Dose–Response Relationship

Pharmacodynamic responses occur at many levels, ranging from single molecules to whole animals. Drugs induce their responses through a number of mechanisms, most of which involve direct or indirect interactions with cell macromolecules and generally proteins. Direct interactions with nonprotein molecules are less common, but examples include nucleic acids (e.g., cancer chemotherapeutic agents), metal chelating drugs, or antacids used to chemically neutralize gastric acid. Drug responses more commonly reflect the interaction of the drug, acting as a ligand, with receptors (Figure 1-2). A receptor most commonly is a large protein macromolecule (e.g., structural, enzymatic, carrier, or ion channel proteins) responsible for cellular signaling. Receptors may be located on or in the cell membrane, in the cytosol, or within an intracellular structure (i.e., nucleus). Physiologic functions of the body generally are regulated by multiple receptor-mediated mechanisms, each responding to different molecular stimuli. Examples of target receptor categories include hormones, neuromodulatory receptors, and neurotransmitters.

Interaction between a drug and its receptor generally results in activation (either directly or indirectly) of cellular biochemical processes (e.g., ion conductance, protein phosphorylation, or DNA transcription) by way of a transduction pathway that ultimately brings about the pharmacologic effect.¹ A time lag may be associated with transduction (Figure 1-2). Activation reflects the drug’s mechanism of action, whereas the sequelae of the stimulation at the molecular, cellular, or tissue level reflect the drug’s pharmacodynamic effects. Secondary intracellular messenger molecules are often activated by drug–receptor interaction; they subsequently set in motion a cascade of events that eventually causes the response. Among the most common receptors are transmembrane receptors linked to guanosine triphosphate–binding proteins (G proteins). These then activate second messenger systems such as adenylyl cyclase (e.g., beta-adrenoceptors), the cytosolic inositol triphosphate pathway (e.g., alpha-adrenoceptors), or membrane-bound diacylglycerol (DAG).

Figure 1-2 Examples of drug–receptor interactions at the cell membrane, cytosol or organelle site, and the secondary amplification cascades that ultimately result in the pharmacodynamic response.

Two properties describe drug-receptor interactions: affinity, or the capacity of a drug to bind to a receptor, and intrinsic efficacy (or activity), or the capacity of a drug to activate or inactivate a receptor. The latter is a complex relationship dependent on drug concentration, receptor activation, and cellular response. Affinity is usually mathematically defined as the reciprocal of the dissociation constant of the drug for the receptor.¹ A receptor often is characterized by multiple types (e.g., alpha- and beta-adrenergics; mu, kappa, and delta opioid receptors) and subtypes (e.g., alpha 1 and 2, beta 1, 2, or 3; mu 1 or 2). The selectivity of a drug action generally reflects the specificity of the drug for the target receptor binding. Drugs often target multiple receptors, although interactions may be concentration dependent or may result in blocking rather than activating specific receptors. Receptor characteristics (e.g., numbers and affinities) are influenced by both external and intracellular conditions. Tissues vary in receptor numbers and subtypes; indeed, proper physiologic responses are dependent on this variability. The relationship between a drug and pharmacologic response was at one time assumed to be directly proportional to the number of receptors occupied by the drug, with a maximal response reflecting 100% occupancy and activation (i.e., the drug receptor theory). However, the interactions are much more complex than that described by a simple linear relationship. Different kinetic relationships (linear, log-linear, polynomial), multiple activation states, (active, inactive, resting), cell amplification of the drug-receptor signal, and existence of spare receptors are some examples of the complexities that determine the relationship between drug concentration and response. The scientific description, examination, and ultimate prediction of drug–receptor interactions are often accomplished by generation of dose–response curves; the graphic representation most generally is represented by a sigmoidal curve (Figure 1-3; see also Fig. 1-1). The curve indicates that increasing drug concentration at the receptor site increases the number of bound receptors and thus drug effect. If concentration–response curves are plotted on a logarithmic (x) axis, the portion of the curve that lies between 20% and 80% of the maximal response is generally linear. This is the portion most relevant to therapeutic concentrations and thus encompasses the therapeutic range. Increasing a drug dose within this range generally results in a proportional increase in response. However, once the 80% mark is passed, as receptors become saturated, a much larger increase in concentration (dose) is necessary to increase response. Although this may increase the risk of adverse effects, for drugs which are safe, it may also prolong the dosing interval since the response will not change much as concentrations decline to the 80% level. At that point, drug concentration declines exponentially (generally first order), and response will also decline log-linearly with time (e.g., 50% decline with one half-life). Note that for some drugs (i.e., drugs that irreversibly interact with receptors, drugs with active metabolites,), response may not be related to plasma (tissue) drug concentrations.

Figure 1-3 Drugs that are equally effective will cause the maximum response but may not be equally potent, i.e., they may not have the same relationship between dose (concentration) and response (A). Because drugs A and C result in the same maximum response (E_max), they are equally effective, whereas drug B is less effective (B). However, drug B is more potent than drug C, and drug A is more potent than both because the dose or concentration of A necessary to achieve a 50% maximum response (ED₅₀ or EC₅₀) is less than that for B or C. A similar set of curves can be used to describe competitive and noncompetitive inhibition. A drug that noncompetitively inhibits another drug will prevent it from reaching its maximum effect, and thus decrease the E_max (plot B, with noncompetitive drug present, plot A without it). In contrast, a drug that competitively inhibits another drug will not alter its E_max, but will increase the concentration of the drug necessary to achieve it (plot C represents a drug with a competitor present; plot A, drug without competitor).

