Basic Principles of Pharmacokinetics*
`
`LESLIE Z. BENET AND PARNIAN ZIA-AMIRHOSSEINI
`
`University of California, San Francisco. California 94143-0446
`
`Pharmacokinetics may be defined as what the body does to a drug. It deals with the absorption, distribution,
`and elimination of drugs but also has utility in evaluating the time course of environmental (exogenous)
`toxicologic agents as well as endogenous compounds. An understanding of 4 fundamental pharmacokinetic
`parameters will give the toxicologic pathologist a strong basis from which to appreciate how pharmacokinetics
`may be useful. These parameters are clearance, volume of distribution, half-life, and bioavailability.
`Kevwords. Clearance; volume of distribution; half-life; bioavailability; extraction ratio
`
`INTRODUCTION
`An understanding of the basic principles of phar-
`macokinetics is necessary to appreciate how this
`discipline may serve as a tool for the toxicologic
`pathologist in understanding models that can be used
`for predicting and assessing drug-related toxic re-
`sponses. Pharmacokinetics may be defined as what
`the body does to a drug. It deals with the absorption,
`distribution, and elimination of drugs but also has
`utility in evaluating the time course of environ-
`mental (exogenous) toxicologic agents as well as en-
`dogenous compounds. A fundamental hypothesis of
`pharmacokinetics is that a relationship exists be-
`tween a pharmacologic or toxic effect of a drug and
`the concentration of that drug in a readily accessible
`site of the body (e.g., blood). This hypothesis has
`been documented for many drugs (5, 6), although
`for some drugs no clear relationship has, as yet, been
`found between pharmacologic effect and plasma or
`blood concentrations. An understanding of 4 fun-
`damental pharmacokinetic parameters will give the
`toxicologic pathologist a firm basis from which to
`appreciate how pharmacokinetics may be useful.
`These parameters are clearance, a measure of the
`body’s ability to eliminate drug; volume of distri-
`bution, a measure of the apparent space in the body
`available to contain the drug; half-life, a measure of
`the time required for a substance to change from
`one concentration to another; and bioavailability,
`the fraction of drug absorbed as such as the systemic
`circulation. These 4 parameters will be discussed
`here in detail. A number of classic pharmacokinetic
`
`* Address correspondence to: Dr. Leslie Z. Benet. Department
`of Pharmacy. University of California. San Francisco, California
`94143-0446.
`
`texts may be consulted for further elucidation of
`these and other more detailed principles (4, 5, 8, 12,
`15).
`
`CLEARANCE
`Clearance is the measure of the ability of the body
`to eliminate a drug. Clearance is expressed as a vol-
`ume per unit of time. Clearance is usually further
`defined as blood clearance (CL,), plasma clearance
`(CLp), or clearance based on the concentration of
`unbound or free drug (CL.), depending on the con-
`centration measured (Cb, Cp, or CJ.
`Clearance by means of various organs of elimi-
`nation is additive. Elimination of drug may occur
`as a result of processes that occur in the liver, kidney,
`and other organs. Division of the rate of elimination
`for each organ by a concentration of drug (e.g., sys-
`temic concentration) will yield the respective clear-
`ance by that organ. Added together, these separate
`clearances will equal total systemic clearance:
`C~CpatlC + CL-n.1 + CLo1hcr = CLyS1Cfi11O~
`Other routes of elimination could include that in
`saliva or sweat, partition into the gut, and metab-
`olism at sites other than the liver (e.g., nitroglycerin,
`which is metabolized in all tissues of the body).
`Figure 1 depicts how a drug is removed from the
`systemic circulation when it passes through an elim-
`inating organ. The rate of presentation of a drug to
`a drug-eliminating organ is the product of organ
`blood flow (Q) and the concentration of drug in the
`arterial blood entering the organ 1C~). The rate of
`exit of a drug from the drug eliminating organ is the
`product of the organ blood flow (Q) and the con-
`centration of the drug in the venous blood leaving
`the organ (C~ ). By mass balance, the rate of elimi-
`
`( I )
`
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`116
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`FIG. 1.-A schematic representation of the concentration-clearance relationship.
`
`nation (or extraction) of a drug by a drug-eliminating
`organ is the difference between the rate of presen-
`tation and the rate of exit:
`
`Extraction ratio (ER) of an organ can be defined as
`the ratio of the rate of elimination to the rate of
`presentation:
`
`The maximum possible extraction ratio is 1.0 when
`no drug emerges into the venous blood upon pre-
`sentation to the eliminating organ (i.e., C,, = 0). The
`lowest possible extraction ratio is zero when all the
`drug passing through the potential drug-eliminating
`organ appears in the venous blood (i.e., Cy = CB).
