Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics PDF

2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics SHINJU OBARA AND TALMAGE D. EGAN CHAPTER OUTLINE Historical Perspective Unique Aspects of Anesthetic Pharmacology Anesthesiology Compared With Other Disciplines A Surfing Analogy as a Simple Conceptual Framework Clinical Ph...

2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics SHINJU OBARA AND TALMAGE D. EGAN CHAPTER OUTLINE Historical Perspective Unique Aspects of Anesthetic Pharmacology Anesthesiology Compared With Other Disciplines A Surfing Analogy as a Simple Conceptual Framework Clinical Pharmacology Posology General Schema Pharmacokinetics Pharmacodynamics The Biophase Drug Interactions Pharmacologic Modeling PK-PD Models as Versions of Pharmacologic Reality PK-PD Model Building Methods Limitations in Building & Applying PK-PD Models Early Model Misspecification Stereochemistry Active Metabolites Variability Pharmacologic Simulation Unimportance of Individual PK-PD Model Parameters Importance of PK-PD Model Simulation PK-PD Model Simulation and Anesthesia Posology Bolus Front-End and Back-End Kinetics Infusion Front-End Kinetics Infusion Back-End Kinetics Influence of Dose on Bolus Onset and Offset of Effect Influence of Loading Dose on Infusion Front-End and Back-End Kinetics Influence of Special Populations Influence of a Second Drug on Effect PK-PD Models and Technology Target-Controlled Infusion Emerging Developments PK-PD Advisory Displays Propofol Measurement in Expired Gas Allometric Scaling in Pharmacokinetics T he science broadly referred to as clinical pharmacology is the foundation on which anesthesiologists base their therapeutic decisions, including the rational selection of anesthetics and the formulation of safe and effective dosage regimens. Focusing exclusively on intravenous anesthetics, this chapter reviews the fundamental theory and practical application of clinical pharmacology in anesthesia, including pharmacokinetics, pharmacodynamics, the “biophase” concept, compartmental models, and pharmacologic simulation. Although clinical pharmacology is grounded in complex mathematics, the chapter avoids excessive reliance on equations by emphasizing a conceptual understanding of the quantitative ideas, and highlights the intuitive understanding that comes from computer simulation of pharmacologic models. Understanding what a pharmacologic model is and how such a model is built and applied is therefore an important focus of the chapter. The ultimate goal of the chapter is to provide the clinician with a solid understanding of the fundamental concepts of clinical pharmacology, thereby enabling practical clinical application of these concepts, primarily through the use of pharmacologic simulation. From a pharmacology perspective, there is perhaps nothing more relevant to day-to-day decision making in anesthesiology than the theories explained here. These concepts are the scientific foundation to answer a very important clinical question: “What are the right drug and the optimal dose for my patient?” Historical Perspective From the earliest days of modern anesthesia, anesthesiologists sought to understand the dose-response relationship. Using dose escalation study methods, clinician-scientists quantified the magnitude and duration of anesthetic effect over a spectrum of doses, thereby identifying a dosage range that would produce anesthesia without excessive toxicity. For many decades, modern anesthesia practice relied on such dose-response studies as the basis for rational drug administration schemes. With advances in analytical chemistry and the widespread availability of computing technology, new approaches to understanding drug behavior emerged. By measuring blood anesthetic concentrations over time using techniques such as radioimmunoassay or gas chromatography, it became possible to characterize the relationship between drug dose and the time course of drug levels in the bloodstream, a field of study called pharmacokinetics (often 20 Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics Abstract Keywords This chapter presents a review of modern pharmacokinetic and pharmacodynamic concepts that comprise the scientific foundation of rational drug selection and administration of intravenous anesthetics. intravenous anesthetics pharmacokinetics pharmacodynamics drug interactions clinical pharmacology pharmacologic simulation Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 20.e1 CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics abbreviated as PKsa). A natural extension of this new discipline of pharmacokinetics was the characterization of the relationship between the concentration of the drug and the magnitude of effect, a branch of pharmacology called pharmacodynamics (abbreviated as PDsb). Coherent linkage of these two pharmacologic disciplines, pharmacokinetics and pharmacodynamics, necessitated creation of the biophase concept wherein plasma drug concentrations from PK studies are translated into apparent “effect site” concentrations, which are then related to drug effects measured in PD studies. The underlying theory of pharmacokinetics was largely developed in therapeutic areas unrelated to anesthesiology.1–3 However, because the clinical pharmacology of anesthesia is so unique4,5 (e.g., the necessity to predict onset and offset of drug effect very accurately), some PK concepts have been developed by anesthesia investigators for specific application in anesthesia.6–8 Moreover, because of the ease with which profound anesthetic effects can be noninvasively measured in real time (e.g., the peripheral nerve stimulator for neuromuscular blockers, the electroencephalogram [EEG] for hypnotics, among others), many important theoretical advances in pharmacodynamics applicable to other fields of medicine have originated from the study of anesthetics. An especially notable example is the conception of the biophase or effect site concept.9 Compared with old-fashioned dose-response methods, a major advantage of these more sophisticated PK-PD studies is that the analysis results in a quantitative model of drug behavior. Using nonlinear regression techniques, equations are fit to raw PK and PD data, yielding a set of PK-PD parameters estimates (i.e., distribution volumes, clearances, potencies) that constitute a quantitative model.10 Unlike dose-response studies of the past, these quantitative PK-PD models can be applied to more diverse and clinically relevant circumstances through computer simulation.11 The application of modern PK-PD concepts into anesthesia practice has blossomed in unanticipated ways. Automated administration of intravenous anesthetics according to a PK model, a technology known as target-controlled infusion (TCI), is now commonplace.12 The use of real-time PK-PD simulation to guide anesthetic administration, wherein a PK-PD prediction module is placed alongside a traditional physiologic monitor, is also an emerging technology with promising potential.13 Unique Aspects of Anesthetic Pharmacology Anesthesiology Compared With Other Disciplines The pharmacology of anesthesia is unique compared with other disciplines within medicine (Table 2.1). Perhaps the most obvious difference relates to the safety of anesthetic drugs. Many drugs within the anesthesia formulary produce profound physiologic alterations (e.g., unresponsiveness, paralysis, ventilatory and hemodynamic depression) and have a very low therapeutic index. There are few therapeutic areas in medicine where 2 to 3 times the typical therapeutic dose is often associated with severe adverse or even lethal effects (see Chapter 7). It is perhaps for this reason more than any other that the specialty of anesthesiology evolved. The consequences of “under” or “over” dosing anesthetics can be catastrophic. a When used as an adjective in this chapter, “pharmacokinetic” is abbreviated as “PK.” b When used as an adjective in this chapter, “pharmacodynamic” is abbreviated as “PD.” 21 TABLE Unique Aspects of Anesthesia Clinical 2.1 Pharmacology Related to Safety and Efficiency Safety Issues Very low therapeutic index drugs Severe consequences to “under” or “over” dosing Necessity to adjust the level of drug effect frequently Efficiency Issues Necessity to produce onset of drug effect quickly Necessity to produce offset of drug effect quickly Another important difference between anesthesiology and other therapeutic areas relates to efficiency. Most settings in clinical medicine do not require immediate onset and rapid offset of pharmacologic effect. When an internist prescribes an antihypertensive, for example, the fact that