Dhanesh K. Gupta
Thomas K. Henthorn
1. Most drugs must pass through cell membranes to reach their sites of action. Consequently, drugs tend to be relatively lipophilic, rather than hydrophilic.
2. The highly lipophilic anesthetic drugs have a rapid onset of action because they rapidly diffuse into the highly perfused brain tissue. They have a very short duration of action because of redistribution of drug from the central nervous system to the blood.
3. The cytochrome P450 (CYP) superfamily is the most important group of enzymes involved in drug metabolism. It and other drug-metabolizing enzymes exhibit genetic polymorphism.
4. The kidneys eliminate hydrophilic drugs and relatively hydrophilic metabolites of lipophilic drugs. Renal elimination of lipophilic compounds is negligible.
5. The liver is the most important organ for metabolism of drugs. Hepatic drug clearance depends on three factors: the intrinsic ability of the liver to metabolize a drug, hepatic blood flow, and the extent of binding of the drug to blood components.
6. The volume of distribution quantifies the extent of drug distribution. The greater the affinity of tissues for a drug relative to blood, the greater its volume of distribution (i.e., lipophilic drugs have greater volumes of distribution).
7. Elimination clearance is the parameter that characterizes the ability of drug-eliminating organs to irreversibly remove drugs from the body. The efficiency of the body to remove a drug from the body is proportional to the elimination clearance.
8. All else being equal, an increase in the volume of distribution of a drug will increase its elimination half-life; an increase in elimination clearance will decrease elimination half-life.
9. Most drugs bring about a pharmacologic effect by binding to a specific receptor that brings about a change in cellular function to produce the pharmacologic effect.
10. Although most pharmacologic effects can be characterized by both dose-response curves and concentration-response curves, the dose-response curves are unable to determine whether variations in pharmacologic response are caused by differences in pharmacokinetics, pharmacodynamics, or both.
11. Integrated pharmacokinetic-pharmacodynamic models allow temporal characterization of the relationship between dose, plasma concentration, and pharmacologic effect.
12. Simulations of multicompartmental pharmacokinetic models that describe intravenous anesthetics demonstrate that for most anesthetic dosing regimens, the distribution of drug from the plasma to the pharmacologically inert peripheral tissues has a greater influence on the plasma concentration profile of the drug than the elimination of drug from the body.
13. Target-controlled infusions are achieved with computer-controlled infusion pumps worldwide (not yet approved by the Food and Drug Administration [FDA] in the United States) and permit clinicians to make use of the drug concentration–effect relationship, optimally accounting for pharmacokinetics and predicting the offset of drug effect.
14. By understanding the interactions between the opioids and the sedative-hypnotics (e.g., response surface models), it is possible to select target concentration pairs of the two drugs that produce the desired clinical effect while minimizing unwanted side effects associated with high concentrations of a single drug.
15. The time until a patient regains responsiveness from a single drug anesthetic is determined by the pharmacokinetics of the individual drug, the concentration-effect relationship, and the duration of administration of the drug (context-sensitive decrement time). For two-drug anesthetics, the time to awakening not only depends on the individual drug pharmacokinetics and the duration of administration of the anesthetics, but it also depends on the pharmacodynamic interactions of the two drugs.
In 1943, Halford1 labeled thiopental as “an ideal method of euthanasia” for war surgical patients and pronounced that “open drop ether still retains primacy!” Based on this recount of the experience with thiopental at Pearl Harbor, it is impressive that cooler heads prevailed—Adams and Gray2 detailed a case of a civilian gunshot wound in which they carefully titrated incremental doses of thiopental without any adverse respiratory or cardiovascular events. To highlight the importance of the quiet case report versus the animated condemnation of intravenous anesthesia for patients with hemorrhagic shock, an anonymous editorial appeared in the same issue of Anesthesiology that attempted to give some scientific justification for the discrepancy in opinions.3 As the editorial detailed, thiopental had a small therapeutic index and the tolerance to normal doses was decreased in extreme physical conditions (e.g., blood loss, sepsis). Therefore, as with open-drop ether, small doses of thiopental should be titrated to achieve the desired affects and avoid side effects associated with overdose. Fortuitously, the anesthesia community did not simply abandon the use of thiopental, and in 1960, Price4 used mathematical models in order to describe the effects of hypovolemia on thiopental distribution.
Anesthetic drugs are administered with the goal of rapidly establishing and maintaining a therapeutic effect while minimizing undesired side effects. Although open-drop ether and chloroform were administered using knowledge of a dose-effect relationship, the more potent volatile agents, along with the intravenous hypnotics, neuromuscular junction blocking agents, and intravenous opioids, require a sound knowledge of pharmacokinetics and pharmacodynamics in order to accurately achieve the desired the pharmacologic effect for the desired period of time without any drug toxicity.
This chapter attempts to guide the reader through the fundamental knowledge of what the body does to a drug (i.e., pharmacokinetics) and what a drug does to the body (i.e., pharmacodynamics). The initial section of this chapter discusses the biologic and pharmacologic factors that influence the absorption, distribution, and elimination of a drug from the body. Where necessary, quantitative analyses of these processes are discussed to give readers insight into the intricacies of pharmacokinetics that cannot be easily described by text alone. The second section concentrates on the factors that determine the relationship between drug concentration and pharmacologic effect. Once again, mathematical models are presented as needed in order to clarify pharmacodynamic concepts. The final section builds on the reader's knowledge gained from the first two sections to apply the principles of pharmacokinetics and pharmacodynamics to determine the target concentration of intravenous anesthetics required and the dosing strategies necessary to produce an adequate anesthetic state. Understanding these concepts should allow the reader to integrate the anesthetic drugs of the future into a rational anesthetic regimen. Although specific drugs are used to illustrate pharmacokinetic and pharmacodynamic principles throughout this chapter, detailed pharmacologic information of anesthetic pharmacopeia are presented in subsequent chapters of this book.
Drug Absorption and Routes of Administration
Transfer of Drugs Across Membranes
For even the simplest drug that is directly administered into the blood to exert its action, it must move across at least one cell membrane to its site of action. Because biologic membranes are lipid bilayers composed of a lipophilic core sandwiched between two hydrophilic layers, only small lipophilic drugs can passively diffuse across the membrane down its concentration gradient. In order for water-soluble drugs to passively diffuse across the membrane down its concentration gradient, transmembrane proteins that form a hydrophilic channel are required. Because of the abundance of these nonspecific hydrophilic channels in the capillary endothelium of all organs except for the central nervous system (CNS), where the blood–brain barrier capillary endothelial cells have very limited numbers of transmembrane hydrophilic channels, passive transport of drugs from the intravascular space into the interstitium of various organs is limited by blood flow, not by the lipid solubility of the drug.5
Hydrophilic drugs can only enter the CNS after binding to drug-specific transmembrane proteins that actively transport the hydrophilic drug across the capillary endothelium into the CNS interstitium. When these transmembrane carrier proteins require energy to transport the drug across the membrane, they are able to shuttle proteins against their concentration gradients, a process called active transport. In contrast, when these carrier proteins do not require energy to shuttle drugs, they cannot overcome concentration gradients, a process called facilitated diffusion. Therefore, active transport is not limited to the CNS but is also found in the organs related to drug elimination (e.g., hepatocytes, renal tubular cells, pulmonary capillary endothelium), where the ability to transport drugs against the concentration gradient has specific biologic advantages. Both active transport and facilitated diffusion of drugs are saturable processes that are limited only by the number of carrier proteins available to shuttle a specific drug.5
For lipophilic compounds, transporters are not needed for the drug to diffuse across the capillary wall into tissues, but the presence of transporters does affect the concentration gradients that exist. For instance, some lipophilic drugs are transported out of tissues by adenosine triphosphate-dependent transporters such as p-glycoprotein. The lipophilic potent µ-opioid agonist, loperamide, used for the treatment of diarrhea, has limited bioavailability because of p-glycoprotein transporters at the intestine-portal capillary interface, and then what does reach the circulation has its CNS penetrance limited by p-glycoprotein at the blood–brain barrier.6 Conversely, lipophilic compounds can be transported into tissues, increasing the tissue concentration of the drug beyond what would be accomplished by passive diffusion. The class of transporters called organic anion polypeptide transporters, like p-glycoprotein, is located in the microvascular endothelium of the brain and transport endogenous opioids into the brain.7,8 These organic anion polypeptide transporters also transport drugs. The degree to which transporter proteins may account for intra- and interindividual responses to anesthetic drugs has not been well studied to date.9
In order for a drug to be delivered to the site of drug action, the drug must be absorbed into the systemic circulation. Therefore, intravenous administration results in rapid increases in drug concentration. Although this can lead to a very rapid onset of drug effect, for drugs that have a low therapeutic index (the ratio of the intravenous dose that produces a toxic effect in 50% of the population to the intravenous dose that produces a therapeutic effect in 50% of the population), rapid overshoot of the desired plasma concentration can potentially result in immediate and severe side effects. Except for intravenous administration, the absorption of a drug into the systemic circulation is an important determinant of the time course of drug action and the maximum drug effect produced. As the absorption of drug is slowed, the maximum
plasma concentration achieved—and therefore the maximum drug effect achieved—is limited. However, as long as the plasma concentration is maintained at a level above the minimum effective plasma concentration, the drug will produce a drug effect.10 Therefore, nonintravenous methods of drug administration can produce a sustained and significant drug effect that may be more advantageous than administering drugs by the intravenous route.11
Bioavailability is the relative amount of a drug dose that reaches the systemic circulation unchanged and the rate at which this occurs. For most intravenously administered drugs, the absolute bioavailability of drug available is close to unity and the rate is nearly instantaneous. However, the pulmonary endothelium can slow the rate at which intravenously administered drugs reach the systemic circulation if distribution into the alveolar endothelium is extensive, such as occurs with the pulmonary uptake of fentanyl. The pulmonary endothelium also contains enzymes that may metabolize intravenously administered drugs (e.g., propofol) on first pass and reduce their absolute bioavailability.12
For almost all therapeutic agents in all fields of medicine, oral administration is the safest and most convenient method of administration. However, this route is not used significantly in anesthetic practice because of the limited and variable rate of bioavailability. The absorption rate in the gastrointestinal tract is highly variable because the main determinant of the timing of absorption is gastric emptying into the small intestines where the surface area for absorption is several orders of magnitude greater than that of the stomach or large intestines. Additionally, the active metabolism of drug by the small intestine mucosal epithelium, and the obligatory path through the portal circulation before entering the systemic circulation, contribute to decreased bioavailability of orally administered drugs.13 In fact, the metabolic capacity of the liver for drugs is so high that only a small fraction of most lipophilic drugs actually reach the systemic circulation. Because of this extensive first-pass metabolism, the oral dose of most drugs must be significantly higher to generate a therapeutic plasma concentration. Coupled with the prolonged and variable time until peak concentrations are usually achieved from oral administration (between tens of minutes to hours), it is nearly impractical to use this mode to administer perioperative anesthetic agents.
Highly lipophilic drugs that can maintain a high contact time with nasal or oral (sublingual) mucosa can be absorbed without needing to traverse the gastrointestinal tract. Sublingual administration of drug has the additional advantage over gastrointestinal absorption in that absorbed drug directly enters the systemic venous circulation and therefore is able to bypass the metabolically active intestinal mucosa and the hepatic first-pass metabolism. Therefore, small amounts of drug can rapidly produce a significant plasma concentration and therapeutic effect.14 However, because of formulation limitations and the small amount of surface area available for absorption, sublingual administration is limited to drugs that fortuitously meet these requirements and require a rapid onset of drug action (e.g., nitroglycerin, fentanyl).
A few lipophilic drugs have been manufactured in formulations that are sufficient to allow penetration of intact skin. Although scopolamine, nitroglycerin, opioids, and clonidine all produce therapeutic systemic plasma concentrations when administered as “drug patches,” the extended amount of time that it takes to achieve an effective therapeutic concentration limits practical application except for maintenance therapy. Attempts to speed the passive diffusion of these drugs using an electric current has been described for fentanyl,15 but is still limited in its practicality.
Intramuscular and Subcutaneous Administration
Absorption of drugs from the depots in the subcutaneous tissue or in muscle tissue is directly dependent on the drug formulation and the blood flow to the depot. Because of the high blood flow to muscles in most physiologic states, intramuscular absorption of drugs in solution is relatively rapid and complete. Therefore, some aqueous drugs can be administered as intramuscular injection with rapid and predictable effects (e.g., neuromuscular junction blocking agents). The subcutaneous route of drug absorption is more variable in its onset because of the variability of subcutaneous blood flow during varying physiologic states—this is the primary reason that subcutaneous regular insulin administered in the operating room has a variable time of onset and maximum effect.
Intrathecal, Epidural, and Perineural Injection
Because the spinal cord is the primary site of action of many anesthetic agents, direct injection of local anesthetics and opioids directly into the intrathecal space bypasses the limitations of drug absorption and drug distribution of any other route of administration. This is not the case for epidural and perineural administration of local anesthetics because not delivering the drug directly into the cerebrospinal fluid necessitates that the drug be absorbed through the dura or nerve sheath in order to reach the site of drug action. The major downside to all of these techniques is the relative expertise required to perform regional anesthetics relative to oral, intravenous, and inhalational administration of drug.
The large surface area of the pulmonary alveoli available for exchange with the large volumetric flow of blood found in the pulmonary capillaries makes inhalational administration an extremely attractive method by which to administer drugs.16 New technologies have been developed that can rapidly and predictably aerosolize a wide range of drugs and thus approximate intravenous administration.17 These devices are currently in phase 2 FDA trials.
Once the drug has entered the systemic circulation, it is transported through bulk flow of blood to all of the organs throughout the body. The relative distribution of cardiac output among organ vascular beds determines the speed at which organs are exposed to the drug. The highly perfused core circulatory components—the brain, lungs, heart, and kidneys—receive the highest relative distribution of cardiac output and therefore are the initial organs to reach equilibrium with plasma drug concentrations.4 Drug concentrations then equilibrate with the less well-perfused muscles and liver and then, finally, with the relatively poorly perfused splanchnic vasculature, adipose tissue, and bone.
Whether by passive diffusion or transporter-mediation, drug transport at the capillaries is not usually saturable, so the amount of drug uptake by tissues and organs is limited by the blood flow they receive (i.e., flow-limited drug uptake).