The interaction of a drug with a receptor is similar to that between a substrate binding to the active site of an enzyme. As such, similar equations and parameters are used to describe the relationship between dose and response. The effective dose (ED) is the quantity of administered drug that will produce the (desired) effects for which it is administered. The median effective dose (ED₅₀) is the dose that produces the desired effect in 50% of a population. However, dose is a less accurate descriptor of what is happening at the receptor than is effective concentration (EC). The affinity of the drug for the receptor is described by the (effective concentration) EC₅₀, the drug concentration that yields 50% of the maximal response (see Figure 1-3, A). The different actions of a drug, such as therapeutic and adverse effects, are often due to the drug binding to different receptors with different EC₅₀ values. Ideally, the EC₅₀ for an adverse event is higher than that of a therapeutic response. The ratio of adverse event EC₅₀ to the therapeutic effect EC₅₀ is the therapeutic index and provides some indication of drug safety in that the larger the index, the safer the drug. Efficacy and potency are two terms used to describe the relationship among drug, concentration, and response. Efficacy refers to the maximum effect (E_max) a drug can have (e = 1 indicates a full response), whereas potency is a comparative term that describes the concentration of two drugs necessary to induce the same magnitude of response. Generally, plots describing efficacy and potency are based on log ₁₀ concentration versus percent response curve. (see Figure1-3, A). Drugs are considered equal in efficacy if they can cause the same magnitude of response; the more potent drug will cause an EC₅₀ at a lower concentration. As such, the dose of a less potent drug may simply need to be increased to achieve the same effect of the more potent drug.

Drug–receptor interactions do not always yield the maximal response. Receptor interaction with a drug that acts as an agonist (generally, a structural analog of the targeted receptor) results in some level of activation. The occupation theory of drug–receptor interaction indicates that the magnitude of the response produced by an agonist is directly proportional to the number of receptors occupied.¹ Pharmacodynamic antagonism occurs when one drug inhibits the agonistic effects of another through actions at the same pathway, although this does not have to occur at the receptor. Like an agonist, an antagonist interacts selectively with receptors, but it lacks intrinsic efficacy and thus is able to block or reduce the action of an agonist at the receptor. Drugs that target opioid receptors (at least three types, with mu receptors having at least two subtypes) offer an example of the different sequelae of drug–receptor interactions. The “full” agonist (e.g., fentanyl) results in the maximal effect (e.g., at mu receptors). A drug that acts as a “reversal” agent would reduce the effect of an exogenous agonist (e.g., naloxone reverses the effects of fentanyl) whereas a “blocking” drug antagonizes endogenous agonists (e.g., catecholamines targeted by beta- or alpha-blockers). Drugs might have dual agonist and antagonist properties at the same receptor (although to variable degrees in different tissues). Because the response is not maximal, they are referred to as partial (low-efficacy) agonists; buprenorphine is a partial agonist opioid at mu receptors. Drugs might also act as an agonist at some receptors and an antagonist at other receptors. Butorphanol is a mixed agonist/antagonist (at kappa and mu receptors, respectively).

The relationship between an antagonist and receptor can be described as competitive or noncompetitive. Competition between compounds occurs at the same receptors and can be reversible or irreversible. Reversible antagonists easily dissociate from the receptor, whereas irreversible antagonists form a stable chemical bond with the receptor (e.g., in alkylation). If the interaction is reversible, an agonist present at sufficiently high concentrations can displace an antagonist. As such, reversal of the agonist or the response may require a higher dose (or a repeat dose) of the antagonist (see Figure 1-3, B). In contrast, an irreversible antagonist cannot be displaced from the receptor. As such, the cellular response can not occur until the receptor is replaced (duration dependent on rate of receptor turnover) and any remaining unbound antagonist has been removed from the body. The presence of a reversible competitive inhibitor will decrease the potency of a drug because a higher concentration will be necessary to induce the same pharmacologic response.

In contrast, the presence of an irreversible competitive inhibitor will decrease the efficacy of the drug by preventing the maximal possible response. In contrast to competitive antagonists, noncompetitive antagonists interact with receptors at a site different from the agonist–receptor interaction site. The interaction often involves a site in the transduction pathway between the receptor and the pharmacodynamic response.¹ Noncompetitive interactions are generally, but not always, reversible. Note that three other types of antagonism, in addition to pharmacodynamic, can occur between drugs: chemical antagonism results from a direct chemical interaction between two drugs (i.e., a weak acid and weak base), physiologic antagonism occurs when two drugs act in the same physiologic system but act on different receptors or pathways, and pharmacokinetic antagonism occurs when one drug alters the response to another drug through changes in disposition (see Chapter 2).

Pharmacodynamic responses are also influenced by the presence of drugs beyond activation. Receptor upregulation and downregulation is an adaptive mechanism that may affect clinical response. Sequelae may include but are not limited to tachyphylaxis, a rapidly decreasing response to a drug after administration of only a few doses; tolerance, a decreasing response to repeated constant doses of a drug that will necessitate a concentration and thus dose increase, if the response is to be maintained; and withdrawal, the syndrome of often painful physical and psychological symptoms that occurs when an addictive substance is discontinued.