a few days may be required for establishment of a steady-state therapeutic effect is of little consequence. Similarly, when terminating therapy, the necessity to wait a few days to achieve complete dissipation of drug effect is usually of no clinical importance. Anesthesiologists, in contrast, must respond to the dynamic needs of patients under anesthesia during which the optimal degree of central nervous system depression can vary widely and frequently, requiring continuous adjustment of drug concentrations. In addition, the anesthesiologist must respond to the practical realities of modern medical practice in terms of operating room efficiency and the outpatient revolution; the anesthesiologist must rapidly anesthetize the patient and then quickly reanimate him or her when the surgeons have finished their work, enabling the patient to transition quickly through the recovery process in preparation for going home. Thus optimal anesthesia posology exists at the nexus of at least three domains: safety, effectiveness, and efficiency. Most other therapeutic areas in medical practice are not constrained by this efficiency imperative (Fig. 2.1). In summary, the profound physiologic alterations of the anesthetized state (and their reversal) must be produced on demand to ensure the rapid achievement and maintenance of the anesthetic state intraoperatively with return of responsiveness, spontaneous ventilation, and other vital functions at the appropriate time. To achieve this degree of pharmacologic control, anesthesiologists in the modern era increasingly rely on the application of advanced PK-PD concepts and technology to formulate and implement rational dosing schemes.14,15 In addition, anesthesiologists take advantage of drugs that were specifically developed to address the unique concerns of anesthesia pharmacology (i.e., drugs with rapid onset and predictable offset of effect).4 A Surfing Analogy as a Simple Conceptual Framework A surfing analogy is helpful in simply conceptualizing how PK-PD principles can be applied to the problem of rational drug administration in anesthesia.16 The anesthesiologist typically targets the upper portion of the steep part of the concentration-effect relationship; that is, the concentration that produces considerable drug effect but from which drug effect will recover quickly once drug administration is terminated. This can be visualized as a surfer riding near the crest of a wave as in Fig. 2.2. Targeting (“surfing”) the steep portion of the concentration-effect relationship makes it Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 22 Basic Principles of Pharmacology SE C T I O N I Most therapeutic areas Safe Effective A Anesthesia therapeutics Efficient Anesthesia posology is optimized here! Safe Effective B Fig. 2.1 Venn diagrams comparing the posology of most therapeutic areas with anesthesia therapeutics. In most therapeutic areas (A), there is considerable overlap between safe doses and effective doses. In contrast, in anesthesia practice the overlap between safe doses and effective doses is much smaller (B). In addition, anesthesiologists must also adjust the dosage to achieve practical efficiency (see text for full explanation). (Adapted with permission from Kuck K, Egan TD. Getting the dose right: anaesthetic drug delivery and the posological sweet spot. Br J Anaesth. 2017 1;119(5):862-864.) Emax Dynamic Effect Pharmaceutic Kinetic γ E0 Low EC50 High Concentration concentration achieved. Propofol titrated to a specific processed EEG target or a neuromuscular blocker administered to maintain a specific degree of twitch depression as measured by a peripheral nerve stimulator are examples of this PD approach. Another common approach in targeting the steep portion of the concentration-effect relationship is the PK approach. Drawing on knowledge about the concentration-effect relationship (i.e., therapeutic windows), the PK approach targets drug concentrations that are typically appropriate for a given anesthetic application. The use of an agent specific vaporizer to deliver some fraction or multiple of an inhaled agent’s minimum alveolar concentration (MAC), and the use of a TCI device to infuse propofol to a specified concentration (e.g., the Diprifusor, AstraZeneca, Cambridge, England; and others) are sophisticated examples of this approach. Of course, even in situations when an advanced delivery technology is not used, standard dosage regimens for drugs in anesthesia are devised to achieve concentrations that are within the therapeutic window based on the drug’s pharmacokinetics. A third approach to targeting the steep portion of the concentration-effect relationship can be referred to as the “forgiving drug” or “pharmaceutic” approach. The pharmaceutic approach takes advantage of the responsive pharmacokinetic profiles of modern anesthetic agents. With this approach, within the constraints of acceptable adverse effects such as hemodynamic depression, it is unnecessary to hit the target with as much precision and accuracy as with the other approaches. Because short-acting agent concentrations can be manipulated up or down rapidly, adjustments can be made quickly as suggested by PD feedback. If the empirical dosage scheme is obviously too high or too low, the anesthetist can achieve a more appropriate level of drug effect in short order. Short-acting agents essentially make it unnecessary to hit the target perfectly. As a practical matter, of course, anesthetists combine all three approaches (i.e., the PD, PK, and pharmaceutic approaches). Typically, pharmacokinetically responsive agents are administered by advanced, target-controlled delivery devices according to PD feedback. Adjusting the propofol TCI target based on feedback from a processed EEG brain function monitor is an example of this combined approach to anesthesia drug delivery. The pharmacologic science underpinning this three-pronged approach to rational drug selection and administration for intravenous anesthesia is the focus of this chapter. Clinical Pharmacology Fig. 2.2 Posology possible to achieve large reductions in effect with relatively small decreases in concentration. In clinical pharmacology terms, there are essentially three approaches to targeting this area of the concentration-effect relationship. Perhaps the most straightforward among them is the PD approach, wherein a drug effect measure is used as a feedback signal to guide drug administration irrespective of the drug Although defining exactly what comprises the field of “clinical pharmacology” is challenging,17 it consists of numerous branches, including pharmacokinetics, pharmacodynamics, toxicology, drug interactions, and clinical drug development. Defined in general terms, clinical pharmacology is the branch of pharmacology concerned with the safe and effective use of drugs. Articulated in a more practical way, the ultimate goal of clinical pharmacology is the translation of the relevant pharmacologic science into rational drug selection and dosing strategies. Posology, although a little used term, is the science of drug dosage and is thus also a branch of clinical pharmacology (or perhaps a synonym). Combining the Greek words posos (how much) and logos (science), posology can be thought of more simply as “dosology.” In the posology of anesthesia, the fundamental question “What is the optimal dose for my patient?” has numerous, clinically important permutations as shown in Table 2.2. All of these questions A surfing analogy as a graphical explanation of how anesthesiologists use a combination of three approaches (i.e., pharmacokinetic, pharmacodynamic, and pharmaceutic) to administer anesthetics to maintain the anesthetic effect while making rapid recovery possible. See the accompanying text for a detailed explanation. E0, Effect at zero drug concentration; Emax, maximal drug effect; EC50, concentration that produces 50% of maximal drug effect; γ, steepness of the curve. (Reproduced with permission from Egan TD, Shafer SL. Target-controlled infusions for intravenous anesthetics: surfing USA not! Anesthesiology. 2003;99:1039–1041.) Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics have obvious clinical relevance in the day-to-day practice of anesthesia. The accurate and precise prediction of the time course and magnitude of drug effect is the primary pharmacology-related task of anesthesia. Given the unique challenges of anesthesia pharmacology, one could argue that pharmacokinetics and pharmacodynamics are perhaps more relevant in anesthesia than in any other therapeutic area of medicine. Indeed, despite the conspicuous unpopularity of these mathematically oriented fields among anesthesia practitioners, perhaps without conscious acknowledgment, anesthesiologists are real-time clinical pharmacologists applying PK-PD TABLE Selected Clinically Important Questions in the 2.2 Posology of Anesthesia What is an appropriate initial dose? How soon will the intended effect begin? When will the effect peak? How long will the effect last? Should the drug be given by bolus or infusion or both? When will repeat bolus doses or infusion rate changes be necessary? When should drug administration stop to promote timely emergence? What are the typical therapeutic target concentrations? What are the expected consequences of underdosing or overdosing? Will tolerance develop? What factors might alter the dosage requirement (e.g., demographic, pathologic, genomic)? What is the expected amount of variability in drug response? How will drug interactions influence outcome? principles to the optimization of anesthetic posology (and the myriad posologic questions suggested by Table 2.2). General Schema A general schema summarizing a framework for understanding clinical pharmacology is presented in Fig. 2.3. The topic can be considered clinically from three domains: the dosage, concentration, and effect domains. Similarly, the underlying science can be divided into three areas of study: pharmacokinetics, the biophase, and pharmacodynamics. Before advances in clinical pharmacology the clinician could consider only the adequacy of intravenous anesthetic therapy in terms of dosage or effect (i.e., without the aid of a computer model, predicted concentrations in the plasma and effect site were not available and thus the concentration domain was unknowable). Likewise, before the development of modern pharmacologic modeling theory, the three distinct disciplines of clinical pharmacology (i.e., pharmacokinetics, the biophase, and pharmacodynamics) were naively lumped together in the study of the dose-response relationship. From the practitioner’s standpoint, the adequacy of therapy can be considered in any of the three clinical domains. Is the dosage adequate? Are the predicted concentrations adequate? Is the intended effect adequate? From the scientist’s perspective, the answers to these clinically oriented questions are grounded in the principles of pharmacokinetics, pharmacodynamics, and the biophase. For some drugs (now mostly older drugs), because a suitable PK model does not exist, consideration of the concentration domain cannot contribute to therapeutic decisions. Similarly, because for some drugs the measurement of drug effect in real time is difficult (e.g., opioids in unresponsive, mechanically ventilated patients), consideration of the effect domain plays a lesser role in guiding therapy. General Clinical Pharmacology Schema Dose domain 23 Concentration domain Effect domain Drug in syringe Drug in bloodstream Drug at target cells Drug interacting with receptor Dose (mass) Plasma concentration (mass/volume) Effect site concentration (mass/volume) Effect (various units) Pharmacokinetics (PKs) (dose-concentration relationship) The biophase (PK-PD link) (plasma-effect site relationship) Pharmacodynamics (PDs) (concentration-effect relationship) Fig. 2.3 A general schema of clinical pharmacology divided into dose, concentration, and effect domains. The science underpinning the field can be divided into the disciplines of pharmacokinetics, pharmacobiophasics, and pharmacodynamics. See the accompanying text for a detailed explanation. The purple triangles represent drug molecules. PDs, pharmacodynamics; PKs, pharmacokinetics. Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 24 SE C T I O N I Basic Principles of Pharmacology Consider the fate of drug molecules as summarized in Fig. 2.3. The anesthesiologist administers the desired dose intravenously using a handheld syringe or pump (the dose domain). The drug is then distributed via the circulation to body tissues and eventually eliminated through biotransformation and/or excretion according to the drug’s pharmacokinetics. The predicted plasma (or blood) concentration versus time profile can be the basis of therapeutic decisions regarding subsequent doses (the concentration domain), although the plasma concentration is sometimes misleading because it might not be in equilibrium with the site of action. Meanwhile, some very small fraction of the administered drug is distributed from the blood to the target cells in the effect site or biophase according to the drug’s biophase behavior. The predicted concentration in the effect site (also the concentration domain) is a more reliable indicator of the adequacy of therapy than is the blood concentration because the target receptors are always in equilibrium with this concentration. Finally, the drug molecules in the biophase interact with the relevant receptors, producing the intended effect (the effect domain). For drugs with easily measurable effects, the dose and concentration domain are obviously less relevant to successful therapy because drug effect is the ultimate goal of therapy; when there is a reliable, real-time effect measurement, the drug can be administered to the targeted level of effect irrespective of what the dose or predicted concentration may be. Pharmacokinetics Pharmacokinetics is typically defined in introductory pharmacology courses as “what the body does to the drug.” A much better and clinically useful definition is the study of the relationship between the dose of a drug and the resulting concentrations in the body over time (the dose-concentration relationship; see Fig. 2.3). In simple terms, pharmacokinetics is the drug’s disposition in the body. Commonly considered PK parameters include distribution volumes, clearances, and half-lives; other, less intuitively meaningful PK parameters such as microrate constants are mathematical transformations of these more common parameters.18 A simple hydraulic model representation of these fundamental parameters for a one-compartment model is presented in Fig. 2.4. The pharmacokinetics of most anesthetic drugs are described by more complex models with two or three compartments (see also “PK-PD Model Building Methods” in later text). When conceptualized in terms of an hydraulic model, of course, multicompartment models consist of additional containers (i.e., volumes) connected to the central volume by pipes of varying sizes. Distribution volumes, expressed in units of volume such as liters or liters per kilogram, are “apparent” in that they are estimated based on the volume of water into which the drug appears to have distributed; they do not represent any actual volume or anatomic space within the body. Clearance parameters, expressed in units of flow such as liters per minute or liters per kilogram per minute, simply quantify the volume of plasma from which the drug is completely cleared per unit of time. For drugs with a very high hepatic extraction ratio (i.e., the liver biotransforms almost all the drug delivered to it), the central clearance is nearly equal to hepatic blood flow (e.g., about 1 L/min). Half-lives, perhaps the most commonly known PK parameter, are expressed in units of time and represent the time required for the concentration to decrease by 50% after drug administration has ceased. Half-life varies directly with volume of distribution and inversely with clearance; these relationships make intuitive sense given that a larger volume will Drug infusion (mass/time) Drug concentration (mass/volume) Concentration after one half-life (time) Clearance (volume/time) Volume of distribution (volume) Fig. 2.4 A hydraulic representation of a one-compartment pharmacokinetic (PK) model simply illustrating various PK parameters. Water running from the faucet into the container represents an infusion of drug. The size of the container represents the volume into which the drug will distribute (i.e., the volume of distribution). The height of the water level is the drug concentration. The water flowing out of the pipe at the bottom of the container represents drug elimination (i.e., clearance). The half-life of the drug after the infusion is stopped is also shown. take longer to clear and that a higher clearance will obviously speed the decline of drug levels. Pharmacodynamics Pharmacodynamics is typically defined as “what the drug does to the body.” A better definition is the study of the relationship between the concentration of the drug in the body and its effects (i.e., the concentration-effect relationship; see Fig. 2.3). In straightforward terms, pharmacodynamics is a description of drug effects, both therapeutic and adverse. Particularly important PD