`Drugs with an extraction ratio more than 0.7 are by
`convention considered as high extraction ratio drugs,
`whereas those with an extraction ratio less than 0.3
`are considered as low extraction ratio drugs.
`The product of organ blood flow and extraction
`ratio of an organ represents a rate at which a certain
`volume of blood is completely cleared of a drug.
`This expression defines the organ clearance (CLorgan)
`of a drug.
`
`It is obvious from Equation 6 that an organ’s clear-
`ance is limited by the blood flow to that organ (i.e.,
`when ER = 1 ). Among the many organs that are
`capable of eliminating drugs, the liver has the high-
`est metabolic capability. The liver may also clear
`drug by excretion in the bile. Kidney eliminates drugs
`primarily by excretion into the urine, but kidney
`metabolism may occur for some drugs.
`Drug in blood is bound to blood cells and plasma
`proteins such as albumin and al-acid glycoprotein.
`Only unbound drug molecules can pass through he-
`patic membranes into the hepatocytes where they
`are metabolized by hepatic enzymes or transported
`into the bile. Thus, to be eliminated, the drug mol-
`ecules must partition out of the red blood cells and
`dissociate from plasma proteins to become unbound
`or free drug molecules. The ratio of the unbound
`drug concentration (C&dquo;) to total drug concentration
`(C) is defined as the fraction unbound (fu):
`
`Because an equilibrium exists between the unbound
`drug molecules in the blood cells and the plasma,
`the rate of elimination of unbound drugs is the same
`in the whole blood as in the plasma at steady state.
`Thus,
`
`where the subscripts p, b, and u refer to plasma,
`blood, and unbound, respectively.
`
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`Since the pioneering discussions of clearance in
`the early 1970s (11. 13), much has been made of
`the differences between high and low clearance (ex-
`traction ratio) drugs and the interpretation of the
`effects of pathological and physiologic changes on
`the kinetics of drug elimination processes. Utilizing
`the simplest model of organ elimination. designated
`the venous equilibration or well-stirred model, the
`blood clearance of an organ can be expressed ac-
`cording to the following relationship:
`
`ir B
`
`roT
`
`Here, (fu)b represents fraction unbound in the blood
`and CLi,,, represents intrinsic clearance of the organ,
`that is, the ability of the organ to clear unbound
`drug when there are no limitations due to flow or
`binding considerations. Knowing that organ clear-
`ance is equal to the product of organ blood flow and
`extraction ratio of the organ (Equation 6), according
`to the well-stirred model, then
`
`Examining Equations 9 and 10, one finds that for
`drugs with a low extraction ratio Qorgan is much great-
`er than (f~)~ . CL,~,; thus, clearance is approximated
`by (f~)~ . CL;~,. However, in the case of a high ex-
`traction ratio drug (i.e., ER approaching 1.0), (fJb’
`CL;~, is much greater than Qorgan, and clearance ap-
`proaches Qorgan- Therefore, the clearance of a high
`extraction ratio drug is perfusion rate-limited.
`Eauations 11 and 12 describe these two cases:
`
`Examples of low and high extraction ratio drugs
`are chlordiazepoxide and imipramine, respectively.
`The pharmacokinetic parameters for both drugs in
`humans are shown in Table I (6). Due to the low
`recovery in the urine (% excreted unchanged), one
`may assume that these drugs are mainly eliminated
`by the liver. Thus, hepatic extraction ratios for
`chlordiazepoxide and imipramine are 0.02 and 0.7,
`respectively. Note that the value of (fJb -CLint (35.8)
`for chlordiazepoxide is much lower than liver blood
`flow (1,500 mlimin) and conversely the value of
`(fu)b’ CLmt for imipramine is more than twice the
`value of liver blood flow. Thus, elimination (clear-
`ance) of chlordiazepoxide is limited by fraction un-
`bound and the intrinsic clearance of the li~=er. where-
`as that of imipramine is limited by liver blood flow.
`
`TABLE 1. - Pharmacokinetic parameters of chlordiaz-
`epoxide and imipramine in 70-kg humans.