The pharmacodynamic response to a drug ideally will occur with any given dose within a therapeutic range. The therapeutic range provides a target for the dosing regimen. It consists of a minimum effective plasma drug concentration (PDC) (trough or C_min), below which therapeutic failure is likely to occur, and a maximum effective PDC (peak or C_max), above which a type A adverse reaction (see Chapter 4) is more likely to occur (see Figures 1-1 and 1-3).^2,3 Dosing regimens are composed of a dose (e.g., mg/kg) and an interval (e.g., every 8 hours) for each route. The dose of the regimen generally is designed to achieve and maintain PDC within the therapeutic range throughout most of the dosing interval. Thus targeted peak PDCs often approximate but do not exceed C_max, whereas trough concentrations approximate but generally do not drop below C_min. However, a therapeutic range is a population statistic that describes the concentrations between which most animals will exhibit the (desired) pharmacodynamic response; each animal will respond (therapeutically or adversely) at a different point in the range. Although most animals will respond at some point within the range (the majority in the middle of the range), a small percentage will respond above or below the range. Therapeutic drug monitoring (see Chapter 5) is used to establish where in the therapeutic range the individual animal will respond; in other words, it will establish the patient’s therapeutic range. Ideally, studies that determine the dosing regimen in a target species reflect integration of pharmacokinetic and pharmacodynamic studies in that species.⁴ Two primary components of a dosing regimen are dose interval. In general, dose, which ultimately determines PDC, is influenced primarily by the tissue that dilutes the drug (i.e., volume of distribution), whereas interval is influenced by elimination of the drug (i.e., half-life). Unfortunately, studies that describe the time course of a drug in animals are limited and, when available, generally focus on healthy rather than diseased animals. As such, clinicians are faced with individualizing dosing regimens in the patient according to the principles of clinical pharmacology—that is, the study of drugs⁵ and their behavior (disposition)⁶ in animals.

Determinants of Drug Disposition

Mechanisms of Drug Movement

Drugs move through the body by two major mechanisms: bulk flow and passive diffusion. The cardiovascular system is the primary determinant of bulk flow; glomerular filtration is one of the more important specific examples. The chemical nature of the drug does not affect bulk flow. Most drugs are characterized by a molecular weight (MW) of 350 or less, ensuring movement of unbound drug between endothelial cells despite the presence of protein filters in the endothelial gaps. Exceptions are made for those tissues whose capillaries are not fenestrated, because endothelial cell junctions are tight. Drug movement for these tissues must occur across cell membranes. Drugs can move through cells directly through the lipid layers of the cell (e.g., passive diffusion), through aqueous pores formed by aquaporins (proteins) that span the width of the membrane, by combination with transmembrane carrier proteins, and by pinocytosis. Of these, transmembrane (passive) diffusion and carrier-mediated movement are most important.

KEY POINT 1-1

Passive diffusion is the most common method by which compounds move through the body. It is most influenced by the concentration gradient of diffusible drug across the membrane to be diffused.

Passive diffusion occurs independent of any other mechanism of drug movement and requires no energy. Passive diffusion through cell membranes depends on a number of factors. The single most important factor is concentration of diffusible drug, which is most easily manipulated by increasing the dose. Additionally, host and drug factors will also influence the concentration of diffusible drug. Host determinants of passive diffusion are subject to change and include thickness of the membrane to be traversed (inversely proportional; e.g., edematous compared with normal tissues), surface area (directly proportional; e.g., small intestine versus stomach), environmental pH (see ionization), and temperature (directly proportional). In contrast, drug characteristics influencing passive diffusion are not subject to change, and thus cannot be easily manipulated. They largely influence lipid solubility of the drug.^2,3 Lipid solubility is, in turn, influenced by a number of drug characteristics, including the inherent chemical structure of a drug, such as molecular weight (smaller molecules diffuse more easily) and partition coefficient (PC). The PC is an experimental measure of relative lipid solubility as influenced by the chemical structure of the drug. The ratio is determined by mixing the drug in a combination of water and an organic solvent (e.g., octanyl). The difference in drug concentration between the two solvents once mixing is complete reflects, in part, the inherent lipid versus water solubility of the drug. Measurement of the concentration of drug in each solvent generates an octanyl:water coefficient or PC, which might be useful for predicting the ability of a drug to pass through cell membranes. A ratio greater than 1 suggests greater distribution to the organic phase, indicating lipid solubility. For example, in regards to providing analgesia, fentanyl (PC of 717) is both more potent and more rapid acting, but shorter in duration, compared to morphine (PC of 0.7), presumably because it can move more rapidly through the blood–brain barrier (Figure 1-4). Benzene rings, carbon double bonds and methyl groups tend to make a drug more lipid soluble, whereas polar compounds such as amine or hydroxyl groups contribute to drug-water solubility.