parameters include potency and the steepness of the concentration-effect relationship (see “PK-PD Model Building Methods” in later text). Expressed in units of mass per volume (e.g., micrograms per milliliter; nanograms per milliliter), potency is usually estimated as the concentration required to produce 50% of maximal effect, often abbreviated as the C50 (sometimes called the EC50, the effective concentration producing 50% of maximal effect; see Fig. 2.2). Obviously, the lower the EC50, the more potent is the drug. The EC50 is important in determining the range of target concentrations that will be necessary for effective therapy (i.e., the therapeutic window). The steepness of the concentration-effect relationship is typically quantified by a parameter called “gamma,” a unitless number that reflects the verticality of the concentration-effect relationship. A highly vertical concentration-effect relationship (i.e., large gamma) means that small changes in drug concentration are associated with large changes in drug effect; some groups of drugs (e.g., opioids) have steeper concentration-effect relationships than others.19 Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics 25 Drug administration Fig. 2.5 A schematic representation of a three-compartment model with an effect compartment attached to the central compartment to account for the equilibration delay between concentration in the central compartment and drug effect. I, Drug input; k12, k13, and so on, rate constants characterizing drug movement between compartments and out of the system; ke0, rate constant for drug elimination out of the effect compartment; V1, V2, and so on, compartment volumes. See the accompanying text for a detailed explanation. I V2 Rapidly equilibrating compartment k21 k12 V1 Central compartment k10 k13 k31 V3 Slowly equilibrating compartment k1e Effect site Ve The Biophase The biophase concept is a nuance of clinical pharmacology that is perhaps not as widely covered in pharmacology courses because its clinical application is most relevant to just a few acute care disciplines like anesthesiology. “Pharmacobiophasics,” a neologism not in common usage (coined by author TDE), is the study of drug behavior in the biophase. The biophase is the site of drug action, often referred to as the effect site (e.g., target cells and receptors within the brain, the neuromuscular junction, the spinal cord). The biophase concept is essential to clinical anesthetic pharmacology because during non–steady-state conditions (i.e., after a bolus injection or an infusion rate change) the concentration of drug in the blood does not correlate well with drug effect. After a bolus injection, compartmental models predict that peak plasma drug concentration occurs immediately (i.e., a key “well stirred” model assumption), and yet peak drug effect does not occur immediately. This is because most drugs do not exert their effect in the blood; rather, they must be delivered to the site of action (i.e., the biophase) before they can elicit the desired therapeutic effect. Thus predictions regarding the magnitude of drug effect based on plasma concentrations can be misleading, particularly when plasma drug concentrations are rapidly changing such as after a bolus injection. As originally proposed by investigators working with d-tubocurarine and pancuronium,9,20,21 the biophase (effect site) concept has revolutionized the ability to predict the time to maximal drug effect during non–steady-state conditions. As shown in Fig. 2.5, incorporating a theoretical “effect compartment” into a standard compartmental PK model enables characterization of the plasma-biophase equilibration process. It is the central compartment concentration (i.e., the concentration in the arterial blood) that drives the concentration in the effect site. The key pharmacobiophasics parameter, expressed in units of inverse time, is a rate constant called ke0 (see “PK-PD Model Building Methods” in later text).9,20,22 The ke0 characterizes the rate of equilibration between plasma and effect site concentrations. When ke0 is known for a drug, it is possible to predict the time course of “apparent” effect site concentrations based on the time course of plasma concentration. These effect site concentrations correlate directly with drug effect. Thus the biophase can be viewed as the link between drug disposition in the blood (pharmacokinetics) and drug effect at the site of action (pharmacodynamics). The time required to achieve peak effect site concentration after bolus administration is a function of the drug’s physicochemical properties in vivo. Small, lipid-soluble, un-ionized, unbound molecules (i.e., drugs with a high “diffusible fraction”) reach peak ke0 Faster onset Slower onset +/– Rx Rx Lipid H2O in ote in nd Bi r gp Fig. 2.6 A schematic representation of the physicochemical properties that hasten or slow the achievement of peak effect site concentration. Small, lipid-soluble, un-ionized, unbound molecules reach peak effect site concentration more rapidly. Molecular weight, the octanol-water partition coefficient, pKa, and the percent protein bound are the parameters that quantify these physicochemical properties. Rx indicates a drug molecule. The lipid droplet indicates high lipid solubility. The H2O droplet represents high water solubility. The +/− lightning bolt indicates a charged molecule. The ribbon-like structure represents a protein binding molecule such as albumin. effect site concentration more rapidly than larger, less lipid-soluble, charged, highly protein-bound drugs (Fig. 2.6). For drugs that achieve a peak effect site concentration more slowly, the onset of therapeutic effect can be hastened with higher doses (see Fig. 2.16). Drug Interactions In anesthesiology, unlike most medical disciplines, PD drug interactions are frequently produced by design. Anesthesiologists take advantage of the PD synergy that results when two drugs with different mechanisms of action but similar therapeutic effects are combined.23 These synergistic combinations can be advantageous because the therapeutic goals of the anesthetic can often be achieved with less toxicity and faster recovery than when individual drugs are used alone in higher doses. In fact, except for specific, limited clinical circumstances in which a volatile agent or propofol alone is an acceptable approach (e.g., a brief procedure in a pediatric patient such as tympanostomy tubes or radiation therapy), modernday anesthesia involves at least a two-drug combination consisting of an analgesic (typically an opioid) and an hypnotic (e.g., an inhaled agent or propofol).24 Therefore from a strictly pharmacologic perspective, anesthesiology can be thought of as the practice of PD synergism using central nervous system depressants. Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 26 SE C T I O N I Basic Principles of Pharmacology Because anesthetics are rarely administered alone, understanding the interactions between drugs is critical to their safe and effective use.25,26 Although PK interactions (i.e., where one drug alters the concentration of another) are sometimes observed in select clinical circumstances,27 PD interactions are an important part of nearly every anesthetic. This topic is of such importance in anesthesia pharmacology that an entire chapter is devoted to it (see Chapter 6); a limited discussion is included here. The study of drug interactions in anesthesiology has traditionally been approached using the “isobologram” method.28,29 An isobologram is a curve defining the concentrations of two drugs that, when given together, produce the same effect (the isobole is an “iso” or “equal” effect curve). Perhaps the most common example of an isobole in anesthesiology is a plot showing the reduction in the MAC of an inhaled agent produced by an opioid.30,31 The main limitation of an isobologram is that the curve applies to only one level of drug effect. This is a problem in anesthesiology because during anesthesia patients experience a spectrum of drug effect ranging from minimal sedation to profound central nervous system depression. Response surface methods address this shortcoming of the isobologram. The response surface approach creates a threedimensional plot of the two drug concentrations (e.g., propofol and fentanyl) versus drug effect (e.g., sedation), quantitatively describing the PD interaction of the two drugs (see Chapter 6). The response surface method is an advance because it describes the drug interaction over the entire range of drug effect and thereby enables simulation from one clinical state to another. This is critical in anesthesia