`
`117
`
`Elimination of both chlordiazepoxide and imipra-
`mine were studied in an in vitro rat microsomal
`system prepared from livers of rats that were in-
`jected with phenobarbital (an inducer of the P-450
`enzyme family). In this in vitro system, the elimi-
`nation of both drugs was higher in the phenobar-
`bital-induced microsomes than in control micro-
`somes. In vivo measured clearance of chlordiaze-
`poxide in rats who had received phenobarbital was
`higher than the control rats (no phenobarbital ad-
`ministration). This is due to the fact that induction
`of enzymes by phenobarbital increases the hepatic
`CLin, and, because for this low extraction ratio drug
`CL,,cpaUC ~ (fJb’ CLtnto a higher CL is measured in
`the presence of phenobarbital. In contrast, the in
`vivo measured clearance of imipramine in rats that
`received phenobarbital could not be differentiated
`from that measured in control rats. This is due to
`the fact that the value of (fJb’ CL,,,, for imipramine
`is already greater than liver blood flow. Thus, in
`vivo, liver blood flow is the limiting factor for the
`elimination of this drug and, because of this, enzyme
`induction will not substantially affect clearance of
`imipramine.
`The ability of an organ to clear a drug is directly
`proportional to the activity of the metabolic en-
`zymes in the organ. In fact, it is now well recognized
`that the product (fJb’ CLint is the parameter best
`related to the Michaelis-Menten enzymatic satura-
`bility parameters of maximum velocity (Vmax) and
`the Michaelis constant (Km) as given in Equation
`13, where Corpn is the total (bound + unbound)
`concentration ofdrue in the or2.an of elimination:
`
`Thus. only low extraction ratio drugs will exhibit
`saturable elimination kinetics follow ing intravenous
`dosing. However, as shown subsequentIN in Equa-
`tion 29. AUCs (area under the curves) following oral
`doses wilt be inversely related to CL,n, for both high
`and low extraction ratio drugs.
`Most drugs are administered on a multiple dosing
`
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`118
`
`regimen, whereby after some time drug concentra-
`tions reach a steady-state level. At steady state, the
`rate of drug input to the body is equal to the rate of
`drug elimination from the body. The input rate is
`given by the dosing rate (dose/T, where T is the dos-
`ing interval) multiplied by the drug availability (F),
`whereas the rate of elimination is given by clearance
`multiplied by the systemic concentration (C). That
`is, at steady state,
`
`When Equation 15 is integrated over all time from
`0 to infinity, Equation 16 results:
`
`- .. -
`
`,
`
`. -- , , . - - -,
`
`, , ,,
`
`where AUC is the area under the concentration-
`time curve and F is the fraction of dose available
`to the systemic circulation.
`Thus, clearance may be calculated as the available
`dose divided by the AUC:
`
`As described in the text following Equation 12, the
`maximum value for organ clearance is limited by
`the blood flow to the organ. The average blood flows
`to the kidneys and the liver are, respectively, ap-
`proximately 72 and 90 L/hr.
`
`VOLUME OF DISTRIBUTION
`Volume of distribution (V) relates the amount of
`drug in the body to the concentration of drug in the
`blood or plasma, depending on the fluid in which
`concentration is measured. This relationship is de-
`fined by Equation 18:
`
`For an average 70-kg human, the plasma volume
`is 3 L, the blood volume is 5.5 L, the extracellular
`fluid outside the plasma is 12 L, and the total body
`water is approximately 42 L. However, many clas-
`sical drugs exhibit volumes of distribution far in
`excess of these known fluid volumes. The volume
`of distribution for digoxin in a healthy volunteer is
`about 700 L, which is approximately 10 times great-
`er than the total body volume of a 70-kg human.
`This serves to emphasize that the volume of distri-
`bution does not represent a real volume. Rather, it
`is an apparent volume that should be considered as
`the size of the pool of body fluids that would be
`required if the drug were equally distributed
`throughout all portions of the body. In fact, the
`
`relatively hydrophobic digoxin has a high apparent
`volume of distribution because it distributes pre-
`dominantly into muscle and adipose tissue, leaving
`only a very small amount of drug in the plasma in
`which the concentration of drug is measured.
