Pharmacokinetic Interpretation of Data Gathered during Therapeutic Drug Monitoring

Transcription

1 CLIN. CHEM. 22/6, (1976) Pharmacokinetic Interpretation of Data Gathered during Therapeutic Drug Monitoring Barry H. Dvorchik and Elliot S. Vesell We review some pharmacokinetic principles that can facilitate interpretation of data obtained during therapeutic drug monitoring: the one- and two-compartment models, volume of drug distribution, drug clearance, organ clearance, bioavailability, first-pass effect, chronic or repetitive dosing, and use of urine and saliva to measure drug clearance and drug binding to plasma proteins, respectively. We also describe use of saliva to estimate rapidly, conveniently, and noninvasively the concentration of the free, pharmacologically active form of the drug as well as the fraction of drug bound to plasma protein. AddftlonalKeyphrases: biologic half-life of a drug #{149} drug distribution and clearance #{149}drug binding to plasma proteins #{149} urine or saliva as the sample in drug monitoring #{149}dosage/concentration relations Clinical chemists are frequently requested to identify and quantitate a wide variety of drugs in the blood and urine of acutely poisoned patients. To this extent, responsibility for verification and treatment of drug toxicity rests with clinical chemists, because they furnish the information that forms the basis for therapy. Recent developments in pharmacology and medicine indicate that under some circumstances measurement of drug concentration in blood is the best available guide to ascertain each patient s particular dose requirements (1, 2). Such circumstances include: (a) high incidence of toxicity resulting from certain drugs used alone or in combination; (b) failure to attain adequate pharmacologic responses after administration of potent drugs with low therapeutic indices given in the usual doses; (c) interactions of concomitantly administered drugs Departments of Pharmacology and Obstetrics and Gynecology, The Pennsylvania State University College of Medicine, Hershey, Pa Received Feb. 2, 1976; accepted Mar. 26, to change the peak effects and durations of action expected when each drug is used alone, which alterations can involve drug absorption from sites of drug administration, distribution of drugs among various compartments of the body, biotransformation, excretion, or a combination of these processes; (d) assessment of patient compliance, especially when the desired therapeutic effects are not obtained; (e) exposure to compounds abundantly distributed in our environmentsuch as caffeine, nicotine, ethanol, benpyrene and DDT-that may change the capacity of an individual to eliminate therapeutic agents; (f) demonstration that individuals can differ greatly in their inherent capacity to absorb, distribute, metabolie, and excrete drugs. (large interindividual differences in these processes, but especially in rates of hepatic drug metabolism, render fallacious the tacit assumption that administration of a given drug solely by weight or by surface area to all patients with adequate cardiovascular, hepatic, and renal function results in closely similar drug concentrations in blood and other tissues); (g) the increasing number of pharmacogenetic conditions in which specific point mutations inherited in classical mendelian fashion affect the enymes that metabolie drugs, thereby altering their safety, peak effects, and duration of action; and (h) development of new, convenient, accurate, inexpensive, and rapid methods for assay of many drugs in biological fluids, thereby permitting the physician to adjust the dosage of many drugs more precisely according to their concentrations in biological fluids (1, 2). The physician and clinical chemist should discriminate between those drugs that can practically and usefully be measured in blood or some other biological fluid and those that cannot (3). Some drugs cannot be satis- 868 CLINICAL CHEMISTRY, Vol. 22, No. 6, 1976

2 factorily assayed in biological fluids because convenient methods are not yet available for their determination. Although for many drugs a close correlation exists between blood drug concentrations and pharmacological or therapeutic effects, this relationship does not apply for all drugs (2). Some drugs are bound so avidly by certain tissues that they may be virtually undetectable in biological fluids or present in such low concentrations that their true concentrations in other organs are concealed. Drugs of this type, as well as drugs that form irreversible covalent bonds with certain macromolecules, may continue to exert their effects long after they vanish from all other sites in the body. The therapeutic and toxic properties of most pharmacological agents are determined in vivo by the absorption characteristics of the drug and the combined, simultaneously occurring processes of distribution, metabolism, and excretion. The intensity of these pharmacological effects depends on the amount of pharmacologically active substance that gets to the site of drug action (receptor site). Pharmacokinetics is the study of the time course of absorption, distribution, metabolism, and excretion of drugs and their metabolites in the intact organism. The amounts of drug and metabolite(s) in readily available biological fluids are measured as functions of time and dosage. Mathematical models are then established to predict quantitatively these dynamic processes. Thus, knowledge of a drug s pharmacokinetic profile within any individual should allow the clinician to choose an adequate dosage schedule that will rapidly and safely produce and maintain a desired pharmacological effect. Obviously, for any pharmacokinetic analysis to be useful the assays on which the analysis is based must separate the parent drug from any metabolites. Most of the currently used analytical methods meet this requirement. Most pharmacokinetic principles have been obtained by investigating the concentration of a drug in blood or plasma as a function of time (4-7). This paper does not review the enormous body of pharmacokinetic literature; instead, the interested reader is referred elsewhere (5-11). After a discussion of some basic