Although the rate of initial drug delivery may depend on the relative blood flow of the organ, the rate of drug equilibration by the tissue depends on the ratio of blood flow to tissue content. Therefore, drug uptake rapidly approaches equilibrium
in the highly perfused but low-volume brain, kidneys, and lungs in a matter of minutes, whereas drug transfer to the less well perfused, intermediate volume muscle tissue may take hours to approach equilibrium, and drug transfer to the poorly perfused, large cellular volumes of adipose tissue does not equilibrate for days.11
Highly lipophilic drugs such as thiopental and propofol rapidly begin to diffuse into the highly perfused brain tissue usually less than a minute after intravenous injection (see Chapter 18). Because of the low tissue volume but high perfusion of the brain, the drug concentration in the cerebral arterial blood rapidly equilibrates, usually within 3 minutes, with the concentration in the brain tissue. As drug continues to be taken up by other tissues with lower blood flows and higher tissue mass, the plasma concentration of the drug continues to decrease rapidly. Once the concentration of drug in the brain tissue is higher than the plasma concentration of drug, there is a reversal of the drug concentration gradient so that the lipophilic drug readily diffuses back into the blood and is redistributed to the other tissues that are still taking up drug.4,18,19 This process continues for each of the organ beds until, ultimately, the adipose tissue will contain the majority of the lipophilic drug that has not been removed from the body by metabolism or excretion. However, after a single bolus of a highly lipophilic drug, the brain's tissue concentration rapidly decreases below therapeutic levels because of redistribution of drug to muscle tissue, which has a larger perfusion than adipose tissue.4,19 Although single, moderate doses of highly lipophilic drugs have a very short CNS duration of action because of redistribution of drug from the CNS to the blood and other, less well-perfused tissues, repeated injections of a drug allows the rapid establishment of significant peripheral tissue concentrations. When the tissue concentrations of a drug are high enough, the decrease in plasma drug concentration below therapeutic threshold becomes solely dependent on drug elimination from the body.20
Besides being excreted unchanged from the body, a drug can be biotransformed (metabolized) into one or more new compounds that are then eliminated from the body. Either mechanism of elimination will decrease the drug concentration in the body such that the concentration will eventually be negligible and therefore unable to produce drug effect.Elimination is the pharmacokinetic term that describes all the processes that remove a drug from the body. Although the liver and the kidneys are considered the major organs of drug elimination, drug metabolism can occur at many other locations that contain active drug-metabolizing enzymes (e.g., pulmonary vasculature, red blood cells) and drug can be excreted unchanged from other organs (e.g., lungs).
Elimination clearance (drug clearance) is the theoretical volume of blood from which drug is completely and irreversibly removed in a unit of time.21 Elimination clearance has the units of flow—[volume per time]. Total drug clearance can be calculated with pharmacokinetic models of blood concentration versus time data.
Most drugs that are excreted unchanged from the body are hydrophilic and therefore readily passed into urine or stool. Drugs that are not sufficiently hydrophilic to be able to be excreted unchanged require modification into more hydrophilic, excretable compounds. Enzymatic reactions that metabolize drugs can be classified into phase I and phase II biotransformation reactions. Phase I reactions tend to transform a drug into one or more polar, and hence potentially excretable compounds. Phase II reactions transform the original drug by conjugating a variety of endogenous compounds to a polar functional group of the drug, making the metabolite even more hydrophilic. Often drugs will undergo a phase I reaction to produce a new compound with a polar functional group that will then undergo a phase II reaction. However, it is possible for a drug to undergo either a phase I reaction alone or a phase II reaction alone.
Phase I Reactions
Phase I reactions may hydrolyze, oxidize, or reduce the parent compound. Hydrolysis is the insertion of a molecule of water into another molecule, which forms an unstable intermediate compound that subsequently splits apart. Thus, hydrolysis cleaves the original substance into two separate molecules. Hydrolytic reactions are the primary way amides, such as lidocaine and other amide local anesthetics, and esters, such as succinylcholine, are metabolized.
Many drugs are biotransformed by oxidative reactions. Oxidations are defined as reactions that remove electrons from a molecule. The common element of most, if not all, oxidations is an enzymatically mediated reaction that inserts a hydroxyl group (OH) into the drug molecule. In some instances, this produces a chemically stable, more polar hydroxylated metabolite. However, hydroxylation usually creates unstable compounds that spontaneously split into separate molecules. Many different biotransformations are affected by this basic mechanism. Dealkylation (removal of a carbon-containing group), deamination (removal of nitrogen-containing groups), oxidation of nitrogen-containing groups, desulfuration, dehalogenation, and dehydrogenation all follow an initial hydroxylation. Hydrolysis and hydroxylation are comparable processes. Both have an initial, enzymatically mediated step that produces an unstable compound that rapidly dissociates into separate molecules.
Some drugs are metabolized by reductive reactions, that is, reactions that add electrons to a molecule. In contrast to oxidations, where electrons are transferred from nicotinamide adenine dinucleotide phosphate (NADPH) to an oxygen atom, the electrons are transferred to the drug molecule. Oxidation of xenobiotics requires oxygen, but reductive biotransformation is inhibited by oxygen, so it is facilitated when the intracellular oxygen tension is low.
Cytochrome P450 Enzymes
The cytochromes P450 (CYP) is the superfamily of constitutive and inducible enzymes that catalyze most phase I biotransformations. CYP3A4 is the single most important enzyme, accounting for 40 to 45% of all CYP-mediated drug metabolism. CYPs are incorporated into the smooth endoplasmic reticulum of hepatocytes and the membranes of the upper intestinal enterocytes in high concentrations. CYPs are also found in the lungs, kidneys, and skin, but in much smaller amounts. CYP isoenzymes oxidize their substrates primarily by the insertion of an atom of oxygen in the form of a hydroxyl group, while another oxygen atom is reduced to water.
Several constitutive CYPs are involved in the production of various endogenous compounds, such as cholesterol, steroid hormones, prostaglandins, and eicosanoids. In addition to the constitutive forms, production of various CYPs can be induced by a wide variety of xenobiotics. CYP drug-metabolizing activity increases after exposure to various exogenous chemicals,
including many drugs. The number and type of CYPs present at any time depends on exposure to different xenobiotics. The CYP system is able to protect the organism from the deleterious effects of accumulation of exogenous compounds because of its two fundamental characteristics—broad substrate specificity and the capability to adapt to exposure to different substances by induction of different CYP isoenzymes. Table 7-1 groups drugs encountered in anesthetic practice according to the CYP isoenzymes responsible for their biotransformation.
Table 7-1 Substrates for Cytochrome P450 (CYP) Isoenzymes Encountered in Anesthesia
Biotransformations can be inhibited if different substrates compete for the drug-binding site on the same CYP member. The effect of two competing substrates on each other's metabolism depends on their relative affinities for the enzyme. Biotransformation of the compound with the lower affinity is inhibited to a greater degree. This is the mechanism by which the H2 receptor antagonist cimetidine inhibits the metabolism of many drugs, including meperidine, propranolol, and diazepam. The newer H2 antagonist ranitidine has a different structure and causes fewer clinically significant drug interactions. Other drugs, notably calcium channel blockers and antidepressants, also inhibit oxidative drug metabolism in humans. This information allows clinicians to predict which combinations of drugs are more likely to lead to clinically significant interactions because of altered drug metabolism by the cytochrome P450 system.
Phase II Reactions
Phase II reactions are also known as conjugation or synthetic reactions. Many drugs do not have a polar chemical group suitable for conjugation, so conjugation occurs only after a phase I reaction. Other drugs, such as morphine, already have a polar group that serves as a “handle” for conjugation, and they undergo these reactions directly. Various endogenous compounds can be attached to parent drugs or their phase I metabolites to form different conjugation products. These endogenous substrates include glucuronic acid, acetate, and amino acids. Mercapturic acid conjugates result from the binding of exogenous compounds to glutathione. Other conjugation reactions produce sulfated or methylated derivatives of drugs or their metabolites. Like the cytochrome P450 system, the enzymes that catalyze phase II reactions are inducible. Phase II reactions produce conjugates that are polar, water-soluble compounds. This facilitates the ultimate excretion of the drug via the kidneys or hepatobiliary secretion. Like CYP, there are different families and superfamilies of the enzymes that catalyze phase II biotransformations.
Genetic Variations in Drug Metabolism
For most enzymes involved in phase I and phase II reactions, there are several biologically available isoforms. Drug metabolism varies substantially among individuals because of variability in the genes controlling the numerous enzymes responsible for biotransformation (see Chapter 6). For most drugs, individual subjects' rates of metabolism have a unimodal distribution. However, distinct subpopulations with different rates of elimination of some drugs have been identified. The resulting multimodal distribution of individual rates of metabolism is known as polymorphism. For example, different genotypes result in either normal, low, or (rarely) absent plasma pseudocholinesterase activity, accounting for the well-known differences in individuals' responses to succinylcholine, which is hydrolyzed by this enzyme. Many drug-metabolizing enzymes exhibit genetic polymorphism, including CYP and various transferases that catalyze phase II reactions. However, none of these have a sex-related difference.
Chronologic Variations in Drug Metabolism
The activity and capacity of the CYP enzymes increase from subnormal levels in the fetal and neonatal period to reach normal levels at about 1 year of age. Although age is a covariate in mathematical models of drug elimination, it is not clear if these changes are related to chronologic changes in organ
function (age-related organ dysfunction) or a decrease in CYP levels with increasing age. In contrast, it is clear that the neonate has a limited ability to perform phase II conjugation reactions, but after normalizing phase II activity over the initial year of life, advanced age does not affect the capacity to perform phase II reactions.
Renal Drug Clearance
The primary role of the kidneys in drug elimination is to excrete into urine the unchanged, hydrophilic drugs, and the hepatic-derived metabolites from phase I and phase II reactions of lipophilic drugs. The passive elimination of drugs by passive glomerular filtration is a very inefficient process—any significant degree of binding of the drug to plasma proteins or erythrocytes will decrease the renal clearance below the glomerular filtration rate of 20% of renal blood flow. In order to make renal elimination more efficient, discrete active transporters of organic acids and bases exist in the proximal renal tubular cells. Although these transporters are saturable, they allow for the renal clearance of drugs to approach the entire renal blood flow.
In reality, renal drug clearance of actively secreted drugs can be inhibited by both passive tubular reabsorption of lipophilic drugs and active, carrier-mediated tubular reabsorption of hydrophilic drugs. Therefore, the small amount of filtered and secreted lipophilic drug is easily reabsorbed in the distal tubules, making the net renal clearance negligible. In contrast, the large amount of filtered and secreted hydrophilic drug can be passively reabsorbed if renal tubular flow decreases substantially (e.g., oliguria) and/or the urine pH favors the un-ionized form of the hydrophilic drug. Because overall renal function is readily estimated by clearance of endogenous creatinine, renal drug clearance, even for drugs eliminated primarily by tubular secretion, depends on renal function. Therefore, in patients with acute and chronic causes of decreased renal function, including age, low cardiac output states, and hepatorenal syndrome, drug dosing must be altered in order to avoid accumulation of parent compounds and potentially toxic metabolites (e.g., lidocaine, meperidine; Table 7-2; see Chapter 52).
Hepatic Drug Clearance
Drug elimination by the liver depends on the intrinsic ability of the liver to metabolize the drug (intrinsic clearance, Cll), and the amount of drug available to diffuse into the liver. Many types of mathematical models have been developed to attempt to accurately model the relationship between hepatic artery blood flow, portal artery blood flow, intrinsic clearance, and drug binding to plasma proteins.22,23 According to these models, the unbound concentration of drug in the hepatic venous blood (Cv) is in equilibrium with the drug within the liver that is available for elimination. These models also make the assumption that all of the drugs delivered to the liver are available for elimination and that the elimination is a first-order process—a constant fraction of the available drug is eliminated per unit time. The fraction of the drug removed from the blood passing through the liver is the hepatic extraction ratio, E:
Table 7-2 Drugs with Significant Renal Excretion Encountered in Anesthesiology
where Ca is the mixed hepatic arterial–portal venous drug concentration and Cv is the mixed hepatic venous drug concentration. The total hepatic drug clearance, ClH, is:
where Q is hepatic blood flow. Therefore, hepatic clearance is a function of hepatic blood flow and the ability of the liver to extract drug from the blood.
The ability to extract drug depends on the activity of drug-metabolizing enzymes and the capacity for hepatobiliary excretion—the intrinsic clearance of the liver (Cll).
Intrinsic clearance represents the ability of the liver to remove drug from the blood in the absence of any limitations imposed by blood flow or drug binding. The relationship of total hepatic drug clearance to the extraction ratio and intrinsic clearance, Cll, is:
The right-hand side of Equation 7-3 indicates that if intrinsic clearance is very high (many times larger than hepatic blood flow, Cll >> Q), total hepatic clearance approaches hepatic blood flow. On the other hand, if intrinsic clearance is very small (Q + Cll ≈ Q), hepatic clearance will be similar to intrinsic clearance. These relationships are shown in Figure 7-1.
Thus, hepatic drug clearance and extraction are determined by two independent variables, intrinsic clearance and hepatic blood flow. Changes in either will change hepatic clearance. However, the extent of the change depends on the initial relationship between intrinsic clearance and hepatic blood flow, according to the nonlinear relationship:
If the initial intrinsic clearance is small relative to hepatic blood flow, then the extraction ratio is also small, and Equation 7-4 reduces to the following relationship:
Equation 7-4a indicates that doubling intrinsic clearance will produce an almost proportional increment in the extraction ratio, and, consequently, hepatic elimination clearance (Fig. 7-1, inset). However, if intrinsic clearance is much greater than hepatic blood flow, Equation 7-4 reduces to the following relationship:
Equation 7-4b demonstrates that the extraction ratio is independent of intrinsic clearance and therefore a change in
intrinsic clearance has a negligible effect on the extraction ratio and hepatic drug clearance (Fig. 7-1). In nonmathematical terms, high intrinsic clearance indicates efficient hepatic elimination. It is hard to enhance an already efficient process, whereas it is relatively easy to improve on inefficient drug clearance because of low intrinsic clearance.
Figure 7-1. The relationship between hepatic extraction ratio (E, right y-axis), intrinsic clearance (Cll, x-axis), and hepatic clearance (ClH, left y-axis) at the normal hepatic blood flow (Q) of 1.5 L/min. For drugs with a high intrinsic clearance (Cll >> Q), increasing intrinsic clearance has little effect on hepatic extraction and total hepatic clearance and total hepatic clearance approaches hepatic blood flow. In contrast, if the intrinsic clearance is small (Cll ≤ Q), the extraction ratio is similar to the intrinsic clearance (inset). (Adapted from Wilkinson GR, Shand DG: A physiologic approach to hepatic drug clearance. Clin Pharmacol Ther 1975; 18: 377.)
