General Principles of Pharmacokinetics and Pharmacodynamics

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169 General Principles of Pharmacokinetics and Pharmacodynamics

Critically ill patients admitted to intensive care units (ICUs) suffer from a variety of physiologic insults that accompany their severe illness. These insults, combined with the rapidly changing physiologic status of the patient, can make appropriate drug dosing a challenging problem for the clinician. An understanding of the pharmacokinetic implications of these physiologic changes and their subsequent effect on pharmacodynamics is required to properly treat critically ill patients. This chapter reviews the basic principles of pharmacokinetics and pharmacodynamics with an emphasis on how they might be affected by critical illness.

Pharmacokinetics and pharmacodynamics describe, respectively, the amount of drug in the body at a given time and the pharmacologic effects caused by the drug.1 Pharmacokinetics describes the movement of a drug into, within, and out of the body over time, whereas pharmacodynamics explains the effects the drug has on the body that result in a clinical response. A general understanding of pharmacokinetic parameters such as clearance, volume of distribution, half-life, steady state, and absorption, along with pharmacodynamic principles such as receptor theory, potency, affinity, tolerance, and minimum effective concentration greatly enhances the clinician’s ability to make informed choices in the treatment of the critically ill patient.

image General Principles of Pharmacokinetics

Clearance, volume of distribution, half-life, and bioavailability are four pharmacokinetic parameters that allow the clinician to better estimate dosing requirements. If the concentration of a drug in an easily assessable sampled fluid (e.g., plasma, urine, saliva) correlates well with the pharmacologic response (therapeutic or toxic) to the drug, then the application of pharmacokinetics in dosing is likely to be beneficial.2 Usually the concentration of a drug cannot be measured at the exact site of action (e.g., a receptor on the cell surface), so it is necessary that there be a predictable relationship between the concentration that is measurable and the concentration at the site of the effect.3,4 These concentrations do not have to be equal, but they should reflect a similar direction and magnitude of change over time (Figure 169-1).

Measurement of the relationship between drug concentration and therapeutic or toxic response in a large number of patients allows development of a therapeutic range or target concentration for that drug (Figure 169-2).510 Table 169-1 lists a number of drugs commonly used in the ICU for which therapeutic ranges have been established and for which therapeutic drug monitoring is often recommended.11,12 Critically ill patients have a multitude of host factors (e.g., hemodynamic status, decreased organ function, nutritional status, concurrent disease states) that increase the likelihood that individualized drug dosing based on individualized pharmacokinetic assessment will be beneficial (Figure 169-3).1316 There can be gender-related differences in both pharmacokinetic and pharmacodynamic responses.1719 Individual chapters in this text are devoted to many of these agents and their adjustments for dosage in patients with renal or hepatic failure.

TABLE 169-1 Therapeutic Ranges of Drugs Commonly Used in Critical Care

Drug Therapeutic Range
Amikacin Trough < 5 µg/mL
Peak < 30 µg/mL
Cyclosporine Whole blood, 150 ng/mL
Digoxin 0.50-2.0 ng/mL
Gentamicin* Trough < 2 µg/mL
Peak < 10 µg/mL
Lidocaine 1.5-5 µg/mL
Phenytoin 10-20 µg/mL
Quinidine 2-5 µg/mL
Theophylline 10-20 µg/mL
Tobramycin* Trough < 2 µg/mL
Peak < 10 µg/mL
Vancomycin Trough < 5 µg/mL
Peak < 30 µg/mL

* Once daily aminoglycoside dosing may result in different therapeutic ranges.

Vancomycin concentrations are currently focusing on higher peak concentrations, and practice varies considerably between sites.

Pharmacokinetic Models

The pharmacokinetic concepts of clearance, volume of distribution, half-life, and bioavailability are based on physiologic principles.20 The physiologic processes governing these concepts are enormously complex, and many simplifying assumptions must be made before the mathematics describing drug concentrations become tractable. Although sophisticated computer modeling approaches are available in research settings, most of the clinically useful pharmacokinetic equations are based on one- or two-compartment models (Figure 169-4).21

The simplest model and the most basic equations describe the one-compartment model. When the drug enters the compartment, it is assumed to be instantaneously and completely mixed in a given volume of distribution (V) resulting in a uniform concentration throughout the compartment. The parameter K is the first-order rate constant that reflects the usual situation of elimination being a first-order linear process. The drug is assumed to enter the compartment instantaneously in the case of an intravenous bolus dose. If the dosage is administered through oral or intramuscular routes, entry into the compartment is assumed to occur at a rate defined by a first-order absorption rate constant (Ka). Entry into the compartment is assumed to occur at a rate described by a zero-order rate constant (Ro) if the drug is administered by constant intravenous infusion. Bioavailability (F) is defined as the fraction of the administered dose that reaches the systemic circulation.

Clearance (CL) is a primary parameter that can be physiologically associated with a particular organ in the body such as the liver or kidney. Clearance can be calculated according to the equation CL = K × V, leading to the impression that CL is a function of the parameters K and V. However, this arrangement of the equation is not correct from a physiologic point of view. CL and V are both primary parameters, and K is a secondary parameter. The first-order rate is determined by changes in either CL or V, and the equation is correctly written: K = CL/V.