pharmacokinetic principles, we intend to describe the applicability of using biological fluids other than blood, either alone or in combination with blood, to monitor therapeutic drug concentrations and to gain information about drug disposition that cannot be gained conveniently from blood alone. Pharmacokinetic Models ONECOMPARTMENT ONE COMPARIM[NT MODEL BEFORE MODEL IMMEDIATLY ADMINISTRATION AFTER ADMINISTRATION Fig. 1. The one-compartment model Numerous observations performed in vivo on drug distribution, absorption, and excretion led to the concept that a biological system can be treated as if there were boundaries separating the system into parts ( compartments ) and that a drug is transferred from one compartment to another in conformance with first-order kinetics. Although the assumption of firstorder kinetics and rate coefficients that are constants is a gross approximation of a complex biological phenomenon, this approach, when utilied with discretion and understanding, has often proved rewarding; these kinetic assumptions have been validated by drug studies performed in vivo. The One-Compartment Pharmacokinetic Model The simplest pharmacokinetic model, the onecompartment model, assumes that after administration (and absorption for those drugs administered by routes other than intravenous injection) drugs are instantaneously and homogeneously distributed throughout the fluids and tissues of the body (Figure 1). This assumption does not necessarily mean that the concentration of drug in plasma and other body fluids and tissues is the same at the same time. What the one-compartment model does assume, however, is that changes in plasma drug concentration quantitatively reflect changes occurring in drug concentrations of other body fluids and tissues. For drugs whose distribution in the body follows one-compartment pharmacokinetics, a plot of the logarithm of the plasma drug concentration against time will be a straight line. The equation describing the plasma decay curve is C = Ae_tet (1) where he is the first-order rate constant for the overall elimination of drug from the body, C is the concentration of drug at time t, and A is the concentration of drug at time, when all of the drug administered has been absorbed but none has been removed through metabolism or excretion. The apparent first-order rate constant, he, is usually the sum of the rate constants of a number of individual processes such as renal excretion, biliary excretion, and metabolism. The apparent firstorder rate constant for elimination of drug from the body is related to the biologic half-life of the drug by the equation t1b =.693 (2) he Unfortunately, this simple model does not account accurately for the observed time course of most drugs in CLINICAL CHEMISTRY. Vol. 22. No

3 the body, because most drugs occupy two or three compartments, rather than one. Serious errors may be introduced into a pharmacokinetic analysis by the assumption that a drug distributes according to a onecompartment model if this assumption is false (12, 13). The Two-Compartment Pharmacokinetic Model For most pharmacokinetic purposes, the mammalian body may be considered a multicompartment system, with all compartments directly or indirectly in contact with blood. The rate at which exchange of drug between blood and tissues takes place depends on the blood flow through the tissues, the volume of the tissues, and the partition of drug between blood and tissues. On the basis of similarities in blood flow and partition coefficients between blood and tissues, various tissues may be grouped together so that the body may be regarded as a two- or three-compartment model (12). Owing to differences in vasculariation among tissues, drug may rapidly exchange between blood and some tissues. Together with blood these tissues may be considered one compartment, commonly called the central compartment. It should be obvious that this central compartment has, in general, no real physiological meaning but varies in extent with the particular drug under study. The other tissues may be considered as a peripheral compartment, the number of peripheral compartments depending also on the properties of the drug. At some time a state of distribution equilibrium between the central and peripheral compartments is reached, whereupon loss of drug from plasma is described by a monoexponential process indicative of kinetic homogeneity with respect to drug concentrations in all fluids and tissues of the body. The central compartment and one peripheral compartment suffice to describe the pharmacokinetic properties of most drugs (Figure 2). When, for purposes of pharmacokinetic analysis, the body has to be subdivided into a central compartment and one or more peripheral compartments, the semilogarithmic plot of blood concentration vs. time is not linear, but hiphasic or triphasic (14-17). In the case of the two-compartment model represented schematically in Figure 3, where elimination occurs from the central compartment, a semilogarithmic plot of concentration of drug in the blood against time (Figure 4) can be separated into two distinct linear segments, described by the following equation: C = Aet + Bet The initial rapid decrease in drug concentration with time is due to the simultaneously occurring processes of drug distribution and drug elimination. The slope of the distributional phase, a, is obtained by subtracting the extrapolated portion of the 3 phase from the experimental data (Figure 4, also ref. 7, 8). The half-life for the distributive process is determined from eq. 2, where a replaces he. The terminal linear phase, or beta phase, describes irreversible loss of drug from the body, usually as a re- TWOCOMPARTMENT TWOCOMPARTMENT MODEL BEFORE MODEL IMMEDIATLY ADMINISTRATION AFTER ADMINISTRATION DOSE Fig. 2. The two-compartment CENTRAL COMPARTMENT Vc Z A+B A o- < -J m- B C -Jo C-) ke TIME Fig. 4. The logarithm of the drug concentration TWO COMPARTMENT MODEL AFTER DISTRIBUTIVE EQUILIBRIUM model PERIPHERAL TISSUE COMPARTMENT VT EXCRETION Fig. 3. Two-compartment model with elimination occurring from the central compartment in blood plotted against time (solid line) after intravenous administration of a drug whose disposition can be described by a two-compartment model Thedashed line (- -) representsextrapolation of the terminal (/1)phase. The other line (. -) was obtainedby the method of residuals (7, 8) sult of metabolism and renal excretion, although enterohepatic recirculation occurs with certain drugs. The (3\ first-order half-life of this terminal linear phase, commonly called the biologic half-life of drug in the body, can be calculated from eq. 2, where fi replaces ke. The slope, fi, of the terminal linear portion of the curve relating log drug concentration to time does not equal the first-order elimination rate constant, be, from equations 1 and 2, but rather is a function of he, h1, and k2 (7, 9) where 13ke/(1+) (4) See Figure 3 for definition of k1 and k2. 87 CLINICAL CHEMISTRY, Vol. 22, No. 6, 1976