For drugs with a high extraction ratio and a high intrinsic clearance, hepatic elimination clearance is directly proportional to hepatic blood flow. Therefore, any manipulation of hepatic blood flow will be directly reflected by a proportional change in hepatic elimination clearance (Fig. 7-2). In contrast, when the intrinsic clearance is low, changes in hepatic blood flow produce inversely proportional changes in extraction ratio (Fig. 7-3), and therefore the hepatic elimination clearance is essentially independent of hepatic blood flow and exquisitely related to intrinsic clearance (Fig. 7-3). Therefore, classifying drugs as having either low, intermediate, or high extraction ratios (Table 7-3), allows predictions to be made on how intrinsic hepatic clearance and hepatic blood flow effect hepatic elimination clearance. This allows gross adjustments to be made in hepatically metabolized drug dosing to avoid excess accumulation of drugs (decreased hepatic elimination without dose adjustment) or subtherapeutic dosing strategies (increased hepatic elimination without dose adjustment).
Figure 7-2. The relationship between liver blood flow (Q, x-axis) and hepatic clearance (ClH, y-axis) for different values of intrinsic clearance (Cll). When the intrinsic clearance is low, hepatic elimination clearance is independent of liver blood flow—the drug elimination is limited by the capacity of the liver to metabolize the drug (i.e., the intrinsic clearance). In contrast, as intrinsic clearance increases, the hepatic elimination becomes more dependent on hepatic blood flow—the liver is able to metabolize all of the drug that it is exposed to and therefore only limited by the amount of drug that is delivered to the liver (i.e., flow limited metabolism).
Pharmacologic and pathologic manipulations of cardiac output with its consequences on hepatic/splanchnic blood flow
and renal blood flow are important covariates when designing drug-dosing strategies.24 As previously detailed, in states where cardiac output is decreased (e.g., heart failure, shock, spinal anesthesia), high extraction-rate drugs will have a decrease in hepatic elimination, whereas low extraction-rate drugs will have minimal change in clearance.25,26 In contrast, autoregulation of renal blood flow maintains a relatively constant renal elimination clearance until low urine output states eventually allow increased reabsorption of drugs from the distal tubules.27
Table 7-3 Classification of Drugs Encountered in Anesthesiology According to Hepatic Extraction Ratios
Figure 7-3. The relationship between liver blood flow (Q, x-axis) and hepatic extraction ratio (E, y-axis) for different values of intrinsic clearance (Cll). When the intrinsic clearance is low, increases in hepatic blood flows cause a decrease in the extraction ratio because the liver has limited metabolic capabilities. In contrast, when the intrinsic clearance is high, the extraction ratio is essentially independent of hepatic blood flow because the liver's ability to eliminate drug is well above the amount of drug provided by normal hepatic blood flow.
The concentration of drug at its site or sites of action is the fundamental determinant of a drug's pharmacologic effects. Although the blood is rarely the site of action of drug effect, the tissue drug concentration of an individual organ is a function of the blood flow to the organ, the concentration of drug in the arterial inflow of the organ, the capacity of the organ to take up drug, and the diffusivity of the drug between the blood and the organ.
Physiologic versus Compartment Models
Initial pharmacokinetic models of intravenous and inhalational anesthetics used physiologic or perfusion models.4 In these models, body tissues were lumped into groups that had similar distribution of cardiac output and capacity for drug uptake. Highly perfused tissues with a large amount of blood flow per volume of tissue were classified as the vessel-rich group, whereas tissues with a balanced amount of blood flow per volume of tissue were classified as the lean tissue group or fast tissue group. The vessel-poor group (slow tissue group) was composed of tissues that had a large capacity for drug uptake but a limited tissue perfusion. Although identification of the exact organs that made up each tissue group was not possible from the mathematical model, it was apparent that the highly perfused tissues were composed of the brain, lungs, kidneys, and a subset of muscle, the fast equilibrating tissue would be consistent with the majority of muscle and some of the splanchnic bed (e.g., liver), and the slowly equilibrating tissues contained the majority of the adipose tissue and the remainder of the splanchnic organs.
Based on the computationally and experimentally intense physiologic models, Price4 and Price et al.18 were able to demonstrate that awakening after a single dose of thiopental was primarily a result of redistribution of thiopental from the brain to the muscle with little contribution by distribution to less well-perfused tissues or drug metabolism. This fundamental concept of redistribution applies to all lipophilic drugs and was not delineated until an accurate pharmacokinetic model had been constructed.
Perfusion-based physiologic pharmacokinetic models have provided significant insights into how physiologic, pharmacologic, and pathologic distribution of cardiac output can effect drug distribution and elimination.28,29 However, verification of the predictions of these models requires measurement of drug concentrations in many different tissues, which is experimentally inefficient and destructive to the system. Therefore, simpler mathematical models have been developed. In these models, the body is composed of one or more compartments. Drug concentrations in the blood are used to define the relationship between dose and the time course of changes in the drug concentration. The compartments of the compartmental pharmacokinetic models cannot be equated with the tissue groups that make up physiologic pharmacokinetic models because the compartments are theoretical entities that are used to mathematically characterize the blood concentration profile of a drug. These models allow the derivation of pharmacokinetic parameters that can be used to quantify drug distribution and elimination—volume of distribution, clearance, and half-lives.
Although the simplicity of compartmental models, compared with physiologic pharmacokinetic models, has its advantages, it also has some disadvantages. For example, cardiac output is not a parameter of compartmental models, and compartmental models therefore cannot be used to predict directly the effect of cardiac failure on drug disposition.30However, compartmental pharmacokinetic models can still quantify the effects of reduced cardiac output on the disposition of a drug if a group of patients with cardiac failure is compared with a group of otherwise healthy subjects.
The discipline of pharmacokinetics is, to the despair of many, mathematically based. In the succeeding sections, formulas are used to illustrate the concepts needed to understand and interpret pharmacokinetic studies. Readers are encouraged to concentrate on the concepts, not the formulas.
Rate Constants and Half-Lives
The disposition of most drugs follows first-order kinetics. A first-order kinetic process is one in which a constant fraction of the drug is removed during a finite period of time regardless of the drug amount or concentration. This fraction is equivalent to the rate constant of the process. Rate constants are usually denoted by the letter k and have units of “inverse time,” such as min-1 or h-1. If 10% of the drug is eliminated per minute, then the rate constant is 0.1 min-1. Because a constant fraction is removed per unit of time in first-order kinetics, the absolute amount of drug removed is proportional to the concentration of the drug. It follows that, in first-order kinetics, the rate of change of the amount of drug at any given time is proportional to the concentration present at that time. When the concentration is high, more drugs will be removed than when it is low. First-order kinetics apply not only to elimination, but also to absorption and distribution. Rather than using rate constants, the rapidity of pharmacokinetic processes is often described with half-lives—the time required for the concentration to change by a factor of 2. Half-lives are
calculated directly from the corresponding rate constants with this simple equation:
Thus, for a rate constant (k) of 0.1 min-1
the half-life is 6.93 minutes. The half-life of any first-order kinetic process, including drug absorption, distribution, and elimination, can be calculated. First-order processes asymptotically approach completion because a constant fraction of the drug, not an absolute amount, is removed per unit of time. However, after five half-lives, the process will be almost 97% complete (Table 7-4). For practical purposes, this is essentially 100% and therefore there is a negligible amount of drug remaining in the body.
Volume of Distribution
The volume of distribution quantifies the extent of drug distribution. The physiologic factor that governs the extent of drug distribution is the overall capacity of tissues versus the capacity of blood for that drug. Overall tissue capacity for uptake of a drug is in turn a function of the total mass of the tissues into which a drug distributes and their average affinity for the drug. In compartmental pharmacokinetic models, drugs are envisaged as distributing into one or more “boxes,” or compartments. These compartments cannot be equated directly with specific tissues. Rather, they are hypothetical entities that permit analysis of drug distribution and elimination and description of the drug concentration versus time profile.
The volume of distribution is an “apparent” volume because it represents the size of these hypothetical boxes, or compartments, that are necessary to explain the concentration of drug in a reference compartment, usually called the central or plasma compartment. The volume of distribution, Vd, relates the total amount of drug present to the concentration observed in the central compartment:
If a drug is extensively distributed, then the concentration will be lower relative to the amount of drug present, which equates to a larger volume of distribution. For example, if a total of 10 mg of drug is present and the concentration is 2 mg/L, then the apparent volume of distribution is 5 L. On the other hand, if the concentration was 4 mg/L, then the volume of distribution would be 2.5 L.
Table 7-4 Half-Lives and Percent of Drug Removed
Simply stated, the apparent volume of distribution is a numeric index of the extent of drug distribution that does not have any relationship to the actual volume of any tissue or group of tissues. It may be as small as plasma volume, or, if overall tissue uptake is extensive, the apparent volume of distribution may greatly exceed the actual total volume of the body. In general, lipophilic drugs have larger volumes of distribution than hydrophilic drugs. Because the volume of distribution is a mathematical construct to model the distribution of a drug in the body, the volume of distribution cannot provide any information regarding the actual tissue concentration in any specific real organ in the body. However, this simple mathematical construct provides a useful summary description of the behavior of the drug in the body. In fact, the loading dose of drug required to achieve a target plasma concentration can be easily calculated by rearranging Equation 7-7 as follows:
Based on this equation, it is clear that an increase in the volume of distribution means that a larger loading dose will be required to “fill up the box” and achieve the same concentration. Therefore any change in state because of changes in physiologic and pathologic conditions can alter the volume of distribution, necessitating therapeutic adjustments.
Total Drug (Elimination) Clearance
Elimination clearance (drug clearance) is the theoretical volume of blood from which drug is completely and irreversibly removed in a unit of time. Elimination clearance has the units of flow—[volume per time]. Total drug clearance can be calculated with pharmacokinetic models of blood concentration versus time data. Drug clearance is often corrected for weight or body surface area, in which case the units are mL/min/kg or mL/min/m2, respectively.
Elimination clearance, Cl, can be calculated from the declining blood levels observed after an intravenous injection, as follows:
If a drug is rapidly removed from the plasma, its concentration will fall more quickly than the concentration of a drug that is less readily eliminated. This results in a smaller area under the concentration versus time curve, which equates to greater clearance (Fig. 7-4).
Figure 7-4. The plasma concentration (y-axis) versus time (x-axis) curve for two drugs that differ only in their elimination clearance. Notice that the areas under the curves are different, signifying that the drug that has the smaller area under the curve is more rapidly eliminated from the body than the drug that has the slower elimination clearance.
Without additional organ-specific data (e.g., urine drug concentration measurements, drug arterial inflow concentration), calculating elimination clearance from compartmental pharmacokinetic models usually does not specify the relative contribution of different organs to drug elimination. Nonetheless, estimation of drug clearance with these models has made important contributions to clinical pharmacology. In particular, these models have provided a great deal of clinically useful information regarding altered drug elimination in various pathologic conditions.
Although the elimination clearance is the pharmacokinetic parameter that best describes the physiologic process of drug elimination (i.e., drug delivery to organs of elimination coupled with the capacity of the organ to eliminate the drug), the pharmacokinetic variable most often reported in textbooks and literature is the elimination half-life of a drug (t1/2β). The elimination half-life is the time during which the amount of drug in the body decreases by 50%. Although this parameter appears to be a simple summary of the physiology of drug elimination, it is actually a complex parameter, influenced by the distribution and the elimination of the drug, as follows:
Therefore, when a physiologic or pathologic perturbation changes the elimination half-life of a drug, it is not a simple reflection of the change in the body's ability to metabolize or eliminate the drug. For example, the elimination half-life of thiopental is prolonged in the elderly; however, the elimination clearance is unchanged and the volume of distribution is increased.31 Therefore, elderly patients need dosing strategies that accommodate for the change in the distribution of the drug rather than a decreased metabolism of the drug. In contrast, in patients with renal insufficiency, the increase in the elimination half-life of pancuronium is due to a simple decrease in renal elimination of the drug and the volume of distribution is unchanged.32
Besides its inability to give insight into the mechanism by which a drug is retained in the body, the elimination half-life is unable to give insight into the time that it takes for a single or a series of repeated drug doses to terminate its effect. Although elimination of drug from the body begins the moment the drug is delivered to the organs of elimination, the rapid termination of effect of a bolus of an intravenous agent is due to redistribution of drug from the brain to the blood and subsequently other tissue (e.g., muscle). Therefore, the effects of most anesthetics have waned long before even one elimination half-life has been completed, making this measure of drug kinetics incapable of providing useful information regarding the duration of action following the administration of intravenous agents. Thus the elimination half-life has limited utility in anesthetic practice.10
Effect of Hepatic or Renal Disease on Pharmacokinetic Parameters
Diverse pathophysiologic changes preclude precise prediction of the pharmacokinetics of a given drug in individual patients with hepatic or renal disease. In addition, liver function tests (e.g., transaminases) are unreliable predictors of the degree of liver function and the remaining metabolic capacity for drug elimination. However, some generalizations can be made. In patients with hepatic disease, the elimination half-life of drugs metabolized or excreted by the liver is often increased because of decreased clearance, and, possibly, increased volume of distribution caused by ascites and altered protein binding.10,33 Drug concentration at steady-state is inversely proportional to elimination clearance. Therefore, when hepatic drug clearance is reduced, repeated bolus dosing or continuous infusion of such drugs as benzodiazepines, opioids, and barbiturates may result in excessive accumulation of drug as well as excessive and prolonged pharmacologic effects. Since recovery from small doses of drugs such as thiopental and fentanyl is largely the result of redistribution, recovery from conservative doses will be minimally affected by reductions in elimination clearance. In patients with renal failure, similar concerns apply to the administration of drugs excreted by the kidneys. It is almost always better to underestimate a patient's dose requirement, observe the response, and give additional drug if necessary.
The physiologic and compartmental models thus far discussed are based on the assumption that drug distribution and elimination are first-order processes. Therefore, their parameters, such as clearance and elimination half-life, are independent of the dose or concentration of the drug. However, the rate of elimination of a few drugs is dose-dependent, or nonlinear.