`At equilibrium, the distribution of a drug within
`the body depends on binding to blood cells, plasma
`proteins, and tissue components. Only the unbound
`drug is capable of entering and leaving the plasma
`and tissue compartments. Thus, the apparent vol-
`ume can be expressed as follows:
`
`f
`
`where Vp is the volume of plasma, VTW is the aque-
`ous volume outside the plasma, fu is the fraction
`unbound in plasma, and fu,, is the fraction unbound
`in tissue. Thus, a drug that has a high degree of
`binding to plasma proteins (i.e., low fu) will generally
`exhibit a small volume of distribution. Unlike plas-
`ma protein binding, tissue binding of a drug cannot
`be measured directly. Generally, this parameter is
`assumed to be constant unless indicated otherwise.
`Several volume terms are commonly used to de-
`scribe drug distribution, and they have been derived
`in a number of ways. The volume of distribution
`defined in Equation 19, considers the body as a
`single homogeneous pool (or compartment) of body
`fluids. In this 1-compartment model, all drug ad-
`ministration occurs directly into the central com-
`partment (the site of measurement of drug concen-
`tration, usually plasma), and distribution of drug is
`considered to be instantaneous throughout the vol-
`ume. Clearance of drug from this compartment oc-
`curs in a first-order fashion, as defined in Equation
`20; that is, the amount of drug eliminated per unit
`time depends on the amount (concentration) of drug
`in the body compartment. Figure 2A and Equation
`20 describe the decline of plasma concentration with
`time for a drug introduced into this compartment:
`
`where k is the rate constant for elimination of the
`drug from the compartment. This rate constant is
`inversely related to the half-life of the drug (k =
`0,693/t,/,),
`In this case (Fig. 2A), drug concentrations were
`measured in plasma 2 hr after the dose was admin-
`istered. The semi-logarithmic plot of plasma con-
`centration versus time appears to indicate that the
`drug is eliminated from a single compartment by a
`first-order process (Equation 20) with a half-life of
`4 hr (k = 0.693/t, = O.I73 hr-’). The volume of
`distribution may be determined from the value of
`
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`119
`
`FIG. 2.-Plasma concentration-time curves following intravenous administration of a drug (500 mg) to a 70-kg human.
`
`Cp obtained by extrapolation to t = 0 (Cp° = 16 lagl
`ml). In this example, the volume of distribution for
`the I-compartment model is 31.3 L or 0.45 L/kg (V
`= dose/CPO). The clearance for this drug is 92 ml/
`min; for a 1-compartment model, CL = k ~ V .
`For most drugs, however, the idealized
`1-compartment model discussed earlier does not de-
`scribe the entire time course of the systemic con-
`centrations. That is, certain tissue reservoirs can be
`distinguished from the central compartment, and
`the drug concentration appears to decay in a manner
`that can be described by multiple exponential terms
`(Fig. 2B). Two different terms have been used to
`describe the volume of distribution for drugs that
`follow multiple exponential decay. The first, des-
`ignated Vare3’ is calculated as the ratio of clearance
`to the rate constant describing the terminal decline
`of concentration during the elimination (final) phase
`of the logarithmic concentration versus time curve:
`
`n
`
`n,&dquo;--~J
`
`The calculation of this parameter is straightfor-
`ward, and the volume term may be determined after
`administration of drug by intravenous or enteral
`routes (where the dose used must be corrected for
`bioavailability). However, another multicompart-
`ment volume of distribution may be more useful,
`especially when the effect of disease states on phar-
`macokinetics is to be determined. The volume of
`distribution at steady state (V ss) represents the vol-
`ume in which a drug would appear to be distributed
`during steady state if the drug existed throughout
`
`that volume at the same concentration as that in the
`measured fluid (plasma or blood). This volume can
`be determined by the use of areas, as described by
`Benet and Galeazzi (3):
`
`~ -1 - - -&dquo;
`
`í ... T T’ 6 r&dquo;&dquo;’B.
`
`where AUMC is the area under the first moment of
`the curve that describes the time course of the plas-
`ma or blood concentration, that is, the area under
`the curve of the product of time t and plasma or
`blood concentration C over the time span 0 to in-
`finity.
`Although Varea is a convenient and easily calcu-
`lated parameter, it varies when the rate constant for
`drug elimination changes, even when there has been
`no change in the distribution space. This is because
`the terminal rate of decline of the concentration of
`drug in blood or plasma depends not only on clear-
`ance but also on the rates of distribution of drug
`between the central and final volumes. V_ does not
`suffer from this disadvantage (4).
