water is the overall amount of fluid inside the organs (e.g. the cerebrospinal fluid, the ocular fluid and the gastrointestinal juices). The transcellular water is usually ignored in calculations.
37
Absorption and distribution are similar procedures from many respects; crossing an anatomical barrier is a key element in both. Some of the factors determining the distribution of APIs: the ability of the API to cross the capillary wall; the ability of the API to cross the cell membrane; the lipid solubility of the API; the binding of the API to plasma proteins; the pH of the given organ or tissue; the affinity of the API for any cell component. Many APIs can reach very high concentrations in some tissues, sometimes without any short-term effect. Agents that dissolve well in lipids can accumulate in the depot fat. The consequences are complex: the slow, but continuous tissue uptake can decrease the therapeutic activity. When the amount of fat is substantially decreased, the stored API is released into the bloodstream and an unexpected response may be observed. Some metals (lead and strontium) and tetracycline antibiotics can accumulate in the bones, while phenothiazines can become concentrated intraocularly.
4.2.2. Volume of distribution
The volume of distribution (VD) is used to express the amount of API present in the plasma volume in the body. It is independent of the body fluids because it is not restricted by anatomical borders. It is the hypothetical volume that would be needed to dissolve the total amount of API present in the body at the same concentration as that found in the plasma. It can be much larger than the actual water content of the body. VD can sometimes be several hundreds of l; it is expressed as the “apparent volume of distribution”. This surprising finding can be explained by the inhomogeneous distribution of the API in the body; its concentrations in the various tissues can differ substantially. When VD is calculated from the given dose and the plasma concentration, its homogeneous distribution is assumed, but this is generally not true; many APIs concentrate in specific tissues. In spite of the theoretical and “apparent“ nature of VD, it is routinely used in calculations to establish dosage regimen.
38
4.2.3. Binding to plasma proteins
APIs entering the bloodstream may bind reversibly to plasma proteins, and especially to albumin. The protein binding of APIs is aspecific, but there are some proteins in the plasma which possess specific binding and transport functions (e.g. transcortin, transferrin and cyanocobalamin) and which can take up some APIs more selectively. Pharmacons exhibit much lower affinity for plasma proteins than that for their therapeutic targets. Since the physiological concentration of albumin is higher than that of most APIs (~0.6 mM or 4.6 g/dl), it has a high capacity and the binding behaves as unsaturable. As a consequence, in the usual range of concentrations, the amount of an API bound to plasma proteins is constant and characteristic of the given drug. In the plasma, the bound and unbound fractions are in equilibrium, and the rate of protein binding has a profound impact on the fate of the API. Only the unbound API can cross membranes, and only this fraction can directly exert its pharmacological effect at the site of action (e.g. on a receptor, an enzyme or an ion channel). Furthermore, only unbound molecules have direct access to a metabolic enzyme or an excretion mechanism (e.g. glomerular filtration). The bound fraction can be regarded as a depot, and excessive protein binding may prolong the duration of action. As a general rule, the lower the aqueous solubility of an agent, the higher the fraction bound to albumin. Typically, one or two acidic molecules can be bound to this protein, but the binding is relatively strong. In contrast, a higher number of basic or positively charged molecules can be weakly attached to albumin. Although the binding capacity of plasma proteins is huge, two or more APIs can displace each other from albumin, and the free fraction is therefore elevated. This is a typical pharmacokinetic interaction, in which the action of the displaced agent is increased, which may be clinically relevant when the protein binding is high (e.g. warfarin) or when the therapeutic range is narrow (e.g. cardenolides).
4.2.4. Special drug distributions: the blood brain–barrier (BBB) and the placental barrier
The wall of the capillaries in the brain is much less permeable to many APIs than anywhere else in the body, resulting in limited cerebral exposure to such APIs. This phenomenon of low permeability is known as the BBB. Highly lipid-soluble drugs generally exhibit better
39 permeation into the central nervous system (CNS). On the other hand, only the unbound fraction of an API can cross the vessels, and extensive protein binding therefore limits entry to the CNS. The background of the BBB is partly structural and partly functional. The capillaries in the CNS are less fenestrated and are covered with an additional layer of astrocytes. On the other hand, the ATP-driven transporters of the ABC family are expressed on the luminal side of the endothelial cells, pumping substrates back into the blood. Since the activities of the ABC transporters can be inhibited pharmacologically, the BBB can be “switched off” with drugs. Although the placenta serves as an interface between the maternal and foetal circulations, its barrier functions are generally limited to macromolecules. Small molecules usually reach the foetal body and exert their action on that too. Since the pH of the foetal blood is slightly lower than that of the mother (~7.30 and ~7.44, respectively), weak bases can concentrate in the foetal compartment.
Used abbreviations: ABC ATP-binding cassette API active pharmaceutical ingredient BBB blood brain–barrier
C0 concentrations of the drug at the site of application CNS central nervous system
Cp concentrations of the drug in the circulation D diffusion coefficient h thickness of the membrane K lipid–water partition coefficient ka absorption constant
Ka_acid dissociation constant of the weak acid
Ka_base dissociation constant of the weak base
KM Michaelis–Menten constant PI percentage ionization pKa negative logarithm of Ka t½a absorption half-life
VD volume of distribution
40
Questions
1. What is the meaning of ka? A. The time needed for the complete absorption of a drug. B. The time needed for the absorption of half of the administered drug. C. The proportion of the administered drug that is absorbed during unit time. D. The proportion of the given drug that reaches the systemic circulation.
2. What is true for the apparent volume of distribution? A. It must be less than the total water content of the body. B. It can be higher than the total water content of the body. C. It is usually equal to the intracellular water content of the body. D. It is equal to any of the anatomically described water compartments of the body.
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5. The drug metabolism 5.1. The main features of the drug metabolism
The term metabolism in its widest meaning refers to any kind of chemical conversion within the body. Three principal functions may be involved: The generation of energy for all energy-dependent vital functions. The catabolism (breaking down) of the ingested substances in order to obtain building elements for the biosynthesis of other molecules. The conversion of exogenous compounds (xenobiotics: drugs, environmental pollutants, cosmetics, etc.) to metabolites with higher aqueous solubility in order to excrete them more easily. It is noteworthy that most pharmacologically active agents exhibit some degree of lipid solubility, which is needed when they cross membranes to reach the sites of their action. The overall excretion of such substances is slow, however, because of the efficient reabsorption after glomerular filtration or biliary excretion. The polarity of xenobiotics is therefore increased as a precondition of efficient excretion. The metabolism of drugs is often regarded as detoxification, indicating that the metabolites of the given drug are ineffective or less effective than the parent drug itself. This is generally true, but there are many examples of drugs with active metabolites which can contribute substantially to the overall action (e.g. diazepam → nordazepam or imipramine → desipramine). There is a further common situation, when the parent drug is ineffective, but its metabolite is responsible for the therapeutic action (e.g. enalapril → enelaprilate or spironolactone → canrenone). Such parent drugs are called prodrugs. The enzymes involved in drug metabolism are not specific for their substrates; they can transform a very wide range of compounds, including synthetic molecules and drugs that have not yet been discovered. Most tissues have the capacity to metabolize drugs, but the highest activities are found in the gastrointestinal tract the (small intestine, liver and the microbial flora of the colon). The drug metabolism consists of two phases: phase I and phase II. During phase I, the non-synthetic or functionalization phase, the basic structure of the drug in not changed, but novel functional groups are introduced or the previous functional groups are changed. As a consequence, a certain degree of pharmacological activity is retained and the polarity is moderately increased. In phase
42
II, the synthetic or conjugation phase, the newly introduced or modified functional groups are used to couple to the xenobiotics, relatively bulky, endogenous and highly water-soluble molecules (e.g. glucuronic acid) to increase the overall polarity of the product. This means a fundamental change in the structure of the drug, and phase II metabolites are therefore pharmacologically ineffective. Most enzymes catalyse phase I reactions, and UDP- glucuronosyltranferases (UGTs) are located in the endoplasmic reticulum of the cell, while enzymes involved in phase II reactions are found in the cytosol.
5.2. Phase I of the drug metabolism
The most relevant phase I metabolic reactions include oxidation, hydrolysis and reduction. Oxidative reactions may be grouped as follows (Fig. 5.1): Aliphatic oxidations, which follow the ω – 1 rule: hydroxylation of a long carbon chain takes place on the carbon atom before the last one. In the case of a secondary carbon atom, the oxidative reaction can continue, and the final product is a ketone. Aromatic hydroxylations through an unstable epoxide. The hydroxy group is added opposite the substituent on the aromatic ring. Besides the most common phenolic compounds, more complex aromatic skeletons (e.g. heteroaromatic rings or condensed rings) can also be oxidized in this way. N-Dealkylation is considered to be oxidative because the group that is removed is oxidized (most commonly, a methyl group is eliminated as formaldehyde). The dimethylamino function is frequently demethylated in this way (e.g. imipramine or tamoxifen), but diazepam, morphine and caffeine are also substrates for such reactions. Deamination results in the elimination of a primary amino function and the formation of a ketone. Among others, histamine and amphetamine are metabolized through deamination. The N-oxidation of primary and secondary animes results in hydroxylamines. The hepatotoxic metabolite of paracetamol (N-acetyl-p-benzoquinoimine) is formed through this kind of oxidative reaction. Tertiary amines too may be oxidized into the corresponding N-oxides (e.g. chlorpromazine).
43
O-Dealkylation is typical for methyl ethers, and reaction results in an alcohol and an aldehyde (mostly formaldehyde). This is the basis of the conversion of codeine to morphine. S-Oxidation can take place in two steps; addition of one oxygen atom to the sulfur atom results in the corresponding sulfoxide, and the second oxygen is needed for a sulfone. Phenothiazines are substrates for this reaction. S-Dealkylation is similar to O-dealkylation; it is restricted to a few thioethers (e.g. 6- methyl thiopurine). Desulfuration and epoxidation are also restricted to a limited number of drugs (e.g. thiobarbiturates and carbamazepine, respectively).
44
Fig. 5.1. The most relevant phase I oxidative reactions. Aliphatic oxidation (A), aromatic hydroxylation (B), N-dealkylation (C), deamination (D), N-oxidation (E), O-dealkylation (F), S-oxidation (G) and S-dealkylation (G).
45
The most relevant oxidative enzymes involved in the phase I reaction are the members of the cytochrome P450 family (CYPs). CYPs are haeme-containing proteins requiring molecular oxygen, NADPH and a NADPH-CYP oxidoreductase for the catalysis of endogenous reactions and the transformation of xenobiotics. CYPs are able to oxidize structurally very diverse chaemicals with relatively low catalytic rates. The human genome contains 57 CYP genes and the corresponding enzymes are classified into 18 families and 43 subfamilies on the basis of their structural features. Thus, CYP2D6 means enzyme number 6 in subfamily D in family 2. In humans, families 1–3, containing 12 CYPs, are primarily responsible for the metabolism of xenobiotics. These enzymes exhibit relatively low substrate affinities and are mostly expressed in the intestinal tract and in the liver. The most relevant subfamilies are CYP2C, CYP2D and CYP3A. CYP3A4 is the most abundant CYP, and is involved in about 50% of currently used agents. CYPs belonging in further families have their roles in an endogenous biochemical pathway and are expressed in the corresponding organs. These CYPs participate in the conversions of lipid-like substances such as steroids, fatty acids or vitamin A. For example, CYP5A1 is involved in thromboxane synthesis, while CYP51A1 (also called lanosterol 14-α- demethylase) catalyses a step of cholesterol synthesis. CYP19A1 (commonly called aromatase) promotes the formation of oestrogens. The overall reaction catalysed by the CYPs can be described as follows: + + RH + O2 + NADPH + H → ROH + H2O + NADP 5.1 where RH and ROH are the parent drug and its oxidized metabolite, respectively (Fig. 5.2).
46
Fig. 5.2. Schematic diagram of oxidative reaction catalyzed by CYPs.
CYPs commonly take part in drug interactions and unexpected drug actions. An interaction may occur when two agents are metabolized by the same CYP and they therefore compete for the enzyme. The rates of metabolism of both drugs usually decrease in this case, resulting in more pronounced action and probably increased toxicity. Some agents are CYP inhibitors, independently of their action and metabolic pathway, which results in elevated concentrations of coadministered drugs being metabolized through that given CYP. As an example, the antifungal drug ketoconazole inhibits CYP3A4 and may therefore increase the exposure of all drugs metabolized by this enzyme. The interpretation of interactions has recently been extended to foods. Grapefuit contains some furanocoumarins (e.g. bergamottin) that are very potent CYP3A4 inhibitors and may induce life-threatening drug–food interactions. Other drugs are able to increase the expressions and activities of CYPs. This phenomenon is called enzyme induction. Typical enzyme inducers are traditional antiepileptics (e.g. phenobarbital, phenytoin or carbamazepine), some antihistamines or rifampicin. The elimination of coadministered substrates is faster and the drugs, especially those with a narrow therapeutic range, can be inefficient. Enzyme induction requires 1-2 weeks of continuous treatment, and the metabolism of the inducer usually becomes faster too, this being referred to as autoinduction. 47
The flavin-containing monooxygenases (FMOs) are another superfamily of oxidative enzymes. FMOs have only a minor role in drug metabolism, as they are involved in the elimination of merely a few agents (e.g. ranitidine and clozapine). Since FMOs cannot be inhibited or induced by current drugs, they are not often involved in interactions. Hydrolytic reactions are also common during phase I of the drug metabolism. Since most tissues and plasma exhibit esterase activity, the hydrolysis of esters is relatively fast. The duration of action of this kind of drugs is usually short (e.g. cocaine, acetylcholine and aspirin). The hydrolytic decomposition of amides is slower and more restricted to the liver (e.g. lidocaine or procainamide). The hydrolysis of epoxides is a not very common catalytic step in the drug metabolism, involving only a few agents (e.g. oxcarbazepine). This reaction is catalysed by epoxide hydrolases. Reductions are other not too crucial phase I reactions, but a few basic drugs do participate in them. Reduction of an aldehyde leads to the corresponding primary alcohol (e.g. chloral hydrate → trichloroethanol). Nitroreduction results in the amino derivatives of nitro compounds (e.g. nitrazepam, chloramphenicol). Disulfide reduction involves the cleavage of a disulfide bond and the formation of two thiol functions (e.g. disulfiram).
5.3. Phase II of the drug metabolism
During phase II reactions, the metabolites of phase I become conjugated with an endogenous substance, leading to highly water-soluble products. If the parent drug contains functional groups suitable for conjugation (e.g. a hydroxy group), it can undergo phase II directly, and phase I can therefore be bypassed. With the exception of glucuronidation, which takes place in the endoplasmatic reticulum, all phase II reactions occur in the cytosol. The rates of conjugating reactions are generally substantially higher than those of phase I transformations, which means that the rate of the overall drug metabolism is determined by the phase I reactions.
48
Glucuronidation is the most common phase II reaction. It requires uridine 5'- diphosphoglucuronic acid (UDPGA) as cofactor and one of the UDP- glucuronosyltransferases (UGTs). UGTs transfer glucuronic acid from the cofactor to the substrate to form a glucuronide. The functional groups suitable for glucuronidation include phenolic and alcoholic hydroxy, carboxyl, thiol and amine functions. The relevance of glucuronidation is indicated by the fact that humans possess 19 UGTs, and such reactions are commonly used to promote the elimination of endogenous substances (e.g. steroids or bilirubin). The highest expressions of UGTs are detected in the gastrointestinal tract and they can be induced by drugs. The glucuronide formed has a substantially higher molecular weight, which favours biliary excretion. Since the conjugate is water-soluble, its reabsorption is not possible from the small intestine, but glucuronidases in the bacterial flora of the colon may hydrolyse the conjugate; the more lipid-soluble parent compound or phase I metabolite is liberated, and this can undergo reabsorption. The overall process is referred to as the enterohepatic circulation (EHC). Sulfation or sulfate conjugation is a further crucial phase II reaction; it requires 3’- phosphoadenosine-5’-phosphosulfate (PAPS) and is catalysed by the family of 11 sulfotransferases (SULTs). This reaction has a broad range of endogenous substrates, including cholesterol, thyroid hormones, catecholamines and oestrogens. Some of the SULTs are expressed in foetal tissues, and sulfation is the only phase II reaction that is functional immediately after delivery of the foetus. During glutathione (GSH) conjugation, catalysed by glutathione-S-transferases (GSTs), the xenobiotics are coupled to the middle amino acid of the tripeptide (Glu-Cys-Gly) through a disulfide bond. GSH itself is present at relatively high concentration in the hepatocytes and is converted into the oxidized form (GSSG), and it therefore plays a critical role in the defence against oxidative damage. The conjugated drug can be further metabolized; the adduct loses glutamate and glycine, and the residual cysteine is acetylated on the amino group. The commonly formed final product, called the mercapturic acid conjugate of the drug, is typically excreted in the urine. N-Acetylation is catalysed by N-acetyltranferases (NATs), and the donor of the acetyl group is acetyl coenzyme A. Aromatic amine and hydrazine groups can be acetylated in this way and the conjugate exhibits a unique feature: it is less water-soluble than the
49
parent compound. As a consequence, these metabolites can be precipitated during renal excretion when the body is inadequately hydrated. The most relevant drugs involved in this kind of phase II metabolism are the antibacterial sulfonamides. The human genome contains only two NATs (NAT1 and NAT2), but polymorphism is characteristic for NAT2, and the final rate of acetylation can therefore differ substantially, depending on the genetic background. The phenomenon may be described as involving a fast or a slow acetylator phenotype. The slow acetylators exhibit an increased risk of adverse drug reactions, including hypersensitivity. Methylation is a highly substrate-specific conjugation catalysed by a set of methyltransferases (MTs). The source of the methyl group is always S-adenosyl- methionine, and it can be transferred onto O, N and S atoms of endogenous molecules and xenobiotics. Catechol-O-methyltransferase (COMT) methylates molecules containing a catechol moiety (e.g. dopamine or methyldopa). Histamine N-methyltransferase (HNMT) is responsible for the methylation of substances containing an imidazole ring (e.g. histamine). Nicotinamide N-methyltransferase (NNMT) conjugates serotonin, tryptophan and nicotine. Phenylethanolamine N-methyltransferase (PNMT) has only a minor role in the drug metabolism, but it catalyses the conversion of noradrenaline to adrenaline. One of the most relevant MTs is thiopurine S-methyltransferase (TPMT), which catalyses a detoxification step in the metabolic pathway of some antiproliferative agents with a narrow therapeutic range, including azathioprine, 6-mercaptopurine and thioguanine. When TPMT is deficient as a consequence of genetically determined polymorphism, these drugs and their active metabolites accumulate and induce serious toxic reactions. The activity of this MT should therefore be assayed before the administration of such drugs.
5.4. Factors influencing the drug metabolism
Since the drug metabolism is a complex, enzymatically driven multistep procedure, it can be influenced by a broad range of factors. Age is obviously a very important factor. At birth, the only functional metabolic reaction is sulfation. In term infants, all the other phase I and phase II reactions are developed by the age of 3–6 months, but the full metabolic capacity is generally
50 reached only at the age of 8 years. Interestingly, the rate of elimination of some drugs (e.g. theophylline) is maximum between the ages of about 1 and 9 years. The body weight-normalized doses of such agents may be higher for children than for adults. In elderly patients, the activity of phase I enzymes, and especially the CYPs, declines gradually, but the functions of the phase II enzymes are usually preserved. Most drug metabolic enzymes exhibit higher activities in males than in females. Pregnancy may be regarded as a state of enzyme induction. Besides the changes in the body fluid volumes, this induction is another factor that complicates drug therapy during gestation. The therapeutic drug monitoring of agents with a narrow therapeutic range (e.g. antiepileptic drugs) is therefore mandatory. Genetic polymorphism is a frequent and relevant feature many of drug metabolizing enzymes, CYPs being the best-characterized in this respect. The activities of these enzymes (e.g. CYP2D6) are polymodally distributed in the population; the wild type, with average activity, is expressed in most people, called extensive metabolizers (EMs). Minor subpopulations, who carry variants of the enzymes with much lower or much higher activities, are called poor metabolizers (PMs) and ultrarapid metabolizers (UMs), respectively. Since the therapeutic protocols and the dosage regimens are elaborated for EMs, unexpected reactions can accumulate in PMs and UMs. Whereas the drug concentration in PMs can be higher than needed and toxic reactions can be elicited, UMs may experience therapeutic failure as a consequence of the fast drug metabolism. Obviously, in the case of a prodrug, the opposite situation can occur. The distribution of the EM, PM and UM groups displays substantial ethnicity-related differences. Further enzymes may behave similarly. The activity of aldehyde dehydrogenase is considerably lower in people with an Asian genetic background that in Caucasians. As a consequence, the alcohol tolerance of Asians is more limited, because the accumulated acetaldehyde may cause the typical features of alcohol intoxication.