Elimination of drugs involves interactions with either enzymes catalyzing biotransformation reactions or carrier proteins for transmembrane transport. If sufficient drug is present, the capacity of the drug-eliminating systems can be exceeded. When this occurs, it is no longer possible to excrete a constant fraction of the drug present to the eliminating system, and a constant amount of drug is excreted per unit time. Phenytoin is a well-known example of a drug that exhibits nonlinear elimination at therapeutic concentrations,34 whereas in anesthetic practice, the extremely high doses of thiopental used for cerebral protection can demonstrate zero-order elimination.35 In theory, all drugs are cleared in a nonlinear fashion. In practice, the capacity to eliminate most drugs is so great that this is usually not evident, even with toxic concentrations.
Compartmental Pharmacokinetic Models
Although for most drugs the one-compartment model is an oversimplification, it does serve to illustrate the basic relationships among clearance, volume of distribution, and the elimination half-life. In this model, the body is envisaged as a single homogeneous compartment. Drug distribution after injection is assumed to be instantaneous, so there are no concentration gradients within the compartment. The concentration can decrease only by elimination of drug from the system. The plasma concentration versus time curve for a hypothetical drug with one-compartment kinetics is shown in Figure 7-5. The decrease in plasma concentration (C) with time from the initial concentration (C0) can be characterized by the simple monoexponential function:
With the concentration plotted on a logarithmic scale, the concentration versus time curve becomes a straight line. The slope of the logarithm of concentration versus time is equal to the first-order elimination rate constant (ke).
In the one-compartment model, drug clearance, Cl, is equal to the product of the elimination rate constant, ke, and the volume of distribution:
Combining Equations 6 and 10 yields Equation 7-9 (where ke = kβ):
Therefore, when it is appropriate to make the simplifying assumption of instantaneous mixing of drug into a single compartment, the elimination half-life is inversely proportional to the slope of the concentration time curve. For drugs that require
consideration of their multicompartmental pharmacokinetics, the relationship among clearance, volume of distribution, and the elimination half-life is not a simple linear one such asEquation 7-9. However, the same principles apply. All else being equal, the greater the clearance, the shorter the elimination half-life; the larger the volume of distribution, the longer the elimination half-life. Thus, the elimination half-life depends on two other variables, clearance and volume of distribution, that characterize, respectively, the extent of drug distribution and efficiency of drug elimination.
Figure 7-5. The plasma concentration versus time profile plotted on both linear (dashed line, left y-axis) and logarithmic (dotted line, right y-axis) scales for a hypothetical drug exhibiting one-compartment, first-order pharmacokinetics. Note that the slope of the logarithmic concentration profile is equal to the elimination rate constant (ke) and related to the elimination half-life (t1/2β) as described in Equation 7-9.
For many drugs, a graph of the logarithm of the plasma concentration versus time after an intravenous injection is similar to the schematic graph shown in Figure 7-6. There are two discrete phases in the decline of the plasma concentration. The first phase after injection is characterized by a very rapid decrease in concentration. The rapid decrease in concentration during this “distribution phase” is largely caused by passage of drug from the plasma into tissues. The distribution phase is followed by a slower decline of the concentration owing to drug elimination. Elimination also begins immediately after injection, but its contribution to the drop in plasma concentration is initially much smaller than the fall in concentration because of drug distribution.
Figure 7-6. The logarithmic plasma concentration versus time profile for a hypothetical drug exhibiting two-compartment, first-order pharmacokinetics. Note that the distribution phase has a slope that is significantly larger than that of the elimination phase, indicating that the process of distribution is not only more rapid than elimination of the drug from the body, but also responsible for the majority of the decline in plasma concentration in the several minutes after drug administration. IV, intravenous.
Figure 7-7. A schematic of a two-compartment pharmacokinetic model. See text for explanation.
To account for this biphasic behavior, one must consider the body to be made up of two compartments, a central compartment, which includes the plasma, and a peripheral compartment (Fig. 7-7). This two-compartment model assumes that it is the central compartment into which the drug is injected and from which the blood samples for measurement of concentration are obtained, and that drug is eliminated only from the central compartment. Drug distribution within the central compartment is considered to be instantaneous. In reality, this last assumption cannot be true. However, drug uptake into some of the highly perfused tissues is so rapid that it cannot be detected as a discrete phase on the plasma concentration versus time curve.
The distribution and elimination phases can be characterized by graphic analysis of the plasma concentration versus time curve, as shown in Figure 7-6. The elimination phase line is extrapolated back to time zero (the time of injection). In Figure 7-6, the zero time intercepts of the distribution and elimination lines are points A and B, respectively. The hybrid rate constants, α and β, are equal to the slopes of the two lines, and are used to calculate the distribution and elimination half-lives; α and β are called hybrid rate constantsbecause they depend on both distribution and elimination processes.
At any time after an intravenous injection, the plasma concentration of drugs with two-compartment kinetics is equal to the sum of two exponential terms:
where t = time, Cp(t) = plasma concentration at time t, A = y-axis intercept of the distribution phase line, α = hybrid rate constant of the distribution phase, B = y-axis intercept of the elimination phase line, and β = hybrid rate constant of the elimination phase. The first term characterizes the distribution phase and the second term characterizes the elimination phase. Immediately after injection, the first term represents a much larger fraction of the total plasma concentration than the second term. After several distribution half-lives, the value of the first term approaches zero, and the plasma concentration is essentially equal to the value of the second term (see Fig. 7-6).
Figure 7-8. A schematic of a three-compartment pharmacokinetic model. See text for details.
In multicompartmental models, the drug is initially distributed only within the central compartment. Therefore, the initial apparent volume of distribution is the volume of the central compartment. Immediately after injection, the amount of drug present is the dose, and the concentration is the extrapolated concentration at time t = 0, which is equal to the sum of the intercepts of the distribution and elimination lines. The volume of the central compartment, V1, is calculated by modifying Equation 7-7:
The volume of the central compartment is important in clinical anesthesiology because it is the pharmacokinetic parameter that determines the peak plasma concentration after an intravenous bolus injection. Hypovolemia, for example, reduces the volume of the central compartment. If doses are not correspondingly reduced, the higher plasma concentrations will increase the incidence of adverse pharmacologic effects.
Immediately after intravenous injection, all of the drug is in the central compartment. Simultaneously, three processes begin. Drug moves from the central to the peripheral compartment, which also has a volume, V2. This intercompartmental transfer is a first-order process, and its magnitude is quantified by the rate constant k12. As soon as drug appears in the peripheral compartment, some passes back to the central compartment, a process characterized by the rate constant k21. The transfer of drug between the central and peripheral compartments is quantified by the distributional or intercompartmental clearance:
The third process that begins immediately after administration of the drug is irreversible removal of drug from the system via the central compartment. As in the one-compartment model, the elimination rate constant is ke, and elimination clearance is:
The rapidity of the decrease in the central compartment concentration after intravenous injection depends on the magnitude of the compartmental volumes, the intercompartmental clearance, and the elimination clearance.
At equilibrium, the drug is distributed between the central and the peripheral compartments, and by definition, the drug concentrations in the compartments are equal. Therefore, the ultimate volume of distribution, termed the volume of distribution at steady-state (Vss), is the sum of V1 and V2. Extensive tissue uptake of a drug is reflected by a large volume of the peripheral compartment, which, in turn, results in a large Vss. Consequently, Vss can greatly exceed the actual volume of the body.
As in the single-compartment model, in multicompartment models the elimination clearance is equal to the dose divided by the area under the concentration versus time curve. This area, as well as the compartmental volumes and intercompartmental clearances, can be calculated from the intercepts and hybrid rate constants, without having to reach steady-state conditions.
After intravenous injection of some drugs, the initial, rapid distribution phase is followed by a second, slower distribution phase before the elimination phase becomes evident. Therefore, the plasma concentration is the sum of three exponential terms:
where t = time, Cp(t) = plasma concentration at time t, A = intercept of the rapid distribution phase line, α = hybrid rate constant of the rapid distribution phase, B = intercept of the slower distribution phase line, β = hybrid rate constant of the slower distribution phase, G = intercept of the elimination phase line, and γ = hybrid rate constant of the elimination phase. This triphasic behavior is explained by a three-compartment pharmacokinetic model (Fig. 7-8). As in the two-compartment model, the drug is injected into and eliminated from the central compartment. Drug is reversibly transferred between the central compartment and two peripheral compartments, which accounts for two distribution phases. Drug transfer between the central compartment and the more rapidly equilibrating, or “shallow,” peripheral compartment is characterized by the first-order rate constants k12 and k21. Transfer in and out of the more slowly equilibrating, “deep” compartment is characterized by the rate constants k13 and k31. In this model, there are three compartmental volumes:V1, V2, and V3, whose sum equals Vss; and three clearances: the rapid intercompartmental clearance, the slow intercompartmental clearance, and elimination clearance.
The pharmacokinetic parameters of interest to clinicians, such as clearance, volumes of distribution, and distribution and elimination half-lives, are determined by calculations analogous to those used in the two-compartment model. Accurate estimates of these parameters depend on accurate characterization of the measured plasma concentration versus time data. A frequently encountered problem is that the duration of sampling is not long enough to define accurately the elimination phase. Similar problems arise if the assay cannot detect low concentrations of the drug. Conversely, samples are sometimes obtained too infrequently following drug administration to be able to characterize the distribution phases accurately.36,37 Whether a drug exhibits two- or three-compartment kinetics is of no clinical consequence.10 In fact, some drugs have two-compartment kinetics in some patients and three-compartment kinetics in others. In selecting a pharmacokinetic model, the most important factor is that it accurately characterizes the measured concentrations.
In general, the model with the smallest number of compartments or exponents that accurately reflects the data is used. However, it is good to consider that the data collected in a particular study may not be reflective of the clinical pharmacologic issues of concern in another situation, making published pharmacokinetic model parameters potentially irrelevant. For instance, new data indicate that hypotension following intravenous administration of drug X is related to peak arterial plasma drug X concentrations
1 minute after injection, but previous pharmacokinetic models are based on venous plasma drug X concentrations beginning 5 minutes after the dose. In this case, the pharmacokinetic models will not be of use in designing dosing regimens for drug X that avoid toxic drug concentrations at 1 minute.10,38,39
Almost all earlier pharmacokinetic studies used two-stage modeling. With this technique, pharmacokinetic parameters were estimated independently for each subject and then averaged to provide estimates of the typical parameters for the population. One problem with this approach is that if outliers are present, averaging parameters could result in a model that does not accurately predict typical drug concentrations. Currently, most pharmacokinetic models are developed using population pharmacokinetic modeling, which has been made feasible because of advances in modeling software and increased computing power. With these techniques, the pharmacokinetic parameters are estimated using all the concentration versus time data from the entire group of subjects in a single stage, using sophisticated nonlinear regression methods. This modeling technique provides single estimates of the typical parameter values for the population.
Noncompartmental (Stochastic) Pharmacokinetic Models
Often investigators performing pharmacokinetic analyses of drugs want to avoid the experimental requirements of a physiologic model—data or empirical estimations of individual organ inflow and outflow concentration profiles and organ tissue drug concentrations are required in order to identify the components of the model.40 Although compartmental models do not assume any physiologic or anatomic basis for the model structure, investigators often attribute anatomic and physiologic function to these empiric models.41 Even if the disciplined clinical pharmacologist avoids overinterpretation of the meaning of compartment models, the simple fact that several competing models can provide equally good descriptions of the mathematical data or that some subjects in a data set may be better fit with a three-compartment model rather than the two-compartment model that provides the best fit for the other data set subjects leads many to question whether there is a true best model architecture for any given drug. Therefore, some investigators choose to employ mathematical techniques to characterize a pharmacokinetic data set that attempt to avoid any preconceived notion of structure and yet yield the pharmacokinetic parameters that summarize drug distribution and elimination. These techniques are classified as noncompartmental techniques or stochastic techniques and are similar to the methods based on moment analysis used in process analysis of chemical engineering systems. Although these techniques are often called model-independent, like any mathematical construct, assumptions must be made to simplify the mathematics. The basic assumptions of noncompartmental analysis are that all of the elimination clearance occurs directly from the plasma, the distribution and elimination of drug is a linear and first-order process, and the pharmacokinetics of the system does not vary over the time of the data collection (time-invariant). All of these assumptions are also made in the basic compartmental and most physiologic models. Therefore, the main advantage of the noncompartmental pharmacokinetic methods is that a general description of drug absorption, distribution, and elimination can be made without resorting to more complex mathematical modeling techniques.40
Another appealing facet of noncompartmental analysis is that the parameters that describe drug distribution (volume of distribution at steady-state, Vdss) and drug elimination (elimination clearance, ClE) are analogous to parameters found in other pharmacokinetic techniques. In fact, when properly defined, the estimates of these parameters from the noncompartmental approach and a well-defined compartmental model yield similar values. The main unique parameter of noncompartmental analysis is the mean residence time (MRT), which is the average time a drug molecule spends in the body before being eliminated.42 The MRT unfortunately suffers from the main failings of the elimination half-life derived from compartmental models—not only does it fail to capture the contribution of extensive distribution versus limited elimination to allow a drug to linger in the body, but both parameters also fail to describe the situation in which the drug effect can dissipate by redistribution of drug from the site of action back into blood and then into other, less well-perfused tissues.43
Much of the clinical pharmacology efforts of the late 1980s through 1990s were devoted to applying new computational power of desktop personal computers to deciphering the pharmacokinetics of intravenous anesthetics. However, the premise behind developing models to better characterize and understand the effects of various physiologic and pathologic states on drug distribution and elimination was that the efforts of the previous 30 years had clearly characterized the relationship between a dose of drug and its effect(s). As computational power and drug assay technology grew, it became possible to characterize the relationship between a drug concentration and the associated pharmacologic effect. As a result, pharmacodynamic studies since the 1990s have focused on the quantitative analysis of the relationship between the drug concentration in the blood and the resultant effects of the drug on physiologic processes.
Most pharmacologic agents produce their physiologic effects by binding to a drug-specific receptor, which brings about a change in cellular function. The majority of pharmacologic receptors are cell membrane-bound proteins, although some receptors are located in the cytoplasm or the nucleoplasm of the cell.