Half-life (t1/2) is a useful measure of how quickly a drug is eliminated from the body, and it is related to the first-order elimination rate constant:

image

Specifically, t1/2 defines the length of time it takes for the drug concentration to decrease by one-half. In a linear pharmacokinetic system with first-order elimination, the t1/2 is a constant, and it takes the same amount of time for the concentration to fall from 100 to 50 arbitrary units as it does to decline from 50 to 25 arbitrary units (Figure 169-5).

The single-compartment model allows concentration at any point in time to be calculated using the following equation:

image

where Δt is the time elapsed between the measurement of two concentrations, C1 and C2. It is the properties of this equation that give rise to the familiar exponentially decreasing concentration-time curve, which becomes linear when plotted on semilog coordinates.

The human body is not a single well-stirred compartment, and it is amazing that such a simple mathematical model can be so useful in the clinical setting. If the body is conceptualized as consisting of individual tissues and organs, the same mathematical treatment can be applied. The concept of the volume of distribution has to be somewhat modified to recognize not only the physical size of the organ or tissue, but also the fact that drugs accumulate to differing degrees in different tissue spaces.22,23 For example, lipophilic drugs have a high affinity for adipose tissue, and this property is reflected by a large partition coefficient (R). The time constant associated with each tissue is a function of the rate of blood flow to that tissue (Q), the physical volume of the tissue (VT), and the partition coefficient. The time constant determines the rate at which equilibrium is reached. As a result, it is possible to construct a set of exponential equations with a time constant unique to each tissue:

image

There is a branch of pharmacokinetics known as physiologically based pharmacokinetic modeling that uses blood flows, organ volumes, and partition coefficients to characterize concentration-time profiles.2427 According to this approach for pharmacokinetic modeling, each tissue space ultimately contributes to the venous pool (Figure 169-6). However, the overall shape of the concentration-time profile in the venous blood is controlled not by the number of tissue spaces or their effective volumes, but by their time constants. Tissues with similar time constants, Q/(V × R), produce similar drug profiles in their venous outflows and appear as a single exponent in pooled venous blood. Practically speaking, many tissues and organs reach equilibrium over similar time frames, and often no more than two distinct time constants are observed. Therefore, this situation can be described adequately by a two-compartment model, characterized by a rapidly distributing central compartment and a more slowly equilibrating peripheral compartment (Figure 169-7). The equation describing the concentration-time profile for the two-compartment model is:

image

The distinguishing feature of this biexponential equation is that when it is plotted on semilog coordinates, the concentrations are the sum of two distinct straight lines. Hence, there are two half-lives. One is known as the terminal or β half-life, and the other is the rapid distribution or α half-life. Once the rapid distribution exponential becomes negligible in the equation, all that remains is the slower exponential term, and the concentration-time profile resembles that for a single-compartment drug. Consequently, the equation:

image

in which β replaces K, can still be used to predict concentrations, as long as both C1 and C2 are in the postdistributive phase. This sum-of-exponentials approach can be extended to three-compartment or even more complex models, but it is difficult to obtain all the concentrations needed to characterize each exponent.

Clearance

Clearance (CL) is a primary pharmacokinetic parameter that measures the ability of the body to eliminate a drug.28,29 It is often stated that clearance is the volume of blood (plasma) that is completely cleared of drug per unit time. Although this is one way to define clearance, it does not capture the relationship between drug clearance (mL/min) and the rate of drug elimination (mg/h). In pharmacokinetics, the general concept of clearance is defined as the rate of elimination relative to the concentration. In a first-order pharmacokinetic system, the rate of elimination is proportional to the drug concentration, and clearance is this proportionality constant:

image

Clearance is clinically useful because it can be related directly to the organ of elimination. We can talk about renal clearance, hepatic clearance, or biliary clearance, and the sum of each of the individual clearances is the total body clearance.30,31 The immediate clinical consequence is the ability to adjust doses in response to changes in specific organ function. For example, a patient with developing renal failure is likely to require a reduction of the dose of a drug that is eliminated by the kidney, but not necessarily a reduction of the dose of a drug that is eliminated by the liver.32 If the clearance of a drug is known to be 50% renal and 50% hepatic, and renal function is decreased by 50%, it is necessary to reduce the dose by only 25% to maintain the same concentration.

The primary clinical utility of clearance is that it is the single pharmacokinetic parameter that determines overall drug exposure. The area under the curve (AUC) on a plot of drug concentration as a function of time is often taken as a measure of drug exposure, and it is determined from the dose and clearance (CL):

image

This relationship is also observed when the steady-state concentration is considered as the measure of drug exposure. During a continuous intravenous infusion, the steady-state concentration (Css) is solely a function of the infusion rate (Ro) and the clearance (CL):

image

Notice that Css is not a function of the volume of distribution. As counterintuitive as it may seem, doubling the volume of distribution will not result in a halving of Css. The important point to keep in mind is that the equation is predicting the concentration at steady state. During a constant infusion at steady state, the rapid doubling of the volume of distribution will only transiently decrease the concentration by half. If the infusion rate remains unchanged, the concentration will return to the same steady-state concentration, as long as clearance remains unchanged.