Used abbreviations: COMT catechol-O-methyltransferase CYP cytochrome P450 EHC enterohepatic circulation EM extensive metabolizer
51
FMO flavin-containing monooxygenase GSH glutathione GSSG oxidized form of GSH GST glutathione-S-transferase HNMT histamine N-methyltransferase MT methyltransferase NAT N-acetyltranferase NNMT nicotinamide N-methyltransferase PAPS 3’-phosphoadenosine-5’-phosphosulfate PM poor metabolizer PNMT phenylethanolamine N-methyltransferase SULT sulfotransferase TPMT thiopurine S-methyltransferase UDP uridine diphosphate UDPGA uridine 5'-diphosphoglucuronic acid UGT UDP-glucuronosyltranferase UM ultrarapid metabolizer
Questions
1. Which of the following reactions occurs in the first phase of the drug metabolism? A. aromatic hydroxylation; B. nitrogen acetylation; C. methylation; D. conjugation with glutathione.
2. Which of the following conjugations may lead to a metabolite with poor water solubility? A. nitrogen acetylation; B. glucuronidation; C. sulfate conjugation; D. glutathione conjugation.
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6. Elimination, continuous intravenous infusion and multiple dosing regimen 6.1. Elimination
Elimination is the term that describes all of the processes in the body which lead to an irreversible decrease in the concentrations of active substances in the various water compartments. The rates of such decreases in concentration may follow zero-order (e.g. alcohol), first-order (most of the active substances) and non-linear or Michaelis–Menten (e.g. phenitoin) kinetics. The routes of elimination can be excretion, metabolism or deposition in the tissues. Excretion is the process of depletion of active substances from the body via the secretion mechanism of different glands (e.g. the lungs, kidneys, salivary glands, sweat glands, liver, intestinal glands and mammary glands). Metabolism has been discussed in Chapter 5. Deposition is the process of the storage of certain active substances in tissues with poor circulation (e.g. the bones, fat tissue, hair and nails). The concentration of an API in its depot is in equilibrium with its plasma concentration. Consequently, if the plasma concentration of the API decreases, API may be liberated from its depot to restore the equilibrium between the plasma and the depot.
6.1.1. Renal excretion
The most important organ that takes part in excretion is the kidneys. Non-volatile, water-soluble APIs with low molecular weight (Mw < 5,000 Da) can undergo renal excretion. Renal excretion can be divided into two processes: glomerular filtration and tubular secretion. Glomerular filtration occurs in Bowman’s capsule and results in a plasma ultrafiltrate, i.e. a protein-free solution. APIs with low molecular weight (Mw < 5,000 Da) and ions are excreted completely freely. Molecules with Mw in the range 5,000-50,000 Da are filtered by saturable transport mechanisms, whereas APIs bound to plasma proteins (Mw > 50,000 Da) do not pass through the glomerular filter. Inorganic ions, glucose, inulin and creatinine are excreted by glomerular filtration. The main driving force of glomerular filtration is the filtration pressure
(Pfiltr), which can be calculated as the difference between the blood pressure in the glomerular capillaries (Pcap = 50 mmHg), and the sum of the oncotic pressure of the blood
(Posm = 25 mmHg) and the intracapsular tissue pressure of Bowman’s capsule
(PBow = 17 mmHg):
53
= − − = 8 mmHg 6.1
The renal blood flow (RBF) is 1200 ml/min and the renal plasma flow (RPF), the volume of plasma passing into the glomeruli, is 650 ml/min. Creatinine and inulin are suitable compounds with which to determine the amount of primary filtration, because they are filtered freely in the glomeruli, but are not reabsorbed in the tubuli. This gives the glomerular filtration rate (GFR) with an average value of 125 ml/min. The ratio of GFR and RPF gives the filtration fraction (FF): = = 0.2 6.2 This indicates that approximately 20% of the volume of the plasma flowing through the kidneys is filtered into the glomeruli during a unit of time. The amount of API filtered in the glomeruli (f) can be calculated according to Eq. 6.3 if the active substance is not bound to plasma proteins:
= ∙ 6.3 where Cp is the plasma concentration of the API. If the API is bound to plasma proteins, Eq. 6.4 is suitable for the calculation f:
= (1 − ) ∙ ∙ 6.4 where p is the protein-bound fraction of the API. Tubular transport mechanisms can be classified as tubular secretion or tubular reabsorption. Tubular secretion is the movement of APIs from the blood into the tubular lumen. This process can occur by passive diffusion or by active transport. Organic ions are mostly excreted by tubular secretion. Anions and cations have their own transport channels with saturable capacity. Ions with the same charge compete for the same excretion route. As an example, probenecid competes with penicillin for anionic tubular secretion. In the presence of probenecid, the duration of action of penicillin is prolonged because of the decreased tubular secretion of penicillin. Anionic tubular secretion is responsible for the elimination of drugs conjugated with glycine, glucuronic acid or the sulfate group. Some examples of anionic tubular secretion: amino acids, chlorothiazide, salicylates, indomethacin and phenylbutazone. Cations removed from the body by tubular secretion include dopamine, histamine, neostigmine, dihydromorphine and quinine. The extent of tubular secretion via passive diffusion is determined by the pH of the urine and the pKa value of the secreted drug. This means that the tubular secretion of weak acids (e.g. barbituric acid derivatives) will be induced if the urine becomes alkaline. On the
54 other hand, the tubular secretion of weak bases (e.g. morphine) will be induced if the urine becomes acidic. The pH of the urine is increased by sodium bicarbonate infusion, and decreased by ammonium chloride. Tubular reabsorption can also take place by passive diffusion and active transport. A good example demonstrating the importance of tubular reabsorption and its features is the reabsorption of glucose. Glucose is freely filtered in the glomeruli, but no glucose can be detected in the urine in healthy persons. This is due to the complete tubular reabsorption of glucose. This transport mechanism has a limited capacity, appearing glucose in the urine if the blood glucose level is higher than normal (e.g. diabetes mellitus). Other materials with a high + - - level of tubular reabsorption are Na , Cl , HCO3 , uric acid and water.
6.1.2. Excretion by the liver
Bile is produced by the liver, and APIs or their metabolites that are excreted by the liver can be found in this fluid. Molecules with specific chemical structures are excreted by the liver, e.g. heterocycles containing –OH and/or =O groups (e.g. benzodiazepines), metabolites with a glucuronide functional group (e.g. steroidal hormones) or APIs with
Mw > 500 Da, e.g. erythromycin. Passive diffusion, which is a function of pKa and pH, and energy-demanding active transport with limited capacity are the main mechanisms of biliary excretion. As in renal tubular secretion, APIs excreted by the liver via an identical mechanism compete with each other for the same excretion route. The bile with the excreted APIs is discharged into the duodenum, and APIs are depleted with the faeces or reabsorbed from the large intestine via the enterohepatic circulation (see Chapter 5).
6.1.3. Pulmonary excretion
Gases and volatile fluids can be excreted by the lungs. Pulmonary excretion is the major route of elimination of inhalatory anaesthetic drugs (e.g. diethyl ether, isoflurane and nitrous oxide). Several organic solvents (e.g. alcohol, ethyl acetate, acetone and n-hexane) are also excreted by the lungs. The exhalation of carbon dioxide during breathing can be regarded as the excretion of this gas by the lungs. Factors that can influence pulmonary excretion include the partition coefficient (L) between the blood and the alveolar air, the volume (Vd) of distribution of the API, the
55 respiratory volume (Vp) and the rate of pulmonary circulation (Ip). The following equation expresses the elimination half-life (t1/2) of a drug excreted by the lungs:
2 ∙ ∙ ( + ∙ ) / = 6.5 ∙ This equation leads to the conclusion that a change in the respiratory volume and/or the rate of the pulmonary circulation can result in a substantial change in the process of elimination of APIs. This may occur in cardiac decompensation.
6.1.4. Salivary excretion
The saliva is the product of secretion by the salivary glands, and one of its several functions is to participate in drug excretion. Mercury ions are excreted into the saliva, resulting in an unpleasant taste and even stomatitis. After administration of the artificial sweetener saccharine into the small intestine via a duodenal tube, a person can feel a sweet taste in the mouth, because the saccharine is excreted by the salivary glands. The saliva/plasma concentration ratios of several APIs that are excreted into the saliva have been determined. The ratio is < 1 in the cases of penicillin and carbamide, > 1 in the cases of lithium, lidocaine, procainamide and acetaminophen (also known as paracetamol) and = 1 in the cases of theophylline, caffeine and digoxine. On this basis, some drugs can be clinically monitored in the saliva through a non-invasive method.
6.1.5. Excretion through the skin
Dermal excretion is the discharge of APIs via the sweat. There are several examples of the excretion of APIs by this route, e.g. sodium chloride, carbamide and uric acid. Uric acid displays equal concentrations in the sweat and in the plasma. The halogens are also excreted in the sweat. When patients were earlier treated with bromide salts, a typical side-effect, bromacne, regularly developed on the skin. The evaporating oils in onion and garlic are also excreted in the sweat. Sweating can be induced by different substances. If sweating is elicited, the elimination of the above-mentioned APIs is increased. The following drugs can induce the production of sweat: capsaicin, caffeine, aspirin and evaporating oils. Moreover, thermal baths with carbon dioxide can cause a reflectoric increase in sweating, and concurrently the
56 excretion of sodium chloride and carbamide in heart and kidney failures as occured before the discovery of diuretics.
6.1.6. Excretion into the breast milk
Excretion into the breast milk develops as a result of the passive diffusion brought about by the pH difference between the plasma and the breast milk. Since breast milk is more acidic (pH = 7.0) than the blood plasma (pH = 7.4), weak bases can accumulate in the breast milk. Their concentration in the breast milk is higher than in the blood plasma. The acidic compounds in high concentration remain in the blood plasma. Active substances which are excreted into the breast milk include caffeine, nicotine, atropine, morphine, heroin, cocaine, digitalis glycosides, oral anticoagulants, theophylline, antihistamines and sulfonamides. Drugs excreted in the breast milk pass into the gastrointestinal system of the baby, where they are absorbed into the circulatory system, resulting in side- or toxic effects. If the mother is treated with theophylline, this is excreted into the breast milk and then passes into the baby resulting, in restlessness and insomnia, because it excites the central nervous system.
6.1.7. Clearance
Clearance is the process by which a drug is removed from the body, independently of its mechanism. From another point of view, the clearance is the fraction of the volume of water in the body that is cleared of the given drug per unit time. Consequently, clearance is expressed in volume/time (e.g. l/h). In the different water compartments, different types of clearance can be distinguished. The total body clearance (CLT) is the sum of the different organ clearances. In general, it can be calculated from the kinetic parameters of the given drug:
= ∙ 6.6 or = 6.7 where ke is the elimination rate constant, Vd is the volume of distribution, D is the dose of the drug and AUC is the area under the plasma concentration vs. time curve. Its value for a given drug is constant, if the elimination of the drug follows first-order kinetics.
57
The organ clearance is the volume of blood that is cleared of the given drug per unit time during its flow through the organ. It can be determined as the product of the organ blood flow (Q) and its extraction ratio (E):
= ∙ 6.8 where E is the ratio of the drug concentration excreted by the organ and the drug plasma concentration in the arteries ([Carterial - Cvenous]/Carterial). The most important organ clearances are the hepatic and renal clearances.
The renal clearance (CLR) is the blood/plasma volume cleared by the kidneys during unit time. Consequently, it is equal to the plasma clearance if the drug is excreted exclusively by the kidneys. CLR can be calculated as follows:
∙ = 6.9 where Cu is the drug concentration in the urine, V is the volume of urine and Cp is the drug concentration in the plasma.
If the drug is bound to plasma proteins in the circulation, its CLR can be determined through a modification of Eq. 6.9:
∙ = 6.10 (1 − ) ∙ where p is the fraction of the drug bound to plasma proteins. Since creatinine is filtered only by the renal glomeruli, it is suitable to determine the
GFR, which is equal to the CLR of creatinine (CLcreat). para-Aminohippuric acid is secreted only by the renal tubules, and is therefore suitable for determination of the activity of tubular secretion. Its value is equal to the CLR of para-aminohippuric acid (CLPAH).
6.2. Continuous intravenous infusion
A single intravenous bolus injection is unsuitable when it is necessary to maintain the drug plasma concentration within the therapeutic range for a longer duration. In hospitals, a drug solution is commonly infused at a constant infusion rate (Xi). This is called continuous intravenous infusion, and is a precise and easily controlled mode of drug administration. The unit of Xi is mass per unit time (e.g. µg/h), because it is influenced by the flow rate (e.g. ml/h) and the concentration of the drug in solution (e.g. µg/ml). The constant input of a drug is administration with zero-order kinetics. However, the elimination of the drug from the body follows a first-order process.
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Immediately after the start of an infusion, the rate at which drug enters the body is greater than the rate at which it is eliminated. If the administration of the infusion lasts long enough, these two rates will equalize and the drug plasma concentration will accumulate to a certain value with no further increase. This equilibrium is called the plateau of the intravenous infusion (Fig. 6.1).
Fig. 6.1. A graphical representation of the plasma concentration (Cp) vs. time profile following the administration of a drug in a continuous infusion. MTC, minimum toxic concentration; MEC, minimum effective concentration.
6.2.1. Concept of plateau
The plateau is the only maximum in the blood concentration vs. time curve of intravenous infusion (Fig. 6.1). Theoretically, it can be maintained until infinity, because the amount of drug entering the body during unit time is equal to the amount of drug eliminated from the body during unit time. It also means that the elimination of the given drug operates at its maximum. Moreover, the rate of drug administration never exceeds the elimination capacity of the body. A continuous intravenous infusion can be administered without the risk of toxic effects of the drug.
6.2.2. Rate of infusion
The change in the amount of drug in the blood during a continuous infusion can be described as follows:
59
= − 6.11 where dD/dt is the rate of change in the amount of drug in the body, Xi is the constant infusion rate and keD is the first-order elimination rate. After the integration of Eq. 6.11:
= ∙ (1 − ) 6.12 Equation 6.12 means that the amount of drug in the blood will be influenced by the chosen infusion rate and the duration of infusion. Moreover, the amount of drug in the blood at a given time will be proportional to the chosen infusion rate. D can be converted into the concentration (Cp) of the drug in the plasma, because D is the product of Cp and the volume of its distribution (Vd):
= ∙ (1 − ) 6.13 The above statements relating to the amount of drug in the blood are also correct in the case of the drug concentration in the plasma. The drug plasma concentration on the plateau is regarded as a steady-state concentration (Css), which develops when the rate of elimination and the rate of infusion become equal. Hypothetically, this occurs only after infinite time. On the basis of this assumption, Eq. 6.13 can be written as follows:
= ∙ (1 − ) 6.14 However, since is zero, we have:
= 6.15
It is important to note that Vdke is the systemic clearance of a drug, which is a constant parameter of any drug in any healthy patient. If a patient suffers from renal impairment (a lowered creatinine clearance), Xi should be lowered to develop the same Css.
On the other hand, Eq. 6.15 clearly demonstrates that, if Xi is raised, Css will increase proportionally. However, the time at which this steady-state is attained is independent of Xi (Fig. 6.2).
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Fig. 6.2. Plasma concentration (Cp) vs. time curves following the administration of a drug in intravenous infusion at different rates. MTC, minimum toxic concentration; MEC, minimum effective concentration.
6.2.3. Plateau fraction
If we wish to calculate the proportion of the plateau at any time, we divide Eq. 6.13 by Eq. 6.15: ∙ (1 − ) = = = 1 − 6.16 where f is the plateau fraction. With the use of Eq. 6.16, the time interval needed to attain any plateau fraction can be calculated. The time interval needed to attain the 50% of plateau fraction for instance, is equal to the elimination half-time (t1/2) of the drug. A drug with a short t1/2 will attain the chosen plateau fraction during a shorter period of time as compared with a drug with a longer t1/2.
Although, by definition, Css can appear at infinite time, in everyday practice it can be beneficial to estimate the time at which the real drug plasma concentration will approximate to the chosen Css. By convention, if the drug plasma concentration reaches at least 95% of the chosen Css, it is considered to represent the plateau of the continuous infusion. From Eq. 6.16, the time interval necessary to reach 95% of the plateau can be calculated. This value is proportional to the t1/2 value of the given drug, because ke is equal to ln 2/t1/2. If a drug is
61 infused at a constant rate, it will take 4.32 t1/2 for the drug to reach 95% of the chosen Css. Table 6.1 indicates the time intervals needed to attain different plateau fractions.
Table 6.11. The relationship between the fraction of the steady-state plasma concentration
(Css) and the number of elimination half-lives (t1/2).
Fraction of Css; % t1/2 x 50.0 1.00 90.0 3.32 95.0 4.32 96.0 4.64 97.0 5.06 99.0 6.64 99.9 9.96
If the infusion is stopped at the plateau, there will be no more drug input into the body. The drug plasma concentration will therefore be influenced only by the first-order elimination processes (Fig. 6.3).
Fig. 6.3. Plasma concentration (Cp) vs. time during and post infusion. T, time of cessation of infusion; MTC, minimum toxic concentration; MEC, minimum effective concentration.
This means that after one t1/2, the plasma drug concentration will drop to half of the plasma concentration at the plateau. Moreover, after 5 t1/2, the plasma drug concentration will have decreased to practically zero.
62
6.2.4. Loading dose of the infusion
For a drug with a long half-life, it takes a considerable time to approximate to the chosen Css (e.g. if t1/2 = 2 h, then 4.32 x 2 h = 8.64 h is needed). However, in certain situations, immediate therapeutic action is necessary, which demands a rapidly developing Css within the therapeutic range of the drug. This may be achieved by administering a loading intravenous bolus dose (DL). With DL, the desired plasma drug concentration can be attained at time zero. The concomitant infusion will maintain this desired plasma drug concentration. Thus, both the intravenous bolus injection and the continuous infusion will contribute to the development of the plasma drug concentration (Fig. 6.4).
Fig. 6.4. Observed and theoretical plasma concentration (Cp) vs. time profile following the administration of a drug as an intravenous bolus loading dose immediately followed by an infusion. Css, desired steady- state plasma concentration; MTC, minimum toxic concentration; MEC, minimum effective concentration.
On the other hand, the administration of DL results in immediate saturation of the volume of distribution (Vd) of the given drug. Accordingly, DL can be calculated via Eq. 6.17:
= ∙ 6.17
6.3. Multiple dosing regimen
Besides drug administration via single doses or continuous infusions, most of the drugs applied on a continual basis can be administered by multiple dosing. This includes multiple intravenous injections and multiple extravascular administration (e.g. oral tablets).
63
Although the theoretical bases of the two methods are similar, they influence the shape of the drug plasma concentration vs. time curve differently, due to the absence or presence of absorption in the two methods. First-order elimination is assumed in every situation. In the case of multiple intravenous injections, the plasma drug concentration rises immediately until a peak plasma concentration (Cmax) is reached, and it then starts to decrease to reach a minimum plasma concentration (Cmin) before the next drug administration. After the administration of the second dose, the whole process is repeated again and again, and a sawtooth-shaped plasma drug concentration vs. time curve is observed (Fig. 6.5).
Fig. 6.5. Plasma concentration (Cp) vs. time curve following the administration by intravenous bolus of identical doses of a drug at identical dosing intervals.
If multiple extravascular administrations are applied, the absorption phase of the drug can be observed in the shape of the plasma drug concentration vs. time curve, but the plasma drug concentration will fluctuate between Cmax and Cmin (Fig. 6.6).
64
Fig. 6.6. Plasma concentration (Cp) vs. time curve following the administration of identical doses of a drug at identical dosing intervals by an extravascular route. Cmax, peak plasma concentration; Cmin, minimum plasma concentration; MTC, minimum toxic concentration; MEC, minimum effective concentration.
Cmax will always occur at the peak time (tmax). There are other factors, such as the dosing interval (τ [Greek letter tau]), the elimination and absorption (if it exists) rate constants
(ke and ka, respectively), that influence the shape of the plasma drug concentration vs. time curve.
6.3.1. Dosing interval (τ)
τ is the frequency of drug administration expressed in time units (e.g. if τ = 6 h, the drug is administered every 6 h). If the value of τ is greater than 5 t1/2 of the given drug, the
Cmax values will be the same, because the succeeding doses of the drug will be administered after the complete elimination of the previous dose (Fig. 6.7).
65
Fig. 6.7. Plasma concentration (Cp) vs. time curve following the administration of identical doses of a drug at identical dosing intervals (τ) by an extravascular route. The value of τ is greater than 5 t1/2 of the given drug. MTC, minimum toxic concentration; MEC, minimum effective concentration.
If the value of τ is smaller than 5 t1/2 of the given drug, the Cmax values will be higher and higher until a steady-state condition is reached. This is a consequence of the accumulation of the drug in the body. If the value of τ approximates to zero, the mode of administration becomes similar to continuous intravenous infusion. Moreover, the values of τ and ke determine the frequency and height of the “sawteeth” in the plasma drug concentration vs. time curve. The shorter the value of τ, the smaller the fluctuation between Cmax and Cmin.