4 The coefficients A and B in eq. 3 are obtained from the intercepts of the a and $ phase, respectively. The sum of A and B is taken as the drug concentration at t =, on the assumption that the drug is completely absorbed from its site of administration. Once the four terms in eq. 1 are determined, individual rate constants may be calculated. Equations used to calculate the individual pharmacokinetic parameters (i.e., k1, k2, be) are published elsewhere (6-8). The apparent volume of the central compartment (V) expressed in liters or liters per kilogram of body weight can be determined from the following: Perrier and Gibaldi (25) demonstrated that clearance, and not $, is a direct measure of the intrinsic metabolic activity of the liver, if the liver is an integral part of the central compartment. For drugs subject to first-pass metabolism, where the liver is considered to be a compartment peripheral to the central compartment, the use of clearance as an index of hepatic metabolism is limited. Thus, for drugs whose disposition can be described by a two-compartment model (with elimination occurring from the central compartment), clearance is a more meaningful measurement of drug elimination than the disposition rate constant, $. V = dose administered/(a + B) Calculation of the apparent volume of the tissue compartment, VT, requires knowledge of the total apparent volume of distribution, Vd, since Vd = V + VT (5) Organ Clearance (6) Vd may be calculated by at least two methods (7, 8, 18-23). The first, in which the area under the bloodconcentration-time curve (AUC) is used, provides the most useful estimate of Vd after single doses of drugs. AUG is one of the most useful parameters in pharmacokinetics because it is directly proportional to the total amount of drug that reaches the central compartment. The apparent volume of distribution determined by this method relates the amount of drug in the body to its concentration at all times during the beta phase of the curve (7, 8, 2-23) (Vd) = dose/($ X AUC) = dose/( + (7) Another method of calculating Vd is shown in eq. 8: (Vd)= (Vd )ss refers to the volume of distribution at steady state. This method is useful when dealing with constant drug concentrations in blood, attained after multiple dosing or constant intravenous infusion (7,8, 18, 19, 23). This latter method is not recommended for calculating Vd after a single dose of a drug, because the condition under which it was derived applies only for that time at which the net transfer of drug between compartments is ero (19, 2, 22). Clearance Total Body Clearance As stated above, for most drugs the biologic half-life, (t /), is a complex function encompassing several discrete pharmacologic processes: drug distribution, biotransformation, and urinary elimination. Clearance, on the other hand, permits expression of rates of drug removal from the body in a way that is independent of these processes (18, 24-26). The total body clearance of a drug, that resulting from all processes of elimination, may be determined from the expression Clearance = (Vc)(ke) = $(Vd)fl = dose/aug (9) The concept of clearance may also be used to determine the efficiency of any organ in removing a drug irreversibly from the perfusing blood (first-pass effect). The question that arises is whether plasma or blood clearance is the parameter for physiological interpretation of clearance (27-29). For a further discussion of this aspect of pharmacokinetics, see references 24, The rate at which a drug is delivered to the clearing organ(s) is also involved in clearance, because clearance reflects both removal of drug, expressed by the term extraction ratio, and blood flow to the organ(s). In pharmacokinetics, when relating drug clearance to blood flow, one should utilie blood drug clearances and blood flows (27). Rowland et al. (24) and Perrier and Gibaldi (26), using different models, showed that the above interrelationships can be described by the equation F Clintrinsic 1 Organ clearance = Q ( #{176}) Ltc! + UlintrinsicJ (8) Q is the blood flow to the organ and Clintrinsic is the maximal capacity of the organ to remove drug by all pathways in the absence of any flow limitations (i.e., intrinsic organ clearance). The fractional term in eq. 1 is equivalent to the extraction ratio. Figure 5 shows the relationship between liver blood flow and hepatic drug extraction for drugs with various extraction ratios. Figure 6 shows the relationship between liver blood flow and total hepatic clearance for drugs with various extraction ratios. The pharmacokinetic behavior of a particular drug depends on the relative values of Clintrinsic and Q. When Clintrinsic> > Q (extraction ratio >.8), clearance becomes dependent upon blood flow to the eliminating organ. When Q > > Clintrinsic (extraction ratio <.2), clearance becomes independent of organ blood flow and is approximately equal to Clintrinsic. For intermediate conditions (.2 < extraction ratio <.8) clearance is partly flow-dependent (24, 27-29). One cannot conveniently directly determine in vivo the organ clearance of a drug. However, the total body clearance (TBC) of a drug can be determined from eq. 9. If the drug is eliminated both by metabolism and excretion of the unchanged drug and if the fraction of drug excreted unchanged (fe) is known, renal clearance CLINICAL CHEMISTRY, Vol. 22, No. 6,