The same principle applies to intermittent intravenous or oral dosing as well as continuous infusion. With intermittent dosing, drug concentrations go up and come down during each dosing interval. The average concentration at steady state (Css, avg) is a time-averaged concentration (i.e., the mean of all concentrations during the dosing interval); as in the case of a constant infusion, it is a function of clearance and the dosing rate. In the case of oral administration, the dosing rate becomes slightly more complicated, in that it is a function of the dose administered (D), the dosing interval (τ), and bioavailability (F):

image

As before, overall drug exposure is not influenced by volume of distribution, but it does change in proportion to changes in clearance or the dosing rate, through changes in F, D, or τ.

Volume of Distribution

The volume of distribution (V) is another primary pharmacokinetic parameter that is useful in determining the change in drug concentration for a given dose.33 After an intravenous bolus dose in a one-compartment pharmacokinetic model, the change in concentration (ΔC) between Cmax and the concentration immediately before the dose is administered is a function of the dose (D) and the volume of distribution (V):

image

This equation is useful for predicting both the concentration after a first bolus dose and the increase in concentration at any point in time after a bolus dose. If a concentration before administration of a bolus dose is known or can be estimated, the equation can be used to predict the increase in concentration after the dose is administered (see Figure 169-5). It is important to recognize that the calculated value of ΔC must be added onto the pre-dose concentration to estimate the Cmax after the bolus dose. This equation is also useful for estimating the dose needed to reach a given concentration. If it is known that the volume of distribution is 0.45 L/kg, and a Cmax of 10 mg/L is desired after the loading dose, the dose is estimated to be 10 mg/L × 0.45 L/kg = 4.5 mg/kg. It is not necessary to have a steady-state condition to use this equation, a fact that makes it very useful in critical care.

The value for volume of distribution does not necessarily coincide with any particular physiologic space. The veracity of this statement becomes readily apparent when one considers a drug such as digoxin which has a volume of distribution of approximately 440 L. Clearly, a volume of distribution of that magnitude cannot have a relationship to any physiologic space in a standard-sized human. For this reason, the term apparent volume of distribution is often used.

The concept of volume of distribution gets more confusing when more than one compartment is needed to describe the pharmacokinetics of a drug. Mathematically, the volume of distribution is a hypothetical volume that is needed to relate the amount of drug in the body to a measured concentration in a fluid (usually plasma). Unlike the one-compartment model, wherein all of the drug in the body is regarded as being in a single compartment until it is eliminated, drug also circulates through additional compartments in a multicompartment model. In this situation, the volume of distribution must increase as drug distributes to other compartments until pseudodistribution equilibrium among all compartments is reached. Technically, an infinite number of volumes of distribution are observed as this equilibration process occurs, but only three are commonly defined. The volume of distribution of the central compartment (Vc) is the volume of the usual sampling compartment; it is always the smallest volume term. Immediately after administration of an intravenous bolus, all added drug is in the central compartment, and Vc can be used to calculate a change in concentration.

The volume of distribution increases over time until a distribution equilibrium is reached among all compartments. This is the largest value for the volume of distribution. The fact that distribution equilibrium has occurred can be determined from a log-concentration versus time plot (see Figure 169-7). The curve becomes log-linear when the rate of drug entry into each peripheral compartment equals the rate of exit from each compartment. Because it is often calculated using the clearance and the β or terminal elimination half-life, this volume is often called Vβ:

image

The third commonly used volume term is the steady-state volume of distribution (Vss). It is the sum of the volumes of all the compartments in the model. If a drug were infused to steady state, Vss would be the proportionality constant relating the steady-state concentration to the total amount of drug in the body. Practically speaking, Vss is not often used in individualizing drug dosing.

Half-Life

The half-life (t1/2) is a pharmacokinetic parameter defined as the length of time it takes to reduce the drug concentration by half (see Figure 169-5).33 The half-life is referred to as a secondary parameter because it is a function of the two primary parameters, clearance and volume of distribution:

image

A change in either clearance or volume of distribution results in a proportional change in half-life.

Because the half-life characterizes how rapidly concentration decreases over time, the primary clinical application for this parameter is for determining how often to dose a drug. Drugs with rapid half-lives have to be dosed more frequently than drugs with longer half-lives. The dosing of aminoglycoside antibiotics exemplifies this concept. The half-life for an aminoglycoside is relatively short in patients with good renal function (high clearance), and the drug may have to be dosed every 6 hours. In patients with poor renal function, the half-life is relatively longer, and dosing may be prolonged to 12- or 24-hour intervals to maintain appropriate peak and trough concentrations. In the critical care patient, the development of renal failure can significantly change aminoglycoside clearance, and the accompanying change in drug half-life will necessitate a change in dosing interval.

In a one-compartment system with constant clearance and volume of distribution, drug half-life also is constant. However, in a multicompartment model, the volume of distribution increases over time as drug equilibrates into tissue compartments until Vβ is reached. According to the previous equation, the half-life also increases over time and eventually reaches a maximum at t1/2β (see Figure 169-7).

In multicompartment models, there is usually one half-life of interest for each compartment. These half-lives are derived from the hybrid time constants associated with each compartment. In a two-compartment model, these two exponentials are typically called α and β and are arbitrarily termed the rapid and slow exponents, respectively. These time constants give rise to the rapid or distribution t1/2α and the slower or terminal t1/2β. One useful way to think about distribution half-lives is analogous to the standard way of thinking about any half-life. In the one-compartment model, it takes five half-lives for 97% of the drug to be eliminated from the body. The situation is similar for each exponent, but the interpretation is that it takes five distribution half-lives for that exponent to become negligible in the sum of exponentials equation. In other words, it takes five α half-lives before the rapid distribution phase is completed, and the remaining concentration-time profile reflects the elimination or β phase.