`In the case of the example given in Fig. 2, sam-
`pling before 2 hr indicated that the drug follows
`multiexponential kinetics. The terminal disposition
`half-life is 4 hr. clearance is 103 ml~’min (calculated
`from a measurement of AUC and Equation 17), V ana
`is ’~8 L (Equation 21), and V&dquo; is 25.4 L (Equation
`22). The initial, or &dquo;central,&dquo; distribution volume
`for the drug (V = dose CpO) is 16.1 L. This example
`indicates that multicompartment kinetics may be
`overlooked when sampling at early times is neglect-
`ed. In this particular case. there is only a 10% error
`
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`120
`
`in the estimate of clearance when the multicom-
`partment characteristics are ignored. However, for
`many drugs multicompartment kinetics may be ob-
`served for significant periods of time, and failure to
`consider the distribution phase can lead to signifi-
`cant errors in estimates of clearance and in predic-
`tions of the appropriate dosage.
`Volume of distribution is a useful parameter for
`determining loading doses. For drugs with long half-
`lives, the time to reach steady state (see the Half-
`Life section) is appreciable. In these instances, it
`may be desirable to administer a loading dose that
`promptly raises the concentration of drug in plasma
`to the projected steady-state value. The amount of
`drug required to achieve a given steady-state con-
`centration in the plasma is the amount of drug that
`must be in the body when the desired steady state
`is reached. For intermittent dosage schemes, the
`amount is that at the average concentration. The
`volume of distribution is the proportionality factor
`that relates the total amount of drug in the body to
`the concentration in the plasma. When a loading
`dose is administered to achieve the desired steady-
`state concentration, then
`(23)
`loading dose = Cp,ss’ Vss
`For most drugs, the loading dose can be given as
`a single dose by the chosen route of administration.
`However, for drugs that follow complicated multi-
`compartment pharmacokinetics, such as a
`2-compartment model (Fig. 2B), the distribution
`phase cannot be ignored in the calculation of the
`loading dose. If the rate of absorption is rapid rel-
`ative to distribution (this is always true for intra-
`venous bolus administration), the concentration of
`drug in plasma that results from an appropriate
`loading dose can initially be considerably higher than
`desired. Severe toxicity may occur, although tran-
`siently. This may be particularly important, for ex-
`ample, in the administration ofantiarrhythmic drugs,
`where an almost immediate toxic response is ob-
`tained when plasma concentrations exceed a partic-
`ular level. Thus, while the estimation of the amount
`of the loading dose may be quite correct, the rate of
`administration can be crucial in preventing exces-
`sive drug concentrations. Therefore, for drugs such
`as antiarrhythmics, even so-called &dquo;bolus&dquo; doses are
`administered by a slow &dquo;push&dquo; (i.e., no faster than
`50 mg/min).
`
`HALF-LIFE
`The half-life (t,,_) is the time it takes for the plasma
`concentration or the amount of drug in the body to
`be reduced by 50%. When drug is being adminis-
`tered as multiple doses or as a zero-order infusion,
`half-life also represents the time it takes for drug
`
`(24)(24)
`
`
`
`concentrations to reach one-half (or 50%) of the
`expected steady-state concentration. For the sim-
`plest case, the 1-compartment model (Fig. 2A), half-
`life may be determined readily and used to make
`decisions about drug dosage. However, as indicated
`in Fig. 2B, drug concentrations in plasma often fol-
`low a multiexponential pattern of decline; 2 or more
`half-life terms may thus be calculated.
`Early studies of pharmacokinetic properties of
`drugs in disease states were compromised by their
`reliance on half-life as the sole measure of altera-
`tions of drug disposition. Only recently has it been
`appreciated that half-life is a derived parameter that
`changes as a function of both clearance and volume
`of distribution. A useful approximate relationship
`among the clinically relevant half-life, clearance, and
`volume of distribution is given by
`t, = (0.693) ~ C
`tv f-- (0.693). v
`Equation 24 is exact for a drug following
`1-compartment kinetics.
`In the past, the half-life that was usually reported
`corresponded to the terminal log-linear phase of
`elimination. As greater analytical sensitivity has been
`achieved, the lower concentrations measured ap-
`peared to yield longer and longer terminal half-lives.
`For example, a terminal half-life of 5 3 hr is observed
`for gentamicin, and biliary cycling is probably re-
`sponsible for a 120-hr terminal t,/, value reported
`for indomethacin. The relevance of a particular half-
`life may be defined in terms of the fraction of the
`clearance and volume of distribution that is related
`to each half-life and whether plasma concentrations
`or amounts of drug in the body are best related to
`measures of response (1).