Figure 1-4 Lipid solubility of a compound can be predicted on the basis of the octanyl: water partition coefficient (PC), which in turn depends on chemical structure. A, Morphine and fentanyl both reach the central nervous system in sufficient quantity to provide analgesia. However, fentanyl is much more lipid soluble, as is supported by its octanyl:water partition coefficient of 717 compared with that of morphine (0.7). Fentanyl is much more potent and more rapid acting, but it also has a shorter duration of effect. B, The PC among the fluorinated quinolones suggests that enrofloxacin would have better tissue distribution than ciprofloxacin. This is supported by the relative concentrations of enrofloxacin versus ciprofloxacin in serum compared with tissues 60 minutes after administration of 20 mg/kg intravenous enrofloxacin in dogs. Although PC is an important determinant of lipid solubility, it may vary with surrounding pH. (ENRO, enrofloxacin; CIPRO, ciprofloxacin; PRADO, pradofloxacin; MARBO, marbofloxacin.)

KEY POINT 1-2

A drug will be more nonionized and more likely to diffuse into tissues when present in a “like” environment—that is, acidic drugs in an acidic environment.

In addition to lipid solubility, drug pKa and environmental (host) pH will also influence distribution of drug into body compartments. The Henderson-Hasselbalch equation describes the pH partition theory (Figure 1-5). Assuming a drug is sufficiently lipid soluble to cross cell membranes, a steady-state equilibrium will be reached when the amount of drug moving from one area equals the amount moving in the opposite direction and the concentration of diffusible drug will be equivalent on either side of a membrane. However, in its ionized form, a drug is not diffusible, cannot traverse lipid membranes, and becomes trapped and thus “partitioned” by the pH in its surrounding environment. Although the concentration of the nonionized (diffusible) portion on each side of the membrane will be equal (assuming a steady state equilibrium is reached), the total concentration on either side may differ if the pH on either side of the membrane is different (Figure 1-5). The difference depends on the pKa of the drug and the environmental pH on either side of the membrane. Drugs will be trapped by ionization when present in an “unlike” environment. Drug pKa (the pH at which the drug is 50% ionized and 50% nonionized; ratio 1:1), and its behavior as a weak acid or base defines the degree of ionization. For a weak acid, as local pH decreases (becoming more “like”), the nonionized and thus diffusible proportion will increase. In contrast, for a weak acid, an increase in pH (“unlike”) will increase the ionized proportion. The opposite is true for a weak base: increasing pH will increase the nonionized or diffusible proportion, whereas a pH decrease will increase the ionized, nondiffusible portion (Box 1-1).

Figure 1-5 The Henderson-Hasselbalch equation and the pH partition hypothesis predict the behavior of an ionizable compound on the basis of its pKa and the ambient pH. A weak base (bottom) will be predominantly ionized in an acidic environment (i.e., gastric pH), and thus is likely to be trapped. It is less likely to be ionized in a higher pH and thus is more diffusible (i.e., plasma). In contrast, a weak acid (top) is likely to be nonionized in the acidic environment and thus is more likely than the weak base to move across the lipid membrane and be absorbed. However, in the plasma the higher pH will increase the proportion of ionized drug, limiting its diffusion from plasma into cells. (see Box 1-1.)

Box 1-1 The pH Partition Hypothesis

The pH partition hypothesis is the ratio of ionized:nonionized drug and is based on pH (of the environment) and pKa (of the drug) (see Figure 1-5). The proportion of ionized to unionized drug is described by the Henderson-Hasselbalch equation. For acids, the ratio (ionized:nonionized) is 10ⁿ, and for a weak base the ratio is 10^-n. The ratio of the ionized:nonionized (I:U) drug can be useful for predicting movement between tissues. A drug is considered significantly ionized if the ratio (I:U) is greater than 100. Thus for a weak acid the drug is considered ionized in an environmental pH that is 2 or more higher than its pK_a (pH − pKa = 2; 10ⁿ = 10² = 100 I : 1 U) A weak base is considered ionized if the pH is or 2 or more below its pK_a.. (pH − pKa = -2; 10^-n = 10^-(-2) = 10² = 100). Ideally, for drug movement to occur by passive diffusion, the pH will be no more than 2 pH units above the pKa for the acid and no more than 2 pH units below the pKa for the base. The gastrointestinal tract (pH 6.0) offers an example of how pH partition influences drug movement. Orally administered aminoglycosides (weak bases with pK_a approximating 7 to 9) are ionized at a ratio of approximately 1000:1 (6 − 9 = −3, 10 ^-n = 10 ^–(-3), = 10³ = 1000:1 [I:U]. Thus there is only one nonionized or diffusible ion for each 1000 ionized amikacin molecules. The ionized molecules will be trapped and will not be absorbed, limiting absorption of this water-soluble drug. In contrast, the proportion of the ionized weak acid penicillin (pKa about 2) would be 0.0001:1 (2 − 6=10^-4); for every ionized molecule, 10,000 molecules would be nonionized (the inverse of 0.0001:1). As such, if other factors are supportive (e.g., the drug is not destroyed by the gastric acidity), penicillin should be well absorbed from the gastrointestinal tract. The urine is another site where pH partition may influence drug movement. Penicillin located in urine with a pH of 7 would be ionized at a ratio of 10,000:1 (10⁵), whereas the aminoglycoside would be ionized at a ratio of only 100:1. If the urine pH was 8, the ratio of I:U would be 10 for the aminoglycoside, which is not considered significant to preclude drug movement. In either pH the aminoglycoside would be more likely than the penicillin to be passively resorbed and to penetrate microbial membranes. Drug that is partitioned by ionization acts as a reservoir, replacing nonionized drug that may leave the other side of the membrane in an open system. Eventually, assuming the nonionized side remains “open,” both sides of the membrane will eventually be depleted of drug.