Most drugs have a rapid distribution phase that could be detected if concentrations were measured frequently enough. Aminoglycosides again are a good illustrative example of this concept, because they have a rapid, although not instantaneous, distribution phase (Figure 169-8). With a distribution phase half-life of 5 to 10 minutes, it would take approximately 25 to 50 minutes before the log-linear elimination phase could be observed. It is this distribution process that is the basis for the recommendation to wait approximately 1 hour after the end of an infusion before sampling blood to measure the aminoglycoside concentration. If a blood sample is obtained before this time, the drug still will be in the distribution phase, and the concentration measured will lead to underestimation of the drug half-life. In addition, slowly equilibrating compartments have been demonstrated when aminoglycoside concentrations are measured during washout.34 Aminoglycosides are usually dosed frequently enough so that the slowly equilibrating compartment is not detected.

Bioavailability

The extent of drug absorption, termed bioavailability (F), is generally referenced to the amount of drug available systemically when the drug is given intravenously. This parameter is determined by comparing the AUC of the drug given by intravenous administration to that of the same drug given by another route (Figure 169-9). The bioavailability of a drug given via the intravenous route is regarded as being 100% (i.e., F = 1.0), and other routes of administration (e.g., oral dosing, intramuscular injection) often have a reduced bioavailability (e.g., F = 0.8, or 80% bioavailability). A number of drug-related and patient-related factors determine bioavailability. In essence, however, F is a function of the degree of absorption and the amount of drug metabolized or eliminated before entering the systemic circulation (first-pass effect).35 Drugs with low bioavailability either cannot be administered by any route other than the intravenous one (e.g., sodium nitroprusside, dobutamine) or require higher doses when given via the oral route compared with the intravenous route (e.g., furosemide, morphine, propranolol). Alternative routes of administration (e.g., rectal, topical, subcutaneous injection, intramuscular injection) are occasionally used in critically ill patients, owing to poor oral bioavailability. These routes all suffer from problems with delayed or poorly predictable serum concentrations. Vasoconstriction, hypoperfusion, edema, gastric suctioning, ileus, diarrhea, and enhanced gastrointestinal motility are all common problems in critically ill patients that can further adversely affect bioavailability.

The first-pass effect (Figure 169-10) refers to the elimination of drug that is absorbed orally but then is metabolized by enzymes in the gut wall or in the liver before reaching the systemic circulation. As a drug is absorbed and passes through the gut wall, it can be acted upon by transport proteins (primarily P-glycoprotein) that actively pump drug molecules back into the lumen of the gastrointestinal tract.3640 All drug molecules that are not pumped out enter the hepatic circulation and are subject to metabolism in the liver before their first opportunity to be presented to the systemic circulation.41 Drugs that have a high hepatic extraction ratio (i.e., are very efficiently removed by the liver) are most likely to show decreased bioavailability due to this first-pass effect; conversely, the bioavailability of these drugs increases if liver dysfunction decreases the hepatic extraction ratio.

Steady State

After an infusion is started, drug concentrations increase and eventually reach a concentration that does not change over time (Figure 169-11).42 At this point, the amount of drug entering the body is equal to the amount leaving it during a given period of time, and steady-state conditions apply. During intermittent dosing, drug concentrations accumulate over time, and eventually a steady state is attained. Drug concentrations increase as more drug is administered or absorbed and decrease during elimination, but the concentration profile over each interval resembles all the other profiles during steady state (Figure 169-12). In the clinical setting, measurement of drug concentration is often delayed for a period equal to five half-lives, because at that point the concentration will reflect 97% of the final steady-state concentration.

image Pharmacodynamics

Pharmacodynamics is the study of the relationship between the concentration of a drug and its pharmacologic effect.2 Pharmacodynamic models are routinely employed during drug development, where they are used to determine drug-dosing regimens. These models can become quite complex, particularly if they are mechanism-based models.

Although a pharmacodynamic model can involve many linked mathematical submodels, this is not the type of model that is likely to be useful in a clinical setting. The principles underpinning the relatively simple Emax model are often adequate.43 Mathematically, the equation relating effect and concentration can be described with the Emax equation:

image

Graphically, this equation has a hyperbolic shape (Figure 169-13). The parameters of this model are the Emax and the EC50. Emax represents the maximal effect attainable due to the drug. The EC50 is the concentration at which half the maximal effect is observed; it is a measure of drug potency. An important feature of this plot reaffirms the intuitive notion that increasing the dose of the drug to higher and higher amounts does not increase the effect of the drug proportionately; eventually, the effect of the drug begins to reach a plateau. In essence, the law of diminishing returns applies: continually smaller increases in effect are observed as the concentration increases. Practically speaking, if the drug concentration is expected to be at the EC50 or lower, increasing the dose will produce a meaningful increase in effect. However, if the concentration exceeds the EC50, increasing the dose may not be warranted, because only small increases in effect may be expected, and the increased concentrations may place the patient at risk for development of adverse (i.e., off-target) drug-related effects.