5 C) I- >( uj :: E as I C INTRAVENOUS ADMINISTRATION 1. C1I LIVER BLOOD FLOW, LITER/MIN Fig. 5. Relationship between hepatic blood flow and hepatic extraction for drugs with various extraction ratios (ER) Revised from Wilkinson and Shand (29) I- U-) C-) -J JO.OO TIME, HOURS I- U LJJ C-) C-).5 a- I LIVER BLOOD FLOW, LITER/MIN Fig. 6. Relationship between hepatic blood flow and total hepatic clearance for drugs with various extraction ratios (ER) Arrows indicatenormal physiological range of liver blood flow and the extraction values refer to a normal flow of 1.5 1/mm. Revised from Wilkinson and Shand (29) of the drug EClrenai = (fe)(tbc)] can be calculated. The difference [TBC - Clrenai] equals the metabolic clearance of the drug. If the liver is the only organ involved in metabolism of the drug, then this value equals the hepatic clearance of the drug. Several physiological or pathological conditions that alter cardiac output, blood distribution, or both can change hepatic blood flow (cf. 28). One drug may also exert an effect on the elimination of another drug through a hemodynamic interaction or by altering intrinsic clearance (e.g., enyme induction). Alterations in acid-base balance can also affect pharmacokinetic parameters (7,8, 1, 11). When pharmacokinetic principles are used to describe the disposition of any drug in an individual patient one should also be aware of the possibility that supervention of these conditions can cause significant changes in pharmacokinetic parameters for certain drugs and hence in the dosage requirements for these drugs. Figures 7 and 8 show how changes in Clintrinsic and hepatic blood flow, respectively, can alter the curves relating drug concentrations in the blood to time after intravenous or oral administration of totally metabolied compounds. The pharmacokinetic parameters described above can be obtained for any drug by measuring in an individual the concentration of drug in plasma or blood as E 1 18 E 9 95 cent Iters/an Wt 3#{149}727 hters/rnin CI hters/nn CI I.ters/min Fig. 7. Effect of increasing hepatic total intrinsic clearance (Clintrmnsic) on the curves for total drug concentration in blood vs. time, after intravenous and oral administration of equal doses of two totally metabolied drugs The left panels refer to a ckug with an initial Cl1,,,,1. equivalent to an extraction ratio of.1 at a blood flow of 1.5 1/mm. The right panels refer to a drug with an initial extraction ratio of.9. The ALICs after oral administration are inversely proportional to From Wilkinson and Shand (29); reprinted with permission of the publisher a function of time. One should be aware, however, that the parameters obtained always refer to the particular fluid used to measure the drug concentration. Thus, for example, if blood is used, the pharmacokinetic parameters refer to whole blood. Because only nonproteinbound drug is pharmacologically active, it would appear to be beneficial to be able to refer all pharmacokinetic parameters, regardless of whether obtained from whole blood or plasma, to this fraction of the totally determined drug concentration. [Note that clearance may be an exception (27-29).] If the drug concentration is determined from whole blood, one needs to determine the plasma/erythrocyte partition coefficient and the fraction of the drug bound to plasma proteins. If plasma drug concentrations are measured, only the fraction of drug bound to plasma protein need be determined. Knowledge of these factors will permit any pharmacokinetic parameter to be obtained in terms of the nonprotein-bound drug concentration, total concentration in plasma, or total concentration in blood (3). The clinical chemist rarely receives a sufficient number of samples from a given individual to perform a complete pharmacokinetic analysis. Nevertheless, the clinical chemist should be aware of these pharmacokinetic principles, to ensure that his half-life determinations of a drug are based solely on samples obtained during the beta phase. Thus far, the pharmacokinetics of drugs administered only by a single intravenous injection have been discussed. However, most drugs are administered by other routes on an acute and chronic basis. The sections below describe certain aspects of pharmacokinetics after administration of drugs by routes other than single in- 872 CLINICAL CHEMISTRY, Vol. 22, No. 6, 1976

6 INTRAVENOUS ADMINISTRATION 1. C 3 Cmax E as I-. I- U-) C-) C) -J >: #{149}.5 ORAL ADMINISTRATION.1.5 TIME, HOURS Fig. 9. Typical plot of the concentration of a drug in blood after repetitive oral administration of equal doses at equal time intervals TIME, HOURS E 1.18 E.9 95 Q 1,5.75 liters/mm Q Imters/mpn CI liters/rnmn Cl titers/mm Fig. 8. Effects of decreasing hepatic blood flow on the total blood concentration-time curves after intravenous and oral administration of equal doses of two totally metabolied drugs The left panels refer to a drug with a total IntrInsicclearance equivalent to an extraction ratio of.1 when bloodflow equals 1.5 1/mm. The right panels refer to a drug with an intrinsic clearance equivalent to an extraction ratio of.9.from Wilkinson and Shand (29); reprinted with permission of the publisher travenous injection. For more comprehensive discussions, the reader is referred to references 6-1,27, Bioavailablllty The most popular mode of drug administration is the oral route. After administration of a drug by this route, the area under the blood drug concentration-time curve (AUC) reflects the amount of drug that reaches the systemic sampling site. The ratio ofauc,j/auc1. has been taken to be a measure of the bioavailability of the drug after oral administration. All drugs, when administered orally, must pass through the gut wall and, when absorbed via the hepatic portal system, must traverse the liver before reaching the systemic sampling site. On the assumption of complete gastrointestinal absorption of drugs, it is possible that for a certain compound a fraction of the dose absorbed may not reach the sampling site because of metabolism within gut or liver. This first-pass effect, especially with respect to the liver, has received increasing recognition (27-29, 31-4). Thus far only a few drugs have been