6.3.2. Concept of plateau and minimum and peak plasma concentrations
If the value of τ is smaller than 5 t1/2 of the given drug, then after several administrations a steady-state condition (plateau) will be reached. However, this plateau cannot be regarded as identical to the plateau observed on the continuous intravenous infusion. In the event of a multiple dosing regimen, the plasma drug concentration fluctuates between Cmax and Cmin. In the optimum situation, these values are included in the therapeutic range of the drug. Additionally, if these values are plotted in plasma concentration vs. time curves, saturation graphs will be built up from each series of values. Moreover, similarly to continuous infusion, in the case of a multiple dosing regimen the time period needed to reach the plateau is equal to 5 t1/2 of the given drug.
66
6.3.3. Considerations during the application of a multiple dosing regimen
Before a multiple dosing regimen is started, three fundamental aims should be taken into consideration: (1) a therapeutic effect should be elicited as soon as possible, (2) the plasma drug concentration should always be in the therapeutic range, and (3) the plasma drug concentration should not be higher or lower than the therapeutic range, even transitionally. The following principles are applied during a multiple dosing regimen: (1) the minimum effective concentration should be reached during a short period (a loading dose can be used), (2) the maintenance doses should be equal, (3) the dosing intervals should be equal, and (4) the pharmacokinetic parameters should be constant throughout the whole treatment. It is known that kidney or liver failure, drug–drug or food–drug interactions and eating habits may influence the pharmacokinetic parameters. Moreover, the above rules are not applicable if the drug has non-linear pharmacokinetics. For a multiple dosing regimen, there are specific kinetic parameters that are used to calculate the different factors such as Cmax, Cmin and tmax.
maintenance parameter 6.18 =
elimination parameter 6.19 = 1 −
accumulation parameter 1 6.20 = 1 −
Used abbreviations: API active pharmaceutical ingredient AUC area under the plasma concentration vs. time curve
CLcreat creatinine clearance
CLorgan organ clearance
CLPAH para-aminohippuric acid clearance
CLR renal clearance
CLT total body clearance
Cmax peak plasma concentration
Cmin minimum plasma concentration
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Cp plasma concentration of the API
Css steady-state plasma concentration
Cu drug concentration in the urine D dose of the drug E organ extraction ratio FF filtration fraction GFR glomerular filtration rate
Ip rate of pulmonary circulation ke elimination rate constant L partition coefficient between the blood and the alveolar air MEC minimum effective concentration MTC minimum toxic concentration p fraction of the drug bound to plasma proteins
PBow intracapsular tissue pressure of Bowman’s capsule
Pcap blood pressure in the glomerular capillaries
Pfiltr glomerular filtration is the filtration pressure
Posm oncotic pressure of the blood Q organ blood flow RBF renal blood flow RPF renal plasma flow τ dosing interval t1/2 elimination half-life V volume of urine
Vd volume of distribution
Vp respiratory volume
Xi infusion rate
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Questions
1. What is excretion? A. All of the processes in the body which lead to an irreversible decrease in the concentrations of active substances in the various water compartments. B. The depletion of active substances from the body via the secretion mechanism of different glands. C. The drug metabolism by the liver. D. The storage of active substances in the fat tissue.
2. What is the plateau fraction? A. The frequency of drug administration. B. A drug solution is infused at a constant infusion rate. C. The dose of the drug needed to equilibrate its volume of distribution. D. The proportion of the plateau at any time.
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7. Compartmental models
Mathematical modelling has been used to study and predict the behaviour (changes in concentration) of drugs (endogenous or xenobiotics) in biological systems (cell cultures, animals or humans). In other words, pharmacokinetic modelling gives a possibility to predict or calculate different kinetic parameters related to absorption, distribution and elimination (metabolism and excretion). The model is a hypothesis, using mathematical descriptions of the investigated biological systems that express quantitative relationships concisely. There are three different ways in which pharmacokinetic parameters can be determined: the use of – compartmental models, – physiological models or a – model-independent approach.
The models that have been developed give information about the following aspects: – changes in drug concentration in the investigated system (usually in the blood), – a visual representation of the various rate processes in which the drug disposition takes part, – the optimum dosage regimen for individual patients, – bioequivalence between different formulations of the same drug, – the influence of diseases or changes in physiology.
In this chapter, the compartmental model system will be discussed in detail. In the compartmental model, the body is assumed to be a series of discrete sections (pools) into which the drug is distributed kinetically. These sections are called compartments. A compartment is a part of the body (tissues or water) in which the drug concentration presumed to change with the same kinetics (the drug concentration is equal at any point in the compartment at the same time), or the drug is considered to be uniformly distributed within the compartment. A compartment is an artificial concept: it does not correspond to any physiologically or anatomically determined regions of the body (e.g. the intravascular volume, the central nervous system, etc.); its borders are rarely identical with anatomical borders. The human body is usually represented by one or two compartments, but when required, more complex (three or more compartments) models can be used. There are two types of compartments: – the central compartment is the blood plasma and the highly perfused tissues in which drugs are distributed rapidly, – the peripheral compartments are poorly perfused tissues such as the fat, lean tissues and muscles.
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To follow and predict the changes in drug concentrations in the body, the model must account for the route of administration and the pharmacokinetics of the drug. The most common compartmental models are therefore: 1. the one-compartment intravascular model (bolus or infusion), 2. the one-compartment extravascular model (zero-order absorption, first-order absorption), 3. the two-compartment intravascular model (bolus or infusion), 4. the two-compartment extravascular model (zero-order absorption, first-order absorption).
These models make use of the experimental data and empirical formulae with which to estimate changes in drug concentration with time, using the following assumptions: – the body is considered to be a series of compartments (central and peripheral) that communicate with each other reversibly, – the mixing of the drug within the compartment is rapid and homogeneous, and – the rate of movement of the drug between the different compartments follows first-order kinetics.
When there is communication between the model and the environment (influx and outflux), this is an open model; if there is no communication, it is a closed model. The pharmacokinetic model systems are usually open models. In the schematic representation of compartmental models, boxes and arrows are used to represent the compartments and the drug motion, respectively (Fig. 7.1).
influx outflux
compartment
Fig. 7.1. Schematic representation of compartmental models.
7.1. One-compartment open model
In this model, the drug is assumed to be in a homogeneous solution (in the compartment) with no barriers to the movement of the drug. The drug distribution occurs instantaneously and the processes in which the drug takes part follow first-order kinetics. Some of the drugs follow a one-compartment model: pentobarbital, phenytoin, salicylic
71 acid, theophylline, warfarin, etc. Depending on the route of administration, intravascular and extravascular models can be distinguished.
7.1.1. One-compartment intravascular model
This is the simplest model. The drug is usually introduced into the compartment in an intravenous bolus (a rapid single dose) or as an infusion. It is assumed that the drug in the blood very rapidly comes into equilibrium with the drug in the extravascular tissues, and the concentration of the drug in the blood is proportional to the concentration in the extravascular tissues. The scheme of the model is depicted in Fig. 7.2.
D ke Vd cp
Fig. 7.2. Scheme of the one-compartment intravascular model. The box represents the compartment, the arrows show the drug input and output, D is
the dose of the drug, Vd is the apparent volume of distribution, cp is the drug concentration in the compartment at a given time, and ke is the elimination rate constant.
The important characteristics of the model: – there is no absorption, – the distribution rapid, – first-order elimination occurs, – the change in drug concentration determined is only by the elimination. As discussed earlier, the change in the concentration of the drug as a function of time can be described by a simple differential equation: 7.1 − = The integrated form of Eq. 7.1 gives:
= . 7.2 or
= .
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where is the concentration of the drug in the blood at time zero, is the elimination rate constant, cp is the drug concentration and A0 is the dose administered. The concentration of the drug in the blood can be calculated via Eq. 7.2 when and are known. On the other hand, if a sufficient number of time vs. concentration data are known, and can be determined from the blood concentration vs. time curve. The plot of Eq. 7.2 gives an exponential curve (Fig. 7.3), from which it is not obvious how to determine the above-mentioned parameters. However, if the logarithmic form of Eq. 7.2 (either with natural [Eq. 7.3] or with common logarithm [Eq. 7.4]) is plotted, a straight line is obtained (Fig. 7.4). The intercept of the semilogarithmic plot gives ln or log , while the slope is - or - /2.303.
= − 7.3
7.4 = − 2.303 From Eq. 7.3, the elimination rate constant can be expressed as
− = 7.5
If two optional time points (t1 and t2) are chosen, ke can be expressed as follows:
, − , = 7.5 −
cp
time
Fig. 7.3. Linear plot of cp versus time.
73
lnc p logcp
time
Fig. 7.4. Plot of ln cp and log cp versus time. If we introduce the definition of the elimination half-lifetime, Eq. 7.2 can be rewritten as
7.6 = . / 2 and the elimination half-lifetime can be expressed as 2 7.7 / = The concentration in Eq. 7.1 can be replaced by the amount of the drug (A), and Eq. 7.1, Eq. 7.2 and Eq. 7.3 can therefore be written as follows: 7.8 − =
= 7.9
= − 7.10
7.1.2. One-compartment extravascular model
When the drug is given extravascularly (orally, intramuscularly, etc.; see Chapter 1) and distributed in only one compartment, the absorption and elimination together define the blood concentration of the drug (Fig. 7.5).
74
D ke Vd cp ka, f (0 Fig. 7.5. Box diagram of the one-compartment extravascular model. Arrows represent the movement of the drug, the box is the compartment, D is the dose of the drug, f is the fraction of the dose absorbed, ka is the absorption rate constant, Vd is the apparent volume of distribution, cp is the drug concentration in the compartment at a given time, and ke is the elimination rate constant. Absorption is the process of movement of the drug from the site of administration into the blood. Since there is a high concentration gradient, this process occurs in only one direction and generally follows first-order kinetics. The change in the amount (or concentration) of the drug as a function of time can therefore be described by a simple differential equation: 7.11 − = − where A is the amount of the drug in the body; Aa is the amount of absorbable drug at the absorption site at time t, and ka and ke are the first-order absorption and elimination rate constants, respectively. Integration of Eq. 7.11 gives Eq. 7.12: 7.12 = ( − ) − where is the dose. It is known that the drug sometimes not totally absorbed, and an absorption factor, f is therefore introduced. To transform the drug dose to the drug concentration, the Eq. 7.12 is divided by the distribution volume (Vd): 7.13 = ( − ) − If we introduce = − Eq. 7.13 can be transformed to 75 = ( − ) or 7.14 = − 7.15 = − − ( − ) When the absorption does not start immediately following the administration of the drug (e.g. in the case of oral administration), the intercepts of the absorption and elimination terms are not the same (the curve has a lag-time, i.e. the difference in time between the administration and absorption of the drug) and Eq. 7.14 therefore gives Eq. 7.16: = − 7.16 = ( − ) − ( − ) Determination of , and A plot of Eq. 7.16 give a biexponential curve (Fig. 7.6) which displays maximum concentration at time tmax. Before tmax the rate of absorption is higher than the rate of elimination; at tmax, the two rates are equal; and after tmax, the rate of elimination is higher than the rate of absorption. At longer times, the total amount of administered drug is absorbed, and elimination is therefore the only process that influences the change in drug concentration in the compartment. Thus, in the case of semilogarithmic plot (Fig. 7.7), a straight line can be fitted to the elimination part of the ln cp vs. time curve (after tmax). The equation of this straight line is identical to the first term in Eq. 7.15; the intercept is therefore , while the slope of the line is - . 76 l / g m , p c time Fig. 7.6. Concentration versus time plot of one-compartment extravascular model. From Eq. 7.14 or Eq. 7.16, the blood concentration of a drug at a given time can be predicted. The two terms represent the concentrations relating to the elimination and absorption processes. This equation can therefore be written in the form = − where = and = . The term , (i.e. the concentration of the drug caused only by absorption) can therefore be easily expressed: = – This equation shows that the concentration produced by absorption can be calculated as the difference between the concentration defined by the elimination straight line and the observed blood concentration. We choose at least two (more than two would be better) time points (t1,and t2) before the tmax (the absorption phase), which determine two different concentrations for each time: the theoretical ′ ′ concentrations from the elimination straight line ( and ) and actual concentrations from the plasma curve (c1 and c2). We than calculate the differences between the two concentration values: ′ at t1: , = − and ′ at t2: , = − , and , are than plotted in the coordinate system, and a straight line is drawn through them. This is the absorption straight line. The intercept is (Eq. 7.14) or A (Eq. 7.16) and the slope is - (Fig. 7.7). 77 lncp lnA lnc' lnB 3 lnc'4 lnc''3 elimination line lnc4 lnc1 lnc3 lnc''4 lnc2 absorption line time t3 t4 tmax t1 t2 Fig. 7.7. Semilogarithmic plot of cp versus t curve – one-compartment extravascular model. 7.2. Two-compartment open model The two-compartment model is applied when the time for the administered drug to be distributed between the different tissues, organs or fluids is not negligible. The active substance is generally administered into the central compartment, which is highly accessible (soft tissues) for the drug. The peripheral compartment includes tissues with low perfusion (muscle, skin, fat, etc.). Some drugs that follow the two-compartmental model: amphetamine, chlordiazeperoxide, digoxin, digitoxin, epinephrine, gentamycin, lidocaine, etc. 7.2.1. Two-compartment intravascular model When the drug is administered intravascularly and the distribution takes a time comparable to that for the elimination, the active substance quickly appears in the central compartment (usually the blood). The distribution process then starts and the drug moves into the peripheral compartment and back to the central compartment. As soon as the drug reaches the central compartment, elimination starts. The blood concentration of the administered compound is therefore defined by 78 two processes: the distribution and the elimination. The scheme of this model is depicted in Fig. 7.8, which shows that there are two distribution processes (from the central to the peripheral compartment, and from the peripheral to the central compartment), characterized by different rate constants. The combination of the micro constants results in the distribution hybrid constant (, h-1) representing the whole distribution. The elimination can occur from the central compartment, or from the peripheral compartment or from both, and this complex process can therefore be described by a new constant, called the elimination hybrid constant (ß, h-1). peripheral k compartment 20 Vd(p), cp(p) k21 k12 D central k10 compartment Vd(c), cp(c) Fig. 7.8. Box diagram of the two-compartment intravascular model. Arrows represent the movement of the drug, the boxes are the compartments, D is the dose of the drug, Vd is the apparent volume of distribution, cp is the drug concentration in the compartment at a given time, k12 and k21 are the distribution micro constants, and k10 and k20 are the elimination micro constants. Figure 7.9 presents a representative blood concentration vs. time curve. Analysis of the curve shows that this is a biexponential curve representing the distribution phase (a rapid decrease in the concentration in the central compartment; the first part of the curve) and the elimination phase. The curve has no peak, because all of the active substance was administered into the central compartment, and the concentration therefore continuously decreases. 79 l / g m , p c time Fig. 7.9. The two-compartment intravascular model describing the change in the concentration of the drug in the central compartment. If it is assumed that the drug is eliminated in the central compartment, the change in the amount of the active substance is defined by Eq. 7.17: 7.17 − = − − Solution of the Eq. 7.17 yields Eq. 7.18: ( − ) ( − ) 7.18 = + − − X = Vc cp, where Vc is the apparent volume of the central compartment. We therefore have ( − ) ( − ) 7.19 = + ( − ) ( − ) If ( − ) ( − ) = and = ( − ) ( − ) then = + 7.20 where is the distribution hybrid constant (h-1), is the elimination hybrid constant (h-1). When t is 0, Eq. 7.20 gives = + 7.21 The parameters in Eq. 7.20 are determined in the same way as in the case of one- compartment extravascular model. Since is larger than , the time t in the distribution term ( ) approaches zero, while the term still has a finite value, and Eq. 7.21 simplifies to: 80 = 7.22 Extrapolation of the phase of the semilogarithmic plasma curve gives therefore the value of B (the intercept), while the slope of the straight line is equal to - (Fig. 7.10). By application of the method of residuals (see section 7.1.2), the values of and A can be determined. The main steps are as follows: 1. Calculation of the difference between the observed plasma concentration and the extrapolated concentration in the distribution time period: ′ , = − 2. The calculated concentrations in the same semilogarithmic coordinate system are plotted and linear regression analysis is performed to obtain the distribution straight line. 3. The intercept of the distribution straight line is A, while the slope is equals with -. The result of the above-mentioned steps is depicted in Fig. 7.10. Examples: vancomycin and tobramycin. lncp lnA lnc4 lnc''3 lnc3 lnc'3 lnB lnc'4 lnc1 elimination line lnc''4 lnc2 distribution line time t3 t4 t1 t2 Fig. 7.10. Semilogarithmic plot of cp versus t curve – two-compartment intravascular model. 81 7.2.2. Two-compartment extravascular model If the drug is administered extravascularly and the time required for its distribution is not negligible, the change in drug concentration is influenced by three processes: absorption, distribution and elimination. The scheme of this model is depicted in Fig. 7.11. peripheral k compartment 20 Vd(p), cp(p) k21 k12 D central k10 compartment ka, f Vd(c), cp(c) (0 Fig. 7.11. Box diagram of the two-compartment extravascular model. Arrows represent the movement of the drug, the boxes are the compartments, D is the dose of the drug, f is fraction of the dose absorbed, ka is the absoption rate constant, Vd is the apparent volume of distribution, cp is the drug concentration in the compartment at a given time, k12 and k21 are the distribution micro constants, and k10 and k20 are the elimination micro constants. With the same reasoning as in the previous model, it is clear that the final equation describing the change in drug concentration is as follows: = + − 7.23 where the first term represents the distribution, the second term the elimination and the last term the absorption. If it is assumed that the drug concentration in the plasma at the time of administration (t = 0) is zero, Eq. 7.23 gives: = + 7.24 A plot of Eq. 7.23 is depicted in Fig. 7.12. 82 l / g m , p c time Fig. 7.12. The two-compartment extravascular model describing the change in the concentration of the drug in the central compartment. The determination of the rate constants and empirical constants follows the same logic as applied in the case of the two-compartment intravascular model. Briefly: 1. The post-distribution (elimination) phase: extrapolation of the phase of the semilogarithmic plasma curve gives the value of B (the intercept on the y-axis), while the slope of the straight line is equal to -. 2. The distribution phase: the difference between the observed plasma and the extrapolated concentration is calculated in the distribution time period: ′ , = − ′ , = − The calculated difference concentrations are plotted in the same semilogarithmic coordinate system and linear regression analysis is performed to obtain the distribution straight line. The intercept of the distribution straight line is A, while the slope is -. 3. The absorption phase: the differences between the theoretical concentrations on the distribution straight line and the observed plasma concentrations are calculated: 83 ′ , = − ′ , = − The calculated difference concentrations are then plotted in the same semilogarithmic coordinate system and linear regression analysis is performed to obtain the distribution straight line. The intercept of the distribution straight line is , while the slope is -ka. The above-described steps are represented in Fig. 7.13. lnc p lnc lnA 0 lnc''5 lnc' 6 lnc3 lnc''6 lnc4 lnB lnc''6 lnc lnc'' 1 3 elimination line lnc''5 lnc2 absorption line lnc''4 distribution line t t5 t6 t3 t4 t1 t2 Fig 7.13. Determination of pharmacokinetic parameters – two-compartment extravascular model. 