`Clearance is the measure of the body’s ability to
`eliminate a drug. However, the organs of elimina-
`tion can only clear drug from the blood or plasma
`with which they are in direct contact. As clearance
`decreases, due to a disease process, for example,
`half-life would be expected to increase. However,
`this reciprocal relationship is exact only when the
`disease does not change the volume of distribution.
`For example, the half-life of diazepam increases with
`increasing age; however, it is not clearance that
`changes as a function of age but the volume of dis-
`tribution (10). Similarly, changes in protein binding
`of the drug may affect its clearance as well as its
`volume of distribution, leading to unpredictable
`changes in half-life as a function of disease. The half-
`life of tolbutamide, for example, decreases in pa-
`tients with acute viral hepatitis, exactly the opposite
`from what one might expect. The disease appears
`to modify protein binding in both plasma and tis-
`sues, causing no change in volume of distribution
`
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`but an increase in total clearance because higher
`concentrations of free drug are present (14).
`Although it can be a poor index of drug elimi-
`nation, half-life does provide an important indica-
`tion of the time required to reach steady state after
`a dosage regimen is initiated (i.e.. 4 half-lives to
`reach approximately 94% of a new steady state). the
`time for a drug to be removed from the bodn,. and
`a means to estimate the appropriate dosing interval.
`If the dosing interval is long relative to the half-
`life, large fluctuations in drug concentration will oc-
`cur. On the other hand, if the dosing interval is short
`relative to half-life, significant accumulation will oc-
`cur. The half-life parameter also allows one to pre-
`dict drug accumulation within the body and quan-
`titates the approach to plateau that occurs with mul-
`tiple dosing and constant rates of infusion. Con-
`ventionally, 31/3 half-lives are used as the time
`required to achieve steady state under constant in-
`fusion. The concentration level achieved at this time
`is already 90% of the steady-state concentration (Ta-
`ble II), and, clinically, it is difficult to distinguish a
`10% difference in concentrations.
`
`BIOAVAILABILITY
`The bioavailability of a drug product via various
`routes of administration is defined as the fraction
`of unchanged drug that is absorbed intact and reach-
`es the site of action, or the systemic circulation fol-
`lowing administration by any route. For an intra-
`venous dose of a drug, bioavailability is defined as
`unity. For drug administered by other routes of ad-
`ministration, bioavailability is often less than unity.
`Incomplete bioavailability may be due to a number
`of factors that can be subdivided into categories of
`dosage form effects, membrane effects, and site of
`administration effects. Obviously, the most avail-
`able route of administration is direct input at the
`site of action for which the drug is developed. This
`may be difficult to achieve because the site of action
`is not known for some disease states, and in other
`cases the site of action is completely inaccessible
`even when drug is placed into the bloodstream. The
`most commonly used route is oral administration.
`Orally administered drugs may decompose in the
`fluids of the gastrointestinal lumen or be metabo-
`lized as they pass through the gastrointestinal mem-
`brane. Once a drug passes into the hepatic portal
`vein, it may be cleared by the liver before entering
`into the general circulation. The loss of drug as it
`passes through drug-eliminating organs for the first
`time is defined as the first-pass effect. For example,
`in Fig. 1, the availability of an oral dose of a drug
`eliminated by the liver will be less than an intra-
`venous dose, due to the first-pass loss of drug through
`the liver following oral dosing. For high extraction
`
`TABLE II.-Percentages of steady-state concentration
`reached upon multiple dosing or during constant rates of
`infusion as a function of number of half-lives.
`
`121
`
`ratio drugs, this first-pass loss, or decrease in oral
`bioav ailability. will be markedly greater than for low
`extraction ratio drugs.
`The fraction of an oral dose available to the sys-
`temic circulation considering both absorption and
`the first-pass effect can be found by comparing the
`ratio of AUCs following oral and intravenous dos-
`ing:
`
`Assuming the drug is completely absorbed intact
`through the gastrointestinal tract, and that the only
`extraction takes place at the liver, then the maxi-
`mum bioavailability (Fmax) is
`
`Combining Equations 6 and 26 results in the fol-
`lowing relationship for maximum bioavailability:
`
`For high extraction ratio drugs, where CL,,«t,~ ap-
`proaches Qhepauc’ F may, will be small. For low extrac-
`tion ratio drugs, Qhepauc is much greater than B.. ~ f~tlC~
`therefore, F max will be close to 1.