Although less common, drug movements other than passive diffusion and bulk flow influence PDC. Carrier-mediated transport includes both facilitated diffusion (nonactive) or active transport. An example important transport system is the P-glycoprotein system, an MDR-1 gene product best known for imparting multidrug resistance to cancer cells (and to microbes).⁷ However, this transport system occurs in several tissues in the body, including renal tubular brush borders and bile canniculi (responsible for drug excretion from the body); the brain or other “sanctuaries” (responsible for keeping exogenous componds out of critical tissues); characterized by a blood–tissue barrier; and in portals of entry, including the lower gastrointestinal tract (reducing oral drug bioavailability).⁸ Pinocytosis is a rare drug movement exemplified by the uptake of vitamin B₁₂ in the ileum and aminoglycosides by renal tubular cells.

Plasma Drug Concentrations

Although response to a drug reflects concentrations at the tissue (or cellular level), because tissue samples cannot be collected easily, drug concentrations at the tissue site are approximated by measuring PDCs. After administration of a fixed dose of a drug, several drug movements act in concert to determine PDC (Figure 1-6).^2,3,6,9 These movements largely, but not exclusively, depend on passive diffusion of the drug and include absorption (A) from the site of administration to systemic circulation, defined as the major vessels and well-perfused organs; distribution (D) of the drug from systemic circulation to tissues (target and nontarget) and back again; and elimination of the drug from the body by metabolism (M) and excretion (E). These drug movements are dynamic, occurring simultaneously, and their net effects determine PDC at any time during the dosing interval after administration of a fixed dose. Because passive diffusion is the major determinant of each drug movement, each in turn is influenced by a number of other factors. The impact of these factors on the drug movements and the time course of drug in the body as a result of these movements can be described or modeled mathematically, leading to the study of pharmacokinetics. Each drug movement is influenced by host and drug factors that may affect therapeutic success (see Chapter 2).

Figure 1-6 The determinants of plasma drug concentration (ADME) act in concert after administration of a fixed dose. The drug must first be absorbed, most commonly from the gastrointestinal tract (Absorption–A). Orally administered drug passes through the liver before reaching systemic circulation (not shown). Once in circulation, drug not bound to plasma proteins (free drug) is distributed into tissues (Distribution–D), where it can be bound to tissues or distributed back to circulation. Elimination of the drug from the body occurs by hepatic metabolism (Metabolism–M) and renal or biliary excretion (Excretion—E) of the drug or its metabolites. Drugs that are protein bound will not be filtered by the kidney or metabolized by the liver unless actively secreted in the kidneys and or characterized by flow-limitation in the liver. Excreted drugs can be passively reabsorbed by the kidney or following biliary excretion after deconjugation in the gastrointestinal drug (enterohepatic circulation).

(Adapted from Ettinger SJ, Feldman EF, editors: Textbook of veterinary internal medicine, ed 5, Philadelphia, 2000, Saunders.)

KEY POINT 1-3

Plasma drug concentrations at any point in time after administration of a dose reflect the combined effects of four dynamic drug movements: absorption, distribution, metabolism, and excretion.

Absorption

Bioavailability, extent, and rate of absorption

The percentage of an administered dose of drug that reaches systemic circulation and is thus able to induce a response is referred to as bioavailability (F).^2,3,9,10 Bioavailability (see Pharmacokinetics section) is used to predict drug efficacy after different routes of administration or administration of different formulations of the same drug. Absolute bioavailability or extent of absorption is the actual bioavailability and can be determined only by comparing the appearance of the drug preparation to that after intravenous administration of the drug. In contrast, relative bioavailability of two different preparations or by two routes of administration of the same drug can be evaluated by comparing their area under the curve (AUC).¹⁰ The area under the concentration versus time curve (AUC) describes the entire time course of the drug. Because its magnitude depends on maximum drug concentration and rate of elimination, it is influenced by several drug movements, including absorption. The AUC is used to calculate several other pharmacokinetic parameters; clinically, it is useful for determining response to certain drugs, particularly antimicrobials.^11,12

KEY POINT 1-4

Absolute bioavailability of a drug preparation can be determined only by comparing its appearance to 100% availability, which occurs only after intravenous administration.

The greater the bioavailability, or extent of absorption of a drug, the greater the anticipated pharmacologic response. However, pharmacologic response of two different drug preparations or the same drug given by different routes may vary even if equally bioavailable; two products are considered bioequivalent only if neither their rate nor their extent of absorption differ. Differences in the rate of absorption (e.g., absorption half-life [see Pharmacokinetics section]) may cause different time to onset, as well as lower peak concentrations, although the duration of effect may be longer.

Factors impacting drug absorption are most profound for orally administered drugs. Factors impacting other routes are addressed under “Routes of Administration.”

Oral absorption

Most orally administered drugs reach systemic circulation after absorption from the small intestine. The rate and extent of drug absorption in the gastrointestinal tract depend on a number of host factors, most of which affect passive diffusion (Figure 1-7).⁹ These include gastrointestinal pH, which favors absorption of weak acids; surface area, which favors absorption in the small intestine compared with the stomach; motility, which mixes the drug, the concentration of diffusible drug at the site of movement; permeability and thickness of the mucosal epithelium; and intestinal blood flow, which maintains the concentration gradient across the mucosal epithelium. The latter factor of blood flow is important only for drugs capable of rapid transfer across the epithelium.