7.3. Effects of the ratio ka/ke on tmax and cmax Figure 7.14 illustrates the influence of the ratio ka/ke (ke is a constant, while ka has three different values, representing the three different routes of administration) on tmax and cmax. In parallel with a decrease in the value of ka, cmax decreases while tmax increases when the same dose of the drug is administered. Examination of the terminal phase of the curve shows that the lower the value of ka, the higher the plasma drug concentration. For the different routes of administration, the sequence of the absorption rate constants is as follows: intravenous (instantaneous absorption, theoretically ka is ) > intramuscular > oral > rectal; as concerns the extravascular routes of 84 administration, therefore the intramuscular route is associated with the highest cmax and lowest tmax, and the rectal route with the lowest cmax and highest tmax. This has practical consequences: intramuscular drug administration is followed by a rapid onset of action with a high plasma drug level, but the drug is eliminated quickly from the blood, while after rectal drug administration the onset of action is slow, with a lower plasma drug level, but with a longer duration of action. l / g m , p c iv im oral rectal time Fig. 7.14. Effects of the ratio ka/ke on tmax and cmax Used abbreviations: α the hybrid first-order rate constant for the distribution process; units of time−1 A and the hybrid coefficients; units of concentrations B β the hybrid first-order rate constant for the elimination; units of time−1 −1 k10 the first-order elimination rate constant from the central compartment; units of time k12 the first-order transfer rate constant from the central compartment to the peripheral compartment; units of time−1 k21 the first-order transfer rate constant from the peripheral compartment to the central compartment; units of time−1 t1/2α the half-life for the distribution phase; units of time 85 t1/2β the half-life for the elimination phase; units of time Vc the volume of the central compartment; units of volume X the amount of drug in the central compartment; units of mass Questions 1. Which process influences the change in plasma drug concentration in the one-compartment intravascular model? A. absorption B. distribution C. elimination D. all of the above three process E. none of them 2. What is the meaning of ? A. elimination rate constant B. absorption rate constant C. half-lifetime D. elimination hybrid constant E. distribution hybrid constant 86 8. AUC, model-independent pharmacokinetics The area under the concentration vs. time curve (AUC) gives information about the amount of the drug that reaches the systemic circulation. This is a very important parameter, which plays a part in the calculation of physiological availability and bioavailability, the whole-body clearance, the maintenance dose, etc. Thus, the calculation or determination of AUC is a key issue in pharmacokinetics. The AUC reflects the actual body exposure to the API after the administration of a dose of the drug. In other words, the AUC corresponds to the integral of the plasma concentration versus a definite interval of time (Eq. 8.1). The precision of the AUC determination increases with the number of concentration determined. The unit of the AUC is h mg/L. ∞ 8.1 = ∙ where AUCT is the total area under the concentration vs. time curve from t = 0 to t = ; cp is the concentration of the administered drug in the blood at time t. Since = . , the integration of Eq. 8.1 gives: ∞ = ∙ ∞ 8.2 1 ∞ = − = 0 − = − − − where is the concentration at t = 0, and is the elimination rate constant. Several methods are available for determination of the AUC: planimetry (tracing the curve with a planimeter), analytical way (cutting and weighting), a trapezoid method, calculation from primary pharmacokinetic parameters (Cl, Vd) integration of the concentration vs. time equation. The first two methods are old-fashioned, but the remaining three are widely used. 8.1. Trapezoid method The blood concentration vs. time curve is sliced into relatively thin vertical segments. The shape of each segment is a trapezoid (Fig. 8.1). The area of each trapezoid is calculated and the 87 areas are summed to give the total AUC value for the investigated time period. This is a simple numerical estimation of AUC, which requires only time vs. concentration data pairs. The area of a trapezoid is given by the following formula: ( + ) 8.3 = ℎ 2 where b1 and b2 are the length of the parallel sides, h is the altitude. Introducing the concentration vs. time data into Eq. 8.3 gives: , + , 8.4 = ( − ) 2 In the case of extravascular administration, the first segment is a right-angled triangle. Since b1 = 0 and t1 = 0, the area of this triangle is given by a simplified form of Eq. 8.4: ( , ∙ ) = 8.5 ⊿ 2 Equation 8.4 can be used for every route of administration. The sum of the areas is the total area under the concentration vs. time curve: 8.6 , + , = ( − ) 2 10 8 6 4 2 concentration, mg/L concentration, 0 0 1 2 3 4 5 6 7 8 9 10 11 12 time, h Fig. 8.1. Segmentation of a concentration vs. time curve after a single extravascular dose. When the concentration is increasing (during the absorption phase), the trapezoid method underestimates the AUC, while when the concentration is decreasing (elimination or distribution), AUC is overestimated. (Table 1, last row). 88 Table 1. Data for the calculation of AUC using the trapezoid method after an intravascular bolus. Area of Time Concentration individual (h) (mg/L) trapezoid, h mg/L 0 150.81 0.25 145.38 37.02 0.5 135.27 35.08 0.75 112.41 30.96 1 100.18 26.57 2 67.5 83.84 3 46.89 57.20 4 32.84 39.87 6 15.47 48.31 0-6 358.85 6- 39.95 ∑ 398.80 AUC by 382.30 Cl 16.50 It often happens that the last measured plasma concentration (cp,t) is not zero, and the total therefore cannot be calculated by the trapezoid method. If it is assumed that the change in the blood concentration follows a single exponential decline, the residual AUC value can be calculated from an equation similar to Eq. 8.1, but with integration between t and : ∞ 8.7 = ∙ Integration gives ∞ ∙ 8.8 , = − = 0 − = = − − − where , is the last measured concentration. If t = 0 is substituted into Eq. 8.8, we have ∞ 8.9 1 = − = 0 − = − − − Thus, after the administration of an intravascular bolus injection (a one-compartment model), the value of AUC is the quotient of the initial plasma concentration and the elimination rate constant. The value of AUC for the various models can be calculated by use of the following equations: One-compartment extravascular model: 89 8.10 = − Two-compartment intravascular model: 8.11 = + Two-compartment extravascular model: 8.12 = + − where A and B are the two empirical constants (y-axis intercepts), and and are the two rate constants associated with the two phases of the of the plasma concentration versus time plot. 8.2. Determination of AUC based on clearance Combination of Eq. 7.2 and 8.1 (for intravascular administration) gives 8.13 = where X0 is the administered dose of drug, Vd is the volume of distribution. When t = 0 and , we have 8.14 = As = ClT, 8.15 = = For extravascular administration, the combination of Eq. 8.1 and 7.12 and the integration of Eq. 7.12 yields − = + ( − ) When t = 0 and , we have 90 8.16 = where D is the dose of the drug, f is the fraction of the dose absorbed, and ClT is the total clearance. Equations 8.15 and 8.16 reveals that AUCT is directly proportional to D and inversely proportional to ClT (Fig. 8.2). This holds true in the case of linear pharmacokinetics. 40 30 30 20 mg/L mg/L 20 10 AUC, h AUC, AUC, h AUC, 10 0 0 0 50 100 150 0.0 0.1 0.2 0.3 dose, mg 1/Cl, h/L A B Fig. 8.2. Plots of AUC as a function of the dose (A), and the reciprocal of clearance (B). 8.3. Model-independent pharmacokinetics The determination of pharmacokinetic parameters on the basis of compartmental models requires an adequate number of measured blood concentrations of the investigated drug. In clinical practice, it may be difficult to obtain multiple blood samples to build up a complex model. Non- compartmental or model-independent pharmacokinetics provides an opportunity to obtain parameters that are used to determine the optimum dosage regimen for a patient without the use of a specific compartmental model or complex computational methods. The process of model- independent data analysis does not require curve-fitting. It makes use of simple mathematical methods and is easy to apply in clinical medicine, but plasma concentration vs. time profiles cannot be obtained. The principle of non-compartmental analysis is based on the assumptions that the passage of a compound through the body is a random process, and is governed by probability. The level of the drug is measurable in the plasma, and the rate of elimination of the drug is proportional to the plasma concentration. The length of time any individual drug molecule remains in the plasma after administration may be very short, or very long or some intermediate value. However, if large numbers of molecules are considered, there will be a mean residence time (MRT), i.e. the average time a molecule remains in the body. 91 The MRT can be calculated by using the statistical moment theory. A series of statistical moments of the f(t) function is the following: 8.17 ( ) where the exponent m refers numerically to the moment that is being considered. In pharmacokinetics, the first two statistical moments (0 and 1) are applied in calculations. When m = 0 expression 8.17 yields ( ) = [ ] and when m = 1: ( ) = [ ] As pharmacokinetic investigations based on plasma concentration vs. time data, the above equations can be rewritten as follows: = [ ] 8.18 × = [ ] 8.19 where AUMC is the area under the (first) moment curve (Fig. 8.3). cp AUMC AUC time, h Fig. 8.3. AUC and AUMC 92 In this approach, MRT is the ratio of the first-order and zero-order statistical moments: ∫ = = 8.20 ∫ which gives / = 8.21 / 1 = = 1.44 / 8.22 Simplifying the fraction on the right-hand side of Eq. 8.21 leads to = MRT may be defined as the time required for 63% of the dose to be eliminated via all routes of elimination. Combining this definition and the plateau principle, we obtain the following equation: = = 1 − where f is the plateau fraction and css is the steady state concentration. Let us assume that ket = 1, when = 1 − = 0.63 On the basis of the definition of the MRT f has a value of 0.37, i.e. = 1 − = 0.37 Overall, therefore 1 = We know that = 1 and / = 2 = 0.693 hence the ratio of these two equations yields / / = 1/ 2 93 / = = 1.44 × 2 / When the drug is given extravascularly and follows the two-compartment model, its absorption influences the transit time. Analogously to MRT, we can define the mean absorption time (MAT) as the time when 63 % of the administered drug is absorbed. 1 = = 1.44 / , 8.23 where ka is the absorption rate constant and t1/2, abs is the absorption half-lifetime. MRT after extravascular administration is the sum of MAT (absorption) and MRTbolus (elimination): = + 8.24 i.e. 1 1 = + For compounds that follow the two-compartment model, we have + ∝ = 8.25 + If » : 1 ≈ = 1.44 / , There is a second approach through which to determine the MRT after intravascular drug administration: if we sum the residence times of all the molecules, we can calculate their average, which is MRT: ∑ = 8.26 ∑ where ti is the residence time of a molecule, Ni is the number of molecules with residence time ti and ∑ is the total number of molecules. Assuming that every molecule that enters the body leaves it too, that every molecule has the same mass, and that the sum of these masses is equal to the amount of the drug in the body, which is proportional to the plasma concentration, we have: ∫ = = 8.27 ∫ 94 Table 2. Residence time, half-lifetime and calculated MRT of injected molecules. Molecule # Time spent in the body, min 1 2.9 2 14.3 3 26.3 4 33.9 5 42.5 6 65.2 7 79.3 8 98.7 9 114.7 10 146.7 t1/2 42.5 MRT 62.45 8.4. Application of model-independent calculations The determination of MRT allows estimates of the elimination half-lifetime (t1/2), the elimination rate constant (ke), the apparent volume of distribution at the steady state (Vss), the clearance (Cl), and the dosing rate. 8.4.1. Calculation of apparent volume of distribution at steady-state (Vss) It was seen earlier that in the case of intravascular administration = and thus = Since = we have 1 = = and = 8.28 If the D, AUC and AUMC are known, Vd can be calculated as follows: 95 ∙ = ∙ = 8.4.2. Calculation of the clearance (Cl) The total body clearance (ClT) refers to a volume of fluid from which a substance is removed in unit time. It therefore has units of flow, e.g. ml/min or l/h. ClT can be used to describe the behaviour of a drug in both in vitro, as well as in in vivo systems. In non-compartmental analysis, ClT is estimated by the model-independent equations , = and ∙ , = Substituting AUC from Eq. 8.20, we have , = and , = 8.4.3. Calculation of dosing rate For first-order pharmacokinetics, ClT has a constant value, and it is therefore a valuable parameter for calculation of the dosing regimen for a patient. If the average steady-state plasma drug concentration is known, the dosing rate (how many mg of a drug should be administered to a patient in a period of time) can be calculated: ̅ = and ̅ ∙ = where is the dosing rate. For example, a congestive heart failure patient must be treated with digoxin. ClT is 0.0076 l/h, f is 0.7 and the desired steady-state concentration is 1.5 g/l. To maintain the desired plasma 96 concentration, 0.391 mg of digoxin must be administered ones daily. 8.4.4. Calculation of bioavailability The AUC is an important parameter for the determination of bioavailability (BA) and physiological availability. The calculations and definitions are discussed in Chapter 9. In Section 8.3.2., we showed how to calculate ClT for the intravascular and extravascular routes of drug administration. Rearrangement of those two equations leads to 1 = , and ∙ = , The absolute BA (BAabs) can therefore be estimated as ∙ ∙ = = 1 ∙ ∙ Since ClT is constant in linear pharmacokinetics and independent of the route of administration, the BAabs may be calculated as = 8.29 If equal doses are administered orally and intravenously, BAabs is the ratio of the extravascular and intravascular AUC values. Used abbreviations: API active pharmaceutical ingredient AUC area under the concentration vs. time curve AUCT total area under the concentration vs. time curve AUMC the area under the (first) moment curve BA bioavailability ClT total clearance cp concentration of the API concentration at t = 0 97 ke elimination rate constant MAT mean absorption time MRT mean residence time t1/2 elimination half-life time Vd volume of distribution Vss apparent volume of distribution at the steady state Questions 1. Choose the correct answer relating to the area under the plasma drug concentration vs. time curve! A. It is directly proportional to the amount of the absorbed drug. B. It is the ratio of the amounts of the absorbed and the eliminated drug. C. It is the relative bioavailability. D. It is directly proportional to the total body clearance. E. It gives information about the maximum concentration of the drug in the plasma. 2. Choose the correct statement. A. In model-independent pharmacokinetics, one of the most important parameters is tmax. B. Bioavailability calculations are based on the AUMC value. C. The ratio of AUC and AUMC gives the absolute bioavailability. D. The elimination half-lifetime can be calculated from MRT. E. The ratio of MAT and MRT gives the elimination rate constant. 98 9. Physiological and biological availability of drugs; bioequivalence 9.1. Introduction The availability of a drug is the fraction of a dose D which enters the systemic circulation and becomes available at the site of action of the drug. This is not a directly measurable value. However it may be estimated via the AUC of the plasma levels vs. time curve of the investigated drug. In general, an intravenous bolus injection may be regarded as the point of reference, for in this case 100% of the administered dose enters the systemic circulation. The availability of a drug administered by a different route can be calculated by the use of Eq. 9.1, if the administered doses are equal: = 9.1 . where AUCiv. is the AUC of the reference plasma level vs. time curve in the case of the intravenous bolus and AUCx is the AUC of the plasma level vs. time curve in the case of the different administration route. If the administered doses are not equal, we may write: = ∙ . 9.2 . where Div is the dose administered intravenously and Dx is the dose administered by the different route. The availability of a drug usually, but not always, lies in the range 0-1. If a drug does not enter the systemic circulation, its availability is 0. Availability is frequently expressed as a percentage. Even if the AUC values of two APIs are very similar, very different therapeutic effects may be exerted. To determine the relationship between two cases (e.g. two active substances), therefore, other data, such as the peak plasma concentration (Cmax) and the peak time (tmax), are needed. Two main groups of availability can be determined, depending on the type of the standard reference preparations. 9.2. Physiological availability The physiological availability (PA) of an active substance demonstrates the relationship of the active substance and the human organism. It is expressed as the ratio of the AUC values of the plasma level vs. time curves of dilute, aqueous drug solutions. These 99 solutions are applied via different routes of administration (e.g. intramuscular, subcutaneous, inhalation, transdermal etc.), and therefore only the physiological parameters (e.g. the absorption rate constant ka) may differ. In this case, the point of reference is the AUC value of the plasma level vs. time curves for an intravenous bolus injection. It also means that the PA of an intravenous bolus injection is always taken as 100%. The value of PA can be calculated as follows: = ∙ . 9.3 . where AUCiv. is the AUC value of the plasma level vs. time curve for intravenous bolus administration, AUCx is the AUC value of the plasma level vs. time curve for the investigated route of administration, Div is the dose of the drug administered in an intravenous bolus injection and Dx is the dose of the same drug applied via the investigated route of administration. The values of PA for an active substance can be used to determine the best route of administration for the given drug (i.e. the route giving the highest PA). 9.3. Biological availability (bioavailability) The bioavailability (BA) of an active substance demonstrates the relationship of the pharmaceutical product containing the given pharmacon and the human organism. It means the rate and extent to which an active substance present in a pharmaceutical product is absorbed from it and becomes available at the site of action. The BA of a pharmaceutical product is determined (1) during the development of all new pharmaceutical products, (2) to establish the quality of the product during manufacturing, (3) before an active substance is marketed in a new pharmaceutical dosage form or (4) to investigate the bioequivalence of two pharmaceutical products. There are two types of BA: absolute BA (BAabs) and relative BA (BArel). 9.3.1. Absolute bioavailability BAabs is calculated by comparing the AUC values of the plasma level vs. time curves of an extravascular dosage form and that of an intravenous bolus injection containing the same active substance: 100 . . = ∙ 9.4 . . where AUCiv. is the AUC value of the plasma level vs. time curve for intravenous bolus administration, AUCev. is the AUC value of the plasma level vs. time curve for the extravascular dosage form, Div. is the dose of the drug administered in an intravenous bolus injection and Dev. is the dose of the same drug applied via the extravascular route of administration. It is important to note that the value of BAabs can be ≤ 1.0 (or ≤ 100%), but it cannot be greater than 1.0. In some cases, BAabs can be determined as the ratio of the amounts of the active substance accumulated in the urine following intravenous and extravascular administration. 9.3.2. Relative bioavailability BArel is assessed by comparing the AUC values of the plasma level vs. time curves of an active substance administered in two different dosage forms (e.g. tablet and syrup) or via two different routes of administration (e.g. oral and intramuscular). In this case, the dosage form or route of administration in the denominator is taken as the reference condition and the dosage form or the route of administration in the numerator is compared with it. BArel is calculated as follows: = ∙ 9.5 where AUCsyrup is the AUC value of the plasma level vs. time curve of an active substance incorporated in a syrup dosage form, AUCtablet is the AUC value of the plasma level vs. time curve of the same active substance incorporated in a tablet dosage form, Dsyrup is the dose of the active substance administered as a syrup and Dtablet is the dose of the same active substance applied as a tablet. Alternatively, BArel is calculated as follows: . = ∙ 9.6 . where AUCoral is the AUC value of the plasma level vs. time curve of an active substance applied by the oral route of administration, AUCim. is the AUC value of the plasma level vs. time curve of the same active substance applied by the intramuscular route of administration, Doral is the dose of the active substance incorporated in the oral dosage form and Dim. is the dose of the same active substance incorporated in the intramuscular injection. 101 The value of BArel can be ≤ 1.0 (or ≤ 100%) or even higher than 1.0 (or 100%). If the AUC value in the numerator is higher than that in the denominator, the value of BArel for the dosage form or route of administration in the numerator is > 1.0 (or > 100%). This means that a higher amount of active substance will be available at the site of action if we use the investigated pharmaceutical dosage form or route of administration rather than the reference pharmaceutical dosage form or route of administration. Similarly to BAabs, BArel can be determined as the ratio of the amounts of active substance accumulated in the urine following its administration in two different pharmaceutical dosage forms or via two different routes of administration. Various factors can affect bioavailability. They can be classified into two groups: formulation and physiological factors. The formulation factors include the excipients used in the formulation of a dosage form, the particle size of the active substance, and the physicochemical characteristics of the API (the crystal structure, the amount of water of crystallization, or the existence of more than one crystal structure). The physiological factors include gastric emptying, intestinal motility, and changes in the gastrointestinal pH and/or in the nature of the intestinal wall. 9.4. Special cases Some APIs used in therapy do not give a plasma level vs. time curve because they do not absorb, they exert only a local effect or they have no measurable plasma level. In these cases, therefore no AUC can be determined from which PA and BA can be calculated. However, the pharmaceutical products containing these active substances must also be evaluated and compared with each other. For this purpose, acute effect vs. dose curves can be produced and the AUC, the maximum effect and the time to the maximum effect can be determined, so that the comparison of such pharmaceutical products becomes possible. For example, the BA of a bronchodilator is determined from the data of the forced expiratory volume in 1 second (FEV1) vs. dose curve. 9.5. Equivalence A bioequivalence study is a type of BArel study. The aim is to investigate the therapeutic similarity and interchangeability of two pharmaceutical products, one of them a standard (or innovator) and the other a generic product. For this purpose, determination and 102 comparison of the AUC, Cmax and tmax values are inevitable. Equation 9.5 can be applied in the determination of the bioequivalence of two pharmaceutical products, but with a very important restriction: both products must be identical dosage forms. Through bioequivalence studies, various types of equivalence are determined for two pharmaceutical products. 9.5.1. Therapeutic alternatives Two pharmaceutical products are therapeutic alternatives if their therapeutic indication is identical (e.g. pain-killers). They may differ in their active substances, dosage forms, strengths, routes of administration, etc. This means that they cannot be regarded as equivalent products. 9.5.2. Pharmaceutical alternatives Pharmaceutical alternatives are pharmaceutical products that contain the same active substance, but differ in the salt or ester form, in the dosage form, or in the strength. For example codeine chloride and codeine phosphate are examples of different salts. Hydrocortisone butyrate and hydrocortisone acetate are examples of different esters. Panadol rapid caplets (paracetamol) and Panadol rapid effervescent tablets (paracetamol) are examples of different dosage forms. Betaloc CR 23.75 tablets (metoprolol) and Betaloc CR 47.5 tablets are examples of tablets with different strengths. Pharmaceutical alternatives are not interchangeable. 9.5.3. Pharmaceutical (chemical) equivalence Pharmaceutical (chemical) equivalence means that two or more pharmaceutical products contain equal doses of the same active substance(s) in identical chemical forms, identical dosage forms and for identical routes of administration. They may differ in appearance (e.g. colour or shape) and excipients, but they must be identical in some features (e.g. purity, disintegration time, or rate of dissolution). 103 9.5.4. Bioequivalence Bioequivalence means that two or more pharmaceutically equivalent or alternative products produce comparable biological effects in any individual when administered in single or repeated, equivalent molar doses and under the same therapeutic circumstances. In other words, the extents of absorption of the active substances do not differ significantly and any difference in their rates of absorption is intentional or not medically significant. 9.5.5. Therapeutic equivalence Two pharmaceutical products are considered to be therapeutic equivalents if they are bioequivalent and their therapeutic characteristics (e.g. efficacy and tolerability) have been demonstrated to be identical in clinical trials. Bioequivalence and therapeutic equivalence are not identical. Bioequivalence is frequently used in connection with manufacturing of generic products to express drug interchangeability. Unlike bioequivalence, therapeutic equivalence is a theoretical concept. 