Binding of drugs to receptors, like the binding of drugs to plasma proteins, is usually reversible, and follows the law of Mass Action:
This relationship demonstrates that the higher the concentration of free drug or unoccupied receptor, the greater the tendency to form the drug-receptor complex. Plotting the percentage of receptors occupied by a drug against the logarithm of the concentration of the drug yields a sigmoid curve, as shown in Figure 7-9.44
The percentage of receptors occupied by a drug is not equivalent to the percentage of maximal effect produced by the drug. In fact, most receptor systems have more receptors than required to obtain the maximum drug effect.45 The presence of “extra” unoccupied receptors will promote the formation of the drug-receptor complex (law of Mass Action, Equation 7-17), therefore, near-maximal drug effects can occur at very low drug concentrations. This not only allows
extremely efficient responses to drugs, but it provides a large margin of safety—an extremely large number of a drugs receptors must be bound to an antagonist before the drug is unable to produce its pharmacologic effect. For example, at the neuromuscular junction, only 20 to 25% of the postjunctional nicotinic cholinergic receptors need to bind acetylcholine to produce contraction of all the fibers in the muscle whereas 75% of the receptors must be blocked by a nondepolarizing neuromuscular antagonist to produce a significant drop in muscle strength. This accounts for the “margin of safety” of neuromuscular transmission45 (see Chapter 20).
Figure 7-9. A schematic curve of the effect of a drug plotted against dose. In the left panel, the response data are plotted against the dose data on a linear scale. In the right panel, the same response data are plotted against the dose data on a logarithmic scale yielding a sigmoid dose-response curve that is linear between 20 and 80% of the maximal effect.
The binding of drugs to receptors and the resulting changes in cellular function are the last two steps in the complex series of events between administration of the drug and production of its pharmacologic effects. There are two primary schemes by which the binding of an agonist to a receptor changes cellular function: receptor-linked membrane ion channels called ionophores, and guanine nucleotide binding proteins, referred to as G-proteins. The nicotinic cholinergic receptor in the neuromuscular postsynaptic membrane is one example of a receptor-ionophore complex. Binding of acetylcholine opens the cation ionophore, leading to an influx of Na+ ions, propagation of an action potential, and, ultimately, muscle contraction. The β-amino butyric acid (GABA) receptor–chloride ionophore complex is another example of this type of effector mechanism. Binding of either endogenous neurotransmitters (GABA) or exogenous agonists (benzodiazepines and intravenous anesthetics) increases Cl- conductance, which hyperpolarizes the neuron and decreases its excitability. Adrenergic receptors are the prototypical G protein coupled receptors. G proteins change the intracellular concentrations of various so-called second messengers, such as Ca2+ and cyclic AMP in order to transducer their signal and produce modify cellular behavior (see Chapter 15).
Desensitization and Down-Regulation of Receptors
Receptors are not static entities. Rather, they are dynamic cellular components that adapt to their environment. Prolonged exposure of a receptor to its agonist leads to desensitization; subsequent doses of the agonist will produce lower maximal effects. With sustained elevation of the cytosolic second messengers downstream of the G-proteins, pathways to prevent further G protein signaling are activated. Phosphorylation by G-protein receptor kinases and arrestin-mediated blockage of the coupling site needed to form the active heterotrimeric G-protein complex prevents G protein-coupled receptors from becoming active. Arrestins and other cell membrane proteins can tag receptors that have sustained activity so that these non–G protein receptors are internalized and sequestered so they are no longer accessible to agonists. Similar mechanisms will prevent the trafficking of stored receptors to the cell membrane. The combined increased rate of internalization and decreased rate of replenishing of receptor results in down-regulation—a decrease in the total number of receptors. Signals that produce down-regulation with sustained receptor activation are essentially reversed in the face of constant receptor inactivity. Therefore, chronically denervated neuromuscular junctions just like cardiac tissue constantly bathed with adrenergic antagonists will both up-regulate the specific receptors in an attempt to produce a signal in the face of lower concentrations of agonists.
Agonists, Partial Agonists, and Antagonists
Drugs that bind to receptors and produce an effect are called agonists. Drugs may be capable of producing the same maximal effect (EMAX), although they may differ in concentration that produces the effect (i.e., potency). Agonists that differ in potency but bind to the same receptors will have parallel concentration-response curves (curves A and B in Fig. 7-10). Differences in potency of agonists reflect differences in affinity for the receptor. Partial agonists are drugs that are not capable of producing the maximal effect, even at very high concentrations (curve C in Fig. 7-10).
Compounds that bind to receptors without producing any changes in cellular function are referred to as antagonists— antagonists blocking the active binding site(s) inhibit agonist binding to the receptors. Competitive antagonists bind reversibly to receptors, and their blocking effect can be overcome by high concentrations of an agonist (i.e., competition). Therefore, competitive antagonists produce a parallel shift in the dose-response curve, but the maximum effect is not altered (see curves A and B in Fig. 7-10). Noncompetitive antagonists bind irreversibly to receptors. This has the same effect as reducing the number of receptors and shifts the dose-response curve downward and to the right, decreasing both the slope and the maximum effect (curves A and C in Fig. 7-10). The effect of noncompetitive antagonists is reversed only by synthesis of new receptor molecules.
Agonists produce a structural change in the receptor molecule that initiates changes in cellular function. Partial agonists may produce a qualitatively different change in the receptor, whereas antagonists bind without producing a change in the receptor that results in altered cellular function. The underlying mechanisms by which different compounds that bind to the same receptor act as agonists, partial agonists, or antagonists are not fully understood.
Figure 7-10. Schematic pharmacodynamic curves, with dose or concentration on the x-axis and effect or receptor occupancy on the y-axis, that illustrate agonism, partial agonism, and antagonism. Drug A produces a maximum effect, EMAX, and a 50% of maximal effect at dose or concentration E50,A. Drug B, a full agonist, can produce the maximum effect, EMAX; however, it is less potent (E50,B > E50,A). Drug C, a partial agonist, can only produce a maximum effect of approximately 50% EMAX. If a competitive antagonist is given to a patient, the dose response for the agonist would shift from curve A to curve B. Although the receptors would have the same affinity for the agonist, the presence of the competitor would necessitate an increase in agonist in order to produce an effect. In fact, the agonist would still be able to produce a maximal effect if a sufficient overdose was given to displace the competitive antagonist. However, the competitive antagonist would not change the binding characteristics of the receptor for the agonist and so curve B is simply shifted to the right but remains parallel to curve A. In contrast, if a noncompetitive antagonist binds to the receptor, the agonist would no longer be able to produce a maximal effect, no matter how much of an overdose is administered (curve C).
Dose-response studies determine the relationship between increasing doses of a drug and the ensuing changes in pharmacologic effects. Schematic dose-response curves are shown inFigure 7-9, with the dose plotted on both linear and logarithmic scales. There is a curvilinear relationship between dose and the intensity of response. Low doses produce little pharmacologic effect. Once effects become evident, a small increase in dose produces a relatively large change in effect. At near-maximal response, large increases in dose produce little change in effect. Usually the dose is plotted on a logarithmic scale (see Fig. 7-9, right panel), which demonstrates the linear relationship between the logarithm of the dose and the intensity of the response between 20 and 80% of the maximum effect.
Acquiring the pharmacologic effect data from a population of subjects exposed to a variety of doses of a drug provides four key characteristics of the drug dose-response relationship: potency, drug-receptor affinity, efficacy, and population pharmacodynamic variability. The potency of the drug—the dose required to produce a given effect—is usually expressed as the dose required to produce a given effect in 50% of subjects, the ED50. The slope of the curve between 20 and 80% of the maximal effect indicates the rate of increase in effect as the dose is increased and is a reflection of the affinity of the receptor for the drug. The maximum effect is referred to as the efficacy of the drug. Finally, if curves from multiple subjects are generated, the variability in potency, efficacy, and the slope of the dose-response curve can be estimated.
The dose needed to produce a given pharmacologic effect varies considerably, even in “normal” patients. The patient most resistant to the drug usually requires a dose two- to threefold greater than the patient with the lowest dose requirements. This variability is caused by differences among individuals in the relationship between drug concentration and pharmacologic effect, superimposed on differences in pharmacokinetics. Dose-response studies have the disadvantage of not being able to determine whether variations in pharmacologic response are caused by differences in pharmacokinetics, pharmacodynamics, or both.
The onset and duration of pharmacologic effects depend not only on pharmacokinetic factors but also on the pharmacodynamic factors governing the degree of temporal disequilibrium between changes in concentration and changes in effect. The magnitude of the pharmacologic effect is a function of the amount of drug present at the site of action, so increasing the dose increases the peak effect. Larger doses have a more rapid onset of action because pharmacologically active concentrations at the site of action occur sooner. Increasing the dose also increases the duration of action because pharmacologically effective concentrations are maintained for a longer time.
Ideally, the concentration of drug at its site of action should be used to define the concentration-response relationship. Unfortunately, these data are rarely available, so the relationship between the concentration of drug in the blood and pharmacologic effect is studied instead. This relationship is easiest to understand if the changes in pharmacologic effect that occur during and after an intravenous infusion of a hypothetical drug are considered. If a drug is infused at a constant rate, the plasma concentration initially increases rapidly and asymptotically approaches a steady-state level after approximately five elimination half-lives have elapsed (Fig. 7-11). The effect of the drug initially increases very slowly, then more rapidly, and eventually also reaches a steady state. When the infusion is discontinued, indicated by point C in Figure 7-11, the plasma concentration immediately decreases because of drug distribution and elimination. However, the effect stays the same for a short period, and then also begins to decrease;
there is always a time lag between changes in plasma concentration and changes in pharmacologic response. Figure 7-11 also demonstrates that the same plasma concentration is associated with different responses if the concentration is changing. At points A and B in Figure 7-11, the plasma concentrations are the same, but the effects at each time differ. When the concentration is increasing, there is a concentration gradient from blood to the site of action. When the infusion is discontinued, the concentration gradient is reversed. Therefore, at the same plasma concentration, the concentration at the site of action is higher after, compared with during, the infusion. This is associated with a correspondingly greater effect.
Figure 7-11. The changes in plasma drug concentration (Cp) and pharmacologic effect during and after an intravenous infusion. See text for explanation. (Reprinted with permission from Stanski DR, Sheiner LB. Pharmacokinetics and pharmacodynamics of muscle relaxants. Anesthesiology 1979; 51: 103.)
In theory, there must be some degree of temporal disequilibrium between plasma concentration and drug effect for all drugs with extravascular sites of action. However, for some drugs, the time lag may be so short that it cannot be demonstrated. The magnitude of this temporal disequilibrium depends on several factors:
1. The perfusion of the organ on which the drug acts
2. The tissue:blood partition coefficient of the drug
3. The rate of diffusion or transport of the drug from the blood to the cellular site of action
4. The rate and affinity of drug–receptor binding
5. The time required for processes initiated by the drug-receptor interaction to produce changes in cellular function
The consequence of this time lag between changes in concentration and changes in effects is that the plasma concentration will have an unvarying relationship with pharmacologic effect only under steady-state conditions. At steady state, the plasma concentration is in equilibrium with the concentrations throughout the body, and is thus directly proportional to the steady-state concentration at the site of action. Plotting the logarithm of the steady-state plasma concentration versus response generates a curve identical in appearance to the dose-response curve shown in the right panel of Figure 7-9. The Cpss50, the steady-state plasma concentration producing 50% of the maximal response, is determined from the concentration-response curve. Like the ED50, the Cpss50 is a measure of sensitivity to a drug, but the Cpss50 has the advantage of being unaffected by pharmacokinetic variability. Because it takes five elimination half-lives to approach steady-state conditions, it is not practical to determine the Cpss50 directly. For drugs with long elimination half-lives, the pseudoequilibrium during the elimination phase can be used to approximate steady-state conditions because the concentrations in plasma and at the site of action are changing very slowly.
Combined Pharmacokinetic-Pharmacodynamic Models
Integrated pharmacokinetic-pharmacodynamic models fully characterize the relationships among time, dose, plasma concentration, and pharmacologic effect. This is accomplished by adding a hypothetical “effect compartment” (biophase) to a standard compartmental pharmacokinetic model (Fig. 7-12).46,47 Transfer of drug between central compartment and the effect compartment is assumed to be a first-order process, and the pharmacologic effect is assumed to be directly related to the concentration in the biophase. The biophase is a “virtual” compartment, although linked to the pharmacokinetic model, does not actually receive or return drug to the model and, therefore, ensures that the effect-site processes do not influence the pharmacokinetics of the rest of the system. By simultaneously characterizing the pharmacokinetics of the drug and the time course of drug effect, the combined pharmacokinetic-pharmacodynamic model is able to quantify the temporal dissociation between the plasma (central compartment) concentration and effect with the rate constant for equilibration between the plasma and the biophase, ke0. By quantifying the time lag between changes in plasma concentration and changes in pharmacologic effect, these models can also define the Cpss50, even without steady-state conditions. These models have contributed greatly to our understanding of factors influencing the response to intravenous anesthetics,48,49,50 opioids,20,51,52,53 and nondepolarizing muscle relaxants47,54,55 in humans.
Figure 7-12. A schematic of a three-compartment pharmacokinetic model with the effect site linked to the central compartment. The rate constant for transfer between the plasma (central compartment) and the effect site, k1e, and the volume of the effect site are both presumed to be negligible to ensure that the effect site does not influence the pharmacokinetic model. The rate constant for drug removal from the effect site, which relates the concentration in the central compartment to the pharmacologic effect, iske0.
The rate of equilibration between the plasma and the biophase, ke0, can also be characterized by the half life of effect site equilibration (T1/2ke0) using the formula:
T1/2ke0 is the time for the effect site concentration to reach 50% of the plasma concentration when the plasma concentration is held constant. For anesthetics with a short T1/2ke0(high ke0), equilibration between the plasma and the biophase is rapid and therefore there is little delay before an effect is reached when a bolus of drug is administered or an infusion of drug is initiated. However, because the decline in the effect site concentration will also depend on the concentration gradient between the effect site and the plasma, drugs that rapidly equilibrate with the biophase may take longer to redistribute away.56 Therefore, the offset of drug effect is more dependent on the pharmacokinetics of the body than on the rapidity of biophase-plasma equilibration.20,56
Taking into account premedication, perioperative antibiotics, intravenous agents used for induction or maintenance, inhalational anesthetics, opioids, muscle relaxants, the drugs used to restore neuromuscular transmission, and postoperative
analgesics, 10 or more drugs may be given for a relatively “routine” anesthetic. Consequently, thorough understanding of the mechanisms of drug interactions and knowledge of specific interactions with drugs used in anesthesia are essential to the safe practice of anesthesiology (see Chapter 22). Indeed, anesthesiologists often deliberately take advantage of drug interactions. For example, moderate to high doses of opioid are often used to decrease the amount of volatile anesthetic required to provide immobility and hemodynamic stability to surgical incision (e.g., MACa and MACBARb), thereby avoiding the side effects of higher concentrations of inhaled anesthetics (e.g., vasodilation, prolonged awakening; seeChapter 17).