Figure 1-7 The determinants of oral drug absorption include local pH, the surface area to which the dissolved drug is presented, epithelial permeability, mucosal blood flow (particularly for drugs very rapidly absorbed), and smooth muscle motility. The drug must be diffusible, and thus must be in the dissolved state (to establish a concentration gradient). Most drugs are absorbed in the small intestine because of its larger surface area. The drug transport system, P-glycoprotein, decreases bioavailability through drug efflux from the intestinal epithelial cell.

In general, the intestinal surface area is so large that changes seldom are of sufficient magnitude to effect absorption (see Chapter 2). However, changing particle size of the drug preparation may cause differences in the rate or extent of absorption and markedly different bioequivalences. Drug preparations often are specifically designed to alter rates of absorption by manipulation of particle size.

Bioavailability of an orally administered drug also is influenced by factors after it passes into the gastrointestinal epithelium. Bioavailability is decreased if the drug is metabolized by intestinal epithelial cells, microbes, or by the liver. Additionally, enterocytes can decrease oral bioavailability of a drug by causing its efflux from enterocytes, in part because of the presence of active transport proteins located on enterocyte cell membranes.¹³

Transport membranes may act alone or in concert with one another; for some drugs, one transporter may predominate, but for others, none may. Identifying the role of each transporter protein is complicated and difficult to study. Several families have been identified. (1) Transporters located on the apical cell membrane include the family of organic anion-transporting polypeptides (OATPs); these proteins are also located in the liver, kidney, and brain and influence distribution and excretion. These proteins transport a large number of amphipathic drugs (e.g., digoxin, steroids) and endogenous compounds (e.g., steroids, thyroid hormones). (2) Proton-dependent oligopeptide transporters (POTs), driven by a proton gradient, are present in the kidney, brain, and the gastrointestinal tract, where their activity appears to increase from the duodenum to the ileum. Among the drugs influenced by these transporters are beta-lactam antimicrobials, ACE-inhibitors, and prodrugs of selected antivirals. (3) The family of ATP-binding cassette (ABC) superfamily of transporters includes the P-glycoproteins. These include multidrug resistance protein (MRP1) and a multispecific organic anion transporter (MOAT) also located in other tissues. An efflux transporter, P-glycoprotein is characterized by broad substrate specificity. Because it is abundant in enterocytes, it can profoundly decrease the oral bioavailability of target drugs. It is associated and shares substrate specificity with selected cytochrome-P450 enzymes (most notably, CYP3A), which decreases drug that is not effluxed from the cell by the transporter (see Chapter 2).¹³

Hepatic metabolism also can profoundly affect the PDC of an orally administered drug. After gastrointestinal absorption, drugs enter the portal vein and then the liver (Figure 1-8). As such, an orally administered drug is exposed to hepatocytes before it enters the systemic circulation. Drugs characterized by a high hepatic extraction ratio (>70% extracted) are almost completely removed from the blood by hepatocytes during the first passage of blood through the liver. As a result, after oral administration, drugs that undergo first-pass metabolism may not reach systemic circulation in concentrations sufficiently high to cause a pharmacologic response. Despite good to excellent oral absorption, such drugs are characterized by poor bioavailability and are administered either parenterally (e.g., lidocaine) or in oral doses high enough to compensate for first-pass metabolism by the liver. Examples of drugs that are orally administered yet undergo significant hepatic first-pass metabolism include selected cardiac drugs (e.g., propranolol and other beta-blockers, diltiazem in some species, hydralazine, nitroglycerin), diazepam, and opioid analgesics. The negative effects of first-pass metabolism on pharmacologic response may be reduced if the drug metabolites (e.g., propranolol and diazepam) are also pharmacologically active.

Figure 1-8 First-pass metabolism occurs as drug absorbed from the gastrointestinal tract (from the stomach to the lower colon) enters the portal vein and flows to the liver. Once in the liver, drugs that are characterized by a high extraction are removed rapidly from the blood before entering systemic circulation. Plasma concentrations of such drugs may not reach therapeutic concentrations unless the dose is increased to compensate for first-pass metabolism. The amount of drug removed on the first pass from the liver differs among species and ages and according to the presence or absence of disease. First-pass metabolism can be avoided by transmucosal absorption in the oral cavity, or rectal absorption,

Distribution

Once a drug reaches the systemic circulation, it must be distributed from the central (blood) compartment to peripheral tissues to impart a pharmacologic effect. Further, drug in tissues will be distributed back into plasma so that it can be eliminated. The major factors that determine drug distribution to and from tissues include drug lipid solubility and its ability to penetrate cell membranes, the degree to which the drug is bound to plasma or tissue proteins, and regional (organ) blood flow. The presence of transport proteins (p-glycoprotein, OATPs, and POTs) also influence drug distribution, particularly in “sanctuary” tissues characterized by tissue–blood barriers (e.g., brain, cerebrospinal fluid, placenta).¹³