shown to exhibit this first-pass effect, most notably imipramine, lidocaine, meperidine, nortriptyline, phenacetin, and propranolol. A hospitalied patient might initially receive drugs intravenously, rather than orally. As mentioned above, changes in the patient s physiological and pathological state may be reflected in altered body clearance of these drugs, thereby altering their therapeutic impact or effect. Pharmacokinetic considerations reveal that even if no discernible changes occur in the curve relating drug concentration to time (and thus total body drug clearance) when the patient is on intravenous therapy, a switch in the route of administration from intravenous to oral, which commonly occurs when a patient is discharged, can alter the pharmacokinetic profile and dosage requirements (Figures 7 and 8, bottom). For example, consider a drug that stimulates the hepatic enymes that metabolie drugs. If the hepatic clearance of this drug, or of a simultaneously administered drug, approaches hepatic blood flow (i.e., extraction ratio, ER,.9), then even though the hepatic enymes are stimulated, changes in the clearance of the drug may not be observable while the drugs are given intravenously. If the drugs are administered orally, a decrease in bioavailability (as judged by AUC) will be evident (Figure 7, bottom right). Thus, while the body clearance of drug remains unchanged, the patient could be receiving as little as 5% of the intended dose. Chronic and or Repetitive Dosing While some drugs, particularly analgesics, hypnotics, bronchodilators, antihistamines, and neuromuscular blocking agents, may be used effectively in a single dose, numerous therapeutic agents are given chronically. In many instances chronically administered drugs are taken sufficiently frequently that measurable and often pharmacologically significant concentrations of drug persist in the body at the time that a subsequent dose is received. Thus, the drug tends to accumulate at a decreasing rate with increasing number of doses until a steady-state plasma level of drug is achieved (Figure 9). For drugs whose disposition follows first-order kinetics, the average steady-state blood concentration is a function of the dose (D), fraction of dose absorbed (f), dosing interval (r), biologic half-life (t =.693/fl), and apparent volume of distribution (Vd) (41). The relationship between the average steady-state blood concentration (C) and the above factors is given by the equation (42) C = 1.44 (t). (fd)/vd. T (11) Clearance = (f)(d)/c55(r) (12) In some cases the terminal exponential elimination phase is difficult if not impossible to observe, because it occurs only after drug concentrations have decreased CLINICAL CHEMISTRY, Vol. 22, No. 6,

7 C cm cm Because a substantial fraction of the administered dose, either as the unchanged drug or metabolite(s), is usually excreted in the urine, it would be very useful if the urinary excretion data could be used to obtain an estimate of certain pharmacokinetic parameters. For drugs whose disposition can be described by a one compartment model and whose metabolites are rapidly excreted (5) 1og \drug 1 rate of or excretion metabolites of TIME Fig. 1. Relative concentrations of a drug in the central and deep peripheral compartments of a three-compartment system during repetitive administration of equal doses at equal time intervals. The curve and the circles represent the central and the deep peripheral compartments, respectively From Olbaldi et al. (4); reprinted with permission of the publisher by two or more orders of magnitude from those occurring immediately after administration of a single dose. In this case, it is possible to reach an apparent steadystate concentration in plasma while the drug concentration in an organ or tissue that acts as a deep compartment continues to rise. If the site of drug action is in this deep compartment, then this discrepancy in pharmacokinetic behavior between plasma and deep compartment can account for (a) delayed onset of therapeutic activity, (b) increases in pharmacological effects at times when plasma drug concentrations appear to be at steady-state, and (c) occurrence of pharmacological effects despite negligible drug concentrations in the plasma (Figure 1). Use of Urine or Saliva for Obtaining Pharmacokinetic Parameters The pharmacokinetic data discussed above are usually obtained by following the concentration of drug or metabolites in blood as a function of time (4-7). The necessary blood samples must be drawn by skilled personnel in the clinic or hospital, and problems may occur with old or young patients or when serial samples are needed. Use of more accessible body fluids, such as urine or saliva, simplifies sample collection for several reasons. Urine and saliva are more convenient and less discomforting or risky to obtain than blood. Furthermore, these noninvasive methods can offer information on drug disposition that may be either unavailable or difficult to acquire from blood. Drug Kinetics from Urinary Excretion Data Many potent therapeutic agents, especially those with large volumes of distribution, present problems for pharmacokinetic analysis, because even at their peak pharmacological effect the drug concentrations in blood are very low. Thus, depending on the selectivity and sensitivity of the analytical procedure, determination of the drug concentration in the blood may be insufficiently accurate (3). he = log (constant) - (233)t (13) This same relationship holds for drugs whose disposition conforms to a two-compartment model and whose metabolites are rapidly excreted, except that fi replaces he (43). Thus, measurement of the rate of elimination of a drug or any of its metabolites permits estimation of the drug s biologic half-life. In practice, the logarithm of the amount of drug excreted in a series of equal intervals is plotted vs. the mid-point of each time interval. This method requires no knowledge of the total amount of drug or metabolite excreted at infinity, so loss of a urine specimen does not invalidate the experiment. Furthermore, collection of urine can be discontinuous; it can be abandoned overnight and started again the following day. Thus, this