pharmacology because anesthesiologists must take the patient from the awake to the anesthetized state, and then back to the awake state again on demand.4,16 Response surface methods yield a set of parameters that indicate whether the interaction is additive, synergistic, or antagonistic. Pharmacologic Modeling PK-PD Models as Versions of Pharmacologic Reality Scientific models seek to represent empirical objects, biologic phenomena, or physical processes in a coherent and logical way. Models are a way of thinking about and understanding the natural world; models are essentially a simplified version of reality intended to provide scientific insight. By providing a framework for understanding the natural world, models can also be a means of creating new knowledge. Knowledge from models comes in many forms, each with certain advantages and limitations. In biomedical science, for example, models of physiologic processes conducted in test tube experiments provide in vitro knowledge wherein confounding variables can be carefully controlled. Experiments conducted in animal models of disease provide in vivo insight that reflects biologic reality at the whole animal level. Since the advent of computational scientific methods, models of natural phenomena are often represented as a mathematical system (an equation or set of equations); these mathematical models provide in silico understanding, meaning that experiments that might be practically impossible or too expensive in actual subjects can be conducted by computer simulation. PK-PD models are examples of this kind of mathematical model applied to clinical pharmacology.32 Various equations are used to represent the pharmacologic processes of interest.2 Although a PK-PD model is a gross oversimplification of reality (e.g., the body is not a set of three containers connected by pipes as suggested in Fig. 2.5), considerable insight into drug behavior has come from the application of PK-PD models to important questions in anesthesia pharmacology. When applying PK-PD models through simulation, rather than conducting the experiment in a test tube (in vitro) or in an experimental animal (in vivo), the experiment is conducted in the computer (in silico) on a virtual subject or subjects. It is axiomatic that the true utility of a pharmacologic model is a function of its performance in the real world. Clinically useful models adequately describe past observations and satisfactorily predict future observations. Among scientists involved in all kinds of modeling, it is often quipped that “all models are wrong, but some models are useful!”33 There is no question that PK-PD models, despite their limitations, are very useful in refining the posology of anesthesia practice.14,15 PK-PD Model Building Methods A summary of the PK-PD model building process is outlined in Fig. 2.7. The process, of course, begins with the gathering of the raw data in appropriately designed experiments.34,35 Elements of a well-designed PK-PD modeling experiment for an intravenous anesthetic include careful attention to the administered dose by infusion15; frequent, prolonged sampling of arterial blood for concentration measurement36,37;use of a quality-assured, validated drug assay; and administration of sufficient drug to elicit maximal or near-maximal effect (but not too rapidly).20 Without quality raw data it is impossible to characterize the pharmacologic system using modeling techniques. Because the mathematics involved in PK-PD modeling can be complex, it is perhaps best for the clinician to consider the modeling methods from other perspectives.38 As shown in Fig. 2.7, approaching the modeling process from schematic and graphic perspectives makes the mathematics less intimidating for non-mathematicians. Ultimately the mathematical equations involved are simply quantitative expressions of the ideas and concepts represented by the schematic diagrams and plots. Schematically, basic PK processes are well represented by a compartmental model (see upper panel of Fig. 2.7). After injection into the central compartment, a drug is either distributed to other compartments or is eliminated from the central compartment altogether. Graphing these PK processes reveals the distinct distribution and elimination phases typically observed in plasma concentration decay curves. Curves of this general shape can be represented by polyexponential equations of the form shown in upper panel of Fig. 2.7.39 Fig. 2.8 summarizes how raw PK data from a single subject might be modeled in a typical PK model building experiment. Using nonlinear regression techniques, a polyexponential equation is fit to the raw concentration versus time data.40 This is an iterative process in which the nonlinear regression software alters the parameters of the equation repeatedly until the “best model” is obtained, thereby estimating the PK parameters of the model (i.e., distribution volumes, clearances, microrate constants).41 The best model is one that fits the data well (e.g., minimizes the difference between the measured concentration and the concentration predicted by the model).42 The PK model enables prediction of the time course of drug concentrations in blood or plasma. Biophase behavior and pharmacodynamics can be modeled in generally the same way. When the biophase is considered schematically, the delay between peak plasma concentration and peak drug effect is a function of the time required for drug delivery to the site of action (middle panel of Fig. 2.7).10 This delay (or hysteresis Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics 27 Dose Vc Distribution Cp V2 Polyexponential equation Distribution Elimination Cp(t) = Ae–αt + Be–βt Elimination Time Time lag Transport to biophase The biophase Pharmacokinetics Clinical Pharmacology Modeling Concepts Differential equation E Cp dCe dt = k1eCp – keoCe Time Pharmacodynamics Bound drug Emax Sigmoidal equation γ E E = E0 + E0 Emax Ceγ EC50γ + Ceγ EC50 Drug-receptor interaction Ce Schematic Graphic Mathematic Fig. 2.7 A summary of clinical pharmacology modeling concepts for the disciplines of pharmacokinetics, the biophase, and pharmacodynamics. The modeling foundation for each area is presented schematically, graphically, and mathematically. The purple triangles represent a drug. See the accompanying text for a detailed explanation, including discussion of the equations. Ce, effect site concentration; Cp, plasma concentration; E, effect; E0, effect at zero drug concentration; Emax, maximal drug effect; EC50, concentration that produces 50% of maximal drug effect; γ, steepness of the curve. Plasma concentration (ng/mL) 80 Iterative models—poor fits (predicted Cp) 60 40 Final model—best fit (predicted Cp) 20 Raw data (measured Cp) 0 0 10 20 30 40 50 60 Time (min) Fig. 2.8 An example of fitting a model (a polyexponential equation in this case) to raw pharmacokinetic (PK) data from a single experimental subject. The measured plasma concentrations (i.e., the raw data) are represented by the pink circles. Preliminary models (i.e., poor fits) generated during the iterative, nonlinear regression process are shown as dotted lines. The final model (i.e., best fit) is shown as a thick, blue line. The thick, blue line thus represents the predicted concentrations according to the PK model. See the accompanying text for a detailed explanation. in engineering terms) is represented by a simple plot showing a time lag between peak plasma concentration and peak effect, and can be characterized by a simple differential equation of the general form shown. Using nonlinear regression and other techniques, the biophase modeling process estimates the key biophase model parameter called ke0 (see previous text).9,22 The biophase model enables prediction of effect site concentrations. These effect site concentration predictions are essential for the PD modeling process. Considered schematically, the PD system is represented by a drug molecule interacting with a target receptor (bottom panel of Fig. 2.7). This drug-receptor interaction is represented graphically by a sigmoidal curve. In the absence of drug, the level of biologic effect is at baseline (E0). As drug concentration in the effect site (predicted from the biophase model) increases, eventually some drug effect is produced. As the steep portion of the concentrationeffect relationship is approached, more pronounced degrees of drug effect are observed. Further increases in drug concentration produce greater and greater effect, eventually reaching the biologic maximum (Emax). This sigmoidal curve is represented by equations of the general form shown in the bottom panel of Fig. 2.7. Using nonlinear regression techniques such as those illustrated in Fig. 2.8, the PD modeling process fits the sigmoidal equation to the raw PD data, thereby estimating the parameters of the equation. Combined with the PK and biophase model, the PD modeling process enables prediction of the time course of drug effect. Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 28 SE C T I O N I Basic Principles of Pharmacology thrust of PK-PD modeling is to characterize drug behavior in the population for which it is intended, a primary focus of modeling is to build a model that represents the entire population (not just an individual).35 Special techniques such as “mixed-effects” modeling (e.g., the NONMEM program and others)43,44 have been developed and refined to estimate typical PK-PD parameter values for an entire population (and also the intersubject variability of the parameters).45 Sophisticated methods to quantify the influence of “covariate” effects (e.g., age, body weight, metabolic organ failure, among others) on the PK-PD system have also been described.46 Pharmacokinetics and Biophase Concentration Cp(t) = Ae–at + Be–bt + Ce–gt Cp dCe dt = k1eCp – keoCe Ce A As simplified versions of reality, PK-PD models fail to account for certain biologic complexities. In selected situations, these complexities make it difficult or impossible to apply PK-PD models in a useful way. Thus intelligent construction and application of PK-PD models requires awareness of their limitations. Time Effect Pharmacodynamics B E = E0 + Emax Ceg C50g + Ceg Effect site concentration Fig. 2.9 Basic equations for modeling drug plasma concentration (Cp), effect site concentration (Ce), and effect. These equations (or various transformations of these equations) are the mathematical basis for pharmacokinetic-pharmacodynamic modeling. The equations represent curves of the appropriate shape to characterize the raw data. See text for complete explanation. Ce, effect site concentration; Cp, plasma concentration; E0, effect at zero drug concentration; Emax, maximal drug effect; C50, concentration that produces 50% of maximal drug effect; In summary, PK-PD model building is an exercise in fitting appropriate equations to experimental data using nonlinear regression modeling software and other related techniques.41 As summarized in Fig. 2.9, the mathematical equations simply represent the general shape of the relationships being modeled. A polyexponential equation is typically used to characterize the plasma concentration decay curve. A differential equation is the basis for modeling the delay between equilibration of plasma and effect site concentration. A sigmoidal equation is used to characterize the concentration-effect relationship. Fitting the equations to the raw data results in a set of PK-PD parameter estimates that constitute the quantitative model.18 These parameters can then be used to conduct PK-PD simulations to explore the clinical implications of the models. It is important to emphasize that the iterative, nonlinear regression process yields only parameter “estimates;” the true values of the parameters are unknowable.a It is of course possible to fit these equations to an individual subject’s data and also to a group of subjects’ data. Because a main a Limitations in Building & Applying PK-PD Models In this chapter, “parameter estimates” will sometimes be referred to as just “parameters.” Early Model Misspecification A major shortcoming of the standard compartmental PK model is a function of model misspecification during the early period after drug injection.47 Standard compartmental models assume the central volume is well stirred and that peak plasma concentration occurs immediately after injection, an assumption that is obviously invalid. Similarly, standard compartmental models assume that plasma concentration declines monotonically after it reaches a peak; although perhaps less obvious, this assumption is also false.48 Careful study of the early period after drug injection confirms that standard compartmental models sometimes do not reliably predict drug disposition in the first few minutes after injection.47 Model misspecification is important because anesthetics are often intended to exert their most profound effects very soon after a bolus is administered.49 The reasons underpinning this model misspecification in the period shortly after bolus injection are numerous and include the influence of cardiac output on drug distribution, the appearance of a “recirculatory,” second concentration peak (after the first circulation time), and pulmonary uptake of drug, among others.48,50,51 These limitations of compartmental models can be addressed with more complex physiologic and recirculatory models,52–55 although standard compartmental models are more commonly applied clinically despite their sometimes poor performance. These more physiologically based PK modeling approaches have identified factors that influence anesthesia induction doses, such as age, cardiac output, and concomitant use of drugs that alter cardiac function.50,56,57 Stereochemistry Chirality in molecular structure introduces substantial complexity in characterizing drug behavior with PK-PD models if the chiral drug is studied as a racemate.58 Taken from the Greek word chier (meaning hand), “chiral” is the term used to designate a molecule that has a center (or centers) of three-dimensional asymmetry. The appropriateness of the term’s Greek origin is clear when considering that a pair of human hands are perhaps the most common example of chirality (Fig. 2.10). Although they are mirror images of each other, a pair of hands cannot be superimposed. Similarly, chirality in molecular structure results in a set of mirror image molecular twins (i.e., the two enantiomers of a racemic mixture) that cannot be superimposed. This kind of molecular handedness in biologic Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics 29 Fig. 2.10 The concept of molecular chirality compared to the anatomic asymmetry of a pair of human hands. Like a pair of hands, chiral molecules are identical, mirror images of one another, but they cannot be superimposed. The molecular asymmetry of chirality is a function of the tetrahedral bonding characteristics of the carbon atom (carbon is represented in black; the other colors represent any four different groups of atoms). The two molecules shown are considered enantiomers; when combined, they constitute a racemic mixture. Chirality has important pharmacologic implications in terms of pharmacokinetic-pharmacodynamic behavior. Mirror systems is ubiquitous in nature and is almost always a function of the unique, tetrahedral bonding characteristics of the carbon atom.59 Drug chirality is significant because the molecular interactions that are the mechanistic foundation of drug action and disposition occur in three dimensions and therefore can be altered by stereochemical asymmetry (see Chapter 1).60 Thus, pharmacologically, not all enantiomers are created equal! The implications of chirality span the entire PK-PD spectrum. Enantiomers can exhibit differences in absorption and bioavailability, distribution and clearance, potency, and toxicology. When a pharmacologic process discriminates in a relative fashion between enantiomers (e.g., one enantiomer being metabolized more rapidly than the other), it is termed stereoselective. If the discrimination is absolute (e.g., one enantiomer being completely incapable of producing drug effect), the process is termed stereospecific. The implications of chirality on PK-PD modeling are obvious. A PK-PD model of a racemic mixture is really a model of two drugs with presumably different PK and PD behavior and thus must be interpreted with caution. This “racemate” complexity applies to a surprisingly diverse array of anesthetic drugs, including thiopental, methohexital, ketamine, isoflurane, desflurane, mepivacaine, bupivacaine, ibuprofen, ketorolac, and methadone, among others.61 It is for this reason that novel drug development in anesthesia over the past decade has avoided racemic mixtures (there is considerable pressure from regulatory bodies like the United States Food and Drug Administration to do so).62,63 Single enantiomer formulations such as (S)-ketamine, ropivacaine, cisatracurium, and levobupivacaine are all cases in point; single enantiomer formulations often have some clinical advantage in terms of their PK and/ or PD behavior, reflecting the PK-PD differences between enantiomers.61 Active Metabolites When a drug has an active metabolite, applying a PK-PD model of the parent compound to predict overall drug effect is obviously