Binding of lipid-soluble drugs to plasma proteins facilitates their circulation. Drug binding to proteins may influence several determinants of drug movement, including distribution.¹⁴ Weakly acidic drugs tend to bind to albumin, whereas weakly basic drugs tend to bind to α₁‑glycoproteins.¹⁵ The large molecular weight of protein precludes movement of bound drug from circulation into tissues. As such, the protein-bound drug is not pharmacologically active; cannot be filtered in the normal glomerulus, and for some drugs (i.e., capacity-limited, discussed later), cannot reach drug metabolizing enzymes in the hepatocyte (or other organ). Presumably, drugs that are highly protein bound may be more likely to be involved in adverse reactions early in the dosing regimen because displacement of only a small proportion of drug from the protein (e.g., due to competition with other protein-bound drugs or hypoalbuminemia) can increase the total amount of free, active drug (Figure 1-9).^2,3 A drug is considered significantly (highly) protein bound if 80% or more bound; for a drug bound less than 80%, displacing enough drug to significantly increase the unbound proportion is difficult. For example, displacement of only 1% of a drug that is 99% protein bound (e.g., nonsteroidal antiinflammatories) can double the concentration of pharmacologically active drug. In contrast, to double the pharmacologically active form of a drug that is only 80% bound (i.e., going from 20% to 40% unbound) would require displacement of 25% of the bound drug, which is clinically difficult to achieve. Yet even with highly protein-bound drugs, the clinical relevance of displacement and increased concentrations of unbound drug is questionable: in the face of normal renal and hepatic function, clearance of the freed drug by these organs will increase such that “extra” drug is rapidly removed.¹⁶ However, it is not clear that clearance will increase sufficiently in the face of organ dysfunction (e.g., renal or liver disease). Further, the package insert for Converia, which is highly protein bound, indicates that the plasma drug concentration of several other highly protein bound drugs increased with co-administration.

Figure 1-9 Displacement of drug from protein-binding sites becomes significant only if a drug is greater than 80% protein bound. Displacement of only 1% of a drug that is 99% protein bound doubles the pharmacologically active form of the drug (top two diagrams). For a drug that is 80% protein bound, however, 20% of the dose is responsible for pharmacologic actions. Displacement of 25% of the drug is necessary to double the pharmacologically active drug. However, because unbound drug will be cleared more rapidly (assuming normal organ function), displacement of highly bound drugs may not be clinically important.

In addition to its ability to reach target tissues and organs of elimination, distribution of a drug is important because of its influence on PDC and drug elimination. The amount of tissue to which a drug is distributed, often estimated by the theoretical parameter, volume of distribution (Vd) of the drug, directly but inversely influences PDC.^2,3,17 Because it is theoretical, Vd is generally referred to as apparent Vd. The Vd of a drug also describes the ease with which the drug leaves the plasma. Simplistically, volume of distribution is also the volume to which a drug would have to be distributed if it were present throughout the body in the same concentration as that measured in the plasma after intravenous (IV) administration of a known dose. It can be exemplified by adding 5 g of dextrose (considered the dose) to each of two beakers containing a different but unknown volume of water. The dextrose is allowed to distribute equally throughout the beaker (no membranes are present in the beaker) and then the concentration is measured. If the concentration in beaker A is 5% (50 mg/mL or 5 g/100 mL), then the volume of water in the beaker must be 100 mL. If the concentration in beaker B is 2.5% (25 mg/mL or 25 g/100 mL), the volume must be 200 mL. The Vd in beaker A is twice that in beaker B. The Vd of a drug in an animal is determined essentially the same way: a known dose is given intravenously to ensure that all the drug reaches the site being measured, the drug is allowed to distribute until equilibrium (or pseudo-equilibrium) is reached, and the peak drug concentration is determined. The Vd is then calculated by dividing the dose by the peak concentration (the y intercept, Co, A or B): Vd = Dose/Co (see the Pharmacokinetics section).

The PDC (and response to) a drug at a known dose varies inversely with Vd. Vd differences among species and ages (pediatric versus geriatric) can dramatically affect PDC (see Chapter 2). In addition, diseases associated with fluid retention or obesity are likely to increase the Vd of many drugs (and thus decrease PDC), whereas dehydration or weight loss is likely to decrease Vd and thus increase PDC (see Chapter 2). The impact depends upon whether the drug is distributed to total body water (i.e., a lipid-soluble drug) or extracellular fluid (i.e., a water-soluble drug). Because the distribution of a drug to peripheral tissues removes drugs from organs of drug clearance, Vd also directly and proportionately influences elimination half-life (Figure 1-10). Thus any factor that increases Vd will tend to decrease PDC but prolong the elimination half-life and thus the presence of the drug in the body.

Figure 1-10 Despite its theoretical nature, the size of the apparent volume of distribution (Vd) may indicate the body compartment to which the drug is distributed. These include (A) the blood compartment (i.e., a drug tightly bound to plasma proteins), (B) extracellular fluid (e.g., a water-soluble drug), or (C) total body water (i.e., a liphophilic drug that penetrates cell membranes). Increasingly larger volumes represented by these compartment inversely affect plasma drug concentration (PDC) and the slope of the elimination (k_el) curve. This curve determines elimination half-life, which changes directly with Vd.