method is particularly applicable to investigation of progressive changes in the rate of drug elimination that may occur during a course of drug therapy. This method has been successfully used to analye data on urinary salicylamide excretion in adults (44) and diphenylhydantoin elimination in overdosed children (45). One problem with this method is that fluctuations in the rate of drug elimination cause appreciable departures from linearity (43, 46). Another method that can be utilied is termed the Sigma-minus method (43, 46, 47). Derived from classical chemical kinetics, this method discloses the amount of drug in the body from knowledge of the amount of drug or metabolite excreted at any time (U) and the total amount excreted (U..). When elimination is first order Furthermore, log(um - U) = log Uro - (2#{149}3)t 13 (14) (15) where k, is the first-order rate constant for either (a) elimination of metabolite (when elimination is slower than formation), (b) production of metabolite (when production is slower than elimination), or (c) elimination of unchanged drug (43). A represents that fraction of the administered dose reaching the central compartment. When absorption is complete, A is equal to the administered dose. The Sigma-minus method requires knowledge of 874 CLINICAL CHEMISTRY, Vol. 22, No. 6, 1976

8 U..,, and so in theory requires total collection of urine until such time as drug excretion is essentially complete. It has been suggested (48) that urine be collected for a time period equal to 1 times the drug s half-life. This requirement applies to the laboratory concerned with defining the complete pharmacokinetic profile of a drug; the clinical chemist need only carry urine collections through three to five drug half-lives, because 87 to 96%, respectively, of a drug is eliminated from the body during this period. The fraction of the dose of a drug excreted in the urine depends on the ratio of renal clearance to total body clearance. Thus, any factor affecting total body clearance can affect the ultimate fraction of the dose eliminated in urine. Furthermore, renal clearance is a complex function of glomerular filtration, tubular secretion, and tubular reabsorption (49), the precise combination varying from drug to drug. Any factor affecting one or more of the components of renal clearance will also affect the pharmacokinetic parameters (5). Alterations in protein binding and urinary ph can affect the urinary excretion and metabolism of certain drugs (7, 8, 1, 5, 51). In summary, urinary excretion data permit determination of (a) the overall disposition constant, 1, for loss of drug from the body; and (b) the rate constants for urinary elimination of unchanged drug, for production or elimination of metabolites, or for both. A further discussion of these methods is given in references 5-9, 11, 43, The use of urine for pharmacokinetic analysis is particularly promising in pediatric and geriatric patients. Drug Kinetics from Salivary Excretion Data Identification in saliva of most therapeutic agents after their oral or parenteral administration is well documented (52-65). For most drugs thus far examined, transfer from plasma to saliva appears to be passive, ph dependent, and proportional to the concentration of the compound in plasma (43,52, 6,62-65). Lithium is an exception in that transport from blood to saliva appears to be active, thereby accounting for higher lithium concentrations in saliva than plasma (61). The observation that salivary drug concentration is often proportional to plasma drug concentration led to use of saliva as a noninvasive technique for monitoring most drug concentrations in plasma and for obtaining various pharmacokinetic data (43, 57-65). Measurement of drug concentrations in saliva offers several advantages over similar measurements performed in plasma. In the first place, many specimens can be obtained noninvasively, without loss of blood or exposure of pediatric and geriatric patients to discomfort and potential skin irritation and infection. More importantly, however, drug concentrations in saliva represent the free fraction of the drug, whereas data on concentrations in plasma represent both the free and protein-bound forms of the drug (43, 52, 53, 57, 6, 62-65). In plasma, the ratio of free to protein-bound drug varies with age and disease state and may also Table 1. Fraction of Drug Bound to Plasma Proteins as Determined by (a) Equilibrium Dialysis and (b) Relationship between Drug Concentration in Saliva and Plasmaab Drug Aminopyrine Amobarbital Antipyrine Digoxin Diphenylhydantoin Phenacetin Phenobarbital Salicylic acid Theophylline Tolbutamide EquIlib. (r.f. CaicuIat.d no) dial.15 (71).41 (67),.58(64) <.1 (72).23 (68).86 (67),.9(69).3(7).32 (6?) (67) from Concns. in saliva and piasmaa.l (r.f. no).2 (43).6 (64).3 (43).22 (63).9(65).4 (43).36 (7) (58).59 (6).52 (6).91 (62).98 (62) Fraction of acidic drug bound to plasma proteins and Fraction of basic drug bound to plasma proteins DIff.r.nc., IS] /1 + 1IPHp-PK.) [P] s1 + 1(pil-pK,) = 1 - [S](1_+ 1Q-(p-pK,) [P] \i + 1-I-pl These equations are rearrangements of equations described by Matin et al. (62). b Plasma ph = (ph5) = 7.4 and salivary ph (ph,) = 6.5 for the equations above. change appreciably in the same patient, owing to factors such as altered albumin concentrations and the presence of other compounds that can displace the drug from its binding site on albumin. Moreover, the clinical chemist cannot conveniently, inexpensively, and routinely separate the free drug from the bound drug in plasma. Only the free form of the drug is available to produce pharmacological effects, and so measurements of drug concentrations in saliva are more therapeutically meaningful because they represent the concentration of the free fraction of the drug. Salivary drug concentration is proportional to plasma drug concentration. Thus, the same pharmacokinetic principles discussed above for blood and plasma can also be used when salivary drug concentrations are measured. Drug transfer from blood to saliva is ph dependent (52-65); thus, the concentration of total drug in plasma can be calculated from salivary drug concentration by CLINICAL CHEMISTRY, Vol. 22, No. 6,

