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.

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 ).

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.)

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. 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).

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. 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 possible to achieve large reductions in effect with relatively small decreases in concentration.

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. E ₀ , Effect at zero drug concentration; E _max , maximal drug effect; EC ₅₀ , 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.)

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 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.

Posology

Although defining exactly what comprises the field of “clinical pharmacology” is challenging, 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 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 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.

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.

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.

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. 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.

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.

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 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 C ₅₀ (sometimes called the EC ₅₀ , the effective concentration producing 50% of maximal effect; see Fig. 2.2 ). Obviously, the lower the EC ₅₀ , the more potent is the drug. The EC ₅₀ 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.

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, 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.

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; k ₁₂ , k ₁₃ , and so on, rate constants characterizing drug movement between compartments and out of the system; k _e0 , rate constant for drug elimination out of the effect compartment; V ₁ , V ₂ , and so on, compartment volumes. See the accompanying text for a detailed explanation.

The key pharmacobiophasics parameter, expressed in units of inverse time, is a rate constant called k _e0 (see “ PK-PD Model Building Methods ” in later text). The k _e0 characterizes the rate of equilibration between plasma and effect site concentrations. When k _e0 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 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 ).

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 H ₂ O droplet represents high water solubility. The +/− lightning bolt indicates a charged molecule. The ribbon-like structure represents a protein binding molecule such as albumin.

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. 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), modern-day 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). Therefore from a strictly pharmacologic perspective, anesthesiology can be thought of as the practice of PD synergism using central nervous system depressants.

Because anesthetics are rarely administered alone, understanding the interactions between drugs is critical to their safe and effective use. Although PK interactions (i.e., where one drug alters the concentration of another) are sometimes observed in select clinical circumstances, 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. 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. 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 three-dimensional 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. Response surface methods yield a set of parameters that indicate whether the interaction is additive, synergistic, or antagonistic.

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. Various equations are used to represent the pharmacologic processes of interest. 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!” There is no question that PK-PD models, despite their limitations, are very useful in refining the posology of anesthesia practice.

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. Elements of a well-designed PK-PD modeling experiment for an intravenous anesthetic include careful attention to the administered dose by infusion ; frequent, prolonged sampling of arterial blood for concentration measurement ;use of a quality-assured, validated drug assay; and administration of sufficient drug to elicit maximal or near-maximal effect (but not too rapidly). Without quality raw data it is impossible to characterize the pharmacologic system using modeling techniques.

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; E ₀ , effect at zero drug concentration; E _max , maximal drug effect; EC ₅₀ , concentration that produces 50% of maximal drug effect; γ, steepness of the curve.

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. 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 .

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. 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). 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). The PK model enables prediction of the time course of drug concentrations in blood or plasma.

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.

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 ). This delay (or hysteresis 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 k _e0 (see previous text). 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 (E ₀ ). 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 concentration-effect 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 (E _max ). 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.

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. 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. 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

a In this chapter, “parameter estimates” will sometimes be referred to as just “parameters.”

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; E ₀ , effect at zero drug concentration; E _max , maximal drug effect; C ₅₀ , concentration that produces 50% of maximal drug effect;

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 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). Special techniques such as “mixed-effects” modeling (e.g., the NONMEM program and others) have been developed and refined to estimate typical PK-PD parameter values for an entire population (and also the intersubject variability of the parameters). 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.

Limitations in Building & Applying PK-PD Models

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.

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. 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 systems is ubiquitous in nature and is almost always a function of the unique, tetrahedral bonding characteristics of the carbon atom.

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