Several modifications of the basic Emax model are found in the literature. For example, a baseline can be added to the model, the drug may actually be responsible for inhibiting a given effect, the effect can be re-parameterized as a percentage change from baseline, or a sigmoidicity term may be added to create an S-shape in the functional relationship. The same basic features of the plot will be observed. In the absence of drug (i.e., when the concentration equals zero), there will be no effect due to the drug. At the other extreme, there will be a maximal effect that can be elicited by the drug. As concentrations increase beyond EC50, the change in effect due to the drug begins to reach a plateau.

Another point to consider is that time does not appear in the effect model. The concentrations are explicitly defined as steady-state concentrations, and the effect resulting from a given concentration is considered to be a steady-state effect. This model applies when drug in the plasma rapidly equilibrates with drug at the site of action, and there is no indirect mechanism between the concentration at the site of effect and the effect. The more common situation is that the effect lags somewhat behind the concentration (Figure 169-14). If concentrations are going up and coming down over time, as would be expected with an intermittent intravenous or oral dosing schedule, the effect is also expected to go up and down over time, but the time frames may not exactly coincide. For example, the plasma concentration might peak at 1 hour and the effect might peak several hours later. There is a mismatch or disequilibrium between concentration and effect, and a plot of effect versus concentration, with the points connected in time order, yields a hysteresis loop (Figure 169-15). It can be seen that for any given concentration, there are two levels of effect, one on the upswing of the concentration-time curve and the other on the downswing. Both empirical and mechanistic pharmacodynamic modeling approaches have been developed to allow for this disequilibrium. Although the modeling of effect-time curves is achievable, and these models are useful in predicting effects with various dosing regimens, their routine use in clinical settings has been limited.

The pharmacodynamic effects noted with a given drug result from the drug’s interaction with receptors and the resultant activation or inhibition of effects mediated by that receptor. These effects may be either the therapeutic action desired or a toxic effect that is unwanted. Generally it is assumed that the intensity of effect produced by the drug is a function of the quantity of drug at the receptor site, whereas relative potency results from varying degrees of selectivity for the receptor and the receptor’s affinity for binding the drug. More potent drugs elicit a given effect at lower concentrations than less potent drugs.

Drugs that stimulate a response from the receptor are agonists, and those that inhibit a response from the receptor are antagonists. Because antagonists have no effect of their own at the receptor, the net effect depends on both the concentration of the antagonist and that of the agonist that is blocked. The relative concentration of the agonist compared with the antagonist primarily determines the effect observed when an antagonist is competitive for the same binding site as the molecule or drug that stimulates the receptor. Irreversible antagonists, however, either bind with very strong affinity to the receptor so they cannot be displaced or bind to another site on the substrate that interferes with binding at the receptor. The effect of irreversible antagonists is independent of the agonist’s concentration and results in a decrease in the maximal effect of the agonist. The duration of effect for irreversible antagonists is determined by the rate of turnover for the receptor.

Tolerance to a drug is seen when the response at a given dose decreases. This may be a result of receptor down-regulation (decreased number or sensitivity of receptors) or enzyme induction (increased metabolism). Cross-tolerance, as is commonly seen with opioids, occurs when similar drugs act on the same receptor.

Protein Binding

Many drugs are bound to plasma proteins, and the terms bound drug concentration (Cb), unbound (or free) drug concentration (Cu), total (bound plus unbound) drug concentration (Ctot), and unbound (or free) fraction (fu) are frequently used:

image

image

Intuitively, it is clear that when a drug is displaced from its binding sites in the plasma, the increase in unbound drug concentration can lead to adverse reactions. A series of scientific papers published in the mid-1960s set this direction for interpretation of the clinical implications of protein binding. In a study of the interaction between warfarin and phenylbutazone, it was shown that phenylbutazone increases plasma warfarin concentration and also increases prothrombin time.44 In addition, warfarin binding was studied in vitro, and it was clearly shown that phenylbutazone displaces warfarin from binding sites. It was concluded that phenylbutazone potentiates the action of warfarin in vivo by displacing warfarin from its binding to plasma albumin, causing more warfarin to be available to specific sites of biological action. Although it may have been intuitive to relate the in vivo and in vitro observations in a cause-and-effect manner, change in protein binding is not the correct explanation for the drug interaction. It is now known that the drug interaction is mediated through an inhibition of the metabolic clearance of warfarin by phenylbutazone.45

The pharmacokinetic concepts concerning the implications of protein binding were reviewed in 2002 by Benet and Hoener.46 The mathematical approach is not repeated here, but when one employs physiologically based models for clearance, volume of distribution, and protein binding, changes in plasma protein binding can be shown to have little clinical relevance. These clearance concepts illustrate that physiologic parameters (intrinsic clearance, organ blood flow, and protein binding) have an impact on some pharmacokinetic parameters, and these changes result in changes to the shape of the plasma-concentration time profiles. However, these effects do not necessarily translate into clinically relevant changes in effective concentrations. To better understand this concept, the relationship between drug exposure and pharmacodynamic effect must be considered.

One of the more useful measures of exposure is the AUC. When talking about pharmacologic effects, some statement is usually made that effect is related to the unbound concentration. This extrapolates directly to say that the unbound AUC (AUCu) is what is important in determining drug effect.

image

where fu is the fraction unbound, F is the bioavailability, and CL is the clearance.