problematic. Not only will the metabolite contribute to drug effect, but the metabolite will also have a different rate of concentration decay (i.e., different pharmacokinetics). The PK-PD model of the parent drug does not account for this complexity and thus the model must be applied with awareness of this shortcoming.64 Therapeutic drug monitoring of parent drugs with active metabolites has long been known to be fraught with similar problems.65 This active metabolite issue applies to a number of anesthetic drugs, including diazepam, midazolam, codeine, morphine, and ketamine, among others. Particular interest in recent years has been focused on morphine’s active metabolite, morphine-6-glucuronide (M6G). Because M6G accumulates in patients with altered renal clearance mechanisms (unlike the parent drug),66,67 prolonged administration of morphine in patients with kidney failure can be complicated by severe ventilatory depression.68 PK-PD models for morphine that also include the concentration time course and effect of the M6G metabolite provide a scientific explanation for these clinical observations.69 Variability Another major shortcoming in applying PK-PD models clinically is that standard simulations using PK-PD model parameters do not typically include an expression of variability in the PK-PD predictions. As a result, from a statistical perspective, these standard simulations are being applied deterministically rather than probabilistically. Given the well-described and considerable variability in drug behavior in terms of both PK and PD relationships70 (and that PK-PD model parameters are only estimates), this shortcoming of standard PK-PD model simulation is an important one. Applying advanced statistical methods such as Monte Carlo simulation to standard PK-PD analysis is a means of addressing this problem by providing the clinician with a sense of the expected variability in drug behavior.71 Pharmacologic Simulation Unimportance of Individual PK-PD Model Parameters In contrast to well-entrenched conventional wisdom, single PK-PD model parameter estimates considered in isolation are not very helpful in drawing clinically useful conclusions. PK-PD studies in the anesthesia literature traditionally include a table of values for PK-PD parameters such as in the left column of Table 2.3. In Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 30 SE C T I O N I Basic Principles of Pharmacology the early days of PK-PD modeling, it was commonplace for investigators to make clinical inference by comparing a particular parameter value for one drug with the corresponding parameter of another drug. For example, certain clinical conclusions might have been drawn depending on how the half-lives or clearances for a pair of drugs compared. The problem with this simplistic approach is that it fails to account for the complexity of the typical PK model. A standard TABLE Selected Traditional Pharmacokinetic2.3 Pharmacodynamic Model Parameters Versus Practical Model Predictionsa Traditional Parameters (From the Model) Practical Model Predictions (From Model Simulation) Pharmacokinetic Front-End and Back-End Bolus Behavior Distribution volumes Clearances Half-lives Pharmacobiophasics ke0 Pharmacodynamic E0 Emax EC50 Gamma (γ) Time to peak effect after a bolus injection? Time to offset of effect after a bolus injection? Front-End and Back-End Infusion Behavior Time to steady state after beginning an infusion? Time to offset of effect after stopping an infusion? Dosage Domain Issues Dosage necessary to achieve a specified target concentration? Dosage reduction necessary when combining synergistic drugs? Concentration Domain Issue Concentration necessary to achieve specified effect? E0, Effect at zero drug concentration; EC50, concentration that produces 50% of maximal drug effect; Emax, maximal drug effect; gamma (γ), steepness of the curve; ke0, rate constant for drug elimination out of the effect compartment. a Single PK-PD parameters considered in isolation are not clinically useful; predictions from model simulations are very useful (see text for complete explanation). three-compartment model as shown in Fig. 2.5, for example, has six fundamental parameters (i.e., three clearances and three distribution volumes); these fundamental parameters can be converted to a variety of other parameters (e.g., half-lives, microrate constants).18 These multiple parameters interact in a complex way over time in determining the predicted drug concentration.6,72 Thus comparing a single PK parameter value of one drug with that of another drug is of limited value and provides very little clinically relevant intuitive understanding. Importance of PK-PD Model Simulation Understanding the clinical implications of a table of PK-PD parameters is best accomplished through in silico application of the associated model by computer simulation.73 Through simulation, the practically oriented clinical questions shown on the right column of Table 2.3 (among many other questions) can be explored and answered. In contrast to a table of parameter values, PK-PD model simulation provides straightforward, clinically oriented information that the practitioner can apply in actual practice.38 The PK-PD model simulation process is summarized in Fig. 2.11. Using PK-PD model simulation software, the user inputs a dosing scheme of interest. The simulation software predicts the time course and magnitude of drug concentration and effect according to the model. An infinite number of such simulations can be performed in silico to gain insight into anesthesia posology. When presented graphically, the results of PK-PD simulations provide a picture of the time course of drug concentration and effect. Most commonly, drug effect site concentrations are simulated. Combined with knowledge about the concentration-effect relationship (i.e., pharmacodynamics), clinical insight into optimal dosing is gained.74 The simulation in Fig. 2.12 illustrates the power of PK-PD simulation in terms of intuitively understanding the implications of various dosing schemes. The simulation depicts the very different time courses of drug concentration in the biophase when identical total doses of fentanyl (i.e., 300 µg) are administered in three different ways. By providing a simple picture of how a specified dosing scheme translates into effect site concentrations over time (and how the resulting concentration versus time profile compares to therapeutic windows), PK-PD simulation constitutes a powerful tool to study and optimize anesthesia posology. Pharmacologic Simulation Concept Fig. 2.11 A simple representation of the concept of a pharmacokinetic-pharmacodynamic (PK-PD) model simulation. Using PK-PD model simulation software (called “PK-PD Simsoft” in this figure just for illustration purposes; PK-PD Simsoft is not an actual product), the user inputs a dosing scheme of interest. The simulation software predicts plasma concentrations (Cp), effect site concentrations (Ce), and effect (E) according to the parameters of the PK-PD model. In this diagram, PK-PD Simsoft is a fictitious simulation software product. See the accompanying text for a detailed explanation. PK-PD Simsoft Cp C Ce E Time Dose of Interest PK-PD Simulation Software PK/PD Predictions Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. CHAPTER 2 Pharmacokinetic and Pharmacodynamic Principles for Intravenous Anesthetics Bolus Front-End and Back-End Kinetics Influence of Dosage Schedule 8 100 6 100-µg bolus x 3 Infusion of 300 µg total 2 0 Typical analgesic Ce 0 50 100 150 200 250 300 Time (min) Percent of peak Ce (%) Fentanyl Ce (ng/mL) 300-µg bolus 4 31 80 PK-PD Model Simulation and Anesthesia Posology Exploring anesthesia posology through PK-PD simulation equips the practitioner with the knowledge necessary to formulate rational drug selection and administration schemes. Although the possibilities are endless in terms of the number and variety of PK-PD simulations that can be performed, a limited set of straightforward simulations form the foundation on which the answers to many routine anesthesia posology questions are based. Among this fundamental set of simulations, perhaps the most important are those that address the front-end and back-end PK behavior of intravenous anesthetics. Because drug behavior is substantially different for bolus injections compared with infusions,7 the two conditions must be considered separately. Other fundamental simulations include the influence of dose on the onset and offset of effect after bolus injection, the influence of dose on the front and back-end kinetics of infusions, the influence of special populations on drug