9 Table 2. K Factors for Determination of Plasma Protein BIndIng of a Drug from the Drug Concentration In Saliva and Plasma According to Equation 17 Drug <4 4.5 pka Plasma ph 7.4, Acids saliva ph 6.5 a The K factor is derived as follows: Bases.999 K factor8 for acids. K = 1 + 1Ov/1 + 1(5H.-pK) for bases. K = 1 + 1OP/1 + These equations are from Matin et al. (62). Plasma ph 7.4, Acids 2.51 saliva ph 7. Bases > use of a modification of the equations of Jacobs (66) as described by Matin et al. (62). To test the validity of these equations in estimating the fraction of drug bound to plasma proteins, we compared the fraction of drug bound to plasma proteins, as determined by equilibrium dialysis, with that obtained by use of the equations described by Matin et al. (62). Analysis of the data in Table 1 indicates that the values for the fraction of drug bound to plasma proteins derived from these equations agree closely with those obtained from equilibrium dialysis. For most drugs measurement of the concentration in saliva provides a good estimate of the concentration of the free form of the drug in plasma without correction for ph (43). This generaliation applies to acidic drugs whose pka is greater than 8.5 and basic drugs whose pka is 5.5 or less. Measurement of drug concentrations in simultaneously obtained samples of saliva and plasma permits accurate estimation of the percent binding of a drug to plasma proteins without knowledge of plasma or salivary ph. The following equation permits determination of the fraction of drug bound to plasma proteins (FB ) from the salivary and plasma drug decay curves (43): FB 1_K[] (16) which can be equated to the following simplified version of the formulas described by Matin et al. (62): FB=1-Kf (17) where K is a proportionality factor that takes into account plasma and salivary ph as well as the pka of the drug. For drugs whose pka lies within the ranges given above, K = 1 and thus plasma and salivary ph need not be determined. However, for drugs whose pka is outside this range, the effect of ph on the distribution of drug between these two biological fluids must be taken into account. Table 2 provides the value ofk in equation 17 for various pk5 s at salivary ph s of 6.5 and 7.. In normal individuals salivary ph appears to be generally between 6.5 and 7.2 (62, 63). Finally, two methodological considerations arise in connection with the use of saliva to monitor drug concentrations. Precaution should be exercised to avoid having remnants of orally administered drug in the mouth when salivary specimens are collected. Chiou et al. (73) reported this source for several aberrantly high salicylate concentrations measured in saliva. This problem occurs mainly when specimens are collected shortly after drug administration. Washing the mouth before obtaining the specimen of saliva can eliminate this problem, if it should appear. In our experience, this difficulty never arose during measurement of drug concentrations in saliva; our salivary drug-decay curves have been as smooth and consistent with first-order kinetics as the plasma drug-decay curves (43). Saliva collected with or without salivary gland stimulation through the chewing of parafilm yielded similar drug concentrations; therefore, chewing parafilm did not alter the salivary concentrations of the drugs that we investigated (43). In summary, measurement of drug in saliva as a function of time permits determination of pharmacokinetic data usually obtained from plasma. In addition, for most drugs saliva discloses the concentration of the free, pharmacologically active form of the drug, whereas plasma concentrations represent the total drug concentration (free plus protein-bound). If plasma and saliva samples are obtained simultaneously, measurement of their respective drug concentrations permits one to estimate the fraction of drug bound to the plasma proteins. Because binding of drug to plasma proteins can fluctuate widely both between and within patients, measurement of drug concentrations in plasma alone are of limited value, whereas salivary drug concentrations are of more value therapeutically. This work was supported in part by grants 1-ROl-DA and 1-R1-CA16536-O1 from the NIH. 876 CLINiCAL CHEMISTRY, Vol. 22, No

10 References 1. Vesell, E. S., and Passananti, G. T., Utility of clinical chemical determinations ofdrug concentrations in biological fluids. GUn. Chem. 17, 851 (1971). 2. Vase!!, E. S., Relationship between drug distribution and therapeutic effects in man. Annu. Rev. Pharmacol. 14, 249 (1974). 3. Werner, M., Sutherland, E. W., ifi, and Abramson, F. P., Concepts for the rational selection ofassays to be used in monitoring therapeutic drugs. Clin. Chem. 21, 1368 (1975). 4. Gibaldi, M., Levy, G., and Weintraub, H., Drug distribution and pharmacological effects. Clin. Pharmacol. Titer. 12, 734 (1971). 5. Nelson, E., Kinetics of drug absorption, distribution, metabolism and excretion. J. Pharm. Sci. 5, 181 (1961). 6. Wagner, J. G., Biopharmaceutics and Relevant Pharmacokinetics, The Hamilton Press, Hamilton, Ill., Notari, R. E., Biopharm.aceutics and Pharmacokinetics, 2nd ed., Marcel Dekker, New York, N. Y., Gibaldi, M., and Perrier, D., Pharmacokinetics, Marcel Dekker, New York, N. Y., Garrett, E. R., Theoretical pharmacokinetics. In Klinische Pharmakologie und Pharmakotherapie, H. P. Kuemmerle, E. R. Garrett and K. M. Spity, Eds., Urban and Schwarenberg, Munich, van Rossum, J. M., Significance of pharmacokinetics for drug design and the planning of dosage regimens. In Drug Design, Volume 11, I, E. J. Ariens, Ed., Academic Press, New York, N. Y., O Reilly, W. J., Pharmacokinetics in drug metabolism and taxicology. Can. J. Pharm. Sci. 7, 66 (1972). 12. Riegelman, S., Loo, J. C. K., and Rowland, M., Shortcomings in pharmacokinetic analysis by conceiving the body to exhibit properties of a single compartment. J. Pharin. Sci. 57, 117 (1968). 13. Sedman, A. J., and Wagner, J. G., Importance of the use of the appropriate pharmacokinetic model to analye in vivo enyme constants. J. Pharmacoki net. Biopharm. 2, 161 (1974). 14. Balasubramaniam, K., Lucas, S. B., Mawer, G. E., and Simons, P. J., The kinetics of amylobarbitone metabolism in healthy men and women. Br. J. Pharmacol. 