After standard well-stirred model assumptions are made regarding high- and low-clearance drugs, something quite interesting occurs when the appropriate equations for clearance and bioavailability are substituted into the equation for AUCu. For all drugs administered orally and eliminated hepatically, the fu term cancels out of the equation. Overall unbound drug exposure is not a function of fu at steady-state, and there should be no changes in pharmacologic effect with changes in protein binding. Similarly, it can be seen that the AUCu for all drugs with low extraction ratios—whether administered orally or by the intravenous route, and whether eliminated by the liver or nonhepatically—is not a function of fu after the appropriate substitutions are made. Again, changes in protein binding will not result in changes in the steady-state exposure to the unbound drug. It is important to emphasize that AUCu refers to the AUC based on unbound concentrations. The AUC based on total concentrations, AUCtot, is calculated from this equation: AUCtot = AUCu/fu. If the protein binding of a drug changes such that fu is doubled, AUCtot will be halved, and AUCu will remain the same. The expression for AUCu retains a term for protein binding for all high-clearance drugs administered by the intravenous route (regardless of clearance method) and for high-clearance drugs administered orally that are eliminated by extrahepatic pathways.

To address this issue, Benet and Hoener reviewed pharmacokinetic data on 456 drugs from the literature (Table 169-2). No orally administered drug which has a high elimination ratio and is cleared nonhepatically met the criterion for significant (>70%) protein binding. Only 25 (5%) of the 456 drugs had high extraction ratios, were not administered by the oral route, and met the criterion for which protein binding may influence drug exposure. However, many of these 25 agents are routinely used in critical care (Table 169-3).

TABLE 169-2 Circumstances in Which Changes in Protein Binding Will Affect Unbound AUC

  Low-Extraction-Ratio Drugs High-Extraction-Ratio Drugs
IV Administration
Hepatic clearance No Yes*
Nonhepatic clearance No Yes*
Oral Administration
Hepatic clearance No No
Nonhepatic clearance No Yes

AUC, area under the concentration-time curve; IV, intravenous.

* Only 25 of the 456 drugs reviewed met the criteria.

None of the 456 drugs reviewed met the criteria.

TABLE 169-3 25 Drugs for Which Changes in Protein Binding May Influence Clinical Drug Exposure After Intravenous or Intramuscular Administration*

Alfentanil Itraconazole
Amitriptyline Lidocaine
Buprenorphine Methylprednisolone
Chlorpromazine Midazolam
Cocaine Milrinone
Diltiazem Nicardipine
Diphenhydramine Pentamidine
Doxorubicin Propofol
Erythromycin Propranolol
Fentanyl Remifentanil
Gold sodium thiomalate Sufentanil
Haloperidol Verapamil
Idarubicin  

* Criteria for selection included > 70% protein binding and hepatic clearance > 6.0 mL/min/kg or nonhepatic extraction ratio clearance ≥ 0.28 × renal blood flow (>4.8 mL/min/kg).

Modified from Benet LZ, Hoener BA. Changes in plasma protein binding have little clinical relevance. Clin Pharmacol Ther 2002;71:115-21.

In critically ill patients, protein concentrations can change over time. This is particularly true of the acute-phase reactant, α1-acid glycoprotein (AAG). In addition, some patients (e.g., those undergoing dialysis or those with cachexia) have altered protein binding.47,48 Although it might seem intuitive to automatically adjust drug doses in response to changes in protein binding, the information in Table 169-2 should be considered. The extent of protein binding, route of administration, route of elimination, and extraction ratio of the drug all should be considered when determining whether a change in binding is likely to result in a change in effect.49,50

As a final note on protein binding, care must be taken when evaluating drug concentrations in patients with altered protein binding. Consider the case of phenytoin. The percentage of unbound drug is typically 10% but is approximately doubled (to about 20%) in patients receiving hemodialysis (Table 169-4). If phenytoin were administered as a standard dose to all patients, there would not be a problem; phenytoin is a low-clearance drug, and protein binding should not influence overall unbound exposure whether the drug is administered orally or intravenously. However, phenytoin concentrations are often obtained for the purposes of therapeutic drug monitoring, and efforts are made to achieve circulating levels within the commonly accepted therapeutic range of 10 to 20 mg/L. In patients with normal protein binding, this drug level equates to an unbound therapeutic range of 1 to 2 mg/L. However, in patients with a higher percentage of unbound drug, say 20%, the desired unbound concentration is still 1 to 2 mg/L, but the corresponding total concentration is approximately halved. In such cases, if the dose of phenytoin is increased to bring the total concentration into the therapeutic range, toxicities may be observed because the unbound concentration will be approximately twice the desired value.

image Nonlinear Pharmacokinetics

The application of pharmacokinetics to therapeutic drug monitoring becomes considerably more difficult with drugs that exhibit nonlinearities. With linear pharmacokinetics, parameters are stable over time and across concentrations. Doubling of the dose results in doubling of the concentration, and a given dose provides the same AUC regardless of the dosing history, even when the dose in question is the first dose. Nonlinear pharmacokinetics is a term used when the principle of superposition no longer holds. An increase in dose may result in an increase in concentration that is more than or less than proportional, or it may result in clearance changes over time (Figure 169-16). There are several common types of nonlinearities that occur in the clinical setting.51