Drug interactions because of physicochemical properties can occur in vitro. Mixing acidic drugs, such as thiopental, and basic drugs, such as opioids or muscle relaxants, results in the formation of insoluble salts that precipitate. Another type of in vitro reaction is absorption of drugs by plastics. Examples include the uptake of nitroglycerin by polyvinyl chloride infusion sets and the absorption of fentanyl by the apparatus used for cardiopulmonary bypass.
Drugs can alter each other's absorption, distribution, and elimination. Drugs like ranitidine, which alters gastric pH, and metoclopramide, which speeds gastric emptying, alter absorption from the gastrointestinal tract. Vasoconstrictors are added to local anesthetic solutions to prolong their duration of action at the site of injection and to decrease the risk of systemic toxicity from rapid absorption.
Drugs that inhibit or induce the enzymes that catalyze biotransformation reactions can affect clearance of other concomitantly administered drugs. For example, the anticonvulsant phenytoin shortens the duration of action of the nondepolarizing neuromuscular junction blocking agents by inducing CYP and therefore increasing elimination clearance of the drug.55 Clearance can also be affected by drug-induced changes in hepatic blood flow. Drugs that are cleared by the kidneys and have similar physicochemical characteristics compete for the transport mechanisms involved in renal tubular secretion.
Pharmacodynamic interactions fall into two broad classifications. Drugs can interact, either directly or indirectly, at the same receptors. Opioid antagonists directly displace opioids from opiate receptors. Cholinesterase inhibitors indirectly antagonize the effects of neuromuscular blockers by increasing the amount of acetylcholine, which displaces the blocking drug from nicotinic receptors. Pharmacodynamic interactions can also occur if two drugs affect a physiologic system at different sites.57,58 Hypnotics and opioids, each acting on their own specific receptors, appear to interact synergistically.59 The pharmacodynamic interaction between two drugs can be characterized using response surface models.60,61,62,63,64,65The three-dimensional models are useful in delineating the concentration pairs of a hypnotic (e.g., volatile anesthetic, propofol, midazolam) and an opioid (e.g., remifentanil, alfentanil, fentanyl) that produce adequate anesthesia while minimizing undesired side effects.66 (See “Response Surface Models of Drug-Drug Interactions.”)
Clinical Applications of Pharmacokinetic and Pharmacodynamics to the Administration of Intravenous Anesthetics
Although no new inhaled anesthetics have been synthesized since the 1970s,67 intravenous drugs that act on the CNS continue to be developed. Anesthesiologists have become accustomed to the exquisite control of anesthetic blood (and effect site) concentrations afforded by modern volatile anesthetic agents and their vaporizers, coupled to end-tidal anesthetic gas monitoring. Although pharmacokinetic and pharmacodynamic principles and data have contributed greatly to our understanding of the behavior of intravenous anesthetics, their primary utility and ultimate purpose are to determine optimal dosing with as much mathematical precision and clinical accuracy as possible. In most pharmacotherapeutic scenarios outside anesthesia care, the time scales for onset of drug effect, its maintenance, and its offset are measured in days, weeks, or even years. In such cases, global pharmacokinetic variables (and one-compartment models) such as total volume of distribution (VSS), elimination clearance (Cle), and half-life (t1/2) are sufficient and utilitarian parameters for calculating dose regimens. However, in the operating room and intensive care unit, the temporal tolerances for onset and offset of desired drug effects are measured in minutes.38,39 Consequently, these global variables are insufficient to describe the details of kinetic behavior of drugs in the minutes following intravenous administration. This is particularly true of lipid-soluble hypnotics and opioids that rapidly and extensively distribute throughout the various tissues of the body because distribution processes dominate pharmacokinetic behavior during the time frame of most anesthetics. Additionally, the therapeutic indices of many intravenous anesthetic drugs are small and two-tailed (i.e., an underdose, resulting in awareness, which is a “toxic” effect). Optimal dosing in these situations requires use of all the variables of a multicompartmental pharmacokinetic model to account for drug distribution in blood and other tissues.
It is not easy to intuit the pharmacokinetic behavior of a multicompartmental system by simple examination of the kinetic variables.10 Computer simulation is required to meaningfully interpret dosing or to accurately devise new dosing regimens. In addition, there are several pharmacokinetic concepts that are uniquely applicable to intravenous administration of drugs with multicompartmental kinetics and must be taken into account when administering intravenous infusions.
To achieve similar degrees of control of intravenously administered anesthetic drug concentrations in blood and in the CNS, new technologies aimed at improving intravenous infusion devices, as well as new software to manage the daunting pharmacokinetic principles involved, are needed. This section examines the current state of infusion devices and the pharmacokinetic and pharmacodynamic principles specifically required for precise delivery of anesthetic agents.
Rise to Steady-State Concentration
The drug concentration versus time profile for the rise to steady state is the mirror image of its elimination profile. In a one-compartment model with a decline in concentration versus time that is monoexponential following a single dose, the rise of drug concentration to the steady-state concentration (CSS) is likewise monoexponential during a continuous
infusion. That is, in one elimination half-life an infusion is halfway to its eventual steady-state concentration, in another half-life it reaches half of what remains between halfway and steady state (i.e., 75% of the eventual steady state is reached in two elimination half-lives), and so on for each half-life increment. The equation describing this behavior is:
where Cp(t) = the concentration at time t, k is the rate constant related to the elimination half-life, and t is the time from the start of the infusion. This relationship can also be described by:
in which Cp(n) is the concentration at n half-lives. Equation 7-20 indicates that during a constant infusion, the concentration reaches 90% of CSS after 3.3 half-lives, which is usually deemed close enough for clinical purposes.
However, for a drug such as propofol, which partitions extensively to pharmacologically inert body tissues (e.g., muscle, gut), a monoexponential equation, or single-compartment model, is insufficient to describe the time course of propofol concentrations in the first minutes and hours after beginning drug administration. Instead, a multicompartmental or multiexponential model must be used. With such a model, the picture changes drastically for the plasma drug concentration rise toward steady state. The rate of rise toward steady state is determined by the distribution rate constants to the degree that their respective exponential terms contribute to the total area under the concentration versus time curve. Thus, for the three-compartment model describing the pharmacokinetics of propofol, Equation 7-19 becomes:
in which t = time; Cp(t) = plasma concentration at time; A = coefficient of the rapid distribution phase and α = hybrid rate constant of the rapid distribution phase; B = coefficient of the slower distribution phase, and β = hybrid rate constant of the slower distribution; and G = coefficient of elimination phase and γ = hybrid rate constant of the elimination phase.A + B + G is the sum of the coefficients of all the exponential terms. For most lipophilic anesthetics and opioids, A is typically one order of magnitude greater than B, and B is in turn an order of magnitude greater than G. Therefore, distribution-phase kinetics for intravenous anesthetics have a much greater influence on the time to reach CSS than do elimination-phase kinetics.56
For example, with propofol having an elimination half-life of approximately 6 hours, the simple one-compartment rule in Equation 7-20 tells us that it would take 6 hours from the start of a constant rate infusion to reach even 50% of the eventual steady-state propofol plasma concentration and 12 hours to reach 75%. In contrast, with a full three-compartment propofol kinetic model, Equation 7-21 accurately predicts that 50% of steady state is reached in <30 minutes and 75% will be reached in <4 hours. This example emphasizes the necessity of using multicompartment models to describe the clinical pharmacokinetics of intravenous anesthetics.
Manual Bolus and Infusion Dosing Schemes
Based on a one-compartment pharmacokinetic model, a stable steady-state plasma concentration (Cp,SS) can be maintained by administering an infusion at a rate (I) that is proportional to the elimination of drug from the body (ClE):
However, if the drug was administered only by initiating and maintaining this infusion, it would take one elimination half-time to reach 50% of the target plasma concentration and three times that long to reach 90% of the target plasma concentration. In order to decrease the time until the target plasma concentration is achieved, an initial bolus (loading dose) of drug can be administered that would produce the target plasma concentration:
Although this method is very efficient in achieving and maintaining the target plasma concentration of a drug that instantaneously mixes and equilibrates throughout the tissues of the body (e.g., drugs modeled with a one-compartment pharmacokinetic model), using the steady-state elimination clearance and volume of distribution to calculate the loading dose and maintenance infusion rate will result in plasma drug concentrations that are higher throughout the initial distribution phase (see Fig. 7-13).
Using Equations 7-22 and 7-23 and Vd,SS = 262 L and ClE = 1.7 L/min (for a 50-year-old man who is 178 cm tall and weighs 70 kg from Schnider et al.49), the loading dose and infusion rate of propofol that is needed to achieve a steady-state plasma concentration of 5 µg/mL is 1,300 mg (18 mg/kg) and 120 µg/kg/min. Obviously, the loading dose of propofol is too high, compared with clinically used doses (1 to 2 mg/kg) while the infusion rate appears to be a clinically acceptable dose. The erroneous estimate of the loading dose is because the initial bolus of drug is not instantaneously mixed and equilibrated with the entire volume of tissue that will eventually take up drug. Therefore,
manual dosing strategies for intravenous anesthetics need to be modified to account for the fact that when a bolus of drug is administered, it rapidly mixes and equilibrates with the blood and only a small volume of tissue (e.g., the central compartment), and then will distribute over time into other tissues.
Table 7-5 BETa Scheme to Achieve Cp 5 µg/mL for 120 Minutes
Figure 7-13. A computer simulation of the plasma propofol concentration profile during and after the administration of a single bolus and infusion scheme calculated using the steady-state, one-compartment pharmacokinetic parameters (solid line) and the BET scheme from Table 7-5 (dashed line) to achieve a plasma concentration of 5 mcg/mL. Vd,SS= 262 L and ClE = 1.7 L/min for a 50-year-old man who is 178 cm tall and weighs 70 kg. See text for description of BET scheme.
To design a manual bolus that more precisely achieves the desired target plasma concentration, it is necessary to choose a bolus that is based on the small, initial volume of distribution (Vc). To maintain the target plasma concentration, a series of infusions of decreasing rate can be used that match the elimination clearance and compensates for drug loss from the central to the peripheral compartments during the initial period of extensive drug distribution and the second period of moderate drug distribution. This manual dosing scheme has been termed the BET scheme, where B is the loading bolus dose, E is the infusion to replace drug removed by elimination clearance, and T is a continuously decreasing infusion that compensates for transfer of drug to the peripheral tissues (i.e., distribution).68 An example of a BET scheme for propofol to achieve a target plasma concentration of 5 µg/mL is shown in Table 7-5.
To make the calculations of the various infusion rates required to maintain a target plasma concentration for a drug that follows multicompartment pharmacokinetics, a clinician would need access to a basic computer and the software to perform the appropriate simulations. With the appropriate formulas, this is quite feasible to do on any basic computer with any basic spreadsheet. However, even with more sophisticated pharmacokinetic software (e.g., SAAM II, WinNonLin, RugLoop, Stanpump), this is a time-consuming process that diverts the clinician's attention from the patient. In 1994, Shafer69 introduced an isoconcentration nomogram for propofol that used the rise toward steady state described by a multicompartmental system (Fig. 7-14). This graphical tool allows users to employ concentration-effect, rather than dose-effect, relationships when determining optimal dosing of intravenous anesthetic agents. The nomogram is constructed by calculating the plasma drug concentration versus time curve for a constant-rate infusion from a set of pharmacokinetic variables for a particular drug. From this single simulation, one can readily visualize (and estimate) the rise toward steady-state plasma drug concentration described by the drug's pharmacokinetic model. By simulating a range of potential infusion rates, a series of curves of identical shape are then plotted on a single graph with drug concentrations at any time that are directly proportional to the infusion rate.
By placing a horizontal line at the desired plasma drug concentration (y-axis) the times (x-axis) at which the horizontal intersects the line for a particular infusion rate will represent the times at which the infusion rate should be set to the rate on the intercepting line. In the example shown (see Fig. 7-14) with 25 mcg/kg/min increments, the predicted plasma propofol concentrations remain within 10% of the target from 2 minutes onward with a bias of underestimation. If never allowing the estimated concentration to fall below the target is desired, then the time to decrease to the next lower infusion should be at the midpoint of the subsequent interval. Extending the infusions to the subsequent midpoint times will introduce a maximum overestimation bias of approximately 17% with the illustrated infusion increments (Fig. 7-14). Biases would be increased or decreased by constructing nomograms with larger or smaller infusion increments, respectively.
Figure 7-14. Isoconcentration nomogram for determining propofol infusion rates designed to maintain a desired plasma propofol concentration. This nomogram is based on the pharmacokinetics of Schnider et al. and plotted on a log–log scale to better delineate the early time points. Curved lines represent the plasma propofol concentration versus time plots, resulting from the various continuous infusion rates indicated along the right and upper borders (units in µg/kg/min). A horizontal line is placed at the desired target plasma propofol concentration (3 µg/mL in this case) and vertical lines are placed at each intersection of a curved concentration time plot. The vertical lines indicate the times that the infusion rate should be set to the one represented by the next intersected curve as one moves from left to right along the horizontal line drawn at 3 µg/mL. In this example the infusion rate would be reduced from 300 to 275 µg/kg/min at 2.5 minutes, to 250 µg/kg/min at 3 minutes, to 225 µg/kg/min at 4.5 minutes, and so on until it is turned to 100 µg/kg/min at 260 minutes.
The nomogram can also be used to increase or reduce the targeted plasma propofol concentration. To target a new plasma drug concentration, a new horizontal line can be drawn at the desired concentration. The infusion rate that is closest to the current time intersect is the one that should be used initially, followed by the decremented rates dictated by the subsequent intercept times. For best results when increasing the target concentration, a bolus equal to the product of Vc (the central compartment volume) and the incremental change in concentration should be administered. Likewise, when decreasing the concentration the best strategy is to turn off the infusion for the duration predicted by the applicable context-sensitive decrement time and resume the infusion rate predicted for the current time plus the context-sensitive decrement time. For instance, if after 30 minutes one wishes to decrease the target plasma propofol concentration from 3 µg/mL to 2 µg/mL (a 33% decrement at a time context of 30 minutes), one would shut off the infusion for 1 minute and 10 seconds to let the concentration fall by 33% and then restart at 75 µg/kg/min. The estimated plasma
propofol concentrations from this nomogram-guided dosing scheme are shown in Figure 7-15.