39, 564 (197). 15. Kaplan, S. A., Weinfeld, R. E., Abruo, C. W., and Lewis, M., Pharmacokinetic profile of sulfisoxaole following intravenous, intramuscular, and oral administration in man. J. Pharm. Sci. 61,773 (1972). 16. Gibaldi, M., Levy, G., and Hayton, W., Kinetics of the elimination and neuromuscular blocking effect of d-tubocurarine in man. Anesthesiology 36, 213 (1972). 17. Shen, D., Gibaldi, M., Throne, M., et al., Pharmacokinetics of bethanidine in hypertensive patients. Clin. Pharmacol. Ther. 17,363, Riggs, D. S., The Mathematical Approach to Physiological Problems, Williams and Wilkins, Baltimore, Md., Riegelman, S., Loo, J., and Rowland, M., Concept of a volume of distribution and possible errors in evaluation of this parameter. J. Pharm. Sci. 57, 128(1968). 2. Benet, L. Z., and Ronfeld, R. A., Volume terms in pharmacokinetics. J. Pharm. Sci. 58,639 (1969). 21. Gibaldi, M., Effect of mode of administration on drug distribution in a two-compartment open system. J. Pharm. Sci. 58,327 (1969). 22. Gibaldi, M., Nagashima, R., and Levy, G., Relationship between drug concentration in plasma or serum and amount of drug in the body. J. Pharm. Sci. 58, 193 (1969). 23. Perrier, D., and Gibaldi, M., Relationship between plasma or serum drug concentration and amount of drug in the body at steady state upon multiple dosing. J. Pharmacokinet. Biopharm. 1, 17 (1973). 24. Rowland, M., Benet, L. Z., and Graham, G. G., Clearance concepts in pharmacokinetics. J. Pharmacoki net. Biopharm. 1, 123 (1973). 25. Perrier, D., and Gibaldi, M., Clearance and biologic half-life as indices of intrinsic hepatic metabolism. J. Pharmacol. Exp. Ther. 191, 17 (1974). 26. Perrier, D., and Gibaldi, M., Drug clearance in multicompartment systems. Can. J. Pharm. Sci. 9,11(1974). 27. Rowland, M., Influence of route of administration on drug availability. J. Pharm. Sci. 61, 7 (1972). 28. Wilkinson, G. R., Pharmacokinetics of drug disposition: Hemodynamic considerations. Annu. Rev. Pharmacol. 15, 11 (1975). 29. Wilkinson, G. R., and Shand, D. G., A physiological approach to hepatic drug clearance. Clin. Pharrnacol. Ther. 18, 377 (1975). 3. Garrett, E. R., and Lambert, H. J., Pharmacokinetics of trichloroethanol and metabolites and interconversions among variously referenced pharmacokinetic parameters. J. Pharm. Sci. 62, 5 (1973). 31. Harris, P. A., and Riegelman, S., Influence of the route of administration on the area under the plasma concentration-time curve. J. Pharm. Sri. 58, 71 (1969). 32. Gibaldi, M., and Feldman, S., Pharmacokinetic basis for the influence of route of administration on the area under the plasma concentration-time curve. J. Pharm. Sci. 58, 1477 (1969). 33. Gibaldi, M., and Feldman, S., Route ofadministration and drug metabolism. Eur. J. Pharmacol. 19, 323 (1972). 34. Gibaldi, M., and Perrier, D., Route of administration and drug disposition. Drug Metab. Rev. 3, 185 (1974). ha. Gibaldi, M., Boyes, R N., and Feldman, S., Influence of first-pass effect on availability of drugs on oral administration. J. Pharm. Sci. 6, 1338 (1971). 36. Perrier, D., and Gibaldi, M., Influence offirst-pass effect on the systemic availability of propoxyphene. J. Clin. Pharmacol. 12, 449 (1972). 37. Cleaveland, C. R., and Shand, D. G., Effect of route of administration on the relationship between fl-adrenergic blockade and plasma propranolol level. Clin. Pharmacol. Ther. 13, 181 (1972). 38. Saidman, L. J., and Eger, E. I., II, Uptake and distribution of thiopental after oral, rectal, and intramuscular administration: Effect of hepatic metabolism and injection site blood flow. Clin. Pharmacol. Ther. 14, 12 (1973). 39. Gram, L. F., and Christiansen, J., First-pass metabolism of imipramine in man. Clin. Pharmacol. Ther. 17, 555 (1975). 4. Gram, L. F., and Overo, K. F., First-pass metabolism of nortriptyline in man. Clin. Pharmacol. Titer. 18, 35 (1975). 41. Levy, G., Pharmacokinetic control and clinical interpretation of steady-state blood levels of drugs. Clin. Pharmacol. Ther. 16, 13 (1974). 42. van Rossum, J. M., and Tomey, A. H. M., Rate of accumulation and plateau plasma concentration of drugs after chronic medication. J. Pharm. Pharmacol. 2, 39 (1968). 43. Vesell, E. S., Passananti, G. T., Glenwright, P. A., and Dvorchik, B. H., Studies on the disposition of antipyrine, aminopyrine, and phenacetin using plasma, saliva, and urine. Clin. Pharmacol. Ther. 18, 259 (1975). 44. Levy, G., and Matsuawa, T., Pharmacokinetics of salicylamide elimination in man. J. Pharmacol. Exp. Ther. 156, 285 (1967). 45. Garrettson, L. K., and Jusko, W. J., Diphenylhydantoin elimination kinetics in overdosed children. Clin. Pharmacol. Ther. 17,481 (1975). 46. Martin, B. K., Drug urinary excretion data-some aspects concerning the interpretation. Br. J. Pharmacol. Chemother. 29, 181 (1967). 47. Cummings, A. J., Martin, B. K., and Park, G. S., Kinetic considerations relating to the accrual and elimination of drug metabolites. Br. J. Pharmacol. Chemot her. 29, 136 (1967). 48. Wagner, J. G., Some possible errors in the plotting and interpretation of semiogarithmic plots of blood level and urinary excretion data. J. Pharm. Sci. 52, 197 (1963). 49. Pitta, R. F., Physiology of the Kidney and Body Fluids, 2nd ed., Year Book Med. Pub., Inc., Chicago, Ill., Wagner, J. G., Equations for excretion rate and renal clearances of exogenous substances not actively reabsorbed. J. Clin. Pharmacol. 7, 89 (1967). 51. Wagner, J. G., Pharmacokinetics. Annu. Rev. Pharmacol. 8, 67 (1968). 52. Killmann, S. A., and Thaysen, J. H., The permeability of the human parotid gland to a series of sulfonamide compounds, paraaminohippurate and inulin. Scand. J. Clin. Lab. Invest. 7, 86 (1955). 53. Rasmussen, F., Salivary excretion of suiphonamides and barbiturates by cows and goats. Acta Pharmacol. Toxicol. 21, 11 (1964). 54. Borelleca, J. F., and Cherrick, H. M., The excretion of drugs in saliva. Antibiotics. J. Oral Ther. Pharmacol. 2, 18 (1965). 55. Borelleca, J. F., and Doyle, C. H., Excretion of drugs in saliva. Salicylate, barbiturate, sulfanilamide. J. Oral Ther. Pharmacol. 3, 14 (1966). CLINICAL CHEMISTRY, Vol. 22, No. 6,