9.5.6. Generic preparations A generic preparation (a generic drug, generic product or generics) is a pharmaceutical product defined by the US Food and Drug Administration (FDA) as “a drug product that is comparable to a brand/reference listed drug product in dosage form, strength, route of administration, quality and performance characteristics, and intended use.” As mentioned above, bioequivalence studies are performed to compare the BAs of generic preparations and a standard (innovator or brand name) product. If the bioequivalence of these products is established, the same therapeutic effect produced by the two pharmaceutical products can be expected. Consequently, they can be regarded as interchangeable pharmaceutical products. It is important to note that these products are not necessarily therapeutic equivalents. Bioequivalence studies are performed in 12–36 normal, healthy volunteers who have been fully informed before the initiation of the study. They are randomized into two study groups (i.e. arms). One dose of the investigated drug is administered to the volunteers in one of the groups after overnight (10–12 hours) fasting. The other study group is treated with the standard product under the same circumstances. The volunteers may continue to fast for 2–4 hours after the dosing. Blood samples are collected at appropriate time points to obtain well- 104 defined plasma concentration vs. time curves of the pharmaceutical products. Then, after a washout period (generally about 10 elimination half-times), each volunteer receives the other pharmaceutical product to become his or her own control and to reduce the subject-to-subject variation. Blood samples are again collected. This is the basic design of a crossover study. If the suspicion arises that food may affect the BA of the active substance, a food intervention study is needed. During this study, the plasma concentrations of the test and standard products given immediately after a standard, high-fat content breakfast are determined and compared. The pharmacokinetic analysis of the data obtained includes calculation of the AUC(0- ∞), tmax and Cmax values of both pharmaceutical products in each subject. To prove bioequivalence, there must be no statistical difference between these data on the investigated pharmaceutical product and the standard product. The statistical evaluation is performed with the use of a 90% confidence interval for the ratio of the means. For most generic preparations, this means an 80–125% interval for the AUC and Cmax values as compared with those of the standard product. However, there are pharmaceutical products with high interindividual variability, for which the “bioequivalence” interval for the cmax values can be 70–143%, if this is not clinically significant (e.g. Cmax higher than MTC) and the AUC values do not change significantly. For drugs with a narrow therapeutic range (e.g. oral anticoagulants), the interval is only 90-115%. 9.6 Biosimilarity A biosimilar material is a biological medical product which is a copy of an original biological product (e.g. a protein or an antibody) that is manufactured by a different pharmaceutical company. Biosimilars are officially approved versions of original biological products, and can be manufactured, like small-molecule drugs, when the original product patent expires. These biological medical products are synthesized by recombinant DNA technology, which allows the production of proteins with a complex and, if necessary, a modified chemical structure in living cells (e.g. bacteria, yeasts, or animal or human cell lines). However, the follow-on manufacturer does not have detailed information about the whole process of synthesis, purification and drug formulation, although it is widely known that the quality of these products is highly dependent on the manufacturing process. Nowadays, it is possible to produce a biosimilar the safety, effectiveness and quality of which do not differ significantly from those of the original product. However, several product 105 characteristics (e.g. stability, microbiological purity or haphazard glycation of the product) may differ despite the most careful planning of the manufacturing process. Biosimilars may therefore be considered to be therapeutic alternatives. Drug authorities, such as the European Medicine Agency (EMA), the Food and Drug Administration (FDA) and Health Canada, have developed their own guidelines for the establishment of the similarity of two biological products in terms of safety and efficacy. Zarxio was the first biosimilar to be approved in the United States (on 6th March, 2015). It is a biosimilar version of filgrastim, manufactured by Sandoz. Due to the continuous developments in drug manufacturing, a new definition has been introduced in the case of monoclonal antibody-containing medicinal products. Biobetters are enhanced or ‘better’ version of biosimilars or the original product. Most frequently, this means better tolerability (e.g. fewer or milder side-effects) of the new product. Used abbreviations: AUC area under the plasma level vs. time curve AUCiv AUC of the reference plasma level vs. time curve after intravenous bolus AUCx AUC of the plasma level vs. time curve in the case of the different administration BA bioavailability BAabs absolute bioavailability BArel relative bioavailability Cmax peak plasma concentration D dose PA physiological availability tmax Time belonging to peak plasma concentration 106 Questions: 1. What is relative bioavailability? A. The availability of dilute, aqueous solutions. B. The availability of an extravascular dosage form relative to an intravascular bolus injection. C. The amount of active substance of a pharmaceutical product at the site of action relative to that of a reference pharmaceutical product. D. The difference in availability between different routes of administration. 2. What is bioequivalence? A. Two pharmaceutical products may be considered to be bioequivalent if they have the same therapeutic indication. B. Two pharmaceutical products may be considered to be bioequivalent if they have the same therapeutic indication, but differ in their chemical form. C. Two pharmaceutical products may be considered to be bioequivalent if they are pharmaceutically equivalent and exert comparable biological effects under the same therapeutic circumstances. D. Two pharmaceutical products may be considered to be bioequivalent if they differ only in appearance or in their excipients. 107 10. Drug interactions 10.1. Relevance of drug interactions It is difficult to overestimate the importance of unexpected drug actions as a consequence of interactions with coadministered agents. Such interactions can cause a significant number of hospitalizations. In general, as far as possible, monotherapy is preferred to reach a defined therapeutic goal. However, in a considerable proportion of clinical situations, one agent (even the best choice) is not sufficient to achieve the desired result. In such cases, two or more drugs are combined, which allows an increase in efficacy but also makes drug interactions possible. Drug interactions can lead to qualitative or quantitative changes in drug actions because of the presence of another agent. There is a common misunderstanding that drug interactions are mutual, i.e. that each of the participating agents can increase or decrease the effects of the others in synergisms and antagonisms. However, this mutuality is not an inevitable feature of the interaction. Disulfiram administered alone has no effect on the general feeling of the patient, but when it is combined with ethanol, the alcohol-induced malaise is substantially increased. When a drug interaction is indicated, typically the agents are specified. Indication of the action which is changed in the interaction is fundamental. Morphine constricts intestinal sphincters and causes constriction of the pupils (miosis). Atropine also constricts bowel sphincters and dilates the pupils. Thus, there will be synergism between these two drugs as regards the intestinal action, but antagonism as regards the action on the pupils. The indications of the participating drugs and the action in question are therefore needed for the correct definition of an interaction. 10.2. Classification of drug interactions A classification that can be used in practice is obviously needed so that all the possible drug interactions can be considered. Several systematizations of interactions have been suggested; all of them have some advantages and some shortcomings. The basis of one of these classifications is the phase of drug action. Interactions developing during the absorption, distribution, metabolism and excretion are therefore defined. Chelate complex formation in the gastrointestinal tract may disturb the absorption of the components (e.g. iron therapy and tetracycline antibiotics). This kind of interaction is not 108 restricted to orally administered agents; the absorption of a subcutaneously administered agent can be facilitated or delayed when it is combined with hyaluronidase or a local vasoconstrictor, respectively. The tissue distribution of a drug can be basically different in the presence of another one. Many drugs are retained from the central nervous system (CNS) by active transporters (i.e. ATP binding cassette (ABC) transporters). These transporters can be pharmacologically inhibited, and ability of the drug to enter the CNS can therefore be changed. Loperamide is an opiate without CNS action because it is a substrate of the ABCB1 transporter. When combined with quinidine, however, the typical morphine-like CNS effects can be observed as a consequence of its efficient penetration through the blood-brain barrier. In the above-mentioned example of the combination of disulfiram and alcohol, the metabolism of one of the drugs is changed. Drugs can compete for the transporter responsible for tubular secretion or reabsorption, and the pharmacokinetic profiles will therefore be different from those obtained after a single drug administration. Interactions developing on the receptor are difficult to interpret in this system. In another classification, drug interactions are divided into two groups; pharmacokinetic and pharmacodynamic interactions. In pharmacokinetic interactions, the kinetic behaviour of one drug is changed as a consequence of the presence of the other one. The modified action can be explained by the change in the concentration in the circulation or target tissues. All of the other interactions are regarded as pharmacodynamic interactions. In these cases, no combination- related differences can be determined in the kinetic parameters. The basis of a further classification is the direction of the change of the pharmacological effect. The synergisms and antagonisms are subdivided according to the mechanism of the interaction. Here this classification is used, but it should be kept in mind that the aim of all classifications is to help the understanding; all interactions can be interpreted in any of the systems. Accordingly, antagonism or synergism occurs in some phase of the action of the drug and it is pharmacokinetic or pharmacodynamic. 109 10.3. Synergisms 10.3.1. Additive synergism The most characteristic feature of additive synergism is that the main effects of the two drugs (e.g. two cyclooxygenase inhibitors as analgesics) have identical mechanisms. Since both agents utilize the same target (i.e. a receptor, an enzyme, or an ion channel), the action of the combination is the mathematical sum of the effects exerted by the agents separately. Another consequence of the common mechanism is that the maximum effect of the combination is not higher than the maximum effect of either of the participating drugs. The practical importance of this kind of combination has decreased recently; up-to-date therapeutic guidelines do not recommend the coadministration of drugs with the same mechanism. Additive synergism was applied decades ago, to improve the tolerability when the safety profile of the first-chosen drug was not sufficient. Although the main effect is mediated through a common mechanism, the side- effects may differ. Thus, when a combination of drugs with different side-effects is used to achieve the required degree of the main effect, the severity of the side-effects may be expected to be milder. Let us consider the combination of two analgesics. Aspirin can cause gastric irritation as a side-effect, while phenacetin may lead to renal damage. When the half-doses of these drugs are combined, the full main effect is obtained, but both the gastric and the renal side-effects are reduced. The safety profiles of current drugs are good enough for them to be applied for monotherapy, and additive synergism can now be regarded as obsolete. 10.3.2. Potentiating synergism Potentiating synergism is characterized by a substantially increased maximum effect of the combination as compared with the effects obtained with the separately given drugs. The effect of the combination can be higher than the mathematical sum of the separate effects. This is possible when the two drugs have different targets and different mechanisms of action. Two different cases of potentiating synergism should be distinguished. Both of the drugs have the desired effect, but their mechanisms of action are different. Combinations are frequently used in the treatment of hypertension when monotherapy is inefficient (e.g. diuretics and sympatholytics, or diuretics and angiotensin converting 110 enzyme inhibitors). In clinical practice, drugs can be administered in combination, either together or consecutively. Let us administer one of the drugs in a dose that elicits the maximum effect, and then start to administer the other drug in gradually increasing doses. Since their mechanisms are different and independent, the second drug will result in an increase of the maximum effect of the first agent. Similarly, potentiating synergism is utilized in numerous other indications, including antiasthmatic, anticancer or antimicrobial therapy. When given alone, only one of the drugs can exert the effect, but the effect is enhanced in the combination. Typically, one of the drugs changes the pharmacokinetic behaviour of the other drug, with the consequence of increased action. As an example, the CYP3A4 inhibitor ketoconazole (an antifungal agent) does not have antihypertensive action. However, it inhibits the first pass metabolism of coadministered dihydropyridines (e.g. amlodipine), the concentration of which in the systemic circulation is substantially increased. Lopinavir is an antiretroviral protease inhibitor with fast elimination by CYP3A4. It is commonly combined with a subtherapeutic dose of another antiretroviral protease inhibitor, ritonavir, which in low doses is a potent CYP3A4 inhibitor; this results in a prolongation of the effect of lopinavir and an increase of its efficacy. Many similar examples of pharmacokinetic synergism are utilized in clinical practice. 10.4. Antagonisms 10.4.1. Chemical antagonism In chemical antagonism, the development of the interaction does not require a biological system and the interaction itself can be characterized purely as a chemical reaction. Complex formation typically involves this kind of interaction. Similarly, chelators can be used as antidotes in cases of heavy metal poisoning. When the action of the anticoagulant heparin needs to be suspended, the specific antidote protamine sulfate is administered. Heparin is an acidic polysaccharide, and protamine is a basic polypeptide, and together they form a fine precipitate, so that the actions of both are terminated. Interestingly, protamine sulfate given alone exerts anticoagulant action too, though it is used only as an antidote in clinical practice. 111 10.4.2. Biological antagonism In contrast with chemical antagonism, the development of biological antagonism demands a living biological system (in vitro or in vivo). Biological antagonism can be subdivided into functional and specific subtypes. In specific biological antagonism, the two drugs act on the same receptor and in this case competitive and non-competitive antagonism can be distinguished. 10.4.3. Functional antagonism In functional antagonism, the two agents exert opposite actions on a physiological function through different sites of action. For instance, when histamine in released excess, it can decrease the blood pressure, activating its own receptors. This situation can be reversed by administration of a vasoconstrictor (e.g. adrenaline) which elicits its action on the α-adrenergic receptors. It is relevant that both participating agents have a broad range of action, and usually only one effect is antagonized by the other drug. The gastric secretory action of histamine and the arrhythmogenic property of adrenaline are not changed in the combination. Sympathomimetics and parasympathomimetics are in a similar relationship. 10.4.4. Competitive antagonism In competitive antagonism, the two drugs, i.e. the agonist and the antagonist, bind to the same receptors in a reversible fashion. Their concentrations and affinities will therefore determine the saturation of the receptor. It seems obvious that, the higher the concentration and the higher the affinity (i.e. the lower KD) the higher the amounts of both drugs bound to the receptor. Since the total number of receptors is limited, a competition develops between the two drugs. The specific activity of an antagonist is zero, indicating that is cannot elicit any action when given alone. The action of a competitive antagonist can be detected when it is used in combination with an agonist and the result is a decrease in the action of the agonist. Since the binding of the antagonist to the receptor is reversible, it can be displaced by a higher agonist concentration. As a consequence the concentration vs. response curve of the agonist is shifted in 112 parallel to the right in the presence of a competitive antagonist. The extent of this shift is determined by the concentration and the affinity of the antagonist (Fig. 10.1). Fig. 10.1. Concentration vs. response curves of an agonist alone (A) and in the presence of a competitive antagonist (B) The parallel occurrence of the shift means that any degree of action elicited by the agonist alone can be elicited in the presence of the antagonist too, but the agonist concentration should be increased several-fold. This can be described as follows: [A][B] [A] = [A] + 10.1 where [A] and [B] are the concentrations of the agonist and antagonist, respectively, KDB defines the affinity of the antagonist, and n, the dose ratio, indicates how many times the agonist concentration should be increased in order to reach the action elicited by [A] alone. Equation 10.1 can be rearranged: [B] = 1 + 10.2 This reveals that the dose ratio is independent of the concentration of the agonist. Let us consider the situation when n = 2. We than have [B] = KDB. In other words, the antagonist concentration at which the concentration of the agonist should be doubled in order to obtain the action elicited by the agonist alone is equal to the dissociation constant of the antagonist. The negative logarithm of this KDB value is called pA2 and is used to describe the affinity of the 113 antagonist. The value of pA2 can be calculated from experimentally determined results through the Schild equation: pA = pA + log ( − 1) 10.3 where pAx is the concentration of competitive antagonist at which the agonist concentration should be increased x-fold in order to obtain the action elicited by the agonist alone. In therapy, many competitive antagonists are utilized; all the β-adrenergic blockers, antihistamines, and opiate and dopamine antagonists exert their action via competitive antagonism. 10.4.5. Non-competitive antagonism A non-competitive antagonist behaves similarly to a competitive one in some respects; it has affinity for the receptor, but without eliciting any action on it. The crucial property of non- competitive antagonists is their irreversible binding to the receptor, from which it cannot be displaced by any concentration of the agonist. The higher the saturation of the receptors by the antagonist, therefore, the lower the number of receptors available for the agonist. As a consequence, the maximum value in the concentration vs. response curve becomes depressed. The higher the concentration and affinity of the antagonist, the more marked the maximum depression (Fig. 10.2). Fig. 10.2. Concentration vs. response curves of an agonist alone (A) and in the presence of a non-competitive antagonist (B) 114 The affinity of the non-competitive antagonists is described by pD2’; this is the negative logarithm of the antagonist concentration at which the maximum effect of the agonist is depressed by 50%. At this concentration, half of the receptors are saturated with non-competitive antagonists, and consequently the ratio of functioning receptors is 50%. pD2’ can be calculated from experimental results as follows: pD = pD + log ( − 1) 10.4 where pDx is the negative logarithm of the antagonist concentration that elicits a depression level of x (i.e. the ratio of the maximum effect of the agonist when given alone and when given in combination with the non-competitive antagonist). Only a few non-competitive antagonists are utilized in therapy; some alkylating α-adrenergic blockers (e.g. phenoxybenzamine) exert their action through this kind of interaction with noradrenaline. 10.4.6. Additional types of interactions The interpretation of interactions has recently been extended to any exogenous substance that may change the action of a drug in either a quantitative or a qualitative meaning. Many drug– food interactions have been described, among which the relationship between grapefruit and CYP3A4-metabolized drugs is considered to be the most relevant. The extract of Hypericum perforatum is widely used in milder forms of depression. Some components of the extract have the capacity to induce hepatic metabolizing enzymes and a substantial decrease of the effect can therefore be expected. There are interactions in which the pharmacological profile of one of the drugs is modified in the presence of the other. Penicillin-type antibiotics frequently become ineffective against the bacteria that produce the enzyme β-lactamase, which breaks down the backbone of the drug. In this case, the penicillin-type antibiotic can be combined with a β-lactamase inhibitor. These latter agents do not exert any substantial antibacterial activity of their own, but they protect the penicillins from enzymatic decomposition. Ampicillin–sulbactam and piperacillin– tazobactam are commonly used combinations. Ampicillin and sulbactam can be chemically linked into a single molecule (sultamicillin) which releases both active agents after absorption. A special subset of interactions develop between a drug and a physical impact on the organism. The treatment of cancers frequently involves systemic chemotherapy and local 115 irradiation of the tumour tissue, and a synergistic interaction is expected from this combination. A novel modality of cancer treatment is photodynamic therapy, which involves the systemic administration of a photosensitizing agent and the local exposure of the cancer to light. The pharmacological activity of the photosensitizing agent given alone is negligible, but the light initiates a chemical reaction that results in highly reactive products (e.g. free radicals), which can cause serious local tissue damage. The light exposure is therefore a tool which localizes the action to the cancer and the surrounding intact tissues can be spared. Used abbreviations: ABC ATP binding cassette CNS central nervous system KD dissociation constant KDB dissociation constant of the competitive antagonist n dose ratio pA2 negative logarithm of KDB pD2’ negative logarithm of the non- competitive antagonist concentration at which the maximal effect of the agonist is depressed by 50% 116 Questions 1. Which of the following parameters may describe the affinity of a competitive antagonist? A. pD2’ B. pA2 C. the dose ratio D. log (dose ratio – 1) 2. Which of the following are classified as a pharmacokinetic interaction? A. displacement of the agonist from its receptor B. inhibition of an enzyme that metabolizes the agonist C. irreversible inhibition of the receptor of the ligand D. eliciting the same action as that of the agonist with another agent which acts through the same mechanism 117 11. Factors influencing drug action and drug administration Different individuals respond to drug therapy differently. The way in which a person responds to a drug is affected by many things such as physiological, pathological, genetic and environmental factors, interactions with other drugs, etc., and many factors must be considered as concerns the effect of a drug. 11.1. Effects of age – Older patients Drug absorption. With advancing age, physiological decreases occur in the intestinal motility, the blood flow and gastric acid secretion (pH > 4.5), which leads to an increase of the transit time in the gastrointestinal tract. Although the absorption of most drugs from the gastrointestinal tract does not usually change significantly in advanced age, it should be remembered that the delay in gastric emptying allows more contact time in the stomach for potentially ulcerogenic drugs such as the NSAIDs. The changes in the skin structure have to be considered in connection with drug administration. Delayed lipid accumulation and the decrease in the epidermal barrier result in the increased the permeability both of water-soluble and fat-soluble subtances. Drug absorption may also be influenced by nutritional deficiencies and gastric surgery in older patients. Drug distribution. The changes in drug distribution with age may be due to a decreased muscle mass, a reduced quantity of body water and an increased amount of body fat as a percentage of the total body mass. The total body distribution of water-soluble drugs is lower and the serum level of drugs is higher, and the pharmacological effect is therefore enhanced. Diuretics, which increase loss of the water, may increase the effects and toxicity of drugs (e.g. antiarrhythmics and digoxin) in the elderly. Fat-soluble drugs (such as diazepam and lidocaine) have greater distribution volumes, and the effects of these drugs will therefore be prolonged and the drugs will in many cases be under dosed. Moreover the serum albumin concentration decreases with age, and the free drug level may therefore increase in the causes of barbiturates, theophylline, salicylates, etc. Drug metabolism. The weight and blood flow of the liver decrease with age. The reduced hepatic blood flow is often associated with a moderation of the first-pass effect (e.g. -blockers and verapamil). Phase 1 drug biotransformations are variably decreased in aging, 118 whereas hepatic phase 2 enzymatic reactions do not appear to be adversely affected by age and drugs with a phase 2 biotransformation (e.g. oxazepam) are preferable for older patients. Drug elimination. The weight of the kidney, the number and size of the renal glomeruli and the blood flow to the remaining renal glomeruli physiologically decrease during life. These structural changes result in a progressive, age-related decrease in the glomerular filtration rate (GFR). The toxic effects of renally excreted drugs (e.g. ciprofloxacin, digoxin and furosemide) may increase. Estimates are commonly made by using the CockroftGault equation, which incorporates age, weight and the approximate change in muscle mass as represented by the serum creatinine: (140 − age) ∙ body weight (kg) Creatinine clearance (ml min, males) = 72 ∙ serum creatinine contet (mg⁄dl) For males, multiply the results by 0.85 Pharmacodynamic changes. General age-related changes may be observed in the function and structure of the receptors. Some receptors, such as the -adrenergic receptors, display reduced sensitivity and decreased efficiency. Increased sensitivity and increased efficiency have been demonstrated for other receptors, e.g. GABAA and opioid receptors. The numbers of some receptors decrease during aging and the antagonistic effect of drugs (e.g. dimenhydrinate and oxybutinin) is therefore higher in older individuals. The age-related decrease in endogenous mediator synthesis also results in an increase in the antagonistic effect, e.g. in cases of metoclopramide and haloperidol. As a consequence of various chronic diseases, polypharmacy is considerable, and the overuse and misuse of medications can increase the number of hospitalizations and the mortality of the elderly. 