Figure 7-15. Simulated plasma propofol concentration history resulting from the information in the isoconcentration nomogram in Figure 7-14 and extending the times to switch the infusion to the next lower increment to the midpoint of the subsequent time segment (i.e., the switch from 250 to 225 µg/kg/min was at 5 minutes, rather than at 4.5 minutes). Note that for the first 30 minutes, this sequence predicts plasma propofol concentrations that are always slightly above 3 µg/mL (see text). The infusion is stopped at 90 minutes in this case.
Context-Sensitive Decrement Times
During an infusion, drug is taken up by the inert, peripheral tissues.18 Once drug delivery is terminated, recovery occurs when the effect site concentration decreases below a threshold concentration for producing a pharmacologic effect (e.g., MACAWAKE—the concentration where 50% of patients follow commands).56,65 Although the rate of elimination of the drug from the body can give some indication for the time required to reach a subtherapeutic effect site drug concentration, distribution to and from the peripheral tissues also contributes to the time course of decreasing drug concentrations of the central and the effect site. For drugs with multicompartmental kinetics, the elimination half-life will always overestimate the time to recovery from anesthetic drugs. This is best understood by considering the limiting condition of steady state. With a steady-state infusion the amount of drug being infused into the central compartment exactly matches the amount of drug being removed by the eliminating organs, and there is no net transfer between tissue compartments and plasma (central) as their drug concentrations are in equilibrium. When the infusion stops, the elimination clearance rapidly decreases only the central compartment drug concentrations on which it is operating. The compartments thus become “disequilibrated” and drug returns from the tissues to the plasma compartment in amounts determined by the distribution clearances, the concentration gradients, and the size of the peripheral compartment depots. This return of drug from the tissue will gradually slow the rate of decrease in plasma drug concentration until pseudoequilibrium is reached and the process can then proceed at the rate of the elimination half-life. For drugs with large elimination clearances relative to the peripheral drug depot size, the time to reach a concentration half the steady-state concentration (or half-time) will be much shorter than the elimination half-life. Propofol fits this category with an initial half-time of 30 minutes as compared with its half-life of 6 hours even after an infinitely long infusion. For infusions of shorter duration than infinity the tissue depots will contribute drug back to the plasma to a lesser degree, depending on how long the infusion had run, that is, how close to equilibration with the central compartment they were, and the half-times will get progressively shorter until the condition of an infinitely short infusion (bolus dose) is reached.20Therefore, the contribution of redistribution to the rate of decay of the plasma concentration depends on the duration of infusion of a drug. Note that here redistribution describes the drug returning from all tissue compartments, not just from the brain, into plasma as opposed to the previous usage that described redistribution of drug from brain to blood and into inert tissues.
To characterize the contribution of redistribution to the time required to reach a subtherapeutic drug concentration, the duration of infusion must be taken into account. Multicompartment pharmacokinetic models of anesthetic drugs can be used to simulate the time required for a decrease in the plasma or effect site concentration by different percentages after terminating infusions of various durations.20 The time required for the drug concentration of the plasma to decrease by 50% increases as the duration of infusion increases. Once the tissue drug concentrations are completely equilibrated with the plasma, redistribution plays a negligible role in decreasing the plasma concentration, and the time required for a 50% drop in plasma concentration is equal to the elimination half-life. The context-sensitive half-time is defined as the time required for the drug concentration of the plasma to decrease by 50%, where the context is the duration of the infusion.51 The context-sensitive half-time for the common synthetic opioids fentanyl, alfentanil, sufentanil, and remifentanil is illustrated in Figure 7-16.
Although a 50% decrease in plasma concentration is an appealing and comprehensible parameter, larger or smaller decreases in plasma concentrations may be required for recovery from the drug. Simulations show that the time for different percent decreases in plasma concentration is not linear.10,20 Therefore, if a 25% or 75% decrease in plasma concentration is required, simulations must be performed to calculate the context-sensitive 25% decrement time or context sensitive 75% decrement time (Fig. 7-17). In addition, if the concentration of interest is the effect-site concentration rather than the plasma concentration, simulations can be performed to calculate the context-sensitive effect-site decrement time. Finally, if a constant plasma or effect-site concentration is not maintained throughout the delivery of the drug (which is typically the case with manual bolus and infusion schemes and also with varying drug requirements depending on surgical stimulation and so forth), the context-sensitive decrement times are guidelines of recovery rather than an absolute prediction of the
decay in drug concentration. If precise drug administration data are known, it is possible to compute the context-sensitive decrement time for the individual situation or context. Even though the context-sensitive decrement times are limited, this concept has changed the way that intravenous anesthetics are described and has helped foster an increase in accurately and safely administering intravenous anesthetics.
Figure 7-16. The context-sensitive plasma half-time for fentanyl, alfentanil, sufentanil, and remifentanil.
Figure 7-17. The context-sensitive 25%, 50%, and 75% plasma decrement times for fentanyl (A), alfentanil (B), sufentanil (C), and remifentanil (D).
Prior to performing an administering, it is possible to perform the calculations presented here and derive a BET scheme targeted to a predetermined plasma or effect-site concentration. However, in the operating room, once the anesthetic has commenced, without the help of a computer, software, and possibly an assistant, it is laborious and difficult to make any calculations to determine how to adjust the infusion or how to bolus (or stop the infusion) to increase or decrease the target plasma concentration.70 By linking a computer with the appropriate pharmacokinetic model to an infusion pump, it is possible for the physician to enter the desired target plasma concentration of a drug and for the computer to nearly instantaneously calculate the appropriate infusion scheme to achieve this target in a matter of seconds.71 Because drug accumulates at various rates among the various tissues and organs in the body, the computer continually calculates the current drug concentration and adjusts the infusion pump in order to account for the current status of drug uptake, distribution, and elimination. Therefore, the computer-driven BET scheme can in fact control the infusion pump in order to achieve a steady target concentration (Fig. 7-18).
The success of this approach is influenced by the extent to which the drug pharmacokinetic and pharmacodynamic parameters programmed into the computer match those of the particular patient at hand. While this same limitation applies to the more rudimentary (non–target-controlled infusions [TCIs]) dosing done routinely in every clinical setting, we must examine the special ramifications of pharmacokinetic– pharmacodynamic model misspecification with TCI in any discussion of its future importance in the clinical setting.
The mathematical principles governing TCI are actually quite simple. For a computer-control pump to produce and maintain a plasma drug concentration it must first administer a dose equal to the product of the central compartment, V1, and the target concentration (Fig. 7-19). Then for each moment after that, the amount of drug to be administered into the central compartment to maintain the target concentration is equal to drug eliminated from the central compartment plus drug distributed from the central compartment to peripheral compartments minus drug returning to the central compartment
from peripheral compartments. The software keeps track of the estimated drug in each compartment over time and applies the rate constants for intercompartmental drug transfer from the pharmacokinetic model to these amounts to determine drug movement at any given time. It then matches the estimated concentrations to the target concentration at any time to determine the amount of drug that should be infused. The software can also predict future concentrations, usually with the assumption that the infusion will be stopped so that emergence from anesthesia or the dissipation of drug effect will occur optimally according to the context-sensitive decrement time.
Figure 7-18. This is a simulation of a target-controlled infusion in which the plasma concentration is targeted at 5 µg/mL. The solid line represents the predicted plasma propofol concentration of 5 µg/mL, which in theory is attained at time t = 0 and is then maintained by a variable rate infusion. The dashed line is the predicted effect site concentration under the conditions of a constant pseudo–steady-state plasma concentration. Note that 95% of the target concentration is reached in the effect site at approximately 4 minutes.
Because there is a delay or hysteresis between the attainment of a drug concentration in the plasma and the production of a drug effect, it is advantageous to have the mathematics of this delay incorporated into TCI. By adding the kinetics of the effect site it is possible to target effect-site concentrations as would be in keeping with the principle of working as closely to the relevant concentration-effect relationship as possible. A dose scheme that targets concentrations in a compartment remote from the central compartment (i.e., the effect site) has no closed form solution for calculating the infusion rate(s) needed. Instead, the solution is solved numerically and involves some additional concepts that must be considered, namely the time to peak effect, TMAX, and the volume of distribution at peak effect, VDPE. These are discussed later. In principle, targeting the effect site necessitates producing an overshoot in plasma drug concentrations during induction and for subsequent target increases. This is similar in concept to overpressurizing inhaled anesthetic concentrations to achieve a targeted end-tidal concentration. However, unlike the inspiratory limb of an anesthesia circuit, the plasma compartment seems to be closely linked to cardiovascular effects, and large overshoots in plasma drug concentration may produce unwanted side effects.
Figure 7-19. This is a simulation of a target controlled infusion in which the effect-site concentration (Ce) is targeted at 5 µg/mL. The solid line represents the predicted plasma propofol concentration (Cp) that results from a bolus dose, given at time t = 0, that is predicted to purposely overshoot the plasma propofol concentration target until time t = TMAX (1.6 minutes). At TMAX pseudoequilibration between the effect site and the plasma occurs and both concentrations are then predicted to be the same until the target is changed. Note that the effect site attains the target in less than half the time with effect-site targeting compared to the plasma concentration targeting seen in Figure 7-18.
The performance of TCI is influenced by the pharmacokinetic model chosen. Although most modern TCI models, whether they target the plasma or the effect site, seem to be similar in performance: they all produce overshoot for 10 to 20 minutes when increasing the target concentration.36 This is because the dose adjustments made are based on calculations that use a central compartment that ignores the complexity of intravascular mixing, thereby overestimating the central compartment's true volume (VC) and overestimating the rate of transfer to the fast peripheral tissue (ClF) and the size of the peripheral tissue compartment (VF) (Fig. 7-20). The performance of TCI is also influenced by the variance between pharmacokinetic parameters determined from group or population studies and the individual patient. Median
absolute performance errors for fentanyl,72 alfentanil,73 sufentanil,74 midazolam,75,76 and propofol76,77 are in the range of ±30% when literature values for pharmacokinetic parameters are used to drive the TCI device and fall to approximately ±7% when the average kinetics of the test subjects themselves are used.73 Divergence (the percentage change of the absolute performance error) is generally quite low (approximately 1%) when target concentrations remain relatively stable, but increase to nearly 20% when the frequency of concentration steps is as frequent as every 12 minutes.36,77 These data suggest that while a considerable error may exist (±30%) between the targeted drug concentration and the one actually achieved in a patient, the concentration attained will not vary much over time. Thus, incremental adjustments in the target should result in incremental and stable new concentrations in the patient as long as the incremental adjustments are not too frequent.
Figure 7-20. The influence of the misspecification of each of the components of the traditional three-compartment pharmacokinetic models on the prolonged discrepancy (overshoot) between predicted and targeted concentrations with target-controlled infusions (TCIs). The error resulting from elimination clearance was negligible and therefore not illustrated. Notice that the loading dose (based on VC) produces a large amount of error in the initial minutes; however, from 1 to 20 minutes, the deviation from the target concentration is largely due to the overestimation of ClF. The equations listed are for the respective BET infusions of the TCI system. See text for description of BET. (From Avram MJ, Krejcie TC: Using front-end kinetics to optimize target-controlled drug infusions. Anesthesiology 2003; 99: 1078.)
The introduction of the concept of TCIs was first described by Schwilden et al. in early 1980s. Other software systems were developed in North America by groups at Stanford University and Duke University. By the late 1990s a commercially available TCI system for propofol (Diprifusor) was introduced. This greatly increased both anesthesiologists' interest in this mode of delivery and their understanding of the concentration-effect relationships for hypnotics and opioids. In most of the world, devices for delivering propofol by TCI are commercially available from at least three companies (Graseby, Alaris, and Fresenius) with similar performance parameters.78 In the United States, there are still no FDA-approved devices. For investigational purposes, STANPUMPc (developed by Steve Shafer at Stanford University) can be interfaced via an RS232 port to an infusion pump. STANPUMP currently provides pharmacokinetic parameters for 19 different drugs, but has the ability to accept any kinetic model for any drug provided by the user. RUGLOOPd is TCI software (developed by Michel Struys of Ghent University), which is similar to STANPUMP but operates in Windows rather than DOS and is capable of controlling multiple drug infusions simultaneously.
Although the pharmacologic principle of relating a concentration rather than a dose is scientifically sound, few studies have actually attempted to determine whether TCI improves clinical performance or outcome. Only a few limited studies have actually compared manual infusion control versus TCI. Some have shown better control and a more predictable emergence with TCI,78,79 whereas others have simply shown no advantage.80,81
TCI principles continue to be developed beyond the scope of intravenous anesthesia techniques. TCI has been used to provide postoperative analgesia with alfentanil.82,83 In this system, a desired target plasma alfentanil concentration was set in the range of 40 to 100 ng/mL. A demand by the patient automatically increased the target level by 5 ng/mL. Lack of a demand caused the system to gradually reduce the targeted level. The quality of analgesia was judged to be superior to standard morphine patient-controlled analgesia.
Similarly, TCI has been used to provide patient-controlled sedation with propofol.84,85 The TCI was set to 1 µg/mL and a demand by the patient increased the level by 0.2 µg/mL. As with the TCI analgesia system, the lack of a demand caused the system to gradually reduce the targeted plasma propofol concentration. The timing and increment of the decrease were adjusted by the clinician. Over 90% of patients were satisfied with this method of sedation.
Time to Maximum Effect Compartment Concentration
Earlier in this chapter, the delay between attaining a plasma concentration and an effect-site concentration was described (Fig. 7-11). This delay, or hysteresis, is presumed to be a result of transfer of drug between the plasma compartment, VC, and an effect compartment, Ve, as well as the time required for a cellular response. By simultaneously modeling the plasma drug concentration versus time data (pharmacokinetics) and the measured drug effect (pharmacodynamics), an estimate of the drug transfer rate constant, ke0, between plasma and the putative effect site can be estimated.47 However, estimates of ke0, like all rate constants, are model-specific.86,87 That is, ke0 cannot be transported from one set of kinetic parameters determined in one specific pharmacokinetic–pharmacodynamic study to any another set of pharmacokinetic parameters. Likewise, it is not valid to compare estimates of ke0 among studies of the same drug or across different drugs; therefore, one should not be surprised that reported values for ke0 for the same drug vary markedly among studies. The model-independent parameter that characterizes the delay between the plasma and effect site is the time to maximal effect, or TMAX.87 Accordingly, if the TMAX and the pharmacokinetics for a drug are known from independent studies, a ke0 can be estimated by numeric techniques for the independent kinetic set that would produce the known effect-site TMAX.