`The relationship between clearance and bioavail-
`ability for high and low extraction ratio drugs is
`summarized in Fig. 3. Equation 9 describes the sim-
`plest model for organ elimination and the approx-
`imate relationships or boundary conditions are giv-
`en for high and low extraction substances (Equations
`12 and 1 1, respectively). Substituting Equation 9
`into Equation 27, yields Equation 28 as given in Fig.
`3. The boundary conditions for Fm.n are also given.
`Much has been made of the comparison of clearance
`and bioavailability for high and low extraction com-
`pounds. However, in both therapeutics and toxi-
`cology. the primary concern will be with the actual
`exposure following an oral dose. because this is the
`measure of how much drug or toxic substance be-
`comes available following ingestion by the most fre-
`quent route of administration. This measure of ex-
`posure (AUC) following oral dosing is given by
`
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`122
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`FIG. 3.-Critical equations utilizing the well-stirred model to define clearance, maximum oral bioavailability, and
`maximum area under the curve following an oral dose for high and low extraction ratio drugs.
`
`Equation 29. Note that Equation 29 holds for both
`high and low extraction ratio compounds.
`Equation 29 indicates that for drugs like chlor-
`diazepoxide or imipramine, which are essentially
`completely absorbed and eliminated exclusively by
`hepatic metabolism, the area under the concentra-
`tion versus time curve (AUC) is predicted by the
`oral dose divided by the fraction unbound (f&dquo;)b and
`the intrinsic ability of the liver to eliminate the un-
`bound drug (CL;nt).
`As discussed earlier, only the unbound drug can
`exert a pharmacologic effect. Thus, another impor-
`tant parameter to consider is the unbound area un-
`der the curve (AVCJ. If both sides of Equation 29
`are multiplied by (fu)b, it can be seen in Equation
`30 that the area under the curve unbound is a func-
`tion only of the oral dose and the intrinsic ability
`of the liver to eliminate the drug:
`
`Because it is generally believed that pharmacody-
`namic response is related to unbound concentration,
`Equation 30 indicates that only the intrinsic ability
`
`of the liver to remove or clear unbound drug is the
`determining factor following an oral dose.
`This is illustrated by data from hemodialysis pa-
`tients for the nonsteroidal anti-inflammatory drug
`etodolac (7), which revealed a decrease in protein
`binding and total drug concentrations. No change
`in half-life was observed. Looking more carefully at
`data from a subgroup of 5 of these patients, there
`was no difference in unbound etodolac concentra-
`tions compared with normal subjects. Thus, al-
`though protein binding changes in hemodialysis pa-
`tients, the unbound concentration does not change
`as predicted by Equation 30; therefore, altering eto-
`dolac dosage should not be necessary (2).
`Recently, bioavailability and clearance data ob-
`tained from a cross-over study of cyclosporine ki-
`netics before and after rifampin dosing revealed a
`new understanding of drug metabolism isozymes
`and the disposition of this compound (9). Healthy
`volunteers were given cyclosporine, intravenously
`and orally, before and after their cytochrome P-450
`3A enzymes were induced by rifampin. As expected,
`the blood clearance of cyclosporine increased from
`0.31 to 0.42 L/hr/kg due to the induction of the
`drug’s metabolizing enzymes (i.e., an increase in
`
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`in Equation 13). There was no change in vol-
`V m<L’<
`ume of distribution, but there was a dramatic de-
`crease in bioavailability from 27 to 10% in these
`individuals.
`A decrease in bioavailability is to be expected,
`because cyclosporine undergoes some first-pass me-
`tabolism as it goes through the liver following oral
`dosing. But if one predicts on the basis of phar-
`macokinetics what the maximum bioavailability (as
`calculated by Equation 27 with an hepatic blood
`flow of 90 L/hr/70 kg) would be before and after
`rifampin dosing, the maximum bioavailability would
`decrease from 77 to 68%. Thus, there would be an
`expected cyclosporine bioavailability decrease of
`approximately 12% on the basis of the clearance
`changes resulting from inducing P-450 3A enzymes
`in the liver. In fact, there was a bioavailability de-
`crease of 60%. Furthermore, bioavailability was sig-
`nificantly less than the predicted maximum bio-
`availability. While some of that lower bioavailabil-
`ity may be due to formulation effects, the discrep-
`ancy between the theoretical maximum
`bioavailability and the achievable bioavailability of
`cyclosporine remain