11.2. Effects of age – Paediatric patients The Food and Drug Administration Guidance (1998) breaks down the paediatric population into the following groups: neonates (from birth to 1 month), infants (from 1 month to 2 years), developing children (from 2 to 12 years), and adolescents between 12 and 16 years. These groups differ in terms of physical size, body composition, physiology and biochemistry. The body weight and the body surface area (BSA) change rapidly during the first year. All of these changes affect the pharmacokinetic and pharmacodynamic parameters 119 in children. For a paediatric individual, the dose may be modified by consideration of either the BSA or the body weight. Ritschel and Kearns described an approach with which to determine doses in infants. This approach may be illustrated by the following equations the BSA is calculated from the height and the weight, and is around 1.7-1.8/m2: Infant dose = (infant body weight in kg) / 70) x adult dose Infant dose = (infant BSA in m2) / 1.73) x adult dose Drug absorption. The gastric pH is neutral (pH 6-8) at birth because of the presence of alkaline amniotic fluid. It subsequently continuously decreases and reaches the adult level at around 2 years of age. The oral bioavailability for acid-labile compounds is higher, and the oral bioavailability for weak acids is lower in neonates than in adults. The gastric emptying time during the neonatal period up to the age of 6 months is longer than in older children or adults. After oral administration, the absorption of phenobarbital, amoxicillin and cephalosporins is delayed and incomplete in neonates and small infants. The different floras colonizing in the foetal intestine also influence the absorption. The percutaneous absorption of drugs may be higher in neonates and infants, as a result of factors such as the better hydration of the epidermis, the readier perfusion of the subcutaneous layer, and the larger ratio of total BSA to body mass than those in adults. Premature infants have a significantly less effective skin barrier to the absorption of drugs and toxins. These factors may lead to systemic toxicity during the administration of therapeutic drug doses (e.g. lidocaine, corticosteroids, antihistamines or antiseptics) during the first year of life. The absorption of intramuscularly administered drugs is delayed in neonates as a result of the lower blood flow to the skeletal muscles and the inefficient muscular contraction. Rectal absorption is excellent for some agents in children; the less pronounced first- pass effect is due to the lower hepatic clearance of drugs. Drug distribution. Neonates and young infants have a relatively high total body water compartment and their adipose tissue has significantly higher water content than that in adults. (An exception is the children of mothers with diabetes.) These differences result in lower plasma levels for water-soluble drugs. The concentrations of plasma proteins (e.g. albumin) and the affinity of the foetal albumin for drugs are lower, which may lead to a high free fraction of a drug (e.g. diazepam, phenytoin, salicylates or ampicillin). The conjugation 120 of bilirubin to albumin in neonates is important, because a disorder of the bilirubin conjugation can result in toxicity (kernicterus). Drug metabolism. The drug-metabolizing enzymes are generally active to varying degrees in neonates, and the maturation of these enzymes occurs longitudinally. Preterm neonates may have very low enzyme levels and this can give rise to significant drug toxicity (e.g. methylxanthines, third generation cephalosporins and morphine) or a lack of efficacy of prodrugs. The level of CYP3A7, the primary isoenzyme expressed during the prenatal period, declines rapidly after birth. The expressions of CYP2E1, CYP3A4, CYP2C9 and CYP2D6 begin to rise at the time of birth. The activities of these enzymes increase with time, but not linearly. The development of the phase 2 enzymes such as the uridine 5’-diphospho- glucuronosyltransferases (UGTs) is important because 15% of the drugs (e.g. acetaminophen, morphine and zidovudine) is eliminated by this metabolic pathway. The UGTs are present by the gestational age of 24 weeks and their activity increases continuously up to the age of 10 years. Drug elimination. The GFR and tubular secretion processes are low at birth. Maturation of this function is dynamic and is usually complete by the age of 1 year. Immature renal clearance processes result in the inefficient elimination and the lower half-lives of drugs (e.g. antibiotics). 11.3. Sex differences Drug absorption. Females have lower gastric acid levels and longer gastrointestinal transit times than those in males. Medications that require an acidic environment for absorption (e.g. antibiotics) may therefore have a lower bioavailability in females. A longer gastrointestinal transit can increase the absorption of medications such as metoprolol. The lower tidal volumes in females result in the lower bioavailability of drugs which undergo inhalational absorption. Drug distribution. Females generally have larger fat stores than those in males and lipophilic medications, such as the benzodiazepines (diazepam), therefore have a longer duration of action in females. Higher initial plasma concentrations and greater effects are produced in females by hydrophilic substances such as alcohol, which are distributed into smaller volumes. 121 Drug metabolism. Higher CYP activities are generally measured in males than in females (e.g. those of CYP1A2, CYP2A6 and CYP2B6). The activities of CYP2D6 and CYP3A4, which are otherwise higher in females than in males are increased still further during pregnancy. Phase 2 metabolism processes proceed faster in males than in females. Both oestrogens and androgens regulate the expression of phase 2 drug-metabolizing enzymes, and the activity is increased during pregnancy. Drug elimination. The GFR is higher in males than in females. Males produce more creatinine than do females and the factor of gender must always be considered when the GFR is calculated from the creatinine clearance and in calculations of the dosage for drugs which have a narrow therapeutic dose range (e.g. digoxin) or irreversible toxic side-effects (e.g. the aminoglycosides). 11.4. Body weight Total body weight (TBW) is a person’s actual weight Ideal body weight (IBW) in kg: Males = height in cm – 100 Females = height in cm – 110 Lean body weight (LBW) in kg: Males = 50 + 0.9 kg for every cm over 150 cm Females = 45 + 0.9 kg for every cm over 150 cm Pathophysiological changes in weight of patients can affect the drug absorption, distribution and elimination of drugs. As drug administration based on the TBW can result in underdosing or overdosing, depending on the properties of the drug, weight-based dosing scalars must be taken into consideration in obese patients. Drug absorption. Gastric emptying is slower in obese patients and this result in the better absorption of oral medications. Intravenous drug administration to obese patients is difficult, due to the poor access to the veins. The lower subcutaneous absorption of drugs results in a poor subcutaneous blood supply. Intramuscular administration may fail if the needles are too short and can not reach the muscle. Drug distribution. The volume of distribution of lipid-soluble drugs is higher in obese subjects, and the doses of lipid-soluble drugs must be calculate by taking the body weight into consideration. The value of Cmax is lower in obesity and the lipophilic drugs (benzodiazepines 122 and tricyclic antidepressants) then accumulate in the fat tissues and result in a prolonged drug action. There is no change in the volume of distribution of water-soluble drugs, and the dose is determined on the basis of the IBW or the LBW. Drug metabolism. The activities of the enzyme CYP2E1 and phase 2 conjugation are generally higher and the hepatic blood flow is lower in obesity. Drug elimination. The elimination half-life of lipid-soluble drugs is longer due to their accumulation in overweight subjects. The higher GFRs in obese patients with a normal renal function cause a more expressed clearance of drugs that are excreted by the kidneys. Co- existing disease (e.g. diabetes or hypertension) can influence the GFR in overweight patients. 11.5. Pregnancy Drug absorption. High progesterone levels lead to delayed gastric emptying and a longer small bowel transit time. An increase in gastric pH may increase the ionization of weak acids and reduce their absorption. Oral drug absorption can be decreased by nausea and vomiting in early pregnancy. Drug absorption via the lungs is enhanced in pregnancy because the higher cardiac output can increase the rate of drug uptake across the alveoli. The higher levels of extracellular water and blood flow to the skin may enhance the absorption and alter the distribution of topical agents. The elevated peripheral perfusion may also increase the absorption of intramuscular drugs. Drug distribution. The fat accumulation during pregnancy may increase the tissue binding of lipophilic drugs, leading to prolonged drug effects. During pregnancy, there are increases in the intravascular (plasma volume) and extravascular (breasts and uterus) water contents. This larger total body water content creates a larger space within which hydrophilic drugs may distribute, which decreases their active concentration. The decreases in albumin and 1-acid glcoprotein levels during pregnancy may lead to higher free levels in the plasma of such drugs as salicylates and diazepam. In some cases, this increase in free drug levels is balanced by a more rapid hepatic biotransformation or renal elimination. Decreased protein binding can increase the availability of free drug to cross the placenta. Drug metabolism. Sex steroids increase the activity of enzymes in the cytochrome P450 family and phase 2 metabolic enzymes during pregnancy. This induction of activity may result in clinically significant reductions in active drug levels. 123 Drug elimination. The increased renal blood flow and GFR in pregnancy may increase the elimination of some drugs (e.g. digoxin, antibiotics or lithium). The placenta plays a crucial role as a barrier between the circulatory systems of mother and child during pregnancy. Drug transfer occurs mainly via passive diffusion, active transport, facilitated diffusion, phagocytosis and pinocytosis (too slow, and it does not affect the pharmaceutical effect) across the placenta. Passive diffusion is influenced by following factors: molecular weight: for drugs with molecular weights in the range 250-400 Da; drugs with high molecular weights, e.g. heparin and insulin, do not cross the placenta; lipid solubility; ionization state (inversely proportional); structure; protein binding. Several transporter proteins and drug transporters have been identified in the placenta. The best described of placental drug transporters to date, are P-glycoprotein and the breast cancer resistance protein of the ABC drug efflux transporter family. The expression of the drug efflux transporters is regulated by a number of transcription factors and steroid hormones. These transporters are normally involved in the excretion of toxins from cells. Placental transport proteins reduce or eliminate the foetal exposure of the drug. Both the immature foetal liver and the placenta can metabolize drugs. An immature phase 1 and phase 2 metabolisms may be observed in the foetus 8 weeks post-conception. Elimination from the foetus occurs by diffusion back to the maternal compartment. 11.6. Genetic factors The effects of genetic factors on the action and administration of drugs are surveyed in Chapter 12. 11.7. Pathological factors Liver diseases. The liver plays a crucial role in the pharmacokinetics of a majority of drugs. A liver dysfunction may affect the hepatic metabolism, the biliary excretion and the plasma protein level of drugs, thereby influencing the processes of distribution and 124 elimination. Liver cirrhosis and various forms of liver failure may decrease the first-pass effect of drugs after oral administration, leading to a significant increase in the plasma concentration of a drug. Chronic liver diseases are associated with reduced activities of drug- metabolizing enzymes. These patients are more sensitive to the adverse central effects of opioid analgesics and the adverse renal effects of NSAIDs. In contrast, a decreased therapeutic effect for β-adrenergic receptor antagonists and certain diuretics has been noted in cirrhotic patients. Renal diseases. Renal disease can lead to lower levels of renal blood flow, glomerular filtration and tubular transport processes. This can be expected to decrease the clearance of water-soluble drugs and drug metabolites, and in renal failure drug filtration and reabsorption are also insufficient. The plasma protein binding can be further diminished as greater amounts of these proteins are lost from the blood into the urine. The titration of the drug dosage to the renal function as estimated by the creatinine clearance is especially important in renal disease patients. The renal function may be affected, and this may lead to abnormal effects of digoxin, lithium, gentamycin and penicillin. Malnutrition. Nutritional deficiencies influence the plasma protein level. A low protein concentration results in a higher unbound fraction of drugs, together with enhanced effects and toxicity, e.g. for warfarin. Protein and calorie malnutrition similarly decreases the levels of microsomal protein and total P450. Used abbreviations: BSA body surface area CYP cytochrome P450 GFR glomerular filtration rate IBW ideal body weight NSAID non-steroidal anti-inflammatory drug TBW total body weight UGT uridine 5’-diphospho- glucuronosyltransferase 125 Questions: 1. Which of the following are true for absorption in paediatric patients? A. The gastric pH is neutral at birth. B. The gastric pH is acid at birth. C. Rectal absorption is unreliable to children. D. Gastric emptying is quicker in children. E. The percutaneous absorption of drugs is similar in children and in adults. 2. Which of the following factors do not influence the drug metabolism? A. age B. gender C. pregnancy D. education E. liver diseases 126 12. Non-linear pharmacokinetics and therapeutic drug monitoring 12.1. Non-linear pharmacokinetics 12.1.1. Relevance of non-linear pharmacokinetics For most drugs, the pharmacokinetic constants used to describe the kinetic behaviour (e.g. t½, ke and ClT) of the given substance do not depend on the dose. On the other hand, there are typically dose-dependent parameters, including AUC and Cmax, which are directly proportional to the dose in the therapeutic range (Fig. 12.1). The kinetics of these drugs is said to be linear, and the elimination is characterized by a first-order process. For a special subset of drugs, these assumptions are not valid; within the therapeutic range, there is a dose above which the dose- dependent parameters are not directly proportional to the dose, and the fundamental kinetic constants (e.g. t½, ke, Cl and VD) may vary, depending on the dose administered. This phenomenon is non-linear pharmacokinetics or dose-dependent pharmacokinetics. The basic reason for the unexpected behaviour is the saturation of one or more of the kinetic processes (absorption, distribution, metabolism or elimination) of the drug at a certain concentration, and above this concentration the process is going on according to zero-order kinetics, instead of the generally anticipated first-order kinetics. When the concentration increase after the administration of an increased dose is lower than expected on the basis of linearity, the absorption is saturated (Fig. 12.1). Fig. 12.1. Typical linear (blue line) and non-linear (red line) pharmacokinetic behaviour as a consequence of saturated absorption. 127 It seems obvious that the increase in the plasma concentration is higher than proportional when the metabolism or excretion of the agent is saturated. The limited solubility of an orally administered agent (e.g. griseofulvin) may lead to a disproportional increase in the serum concentration; increase of the dose elicits a lower than expected increase in concentration. Saturation of the gut wall transport may lead to a similar situation (e.g. riboflavin). The extent of enteral absorption of amoxicillin decreases with increase of the dose. During the distribution phase, the plasma protein binding of a drug can be saturated within the therapeutic concentration range, and the free fraction of the drug can be disproportionate elevated following an increase of the dose of the drug (e.g. disopyramide). A step in the elimination can also be saturated; in this case, an increase of the dose will elicit a higher than proportional increase in the serum concentration. The saturation of tubular secretion (e.g. penicillin G) can be a basis of this kind of kinetic behaviour. The most frequent reason for non-linear pharmacokinetic behaviour is the saturation of the metabolic capacity; this can also be true for the presystemic metabolism. The absorption of levodopa takes place via an amino acid transporter, and a substantial amount of the given dose is metabolized during the absorption. A limited increase of the daily dose of phenytoin (e.g. from 300 mg to 450 mg) may elicit as much as a 10-fold increase in peak concentration (Cmax). Since the pharmacokinetic behaviour of phenytoin is an example of the most common type of non-linear kinetics, this kind of elimination should be discussed in detail. As a consequence of the saturation of the metabolism, the most relevant means of elimination, a threshold concentration can be defined above which the elimination becomes of zero-order instead of the typical first-order process. Administration of higher doses of this kind of drug does not result in a parallel serum concentration profile (Fig. 12.2). 128 Fig. 12.2. Typical linear (blue line) and non-linear (red line) pharmacokinetic behaviour as a consequence of saturated elimination. 12.1.2. Capacity-limited metabolism The capacity-limited metabolism is also referred to as saturable metabolism, Michaelis– Menten kinetics or mixed-order kinetics. This kind of kinetics is the most basic feature of enzyme kinetics. enzyme + drug → enzyme + metabolite 12.1 According to the Michaelis–Menten principle, the rate of conversion of the drug into the metabolite as a function of drug concentration can be described by a saturation curve (Fig. 12.3). At low drug concentration, the concentration of available enzyme is relatively high and thus the rate-limiting factor of the reaction is the availability of the drug. When the drug concentration is increased, the rate of metabolism is increased proportionally. In this condition, the reaction takes place with first-order kinetics and the kinetics itself is considered linear. When the drug concentration is increased still further, a point is reached above which the rate of metabolism increases less than proportionally because the relative abundance of the enzyme decreases. Upon further increase of the drug concentration, all the available enzyme molecules become saturated and the rate reaches its maximum; even if the drug concentration is increased further, the rate of conversion will not change. 129 Fig. 12.3. Relationship between rate of metabolism and the concentration of a drug that exhibits capacity-limited metabolism. The rate can be described by the following equation: = 12.2 + where V is the rate of metabolism, C means the concentration of the drug, Vmax is the maximum rate and KM is the Michaelis–Menten constant. Vmax depends on the amount of the enzyme. KM defines the concentration of the drug at which the rate of metabolism is half the maximum (Vmax/2). It is also a descriptor of the affinity of the drug for the enzyme; the higher the affinity, the lower the value of KM. Although Eq. 12.2 describes the rate of metabolism for the whole concentration range, it is practical to apply it separately for low and high concentrations. At low drug concentrations when KM >> C, C can therefore be omitted from the denominator of Eq. 12.2: = 12.3 Since the ratio of the two constants is also constant (Vmax/KM = K), at these concentrations the reaction follows first-order kinetics: = 12.4 On the other hand, C >> KM, Eq. 12.2 can be simplified to V = Vmax. 130 12.1.3. Estimation of Michaelis–Menten parameters (Vmax and KM) It is obvious that the development of a proper dose regimen for drugs which follow non- linear kinetics is impossible without a knowledge of Vmax and KM. Theoretically, a single dose could be enough to determine these crucial parameters. In order to avoid absorption, the dose should be given intravenously and should be high enough to reach the plasma concentration in the non-linear range (Fig. 12.3). The rate of elimination can be calculated via the following equation: − = 12.5 − where Cn and Cn+1 are the consecutive plasma concentrations obtained at consecutive time points tn and tn+1, respectively. For each pair of concentrations, the average concentration can be calculated, + = 12.6 2 and the rate of elimination (V) can be plotted against C (Fig. 12.3). The linearized form of the relationship can be used to produce the Lineweaver–Burk plot: 1 1 1 = ∙ + 12.7 The reciprocal of Vmax is obtained as the intercept on the ordinate and the slope of the line is KM/Vmax (Fig. 12.4). Fig. 12.4. Relationship between 1/rate of metabolism and the 1/concentration of a drug that exhibits capacity-limited metabolism. 131 There is another way to linearize 12.2: = 12.2 + ( + ) = 12.8 + = 12.9 = − 12.10 − = 12.11 = − 12.12 At the steady state, the rate of elimination (V) can be substituted by the rate of administration (R), which can be interpreted as the dose administered in unit time. = − 12.13 When the administration is a continuous infusion, it is typically given in mg/h, but it can be used for discrete doses too, e.g. mg/day. In the latter case, the steady-state concentration is the average of the peak and trough (maximum and minimum) concentrations. When R is plotted against R/C, a straight line with negative slope is obtained; the intercept on the ordinate is Vmax and the slope is –KM. It is obvious that at least two pairs of data (R and the corresponding C) are needed for this kind of graphical estimation. 