The concept of a transportable, model-independent parameter that characterizes the kinetics of the effect site is important for robust effect-site–targeted, computer-controlled infusions. This is because there are many more pharmacokinetic studies characterizing a wider variety of patient types and groups in the literature than there are complete pharmacokinetic-pharmacodynamic studies. By making the generally valid assumption that intraindividual differences are small in a drug's rate of effect site equilibration, it is possible with a known TMAX to estimate effect-site kinetics for a drug across a wide variety of patient groups in which only the pharmacokinetics are known. This cannot be done in a valid manner using ke0 or t1/2ke0 alone.86,87
Volume of Distribution at Peak Effect
Although the plasma concentration can be brought rapidly to the targeted drug concentration by administering a bolus dose to the central compartment (C × VC) and then held there by a computer-controlled infusion (Fig. 7-18), the time for the effect site to reach the target concentration will be much longer than TMAX (4 minutes for propofol effect-site concentration to reach 95% of that targeted). It is possible to calculate a bolus dose that will attain the estimated effect site concentration at TMAX without overshoot in the effect site. However, plasma drug concentration will overshoot (Fig. 7-19). This is done by combining the concept of describing drug distribution as an expanding volume of distribution that starts at VC and approaches Vβ (the apparent volume of distribution during the elimination phase) over time with the concept of TMAX .88,89
Volume of distribution over time is calculated by dividing the total amount of drug remaining in the body by the plasma drug concentration at each time, t. The time-dependent volume at the time of peak effect (or TMAX) is VDPE. The product
of the targeted effect-site concentration and VDPE plus the amount lost to elimination in the time to TMAX becomes the proper bolus dose that will attain the target concentration at the effect site as rapidly as possible without overshoot. In practical terms this bolus is given at time t = 0, after which the infusion stops until time t = TMAX. It then resumes infusing drug in its normal “stop loss” manner.
Some software programs for controlling target-controlled infusions include this concept in their algorithms. In the case of the propofol kinetics used to construct the isoconcentration nomogram in Figure 7-14, the pharmacokinetic-pharmacodynamic parameter set of Schnider et al.,49 predicts a TMAX of 1.6 minutes, a VDPE of 16.62 L, and an elimination loss of 23.8% of the dose over 1.6 minutes in a 70-kg man. Thus, the proper propofol bolus for a targeted effect-site propofol concentration of 5 µg/mL is 109 mg. The computer-controlled infusion pump will deliver this dose as rapidly as possible and then begin a targeted infusion for 5 µg/mL at t = 1.6 minutes (see Fig. 7-19).
The term front-end pharmacokinetics refers to the intravascular mixing, pulmonary uptake, and recirculation events that occur in the first few minutes during and after intravenous drug administration.39 These kinetic events and the drug concentration versus time profile that results are important because the peak effect of rapidly acting drugs occurs during this temporal window.17,90,91,92,93 Although it has been suggested that front-end pharmacokinetics be used to guide drug dosing,36 current TCI does not incorporate front-end kinetics into the models from which drug infusion rates are calculated. As previously described, not doing so introduces further error.
TCI relies on pharmacokinetic models that are based on the simplifying assumption of instantaneous and complete mixing within VC. However, the determination of VC is routinely overestimated in most pharmacokinetic studies. Overestimation of VC, when used to calculate TCI infusion rates, results in plasma drug concentrations that overshoot the desired target concentration, especially in the first few minutes after beginning TCI. Furthermore, correct description of drug distribution to tissues depends on an accurate VC estimate, so inaccuracies caused by not taking front-end pharmacokinetics into account may be persistent and result in undershoot as well as overshoot. Simulation indicates that pharmacokinetic parameters derived from studies in which the drug is administered by a short (approximately 2 minutes) infusion better estimate VC and tissue-distribution kinetics than those from a rapid intravenous bolus infusion.36,37 When the latter drug administration method is used, full characterization of the front-end recirculatory pharmacokinetics is required to obtain valid estimates of V for use in TCI.36,37
When a valid, and nearly continuous, measure of drug effect is available, drug delivery can be automatically titrated by feedback control. Such systems have been used experimentally for control of blood pressure,94 oxygen delivery,95 blood glucose,96 neuromuscular blockade,97 and depth of anesthesia.98,99,100,101,102,103,104 A target value for the desired effect measure (the output of the system) is selected and the rate of drug delivery (the input into the system) depends on whether the effect measure is above, below, or at the target value. Thus, the output feeds back and controls the input. Standard controllers (referred to as proportional-integral-derivative [or PID] controllers) adjust drug delivery based on both the integral, or magnitude, of the deviation from target and the rate of deviation, or the derivative.
Under a range of responses, standard PID controllers work quite well. However, they have been shown to develop unstable characteristics in situations in which the output may vary rapidly and widely. Schwilden et al.105 have proposed a controller in which the output (measured response) controls not only the input (drug infusion rate), but also the pharmacokinetic model driving the infusion rate. This is a so-called model-driven or adaptive closed-loop system. Such a system has performed well in clinical trials,99 and in a simulation of extreme conditions it was demonstrated to outperform a standard PID controller.102
Closed-loop systems for anesthesia are the most difficult to design and implement because the precise definition of “anesthesia” remains elusive, as does a robust monitor for “anesthetic depth.”65 Because modification of consciousness must accompany anesthesia, processed electroencephalographic parameters that correlate with level of consciousness, such as the bispectral index, electroencephalographic entropy, and auditory-evoked potentials, make it possible to undertake closed-loop control of anesthesia. There is keen interest in further developing these tools to make them more reliable because advances in pharmacokinetic modeling, including the effect compartment, the implementation of such models into drug-delivery systems, and the creation of adaptive controllers based on these models, have made routine closed-loop delivery of anesthesia imaginable.98 So far it has been difficult to bring a true closed-loop system to market in medical applications because of the regulatory agency hurdles. From a regulatory point of view, an open-loop TCI system is much easier to attain and offers many of the benefits of actual closed-loop systems. Unless there is a regulatory or a design “breakthrough,” closed-loop systems for anesthesia will likely remain in the theoretical and experimental realms.
Response Surface Models of Drug-Drug Interactions
During the course of an operation, the level of anesthetic drug administered is adjusted to ensure amnesia to ongoing events, provide immobility to noxious stimulation, and blunt the sympathetic response to noxious stimulation. Although it is possible to achieve an adequate anesthetic state with a high dose of a sedative-hypnotic alone (i.e., a volatile anesthetic or propofol), the effect-site drug concentration necessary is often associated with excessive hemodynamic depression58 and excessively deep plane of hypnosis that may be associated with long-standing morbidity or mortality.106,107 Therefore, to limit side effects, an opioid and a sedative-hypnotic are administered together. Although the administration of two volatile anesthetics or a volatile anesthetic and propofol produce a net-additive effect, the combination of an opioid and a sedative-hypnotic are synergistic for most pharmacologic effects. By understanding the interactions between the opioids and the sedative-hypnotics, it is possible to select target concentration pairs of the two drugs that produce the desired clinical effect while minimizing unwanted side effects associated with high concentrations of a single drug (e.g., hemodynamic instability, prolonged respiratory depression).
Studies designed to evaluate the pharmacodynamic interactions between an opioid and a sedative-hypnotic have traditionally focused on the effects of adding one or two fixed doses or concentrations of the opioid to several defined concentrations or doses of the sedative-hypnotic.57,58,108,109,110,111,112,113,114,115 Graphical demonstration of these interaction data are most commonly performed
by demonstrating a shift of parallel dose-response curves (Fig. 7-21). An alternative mathematical model is the isobologram—isoeffect curves that show dose combinations that result in equal effect (Fig. 7-22). Isobolographic analysis has the additional benefit of characterizing the interaction between the two drugs as additive, antagonistic, or synergistic (Fig. 7-23), whereas shifts of dose-response curves requires more complex concentrations to determine if the interaction demonstrated by a leftward shift in the curve is more than additive.
Figure 7-21. The effect of adding remifentanil on the concentration-effect curve for sevoflurane-induced analgesia (no hemodynamic response to a 5-second, 50 mA tetanic stimulation in volunteers). Each curve represents the concentration-effect relation for sevoflurane with a fixed effect-site concentration of remifentanil. The leftward shift in the curves indicates that remifentanil decreases the amount of sevoflurane needed to produce adequate analgesia. The changes in the slopes of the concentration-response curves indicate that there is significant pharmacodynamic synergy between sevoflurane-remifentanil. Also note that there is a ceiling effect to this pharmacodynamic interaction—the magnitude of the leftward shift decreases as the remifentanil concentration increases. HR, heart rate; MAC, minimum alveolar concentration. (Adapted from Manyam SC, Gupta DK, Johnson KB, White JL, Pace NL, Westenskow DR, Egan TD: Opioid-volatile anesthetic synergy: A response surface model with remifentanil and sevoflurane as prototypes. Anesthesiology 2006; 105: 267.)
An alternative mathematical model that can fully characterize the complete spectrum of interaction between two drugs for all possible levels of concentration and effects is the response surface model.61,64 The surface morphology of a response surface not only demonstrates whether the interaction is additive, synergistic, or antagonistic, but the model itself can quantitatively describe the degree of interaction between the two drugs. Furthermore, isobolograms can be derived from the projection of the response surface onto the appropriate horizontal effect plane (Fig. 7-24) and concentration-response curves can be derived from taking a vertical slice through a response surface in the plane perpendicular to the fixed-opioid concentration of interest (Fig. 7-24).61,64,65 Therefore, response surface models can be viewed as generalizations of the traditional pharmacodynamic methods of analysis. The major limitation of response surface models is that they require a large number of pharmacodynamic measurements across all possible concentration pair combinations to accurately characterize the entire surface.116 This is most efficiently done in the laboratory setting using volunteers who can be exposed to subtherapeutic (e.g., below the level that guarantees amnesia) and supratherapeutic drug concentration pairs. However, because response surface models characterize the drug concentration pairs that provide adequate anesthesia and also adequate recovery from anesthesia, these models provide information that are not normally available from studies that generate an isobologram from surgical patients.
Figure 7-22. Remifentanil-sevoflurane interaction for sedation (dashed line) and analgesia to electrical tetanic stimulation (solid line) for volunteers. The respective 95% isoboles demonstrate the myriad of target concentration pairs of remifentanil and sevoflurane that have a 95% probability of producing the desired pharmacodynamic end point. (Adapted from Manyam SC, Gupta DK, Johnson KB, White JL, Pace NL, Westenskow DR, Egan TD: Opioid-volatile anesthetic synergy: A response surface model with remifentanil and sevoflurane as prototypes. Anesthesiology 2006; 105: 267.)
Isobolograms and response surface models clearly demonstrate that there are multiple target concentration pairs of an opioid and a sedative-hypnotic that can provide adequate anesthesia—a 95% probability of no hemodynamic response to a noxious stimulus and 95% probability of clinically
adequate sedation.62,63,66 Combining the response surface pharmacodynamic models with pharmacokinetic models allows computer simulations to be performed to identify the target concentration pair of the opioid and the sedative-hypnotic that produces an adequate anesthetic and yet optimizes one or more pharmacodynamic end points, such as the speed of awakening from anesthesia, drug-induced respiratory depression, or drug acquisition costs.59,63 For sevoflurane-remifentanil anesthetics, these types of pharmacokinetic-pharmacodynamic simulations demonstrate the benefit of minimizing the administered dose of even the low solubility volatile anesthetic sevoflurane to near 0.5 MAC to take advantage of the pharmacokinetic efficiency of remifentanil, especially as the duration of anesthesia increases (Fig. 7-25 and Table 7-6).63
Figure 7-23. Isoboles to demonstrate additive (solid line), synergistic (dashed line), and antagonistic (dotted line) interactions between Drug A and Drug B.
Figure 7-24. A response surface model characterizing the remifentanil-sevoflurane interaction for analgesia to electrical tetanic stimulation. The projection of the response surface onto the 50% probability horizontal plane results in the 50% effect isobole while the projection of the response surface onto the 2.5 ng/mL remifentanil effect-site concentration vertical plane results in the sevoflurane concentration-response curve under 2.5 ng/mL of remifentanil. (Adapted from Manyam SC, Gupta DK, Johnson KB, White JL, Pace NL, Westenskow DR, Egan TD: Opioid-volatile anesthetic synergy: A response surface model with remifentanil and sevoflurane as prototypes. Anesthesiology 2006; 105: 267.)
Figure 7-25. The optimal target concentration pairs of remifentanil and sevoflurane to maintain adequate analgesia (95% isobole for analgesia to electrical tetanic stimulation) and result in the most rapid emergence for anesthetics of various durations. For example, for a 2-hour anesthetic, target concentrations of 0.93 vol% sevoflurane and 4.9 ng/mL remifentanil would result in a 5.8-minute time to awakening. As the duration of anesthesia increases, a minimum sevoflurane target concentration of 0.75 vol% is reached. (Adapted from Manyam SC, Gupta DK, Johnson KB, White JL, Pace NL, Westenskow DR, Egan TD: Opioid-volatile anesthetic synergy: A response surface model with remifentanil and sevoflurane as prototypes. Anesthesiology 2006; 105: 267.)
Since World War II, we have moved from characterizing all anesthetics by a dose-response relationship to developing sophisticated models to characterize the synergistic interaction between sedative-hypnotics and opioids and having the physical devices and the computer support to accurately administer drugs to achieve the desired concentrations at the effect site of drug action. The rational selection of drug target concentrations required to achieve adequate anesthesia and minimize side effects (e.g., prolonged awakening, hemodynamic depression) and the methods by which to efficiently achieve those concentration targets with minimal overshoot requires a solid understanding of the clinical pharmacology of anesthetics. As new drugs enter the anesthetic armamentarium, careful characterization of their pharmacokinetic and pharmacodynamic properties will allow them to be safely and appropriately used as part of a balanced anesthetic.65
Table 7-6 Optimal Target Concentration Pairs of Sevoflurane and Remifentanil for Anesthetics 30 to 900 Minutes in Duration
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Editors: Barash, Paul G.; Cullen, Bruce F.; Stoelting, Robert K.; Cahalan, Michael K.; Stock, M. Christine