behavior, and the influence of a second drug on PD effect. Bolus Front-End and Back-End Kinetics As noted in Table 2.2, important posologic questions regarding bolus injections include “How long will it take to reach peak effect and how long will it take for the effect to dissipate?” The simulations plotted in Fig. 2.13 explore these questions for a number of commonly used opioids. After bolus injection, remifentanil and alfentanil predicted effect site concentrations reach a peak quickly and then decline significantly before any of the other opioids have even begun to peak. This rapid achievement of peak effect site concentrations for these two highly lipid-soluble fentanyl congeners is likely a function of their high “diffusible fractions” (i.e., the proportion Morphine 60 Fetanyl 40 Alfentanil 20 Bolus at time zero Remifentanil 0 0 Fig. 2.12 A pharmacokinetic simulation of predicted fentanyl effect site concentrations (Ce) resulting from three different regimens to administer 300 µg of fentanyl (a single 300-µg bolus, three 100-µg boluses every 20 minutes, an infusion of 300 µg at a constant rate over 1 hour). The horizontal dotted line indicates a typical analgesic fentanyl level. The colored vertical dotted lines represent the time at which the fentanyl concentration falls permanently below the typical analgesic level. See the accompanying text for a detailed explanation. The simulations were conducted with pharmacokinetic-pharmacodynamic parameter estimates from the literature.107 Hydromorphone Sufentanil 5 10 15 20 25 30 Minutes after bolus injection (min) Fig. 2.13 A simulation exploring bolus injection front and back-end pharmacokinetic behavior for a variety of commonly used opioids. For comparison purposes, the effect site concentrations (Ce) are normalized to the percentage of the peak. See the accompanying text for a detailed explanation. The simulations were conducted with pharmacokinetic-pharmacodynamic parameter estimates from the literature.69,107–113 that is un-ionized and unbound — see Fig. 2.6). Interestingly, morphine’s front-end kinetics are notably different. Morphine does not approach a substantial fraction of the ultimate peak until 20 to 30 minutes have elapsed. The simulations depicted in Fig. 2.13 have obvious clinical implications. When a brief pulse of opioid effect followed by a quick offset is desirable (such as a brief period of intense analgesia before injection of local anesthetic during a regional block), remifentanil or alfentanil would be rational choices. In contrast, when the clinical situation calls for a slower onset followed by a more sustained period of opioid effect, one of the other opioids may be more appropriate. Given the lockout period of a typical patient-controlled analgesia (PCA) dosing regimen, it is surprising that morphine has been the mainstay of PCA therapy; fentanyl’s latency to peak effect of 4 to 5 minutes is much more favorable for PCA, particularly in terms of avoiding a “dose stacking” problem wherein the patient requests additional doses before the prior doses have reached their peak effect. Infusion Front-End Kinetics The relevant questions concerning the posology of anesthetic infusions are similar to those for bolus injections (see Table 2.2). The simulations plotted in Fig. 2.14 explore the front-end kinetic behavior of a number of opioids when administered by infusion. With the exception of remifentanil, no opioid comes anywhere near the ultimate steady-state level even after many hours of infusion. Remifentanil is the only opioid in common use that can be expected to reach steady state during the time course of typical anesthetic. Several clinically important points are evident from inspection of the simulations presented in Fig. 2.14. Most obviously, although remifentanil is a notable exception, the practitioner must be aware that when an opioid infusion is ongoing, the concentrations will continue to rise for the duration of any conceivable anesthetic (this general rule applies less fully to alfentanil). An extension of Downloaded for Vicente Gonzalez ([email protected]) at Florida International University from ClinicalKey.com by Elsevier on April 29, 2024. For personal use only. No other uses without permission. Copyright ©2024. Elsevier Inc. All rights reserved. 32 SE C T I O N I Basic Principles of Pharmacology Infusion Front-End Kinetics Alfentanil Remifentanil 80 Morphine Sufentanil 60 Fetanyl 40 Hydromorphone 20 Infusion begins Minutes to 50% decrement in Ce Percent of steady-state Ce 100 Infusion Back-End Kinetics 500 400 300 200 100 Ketamine Etomidate 0 100 200 300 400 500 600 Simulations exploring infusion front-end pharmacokinetic behavior for a variety of commonly used opioids. For comparison purposes, effect site concentrations (Ce) are normalized to a percentage of the eventual steady-state concentration. See the accompanying text for a detailed explanation. The simulations were conducted with pharmacokinetic-pharmacodynamic parameter estimates from the literature.69,107–113 this observation is that if the level of opioid effect part way through a long anesthetic is appropriate, it would be necessary to decrease the infusion rate somewhat to maintain the existing therapeutic concentration (without the infusion rate decrease, the concentration will continue to rise). That remifentanil reaches a steady state quickly is at least partially responsible for its popularity as part of a total intravenous anesthetic (TIVA) technique. However, even for remifentanil, it is best to precede an infusion with a bolus injection as a “loading dose” to speed achievement of a steady-state drug level (see later text). Because they take so long to reach steady state, the loading dose concept is even more important when using the other opioids in Fig. 2.14. Infusion Back-End Kinetics The simulations presented graphically in Fig. 2.15 summarize the back-end kinetic behavior for a number of commonly used intravenous sedative-hypnotics when administered by infusion. In terms of anesthesia posology, these simulations are valuable in explaining how various sedative-hypnotics exhibit different recovery profiles depending on the duration of the infusion. The simulation also helps guide therapeutic decision making in terms of the best time to turn off a continuous infusion to promote a timely emergence from anesthesia. The simulations in Fig. 2.15 predict the time necessary to achieve a 50% decrease in drug concentration after termination of a variable length continuous infusion to a steady-state drug level. Using concepts originally developed for opioids,7 these simulations are an attempt to provide context-sensitive half times (CSHTs).6 In this case the context is the duration of a continuous infusion. The CSHT has also been referred to as the 50% decrement time (although the decrement time concept usually refers to simulations of effect site concentrations, not plasma). 8 These simulations illustrate how PK parameters interact in a complex way that can only readily be understood through model simulation.7,72 The 0 100 200 300 Propofol 400 500 600 Infusion duration (min) Infusion duration (min) Fig. 2.14 Midazolam 50 0 0 Thiopental Dexmedetomidine Fig. 2.15 Simulations exploring the infusion back-end pharmacokinetic behavior for a variety of commonly used sedative-hypnotics. This simulation is usually referred to as the context-sensitive half-time (the context being the duration of a continuous, steady-state infusion) or the 50% decrement time (for effect site concentrations). The upper portion of the vertical axis is shown on a more compressed scale than the lower portion. See the accompanying text for a detailed explanation. The simulations were conducted with pharmacokinetic-pharmacodynamic parameter estimates from the literature.114–120 Ce, Effect site concentration. CSHT simulations also illustrate the utter irrelevance of using terminal half-lives to predict drug offset behavior for intravenous anesthetics described by three compartment models.72 Interpreted from a clinical perspective, CSHT simulations are very instructive. For example, they provide an explanation for why propofol has been so widely embraced as an intravenous anesthetic for TIVA; propofol has a relatively short, time-independent CSHT that is well suited for longer infusions. The CSHT simulations also explain at least one reason why thiopental and midazolam never emerged as popular anesthetics for infusion (and why “barbiturate coma” was sometimes complicated by extremely long recovery times). Another interesting clinical correlation from the CSHT simulations is that when infusion duration is very brief (i.e.,