12.1.4. Additional possibilities for non-linear pharmacokinetics Although the saturation of kinetic processes is the most common reason for non-linear pharmacokinetic behaviour, there can be other reasons too. The pharmacokinetics of ethanol is special and relevant from a practical point of view. Ethanol is converted into acetaldehyde by alcohol dehydrogenase and then into acetic acid by acetaldehyde dehydrogenase and the first metabolite is the more toxic. Both metabolic steps require NAD+; the conversion of 1 mol of ethanol into acetic acid requires 2 mol of NAD+, which greatly exceeds the hepatic pool. The availability of NAD+ therefore limits the ethanol metabolism to about 8 g or 10 ml per hour in a 70-kg adult. The metabolism of ethanol is saturated at very low concentrations and it is a zero-order procedure in the whole clinically 132 relevant concentration range. A negligible portion of ingested ethanol (at most 10%) is excreted in the urine, the sweat and the breath and the remainder is metabolized by the hepatic alcohol dehydrogenase and acetaldehyde dehydrogenase. In enzyme autoinduction, the kinetic parameters change as a function of the treatment time. The phenomenon itself may be regarded as an adaptation of the body to the repeated exposure to the xenobiotic. The development of the stimulated activity of the metabolic enzyme requires several days to weeks. The rate of elimination of an autoinducer (e.g. phenobarbital) is therefore lower at the beginning of repeated administration than later, when the induction has been accomplished. The basic pharmacokinetic procedures (e.g. absorption, distribution and excretion) are strongly coupled to physiological functions (e.g. blood flow, motility and secretion). Since most of the physiological functions exhibit a circadian variation, it is conceivable that the pharmacokinetic behaviour of some drugs may change depending on the time of administration. Chromopharmacokinetics is an area of science in which the variation in the pharmacokinetic parameters of drugs is studied as a function of the time of day. A wide range of data have demonstrated that this circadian variation may result in deviations from linear pharmacokinetics. The activities of crucial drug metabolic enzymes (e.g. CYPA34) can exhibit severalfold changes during the day indicating that systemic exposure to orally administered substrates is dependent on the time of the administration. When administered to young patients, propranolol was absorbed faster and exhibited a higher peak plasma concentration in the morning that at night. 12.2. Therapeutic drug monitoring (TDM) 12.2.1. Individualization of drug therapy The relevance of the individualization of drug therapy was probably recognized in the very early age of drug usage. Monotherapy is nowadays preferred to multicomponent preparations, with individualization of the prescribed drug dose according to the requirements of the patient. As concerns the determination of the optimum dosing regimen, drugs can be divided into three groups. 133 A minor proportion of the currently used agents (e.g. beta-lactam antibiotics) are considered to be atoxic; the usual therapeutic doses and the doses that elicit toxic effects are safely different. In other words, the therapeutic range is wide enough. For the vast majority of drugs, the therapeutic range is relatively narrow, meaning that the dose must be carefully considered. Adjustment of the dose can be facilitated by regular evaluation of the therapeutic action of the drug. Most of the actions can be easily determined, and the result of the evaluation can be utilized as input for dose correction iteration (Fig. 12.5). This kind of dose correction, called dose titration, is utilized in treatments with most drugs, including antihypertensive, anticoagulant or antihyperlipidaemic agents. The actions of the applied drugs can be assayed readily (e.g. blood pressure, coagulation time or serum lipid levels). There is a third group of drugs, for which dose titration is not possible for a number of reasons. Some drugs have an extremely narrow therapeutic range and the elicited effects are therefore not suitable for dose titration (e.g. cardiac glycosides or lithium). Other drugs exhibit extremely large individual variability in serum concentration as a consequence of, for example, the Michaelis–Menten kinetics (e.g. phenytoin). For other drugs, the toxicity is difficult to distinguish from the symptom of the underlying disease of the patient (e.g. some antiarrhythmic agents may induce arrhythmia). There are special groups of drugs whose expected action is very difficult or impossible to evaluate. This is especially true when some unwanted event is prevented with drug therapy. Immunosuppressants are typically this kind of drugs; after an organ transplantation, there is no possibility to titrate the dose. If the dose is lower than needed, the graft is rejected, and if it is higher than needed, the dose is generally not tolerated. Antiepileptic agents, and especially traditional ones, are not easily tolerated and dose titration takes an extremely long time. An alternative approach is therefore needed to determine the appropriate dose for the given patient. 12.2.2. Theory of TDM In all of these latter cases, a pharmacokinetic approach is utilized and the relationship between the dose and the action is split into two relationships: the dose vs. concentration and the 134 concentration vs. effect relationship. The given dose is distributed in a volume of distribution, resulting in a concentration, and at the site of action this concentration is directly responsible for the elicited action. The first relationship is highly variable; the same dose may elicit substantially different plasma concentrations as a consequence of many individual and unpredictable factors determining the kinetic behaviour of the given drug (e.g. enzyme induction by smoking or absorption modified by the diet). This second relationship is more reliable; the same concentration elicits more or less the same action. In these difficult cases, therefore, the optimum concentrations suitable for eliciting the required action should be determined first. When the target plasma concentration (usually defined as a range) is available, it can be used as input information for dose optimization (Fig. 12.5). TDM is defined as the regular determination of the plasma concentration of the given drug so as to utilize the obtained data for continuous correction of the dose in order to maximize the therapeutic efficacy and minimize the adverse effects. It is noteworthy that TDM is more than simply an analysis of a drug concentration. Instead, it includes the interpretation of the results on the basis of pharmacokinetic principles and the suggestion relating to the correction of the dose. Besides the indication for TDM listed above, there are additional cases when the occasional determination of serum concentrations may improve the outcome of therapy. For example, when the patient fails to respond to the usual doses, the concentration could be useful to distinguish between a non-compliant and a non-responder patient. A poor metabolizer and an ultra-rapid metabolizer phenotype can be evidenced by measurement of the substrate of the given enzyme in the plasma. The plasma level of a seriously overdosaged agent can be used to predict the degree of target organ damage (e.g. the higher the paracetamol level, the higher the risk of hepatic injury). 135 Fig. 12.5. Possibilities of dose optimization by titration and TDM. 12.2.3. Practice of TDM In current practice, the following agents are utilized with TDM (Table 12.1): Table 12.1. Drugs utilized with TDM Drug class Typical representatives Digitalis glycosides digoxin and digitoxin Antibiotics animoglycosides: gentamycin, amikacin, tobramycin vancomycin Antiepileptics phenobarbital, phenytoin, carbamazepine, valproic acid Antiarrythmic agents amiodarone, disopyramide, quinidine, flecainide, procainamide Immunosuppressants cyclosporine A Antiproliferative agents methotrexate Antiasthmatic agents theophylline As concerns the sampling time, in most cases the determination is performed when the steady-state concentrations has been achieved which requires 5 half-lives. If a loading dose was administered, the targeted steady state can be reached earlier and an earlier determination can be the rationale. Loading doses are usually given when the elimination of the drug is slow and a long time is therefore needed to reach the plateau phase (e.g. digoxin or digitoxin). Two samples are 136 usually collected; a maximum or peak concentration sample and a minimum or trough concentration sample. It is obvious that the trough concentration is determined from the sample obtained just before the next dose is administered. The sample for the peak concentration is collected at tmax after the last dose. tmax is available for all routinely determined agents or preparations. The exact sample timing is one of the most crucial points of TDM; errors in timing can lead to unusable or even misleading results. In the case of intravenous administration, no samples are obtained during the distribution phase. Both peak and trough concentrations are expected to be within the reference ranges published for all drugs. When any of the points are outside this range, the dose should be adequately modified in order to avoid inefficient and also toxic concentrations. Since the typical drug concentrations are very low (e.g. mg/l) and the sample volume is limited, the method of the assay should be sensitive. It should be specific too; the analyte is determined on a biological sample that may contain many similar molecules (e.g. metabolites). Furthermore, the assay should be fast and suitable for automation. These expectations are satisfied with the commercially available kits based on immunoassays (e.g. the enzyme multiplied immunoassay technique). The most widely used method is the fluorescence polarization immunoassay. Chromatographic methods (e.g. HPLC) are suitable for determining practically everything, and therefore the procedure does not depend on the available kits. HPLC methods are regarded as standards for specificity, but the determination is time-consuming and there is no possibility for automation, and HPLC methods are therefore rarely used in TDM. Used abbreviation: AUC area under the curve C concentration of the drug ClT total body clearance Cmax maximum concentration HPLC high-performance liquid chromatography ke elimination rate constant KM Michaelis–Menten constant NAD+ oxidized form of nicotinamide adenine dinucleotide R rate of administration t½ elimination half-life 137 TDM therapeutic drug monitoring V rate of metabolism VD volume of distribution Vmax maximum rate of metabolism Questions 1. Which parameters should be determined for a drug with non-linear kinetics? A. Vmax and KM B. Vmax and t½ C. t½ and ka D. KM and t½ 2. Which of the following drugs are used with therapeutic drug monitoring? A. penicillins B. antihypertensives C. aminoglycosides D. anticoagulants 138 13. Adverse drug reactions 13.1. Classification of adverse drug reactions The expression of adverse drug reaction (ADR) is a broad term referring to unwanted, inconvenient or dangerous effects of a drug which is administered in a standard dose by the proper route for the purpose of prophylaxis, diagnosis or treatment. ADRs can be considered a form of toxicity, because the toxic effect is always dose- related. All drugs have the potential for ADRs; risk-benefit analysis is necessary whenever a drug is prescribed. ADRs may be dose-related or not. Dose-related ADRs are usually predictable, whereas those which are unrelated to dose are usually unpredictable. An ADR may occur following a single dose, following prolonged administration of a drug, or result from the combination of two or more drugs. ADRs may be classified by causes and severity. ADR are classified into the following seven types by causes: dose-related (augmented, A), non-dose-related (bizarre, B), dose-related and time-related (chronic, C), time-related (delayed, D), withdrawal (end of use, E), failure of therapy (failure, F) and genotoxicity (G) (Table 13.1). Table 13.1. classification of adverse drug reactions. Types of reaction Features Examples Dose-related - common (85-90% of ADR) Side-effects: (augmented, A) - related to a pharmacological - hypoglycaemia (antidiabetics) action of the drug - hypokalaemia (diuretics) - predictable - dry mouth (anticholinergics) - low mortality - bradycardia with -adrenoceptor - reproducible with an animal blockers model - reversible Toxic effects: - digoxin toxicity - serotonin syndrome with selective serotonin inhibitors - nephrotoxicity with aminoglycoside antibiotics Non-dose-related - uncommon (10-15% of ADR) Immunological reactions: (bizarre, B) - not related to a pharmacological - anaphylaxis from -lactam antibiotic action of the drug - haemolytic anaemia from pencillin - unpredictable - anaphylaxis from codeine - high mortality - rash from enalapril Non-immunological reactions: 139 Pseudoallergic reactions: - radio contrast dye, ACE inhibitors, opiates, vancomycin, ciprofloxacin reaction Idiosyncratic reactions: -acute porphyria (benzodiazepines) - rhabdomyolysis (clozapine) Intolerance reactions: - urticaria after NSAIDs - codeine-caused hyperemesis - hypotension from enalapril Dose-related and time- - uncommon - extravasation reactions related - related to the cumulative dose - osteonecrosis of the jaw with (chronic, C) bisphosphonates - hypothalamic-pituitary-adrenal axis suppression by corticosteroids Time-related - uncommon - secondary cancers in patients treated (delayed, D) - usually dose-related with alkylating agents (cyclophosphamide) - teratogenesis (diethylstilboestrol: vaginal adenocarcinoma) - tardive dyskinesia caused by antipsychotic medication Withdrawal - uncommon - withdrawal seizures on terminating (end of use, E) - associated with the withdrawal of anticonvulsant therapy a medicine - adrenocortical insufficiency subsequent to glucocorticoids termination - opiate withdrawal syndrome - withdrawal insomnia and anxiety on terminating benzodiazepine therapy Unexpected Failure of - common - inadequate dosage of an oral therapy - dose-related contraceptive, when used with specific (failure, F) - often caused by drug interactions enzyme inducers Genotoxicity, G - cause of irreversible genetic - teratogenic agents, e.g. thalidomide, damage causing genetic damage in the foetus Type A reactions represent an augmentation of the pharmacological actions of a drug. They are dose-dependent, and therefore readily reversible when the dose is reduced or the drug is withdrawn. In contrast, type B adverse reactions are bizarre and cannot be predicted from the known pharmacology of the drug. Type B contains two different types of reactions: immunologic and non- immunologic. Immune-mediated reactions account for 5 to 10 % of all drug reactions and constitute true drug hypersensitivity, with IgE-mediated drug allergies falling into 140 this category. The Gell and Coombs classification system describes the predominant immune mechanisms that lead to clinical symptoms of immune-mediated reactions of drugs (Table 13.2). Table 13.2. Classification of drug hypersensitivity reactions Type Mechanism Example Timing of reactions Type I IgE-mediated Anaphylaxis from Minutes to hours (histamine and -lactam antibiotic after drug exposure inflammatory mediators released from mast cells) Type II Cytotoxic Haemolytic anaemia Variable (IgG and IgM from penicillin antibodies directed at drug- hapten-coated cells) Type III Immune complex Serum sickness from 1 to 3 weeks after (tissue deposition anti-thymocyte drug exposure of drug-antibody globulin complex with complement activation) Type IV Delayed, cell- Contact dermatitis 2 to 7 days after mediated (MHC from topical cutaneous drug presentation of antihistamine exposure drug molecules to T cells with cytokine and inflammatory mediator release) Non-immune and unpredictable drug reactions can be classified as idiosyncratic, pseudoallergic and intolerance reactions. Idiosyncrasy is a term used to refer to an individual’s susceptibility to a drug ADR based on genetic variation. An idiosyncratic drug reaction denotes a non- immunological hypersensitivity to drugs, without connection to pharmacological toxicity. In these cases, genetic testing prior to drug administration will reduce the risk of ADRs. A classical example of an idiosyncratic reaction is drug-induced haemolysis in persons with a glucose-6-phosphate dehydrogenase (G6PD) deficiency. Some 141 patients who respond idiosyncratically do so after the first or second administration of the drug, whereas others require weeks or months of therapy. Other examples are antipsychotic drugs such as chlorpromazine and clozapine, which cause infrequent reactions such as rhabdomyolysis and liver toxicity. Troglitazone also causes life- threatening idiosyncratic reactions (fatal liver failure) in diabetic patients. Pseudoallergic reactions are a result of direct mast cell activation and degranulation by drugs such as angiotensin convering enzyme (ACE) inhibitors, opiates, vancomycin (antibiotic), ciprofloxacin (antibiotic) and radiocontrast media. These reactions may be clinically indistinguishable from type I hypersensitivity because they do not involve drug-specific IgE. Pseudoallergic reaction can refer to ADRs that produce clinical symptoms that mimic allergy, but are not mediated by immunological mechanisms. Inhibition of ACE can lead to an excess of tissue bradykinin triggering angioedema, which is often thought of as an allergic disorder, but in this case is related to the pharmacological effect of the drug. It has been established that pseudoallergic reactions caused by opioid drugs result from the activation of opioid receptors, which present on mast cells to influence histamine liberation. The flushing during a vancomycin infusion and ciprofloxacin is due to the direct stimulation of mast cells and basophiles causing the release of mediators. Radiocontrast media cause an anaphylactic reaction and shock via an unknown mechanism. Intolerance (sensitivity) is a poorly defined term that may refer to an unusually low threshold to the pharmacological side-effect of a drug (e.g. hyperemesis with codeine may be referred to as opiate intolerance) or to an adverse reaction that might be atypical or not understood according to the pharmacology of the drug. NSAIDs can produce intolerance because they cause urticaria, angioedema or asthma. The basis of this reaction is pharmacological, because NSAIDs inhibit the enzyme COX-1, whith a resulting, parallel increase in leukotriene production to intolerance symptoms. The other classification of adverse drug reactions is according to the severity, which may be mild, moderate, severe or lethal. In the event of a mild reaction, no antidote or treatment is required during the ADR, and hospitalization is generally not needed or not prolonged, e.g. sleepiness from antihistamines or constipation from opioids. In moderate ADRs, a change in treatment (e.g. a modified dosage) is considered essential, but discontinuation of the drug is not necessarily required. The hospitalization may be prolonged or specific treatment may be needed. Classical examples of moderate reactions are the venous thrombosis induced by hormonal 142 contraceptives and the hypertension and oedema caused by NSAIDs. Severe ADRs are potentially life-threatening and require cessation of the drug therapy and specific treatment of the ADR, e.g. angioedema caused by ACE inhibitors. Lethal ADRs directly or indirectly contribute to a patient’s death, e.g. an acetaminophen overdosage (liver failure) or haemorrhage in anticoagulant therapy. For dose-related ADRs, modification of the dose or the elimination or reduction of precipitating factors may suffice. Increase of the rate of drug elimination is rarely necessary. For allergic and idiosyncratic ADRs, the drug should usually be discontinued and not tried again. Alternative medications with unrelated chemical structures should be substituted when available, and symptomatic treatment must be administered. Individual variability in drug efficacy and drug safety is a major challenge in current practice and drug development. The increase in the knowledge of pharmacogenetics and human genomics in recent years has dramatically accelerated the discovery of new genetic variations that potentially explain the variability in drug response and has given birth to pharmacogenomics (Fig. 13.1). Pharmacogenetics in drug regulation Genetic polymorphism Pharmacokinetics Pharmacodynamics e.g. – Drug-metabolizing e.g.- Receptors enzymes - Ion channels - Transporter proteins - Immune system - Plasma protein binding - Other enzymes Idiosyncratic response Variability in efficacy or toxicity Fig. 13.1. Role of pharmacogenetics in variabilities of efficacy or toxicity 143 Pharmacogenetics has been defined as the study of the variability in drug response due to heredity. National Center for Biotechnology Information (NCBI) has defined pharmacogenetics as and pharmacogenomics the study of inherited differences (variation) in drug metabolism and response, as the general study of all of the many different genes that determine drug behaviour. Pharmacogenetics determines the effects of genes on the processes of drugs (pharmacokinetics), and the interactions of drugs with receptors, the treatment efficacy and adverse side-effects (pharmacodynamics). The basis of genetic polymorphisms is most often the single nucleotide polymorphisms (SNPs). Each SNP involves a difference in a single nucleotide. For example, an SNP may replace the nucleotide adenine with the nucleotide guanine in a certain stretch of DNA. If more than 1% of a population does not carry the same nucleotide at a specific position in the DNA sequence, this variation can be classified as a SNP. SNPs do not usually cause disorders, but some SNPs are associated with diseases. 13.2. Pharmacodynamic variation of genetic polymorphism Variations in receptor proteins can influence the structure of a receptor and the outcome of the pharmacological reaction. These changes in receptor proteins can give rise to different diseases and ADRs. The 2-adrenergic receptor (2-AR) mediates the relaxation of the smooth muscles in the small airways. The 2-AR agonist is widely used in the therapy of asthma and chronic obstructive pulmonary disease. The 2-AR is highly polymorphic; the changes of arginine to glycine at position 16 and of glutamine to glutamate at position 27 are common SNPs in the Caucasian population. Individuals with the G16 (glycine 16) variant downregulate the 2-ARs, after agonists. Long-acting 2-agonist therapy is not recommended in patients with this variant. Glu 27 results in less downregulation of the 2-ARs in response to agonists. Another example of pharmacodynamic variation is the pharmacogenetics of antidiabetics. The thiazolidinedione drugs (rosiglitasone and pioglitasione) potentiate the binding of the transcription factor peroxisome proliferator-activated receptor- (PPAR-) to its DNA response element. They induce adipocyte differentiation, increase insulin-stimulated lipolysis and insulin suppression of hepatic glucose output, and 144 promote insulin-stimulated glucose uptake into the muscle. The genetic variation Pro12Ala in the PPAR gene influences the pharmacological effect of antidiabetics. The Ala allele has a greater response to rosiglitasone than that of the Pro counterpart. The dopamine D3 receptor gene (DRD3) is important in antipsychotic therapy. The Ser9Gly polymorphism of DRD3 influences the pharmacological response of antipsychotic drugs such as clozapine, which is a high-affinity antagonist of dopamine receptors and widely used in the treatment of schizophrenia. The Ser/Ser genotype has been found to be more frequent among non-responders to clozapine. In the Gly variant, there are changes in the tertiary structure of the receptors, the affinity of dopamine for the receptors is higher and the receptor behaves as a “supersensitive dopamine receptor”. 13.3 Pharmacokinetic variation of genetic polymorphism Cytochrome P450 (CYP) is considered to be the most important enzyme involved in drug metabolism, because many drugs are substrates for this enzyme. A number of reports have demonstrated the association between the therapeutic response and the genetic polymorphisms of the CYP superfamily. Depending on the phenotypes of CYP, extensive metabolizers (EMs), with regular metabolic capacity, and poor metabolizers (PMs), with low metabolic capacity, intermediate metabolizers (IMs), with a metabolic capacity between those of the PMs and EMs and ultra-rapid metabolizers (UMs), with higher metabolic capacity than that of EMs, are distinguished. Pharmacologically, CYP2D6, CYP2C9, CYP2C19 and CYP3A4 are the most studied enzymes. Table 13.3 gives some examples of the substrates of these CYP enzymes. 