If a semipermeable membrane divided the beakers used to exemplify Vd into two compartments, distribution of the dextrose throughout each beaker would have taken longer than if the membrane were not present. At distribution equilibrium, (the amount of drug moving from one side equals the amount of drug moving from the other side. Further, at equilibrium, although the amount of drug passing between the two compartments is equal, membrane or fluid characteristics result in different concentrations of drug on each side of the membrane after equilibrium has been reached. Thus both the rate (i.e., distribution half-life) and extent of drug distribution may be affected by membranes. The body contains many membranes whose characteristics are sufficiently complex that multiple compartments may be formed. Extracellular and intracellular compartments (which together make up total body water) are major compartments to which drugs distribute. Most capillaries are fenestrated and present no barrier to passage of unbound drugs from plasma to interstitial fluid. Hence water-soluble drugs tend to be distributed to extracellular fluid (ECF; 20% to 30% of body weight) and thus are often characterized by a Vd of 0.1 to 0.3 L/kg. Lipid-soluble drugs tend to cross cell membranes and thus distribute into both ECF and intracellular fluid (ICF; i.e., total body water [TBW]) and as such, generally have a larger Vd (>0.6 L/kg). The Vd of highly protein-bound drugs reflects the plasma compartment, and as such is very small (0.05% of the body weight, or 0.05 L/kg). Such drugs may appear to distribute to their total volume almost instantaneously, resulting in a PDC versus time described by a single component, or a one compartment model (see the pharmacokinetics section). However, it is the Vd of the unbound or pharmacologically active drug that is more descriptive of the disposition and pharmacologic effects of a highly bound drug.

Capillaries of selected organs, including the brain, cerebrospinal fluid, eye, testis, and prostate, are not fenestrated, and drugs must diffuse through the capillary endothelium to penetrate these tissues.^18,19 For treatment of such organs, lipid-soluble drugs (i.e., Vd >0.6 L/kg) are more likely than water-soluble drugs to penetrate the endothelial barrier and achieve therapeutic concentrations. However, simply because a drug has a Vd that equals or exceeds the volume of TBW does not assure lipid solubility nor does it guarantee sufficient tissue distribution. Drug distribution to various tissues differs with drug chemistry, and intracellular accumulation may occur for many reasons. Ion trapping was previously discussed; drugs also can bind to intracellular proteins (i.e., Na+ K+ ATPase of digoxin), bone (e.g., Ca²⁺ or Mg⁺ by tetracyclines) or other macromolecules (e.g., lysozymes by aminoglycosides). Bound drug is generally not active (unless binding occurs to target ligands), but bound drug may act as a reservoir for interstitial and plasma drug concentration (e.g., the antimicrobial cefovecin). Ion trapping or binding of a drug will remove it from plasma; as such, as PDC decreases, for any given dose, the Vd will increase. The Vd of a drug characterized by such multicompartments may result in a Vd that is greater than the volume of the animal (e.g., >1 L/kg). Such a drug exemplifies the theoretical nature of Vd in that it simply (mathematically) describes the amount of tissue that is diluting the drug if the concentrations measured in plasma were the same throughout the body. Although Vd is a useful parameter, particularly for calculating drug dose, it should not be used to indicate where (i.e., ECF, ICF, TBW, or selected tissues) a drug has distributed. Further, because the rate and extent of drug distribution to tissues varies, the time to equilibrium also will vary. Calculations for Vd (and determining peak PDC) generally should not occur until distribution equilibrium has been reached.

KEY POINT 1-5

Volume of distribution is used to calculate the dose by estimating the volume of tissue that will dilute the drug after its intravenous administration. It is theoretical because it provides no information regarding the site of distribution. However, it proportionately impacts plasma drug concentration (inversely) and elimination half-life (directly).

The term distribution equilibrium, or steady-state equilibrium, is often used to refer to the state in which the amount of drug leaving plasma for tissues is equivalent to the amount of drug leaving tissues for plasma. The reality is that distribution equilibrium may not ever be achieved because drugs are characterized by an “open” system—that is, drug is continually being eliminated. Hence, the term pseudoequilibrium is more appropriate. Distribution equilibrium is less likely to be achieved for drugs with a short half-life, particularly when administered at a long dosing interval. Drugs that accumulate (given at a dosing interval that is shorter than the half-life; see later discussion) are more likely to reach a state of equilibrium between doses, although the actual concentrations may fluctuate between C^max and C^min during a dosing interval.

Documenting the extent to which a drug distributes to a specific site is difficult because techniques are required that allow collection of interstitial versus intracellular tissue. Measurement of drug in interstitial fluid or ICF might confirm the site of drug distribution. However, collecting a sample of sufficient size using methods that are not traumatic (and thus do not impact drug movement) is difficult. Several techniques have been developed to collect fluid representative of ECF. Examples include tissue cage models; “wick” methods; and more recently and perhaps most appropriately, the use of microfiltration systems that collect directly from ECF using a microprobe. A less representative method of reporting tissue concentrations is measurements of drug in homogenized tissues; this measures both extracellular and intracellular drug. Drugs bound (trapped) inside a cell (e.g., as a result of binding to proteins, or ionization) may markedly increase drug concentrations in homogenized tissue, but the drug may not be pharmacologically active or available to interstitial tissues. However, intracellular drug may act as a reservoir, providing continued input to interstitial fluid even as PDCs decline. Drug-void cells, on the other hand, will artificially dilute actual drug concentrations in the ECF.

KEY POINT 1-6

If a protein-bound drug is displaced from its binding protein, the increase in concentration of free and thus active drug is likely to be short-lived as the free drug is cleared more rapidly in the normal animal, thus potentially offsetting any risk associated with increased concentration.

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