Phenytoin is the classic example for nonlinear elimination. Increases in a phenytoin dose can result in greater than proportional increases in concentration. In any pharmacokinetic system, clearance (CL) is defined as the rate of elimination relative to the concentration (C). Hence, an instantaneous rate of elimination can be defined as follows:

image

In a linear elimination process, clearance is constant, and doubling the concentration doubles the rate of elimination. In the case of phenytoin with nonlinear elimination, the rate of elimination does not increase in proportion to the concentration, and clearance is not a constant. The nonlinear elimination of phenytoin occurs because the metabolic pathway responsible for the elimination of the drug is saturable. The enzyme system has a maximum rate of metabolism that can be approached at therapeutic concentrations of phenytoin. These principles can be better understood by considering the rate of elimination described by the Michaelis-Menten equation (Figure 169-17). It has two parameters, the maximum rate of elimination (Vmax) and the concentration that results in one-half the maximum rate (Km):

image

Although the parameters Vmax and Km are constant, it can be seen that clearance is a function of concentration (C). The clearance of a drug decreases as the concentration increases:

image

Although enzyme systems do have maximal rates, the usual concentrations of drug attained in the clinical setting produce rates of elimination that are far below the maximal rate of the enzyme. In the last equation, if C is considerably lower than Km (i.e., negligible), then the quantity, Vmax ÷ (Km + C), is minimally influenced by concentration, and clearance becomes a constant. Therefore, even though many drugs are metabolized by hepatic enzymes, few drugs of clinical interest display detectable nonlinear elimination.

At steady state, the amount of drug eliminated every day must equal the dose taken, so the elimination rate equals the dosing rate. The equation for the steady-state concentration (Css) is:

image

This equation shows that an increase in dosing rate produces a greater than proportional increase in the steady-state concentration. Furthermore, if the dosing rate exceeds Vmax, a steady-state concentration will never be attained. The nonlinear relationship between phenytoin dosing rate and steady-state concentration can be seen for two patients with different Vmax and Km parameters (Figure 169-18). It is easy to understand the difficulties clinicians can encounter when adjusting doses for a drug such as phenytoin which displays nonlinear elimination kinetics. A dose increase that provides a nearly proportional increase in concentration in one patient could produce a much greater concentration in another. These two curves would be straight lines for drugs that displayed linear pharmacokinetics.

Another type of nonlinearity is time-dependent pharmacokinetics. The classic example in this category is the ability of carbamazepine to induce its own metabolism.52 This autoinduction causes the clearance of carbamazepine to increase over time. It is important to gradually increase the dose of carbamazepine during the first few weeks of therapy up to the expected maintenance dose so as to avoid toxicities related to elevated concentrations.

Protein binding also can become saturable with some drugs. Intuitively, one might think that saturation of protein binding would result in higher unbound drug concentrations available to exert desirable effects and toxicities, but it must be kept in mind that the organs responsible for drug clearance are eliminating unbound drug. Therefore, unless the clearance of a drug also changes, the steady-state unbound concentration will remain constant in the face of saturable protein binding. The total concentration (Ctot) is a function of the unbound concentration (Cu) and the fraction unbound (fu):

image

The fraction unbound does increase at higher unbound concentrations, with the result that total concentrations do not increase in proportion to unbound concentrations. This can be perplexing in therapeutic drug monitoring situations. Increases in dose produce less than expected increases in total concentration. As the dose is pushed higher to reach therapeutic concentrations based on total concentration, toxicities may be observed, because saturable binding causes the unbound concentration to be greater than expected.

image Alterations in the Elderly

The number of people over 65 years of age is increasing in the United States and in many European countries, and this growth in the elderly population will result in an even greater percentage of ICU beds occupied by older patients. Compared with younger patients, elderly patients typically are taking more drugs, have more underlying organ dysfunction (hepatic, renal, central nervous system), are more likely to be malnourished and to have altered protein binding on this basis, and have reduced or increased responses to some medications.53 These age-related changes further complicate management of the superimposed critical illness because of large variations among individuals with respect to disposition of drugs (Figure 169-19).

image

Figure 169-19 Physiologic changes with aging that may affect drug distribution are reflected.

(From Evans WE, Schentag JJ, editors. Applied pharmacokinetics: principles of therapeutic drug monitoring. 3rd ed. Vancouver, WA: Applied Therapeutics; 1992, p. 919-43.)

Elderly patients may have a decreased rate of drug absorption, although the total amount of drug absorbed is usually unchanged. As the body ages, the percentage of body mass that is fat increases. This change results in greater distribution of lipophilic drugs into fat, leading to longer half-lives for certain classes of drugs such as anesthetics, barbiturates, and benzodiazepines. Clearance of many drugs is decreased in the elderly, because the hepatic and renal function decreases with increasing age (Table 169-5). These changes can lead to a greater incidence of toxicity because metabolites associated with adverse effects can accumulate. Overall, the same careful attention to dosing required for all critically ill patients must be extended to the elderly. Drugs should be stopped as soon as possible, and dosage increases should be applied cautiously.