145 Table 13.3. Examples of polymorphism of CYP enzymes. Enzymes Substrates anticoagulants warfarin CYP 2C9 sulfonylureas glibenclamide, glipizide NSAIDs ibuprofen, diclofenac antidepressants fluoxetine, imipramin antihypertensives irbesartan,losartan others phenytoin, tamoxifen benzodiazepines diazepam CYP 2C19 antidepressants amitriptyline, imipramine proton pump imhibitors omeprazole, pantoprazole others progesterone, nelfinavir antiarrhythmics amiodarone, encainide CYP 2D6 opiates codeine, dextromethorphan antihypertensives propanolol, carvedinol antidepressants fluoxetine, citalopram antipsychotics clozapine, haloperidol others ondansetron, metoclopamide immune modulators tacrolimus, cyclosporine CYP 3A4 benzodiazepines diazepam, alprazolam Ca channel blockers diltiazem, verapamil macrolide antibiotics erythromycin antihistamines terfenadine sexual steroids, corticosteroids oestradiol, testosterone, hydrocortisone others cocaine, sildenafil More than 80 CYP2D6 variants have been identified whose functions are associated with four general phenotypes: PM, EM, IM and UM. Opioids, including codeine, are among the pain medications metabolized by CYP2D6. About 5% of codeine is metabolized by CYP2D6 (O-methylation) to morphine, which has an analgesic effect. In PM patients, codeine is ineffective in pain therapy because of the low concentration of morphine, in contrast with the UM phenotype, where it causes toxic reactions. CYP2C9 is involved in the metabolism of an anticoagulant, S-warfarin. The polymorphism for CYP2C9 (Ile359Leu) decreases the enzyme activity and oral clearance for warfarin, and therefore increases the bleeding side-effects. CYP2C19 is involved in the metabolism of omeprazole. The clearance of omeprazole is significantly increased in extensive metabolizers, resulting in lower plasma concentrations of omeprazole and decreased antisecretory action. CYP3A4 plays a role in the metabolism of sexual steroids, and the individual variation in CYP3A4 activity may play a role in 146 breast and prostate carcinogenesis and lipid levels. Grapefruit juice is a potent inhibitor of the CYP3A4-mediated drug metabolism. Phase 2 enzyme pharmacokinetic variations can also impact on drug responses, e.g. thiopurine S-methyltransferase is involved in the metabolism of an anti-leukaemia drug 6-mercaptopurin. Patients with low or medium enzyme activities require smaller doses, because the therapy with standard doses may result in life-threatening side- effects (myelosuppression and pancytopenia). Genetic variations of transport proteins can cause pharmacokinetic changes in drug responses. There are two types of transport superfamilies in the human body, ABC proteins generally acting as efflux pumps and solute-linked carrier (SLC) proteins as influx transporters responsible for the transport of drugs and other substrates. The serotonin transporter SLC6A4 regulates the synaptic concentrations of serotonin and thereby strongly influences perception, mood, emotion, behaviour and cognition. The polymorphism of SLC6A4 is associated with drug dependence, schizophrenia, autism and antidepressant drug response. SLC6A4 polymorphism influences (increases) the therapeutic response to selective serotonin reuptake inhibitors. SLC6A4 polymorphism may also play a role in the disturbances in the gut function in irritable bowel syndrome. Higher levels of serotonin are associated with diarrhoea and abdominal pain in irritable bowel syndrome. Digoxin is a substrate for the ABCB1 (MDR1) gene. It has been suggested that ABCB1 polymorphism and the co-administration of an ABCB1 inhibitor (verapamil) may influence the bioavailability of digoxin. Used abbreviations: ACE angiotensin converting enzyme ADR adverse drug reaction ABC ATP-binding cassette COX-1 cyclooxygenase-1 CYP cytochrome P450 DRD3 dopamine D3 receptor gene EM extensive metabolizer G6PD glucose-6-phosphate dehydrogenase IM intermediate metabolizer NSAID non-steroidal anti-inflammatory drug PPAR-γ peroxisome proliferator-activated receptor-γ 147 PGt pharmacogenetics PGx pharmacogenomics PM poor metabolizer SLC solute-linked carrier SNP single nucleotide polymorphism UM ultra-rapid metabolizer Questions: 1. Which of following answers are true for A type adverse drug reactions? A. They are usually not dose-related. B. They are associated with the withdrawal of a medicine. C. They are not related to a pharmacological action of the drug. D. They are most common type of adverse drug reaction. 2. Which type of CYP phenotype causes a toxic reaction during the use of codeine? A. extensive metabolizers B. poor metabolizers C. intermediate metabolizers D. ultra-rapid metabolizers 148 14. Practical considerations Pharmacokinetics is a complex science; the optimum implementation of pharmacokinetic studies requires a knowledge of other sciences, e. g. – physiology (understanding the functioning of the living body) – biochemistry (the molecular mechanisms of kinetic processes) – physical chemistry (features of drugs, and formulae of kinetics) – mathematics (understanding and solving equations) – analytics (to measure drug concentrations) – statistics (to determine the statistical reliability of model parameters) Pharmacokinetics is particularly useful in the early phases of drug development. Clinical pharmacokinetic studies are performed to examine the absorption, distribution, metabolism and excretion of a potential drug under investigation in healthy volunteers and/or patients. the outcomes of clinical pharmacokinetic studies are useful for determining the appropriate use of medicines. Experimental design is fundamental for successful scientific investigations. Poorly designed experiments lead to the loss of information, which is costly and potentially unethical. When a pharmacokinetic study is being designed, practical design limitations, such as the doses to be employed, the sampling times, the number of samples per subject, and the numbers and type of subjects should be considered. Collecting preliminary information from pilot studies helps to decrease the failures in study design and also leads to a reduction in costs. The steps in the development of pharmacokinetic models are as follows: 1. design an experiment, 2. collect the data, 3. develop a model on the basis of the observed characteristics of the data, 4. express the model mathematically, 5. analyse the data in terms of the model, 6. evaluate the fit of the data to the model, 7. if necessary, revise the model in step 3 and repeat it until the model provides a satisfactory description of the data. Some important characteristics of model development will now be discussed in detail. 149 14.1. Important considerations of pharmacokinetic study design 14.1.1. Subjects Sample size calculation is an important part of the design of applied scientific research such as clinical trials. The optimum number and type of subjects depend on the method applied and on the phase of drug development. Sample size calculation should be based on the procedure for analysis when a population pharmacokinetics study is considered. In the early stage, the subjects are healthy volunteers, except when the drug has a high risk in which case the studies should be conducted in patients with the target disease. In the population pharmacokinetics context, a single blood sample is obtained from each patient shortly before the next dose administered (the trough in the drug concentration), when a single-trough sampling design is implemented. Studies in the late stages of drug development with patients who have the target disease are performed to determine pharmacokinetic profiles. It is advisable to investigate relationships between dosage and drug concentrations in the blood, and between drug concentrations in the blood and therapeutic effects. In the multiple-trough sampling design, two or more blood samples are obtained near the trough of the steady-state concentrations from most or all of the patients. In an experimental population pharmacokinetic design, blood samples should be drawn from subjects at various times. 14.1.2. Types of study There are two methods with which to carry out pharmacokinetic studies: conventional pharmacokinetic studies and population pharmacokinetic studies. In a conventional pharmacokinetic study, the subjects are treated with a single dose or a repeated dose of the drug, and blood and/or urine samples are collected in compliance with a fixed schedule. The drug and/or metabolite concentrations are then measured and the pharmacokinetic profile of the drug is evaluated. In a single-dose study, usually a small number of healthy subjects are included, and the dosage is started with the lowest dose, which is increased in a stepwise fashion. In order to evaluate the relationships between the dosage and the pharmacokinetic parameters, several doses should be used, including the estimated clinical dose and a dose higher than the estimated highest clinical dose. In a repeated-dose study, the appropriate number of subjects should be determined on the basis of the results of single-dose studies. Sampling should be performed at a few points corresponding to trough 150 concentrations or peak concentrations, and a sufficient number of sampling time points should be used to evaluate the elimination rate, and linearity. In a population pharmacokinetic approach, usually a large number of subjects participate in the study, while the number of samples collected from each subject can be small. The sample size depends on the chosen parameter, the sampling design and the method for the analysis of the collected data, among other things. This approach is considered suitable for special populations, such as the elderly and children. 14.1.3. Dosage form, route of administration Special attention should be paid to the route and method of administration of the medicinal product, as this may affect the absorption and disposition of the active ingredient. After the dose of the drug and the route of administration have been chosen a pre-analysis of the dosage form is required. The ampoules and the vials are usually overfilled and the volume to be administered must be carefully checked; it is advisable to make use of aliquots to administer the correct dose. It is possible that the dose of the active substance in the solid dosage form is significantly different from that indicated by the manufacturer. Pre-analysis of replicate doses helps to decrease the uncertainty. 14.1.4. Accuracy in administration of the dose For a new active ingredient in animal models, kinetic studies with at least three different doses should be performed, the central dose being the expected recommended dose. For established active ingredients where dose linearity exists in the target, single-dose studies, corresponding to the highest intended therapeutic dose, are generally sufficient. When a drug with a dosing interval longer than the elimination half-life is repeatedly administered, the drug accumulates within the body. In the case of repeated dose administration, therefore the dose interval () must be less than the elimination half-lifetime (t1/2) while in the case of single- dose administration, a wash-out period longer than 5 t1/2 should be kept. Eventually, the blood concentration reaches a plateau after repetitive administration, when the blood concentration has reached a steady state. The timing depends on the chosen pharmacokinetic approach and the dosage regimen. When an intravascular single-dose administration is intended, the first blood sample should be taken as soon as possible to detect the high concentration part of the curve. A population 151 pharmacokinetic study requires only one or two samples per subject, bearing in mind that the second sample must be taken before complete elimination of the drug. Repeat-dose studies evaluate the safety and tolerability of single and repeat dosing. This gives an insight as to how the pharmacokinetics differs for a repeat dose in comparison with a single dose. In repeat-dose administration, patient compliance (and the appropriate dosage) is very important from the aspect of the development the steady state, so that the elimination phase of the curve can be determined precisely. It has been shown that the materials (the syringe, infusion kit, plastic tubes, etc.) may all cause some loss of the administered drug. 14.1.5. Blood samples The sites of action of the tested drug are not easily accessible, and hence the drug concentration is commonly estimated in bio-matrices (blood, urine, saliva, tears and other body fluids), assuming kinetic homogeneity. There is no doubt that the blood is the most frequently tested body fluid. In cases of sampling from humans, there are three possibilities to collect blood samples: – capillary sampling, – venipuncture, and – arterial blood sampling. Capillary sampling The capillary blood sample sites are the fingers (preferred for adults), the heels and the ear lobes. A finger prick gives of arteriolar, venous and capillary blood. In infants, blood sampling is done by heel prick (age below 6 months) or finger prick (age above 6 months). Venipuncture The median cubital vein is the most commonly used sampling site in adults. In term neonates, venipuncture is preferred because it causes less pain than a heel prick. In the case of difficulties, the area of the puncture is warmed to increase the blood flow. Arterial blood sampling 152 The radial artery is the first choice for arterial sampling, because this involves fewer disadvantages relative to other arteries. There may be differences between the arterial and venous blood concentrations of some drugs which should be taken into consideration. Capillary sampling is the most preferred route of blood sampling in humans for the estimation of drug concentrations. There is a significant correlation between the results of measurements on finger prick and venous samples, but a few drugs have different concentrations in the venous and the capillary blood, leading to differences in the calculated pharmacokinetic parameters. During population pharmacokinetic studies, the finger prick method of blood sampling is preferred for serial sampling from patients, especially in geriatric and paediatric populations, despite the fact that there is some uncertainty in the precise determination of pharmacokinetic parameters. It should also be considered whether anticoagulants can be used during blood sampling, because these can increase the error of the measurement. For example, heparin can increase the free fatty acid concentration in the blood, causing altered plasma protein binding. 14.1.6. Sample handling and timing The stability of the drug in the samples is a key question. There are drugs which are more stable when refrigerated than in frozen samples, while other drugs are able to continue the biotransformation in the samples after sampling. An other important issue is the labelling of samples. The precise documentation of the sampling, the storage conditions and other parameters are crucial. The design of optimum timing is not easy, but there are practical methods for planning optimum sampling strategy, and pilot studies help to increase the quality of the timing procedure. The precise calculation of elimination rate constants requires the correct timing of terminal disposition phase. Incomplete measurement of the elimination phase is a common and serious problem that originates from the inadequate timing of sample collection. When model-independent pharmacokinetics applied, determination of AUC and AUMC (see in Chapter 8) is crucial and depends on a well-calculated elimination rate constant. The systemic clearance (Cls) and the steady-state volume of distribution (Vss) are widely used pharmacokinetic parameters and their determination depends on the AUC value. If there are only a limited number of blood samples, the drug concentration can be measured in the urine 153 or the saliva in order to complete the determination of the slope of the terminal disposition phase. 14.1.7. Curve fitting and statistical considerations Measured data should be analysed from both a pharmacokinetic and a statistical point of view. The observed plasma drug concentrations are sometimes different from those anticipated. The most common reasons for such differences are listed below. An unexpectedly low concentration measured: – an error in the dosage regimen – poor patient compliance – an incorrect dosage form – fast metabolizers – poor bioavailability – incorrect timing of blood sampling – autoinduction of metabolic enzymes An unexpectedly high concentration measured: – poor patient compliance – en error in the dosage regimen – an incorrect dosage form – poor metabolizers – high bioavailability – increased plasma protein binding – inhibition of metabolic enzymes The correct drug concentration is measured, but without a therapeutic response: – a drug interaction at the receptor site – altered receptor sensitivity (tolerance, desensitization or downregulation) – a change in hepatic blood flow The non-compartmental and compartmental evaluation of a pharmacokinetic analysis requires suitable curve fitting of the observed data. The accuracy of curve fitting depends on a number of parameters: – the number and the timing of the experimental data – the integrity of data collection 154 – the linearity of the function – the initial estimates – the data transformation – the applied algorithms – etc. There are several computer packages (PK Solutions, MathWorks, GraphPad Prism, Pmetrics, Pharsight Phoenix, PCNONLINE, SAS, RSTRIP, etc.) that are suitable for the fitting of pharmacokinetic data with different built in models and complexity. It is very important to choose the appropriate model (compartmental, model-independent, linear, non- linear, etc.), to determine the initial estimates (which depend on the chosen model) properly, and to use weighting functions. The design, analysis and interpretation of pharmacokinetic data require many logical uses of statistics. In a study with a sufficient number of data, mean values, variance (between- and within-subjects) and confidence intervals of drug concentrations and pharmacokinetic parameters should be estimated by using appropriate statistical methods that are determined in advance during consideration of the study design. Major variables, such as drug concentrations and pharmacokinetic parameters, should be analysed on the basis of the statistical properties of their distribution, and data transformation such as logarithmic transformation should be performed whenever necessary. The pharmacokinetic models on which the data analyses are based, the methods used for estimation of the pharmacokinetic parameters, the software used for analysis (package), and the handling of outliers and data points lower than the limit of quantization must be clearly stated. 14.2. Pharmacokinetics and clinical situations The most important consequence of pharmacokinetic studies is the clinical application of the determined parameters to design an appropriate dosage regimen for the patients. The goal of the therapy is to achieve an adequate concentration of the active substance at the receptorial milieu in order to trigger the optimum therapeutic response with minimum adverse effects. The choice of the appropriate drug and drug product and the success of the therapy are based on the pharmacokinetic behaviour of the drug and the characteristics of the patient. In modern therapy, individualization of the treatment is an important expectation. A knowledge of the patient’s features (differences in metabolic enzymes, blood circulation, hepatic or renal 155 function, diseases, etc.) and the exact pharmacokinetic parameters of the administered drug is therefore invaluable. Drugs with a high therapeutic index (acetylsalicylic acid, ibuprofen, omeprazol, fexofenadine, etc.) do not require strict individualization. However, for drugs with a narrow safety window (digoxin, amiodarone, warfarin, theophylline, etc.), the individualization of the dosage regimen is important with a view to the avoidance of the intersubject variation of pharmacokinetic processes. This is feasible if the plasma drug concentration is proportional to the main effect or to an adverse effect (anticancer drugs). The reasons why patients differ in their responsiveness to a given dose of a drug vary considerably; they include genetics, pathophysiology, age, body weight, drugs given concomitantly, and other behavioural and environmental factors. The body weight, age, pathophysiology and simultaneously administered drugs are important because they are sources of variability that can be taken into account. When the suitable drug has been chosen, the therapeutic dosage regimen must be planned carefully, taking the above-mentioned factors into consideration. The optimum dosing design can reduce the intensity of side-effects, and therefore the need for drug monitoring, and the costs of the treatment. The initial dosage of the drug is usually estimated by using population pharmacokinetic parameters from the literature. The patient is then monitored (therapeutic response, and plasma drug concentration if required) and, if necessary, considering the individual pharmacokinetic parameters, the initial dosage is changed. Nevertheless, the most precise method of dosage regimen design is to calculate the appropriate dose by using the pharmacokinetic parameters determined in the treated patient. This process cannot be used to calculate the initial dosage. The method most often used to calculate a dosage regimen is based on the average pharmacokinetic parameters obtained from clinical studies published in the drug literature. There are two methods in this approach: a fixed model and an adaptive model. The fixed model assumes that the population-average pharmacokinetic parameters can be used without any modification. In the case of a multiple dosage regimen design, equations based on the principle of superposition are applied to calculate the dose. (The superposition principle states that, under linear conditions, the total concentration of drug in the body is the sum of the concentrations of each administered dose remaining at that point in time when the measurement is made.) The adaptive model takes into consideration any changes in the pathophysiology of the patient and attempts to adapt or modify the dosage regimen according to the needs of the patient. Just as the optimum dosage regimen is very important, so is the dosage form. The desired duration and onset of the therapeutic effect and the route of administration can 156 determine the dosage form, which influences the pharmacokinetic processes and the bioavailability. The patient’s lifestyle (smoking, alcohol consumption, exercise, etc.) and compliance can also modify the pharmacokinetics of a drug. The frequency of dosing influences the size of the drug dose. A higher frequency of dosing, results in the need for a lower drug dose to achieve the same average plasma drug concentration. A long dosing interval (low frequency, high dose) causes intensive fluctuations in drug concentration (cmin and cmax), and can result in a peak plasma concentration close to the toxic level. For intravascular repeated dosage administration, the values of cmin and cmax may be calculated as follows: ∙ ( ⁄ ) ∙ = = 1 − 1 − 14.1 ⁄ ( ) = = 1 − 1 − 14.2 The ratio of these concentrations is therefore 1 = 14.3 and the dosage interval () may be expressed from Eq. 14.3. The maintenance dose may also be calculated from Eq. 14.2: = (1 − ) 14.4 For a given dose and dosage interval, the average concentration in the plasma can be determined: = 14.5 There are other possibilities to consider in relation to the clinical application of pharmacokinetics, but are beyond the scope of this book. Used abbreviations: cmin minimum drug concentration 157 cmax peak drug concentration dosage interval X0 maintenance dose Questions 1. Choose the correct answers. A. Population pharmacokinetics studies require a high number of blood samples per person. B. Classical pharmacokinetic analysis requires one or at most two blood samples per person. C. The timing of blood sampling is not important in pharmacokinetic analysis. D. The most frequent blood sampling method is venipuncture. E. Blood samples should be analysed immediately after blood sampling, because the investigated drug then has no chance to metabolize. 2. Which of these can lead to a plasma concentration higher than expected? A. fast metabolizers B. the autoinduction of metabolic enzymes C. poor metabolizers D. a lower administered dose than the calculated one E. the perfect compliance of the patient 158 15. Suggested readings Costantine MM: Physiologic and pharmacokinetic changes in pregnancy. Front Pharmacol 5:65 (2014) Edwards IR, Aronson JK: Adverse drug reactions: definitions, diagnosis, and management. Lancet 356:1255-9 (2000) Goldstein DB, Tate SK, Sisodiya SM. Pharmacogenetics goes genomic. Nat Rev Genet 4:937-47 (2003) Jambhekar SS, Breen PJ: Basic Pharmacokinetics. Pharmaceutical Press (2012) Lu H, Rosenbaum S: Developmental pharmacokinetics in pediatric populations J Pediatr Pharmacol Ther 19:262-76 (2014) Smith W: Adverse drug reactions. Allergy? Side-effect? Intolerance? Aust Fam Physician 42:12-6 (2013) Verbeeck RK: Pharmacokinetics and dosage adjustment in patients with hepatic dysfunction. Eur J Clin Pharmacol. 64:1147-61 (2008) Waldman SA, Terzic A: Pharmacology and Therapeutics: Principle to Practice. Saunders-Elsevier (2009) Whitley H, Lindsey W: Sex-based differences in drug activity. Am Fam Physician 80:1254-8 (2009) 159