TABLE 169-5 Effects of Aging on Clearance of Some Oxidized and Conjugated Drugs

Drug Effect Reference
Oxidized
Chlordiazepoxide ↓↓ Am J Psychiatry 1977;134:559
Desmethyldiazepam ↓↓ Br J Clin Pharmacol 1979;7:119
Erythromycin ↓↓ Eur J Clin Pharmacol 1990;39:161
Haloperidol ↓↓ Neuropsychobiology 1996;33:12
Midazolam ↓↓ Biochem Pharmacol 1992;44:275
Nicardipine ↓↓ Am Heart J 1989;117:256
Nifedipine ↓↓ Br J Clin Pharmacol 1988;25:297
Phenytoin (free) ↓↓ Clin Pharmacokinet 1981;6:389
Propranolol Br J Clin Pharmacol 1979;7:49
Theophylline ↓↓ Eur J Clin Pharmacol 1989;36:29
Verapamil ↓↓ Acta Med Scand 1984;681(Suppl):25
Conjugated
Acetaminophen Br J Clin Pharmacol 1990;30:634
Lamotrigine J Pharm Med 1991;1:121
Lidocaine ↓↓ J Cardiovasc Pharmacol 1983;5:1093
Lorazepam Clin Pharmacol Ther 1979;26:103
Metronidazole Hum Exp Toxicol 1990;9:155
Morphine Age Ageing 1989;18:258
Oxazepam Clin Pharmacol Ther 1981;30:805

—, no effect; ↓, minor effect; ↓↓, significant effect.

Modified from Woodhouse K, Wynne HA. Age-related changes in hepatic function: implications for drug therapy. Drugs Aging 1992;2:243.

image Pharmacogenomics

The responses to drugs can vary widely among individuals within a population, and pharmacogenetic differences have been identified that help explain some of this variability. Pharmacogenomics is the term applied to the study of the expression and regulation of genes that effect drug response. It was initially reported in the 1960s that the N-acetylation pathway of isoniazid metabolism was under genetic control. Based upon these findings, individuals could be classified as being rapid or slow acetylators. Some of the more commonly known genetic polymorphisms that affect pharmacokinetics are related to various enzymes belonging to the cytochrome P450 family.

It is now recognized that genetic variants exist in drug transporters that influence the distribution of drugs into tissue spaces. Research in this area increased dramatically following the recognition that overexpression of the multidrug-resistance protein, MDR-1, in tumor cells led to a loss of drug effect. This class of efflux proteins functions to pump drugs out of cells and is responsible for reducing drug concentrations in tissues such as the brain, testes, gastrointestinal tract, and biliary tree. There is evidence that the expression of some of these transporters is under genetic control. Concentrations of digoxin reportedly are elevated in patients with low MDR-1 expression.54

Drug effects are often mediated through direct receptor proteins, or proteins that influence control of the cell cycle or signal transduction cascades. Polymorphisms in the expression of these proteins could result in pharmacodynamic differences. For example, a polymorphism has been linked to increased down-regulation of the β2-adrenergic receptor when patients are treated with a β-agonist for amelioration of the symptoms of asthma.55 Genetic polymorphisms leading to altered drug sensitivity also have been identified in angiotensin-converting enzyme, the angiotensin II T1 receptor, and the sulfonylurea receptor.56

Mapping the human genome holds enormous potential for improving our understanding of variations among individuals with regard to responses to drug therapy. The pharmaceutical industry is embracing DNA arrays, high-throughput screening, and bioinformatics in the drug development process. It is conceivable that drugs will be specifically developed for patients with a genetic predisposition to a particular disease, and drug doses will be identified for subgroups of patients with particular genetic polymorphisms. Pharmacogenomics is a field that is clearly in its infancy, but it is quite likely to alter the manner whereby drugs are selected and dosed. However, the full clinical relevance of polymorphisms that effect pharmacokinetics and pharmacodynamic processes is not known. At present, there are no clinical instances that clearly mandate genotyping prior to the selection of a drug or a dosing regimen.

Key Points

Annotated References

Benet LZ, Hoener B. Changes in plasma protein binding have little clinical relevance. Clin Pharmacol Ther. 2002;71:115-121.

This manuscript systematically presents the rationale behind the statement that changes in protein binding have little clinical relevance. The physiology and mathematics needed to understand the rationale are presented in an easily understood fashion.

De Paepe P, Belpaire FM, Buylaert WA. Pharmacokinetic and pharmacodynamic considerations when treating patients with sepsis and septic shock. Clin Pharmacokinet. 2002;41:1135-1151.

This review article details the pharmacokinetic changes observed during sepsis and septic shock. It provides a good discussion of the relationships between drug clearance and organ function.

Gibaldi M, Perrier D. Pharmacokinetics, 2nd ed. New York: Marcel Dekker; 1982.

This text provides detailed coverage of the mathematical aspects of pharmacokinetics. Most of the equations used in clinical pharmacokinetics, and their derivations, are presented.

Renton KW. Alteration of drug biotransformation and elimination during infection and inflammation. Pharmacol Ther. 2001;92:147-163.

This review describes the relationship between cytochrome P450 expression and inflammation. Mechanisms of cytochrome P450 regulation and the impact of cytokines on drug metabolism are presented.

Schulz M, Schmoldt A. Therapeutic and toxic blood concentrations of more than 800 drugs and other xenobiotics. Pharmazie. 2003;58:447-474.

This is an excellent reference article that contains an exhaustive compilation of drugs with their therapeutic, toxic, and fatal concentration ranges. The article also provides half-lives and references for each drug.

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