clinical pharmacokinetics: a simplified approach, parti - NCBI

CLINICAL PHARMACOKINETICS: A SIMPLIFIED APPROACH, PART I Elliott Perlin, MD, Robert E. Taylor, MD, PhD, and Carl Peck, MD Washington, DC, and Bethesda, Maryland

Clinicians often find that the application of pharmacokinetic principles for the calculation of a drug regimen is bewildering and difficult. In this article it is shown that clinically useful calculations can be simply done at the bedside using a handheld calculator. The only requirement is an understanding of the terms that define the pharmacokinetic behavior of a drug. Appropriate manipulation of these terms will allow calculation of loading and maintenance doses, peak and average plasma concentrations, and other useful pharmacological

From the Clinical Pharmacology Section, Departments of Medicine and Pharmacology, Howard University School of Medicine, Washington, DC and the Division of Clinical Pharmacology Departments of Medicine and Pharmacology, Uniformed Services University of the Health Sciences, Bethesda, Maryland. The opinions and/or assertions contained herein are those of the authors and should not be construed as those of the Uniformed Services University of the Health Sciences or the Department of Defense. Requests for reprints should be addressed to Dr. Elliott Perlin, Howard University Hospital, 2041 Georgia Avenue, NW, Washington, DC 20060.

data. The result will be improvement in drug therapy.

DEFINITION OF TERMS Pharmacokinetics (PK) refers to the time course of a drug as it passes through the body. This should not be confused with effect kinetics (EK), which is the time course of a drug's action on the body. The link between PK and EK is pharmacodynamics (PD), the relationship between blood or tissue concentrations and pharmacological effects. Very simply, PK is "what the body does to the drug" and PD "what the drug does to the body."-1 Oral bioavailability (F)2 is the fraction of a drug that enters the body orally, usually in relationship to the intravenous route of administration; it is expressed as a fraction or a percent. Note that it describes the extent of the absorption, not its rate. The extent of distribution is defined in terms of a volume (V or Vd), usually as a percent or multi-

JOURNAL OF THE NATIONAL MEDICAL ASSOCIATION, VOL. 77, NO. 6, 1985

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CLINICAL PHARMACOKINETICS

TABLE 1. ALGORITHM FOR CALCULATING IDEAL BODY WEIGHT

Body Build Medium Small Large

Women

100 Ibs/first 5 ft of height + 5 lbs/additional inch Subtract 10% Add 10%

ple of the body weight. Some drugs distribute mainly throughout the extracellular space; hence their volume of distribution approximates this space, ie, about 20 percent of the body weight. This would be true, for example, of the aminoglycosides. Other drugs distribute throughout both the intracellular and extracellular water, their volumes are about 60 percent of the body weight. An example of this would be the drug theophylline. Many others distribute more extensively into bone, muscle, and fat. The volume will vary with these drugs, depending upon the extent of tissue binding and distribution. In these cases the distribution volume will be a multiple of body weight. Thus, it should be emphasized that distribution volume cannot be interpreted in strictly physiological terms; it will rarely coincide exactly with a discrete body compartment. For example, V for digoxin is 400 to 600 liters in an adult. As volume is inversely proportional to concentration (V cc 1/c) and concentration is directly proportional to dose (C a: D), in order to "explain" a relatively low plasma concentration, a large volume of distribution is required. For this reason, it is sometimes referred to as "apparent volume of distribution." For many drugs (eg, theophylline, digoxin) V appears to be related to a fraction or multiple of "lean body weight." For these drugs lean body weight rather than actual weight should be used to calculate volume (Table 1). To describe the loss of drug from the body, the rate at which the body clears or eliminates this volume of the drug, ie, clearance (CL) is used. Half-life (T 1/2) is the time it takes for one half of the amount of the drug present at any particular 476

Men 106 lbs/first 5 ft of height + 6 lbs/additional inch Subtract 10% Add 10%

time to be eliminated from the body. Dose (D) is the amount of drug administered to the patient. Concentration (C) refers to the amount of drug in a unit volume of the plasma (or other body fluid) at a particular time. Steady state concentration (C,s) is the concentration reached during an infusion or multiple dosing after more than four half-lives have passed. Time to reach steady state (TSS) is equal to four to five times T '/2. Loading dose (LD) is the dose of a drug required to rapidly achieve a target C. Dose rate (Ro) is the amount of drug required per unit time to maintain a specific CSSI

RELATIONSHIPS BETWEEN THE TERMS The individual parameters described above define the pharmacokinetic behavior of a drug as it sojourns in the body. As they are related to one another, the knowledge of these relationships allows calculation of clinically useful pharmacological data.34 Following IV drug administration C is directly proportional to D and inversely proportional to V, ie, C = DNV. Since D will be proportionately reduced by F after oral administration C = FD/V. CL is directly proportional to V and inversely proportional to T 1/2, ie, CL cr V/T l/2. In order to equate CL to V, a proportionality constant of 0.7 is required, ie, CL = 0.7V/T '/2. Note also that T '/2 = 0.7V/CL. C,s is directly related to Ro and inversely related to CL, ie, Css = FRo/CL. Also CL = FRo/C,, and Ro = CSSCL/F. The F factor is again introduced in the latter equations to account for oral bioavailability. Table 2



lists the six simple pharmacokinetic formulae that summarize the foregoing discussion.

EFFECT OF RENAL FUNCTION ON CLEARANCE Many drugs (aminoglycosides, digoxin, cimetidine) are eliminated primarily through the kidney. In these cases, drug clearance is primarily a function of glomerular fitration, as only a relatively small fraction of the clearance may occur through non-renal routes. Creatinine clearance is a reasonable estimate of glomerular filtration. It can be calculated in one of two ways (Table 3). Recent data suggest that the Cockcroft and Gault5 equation, which requires only that serum creatinine concentration be measured, provides a clinically acceptable approximation to glomerular filtration rate (GFR) calculated from plasma and urine creatinine concentration. For a compilation of drug clearance in terms of the clearance of creatinine, the reader can use the tables in Appendix II of the sixth edition of Goodman and Gilman.6 For example, the clearance of tobramycin = CLer 0.66 mL/min/kg.

EFFECT OF HEPATIC FUNCTION ON BIOAVAILABILITY AND DRUG CLEARANCE Other drugs are eliminated by the liver, usually by drug biotransformation. Metabolism by the liver can affect both bioavailability and clearance. When a drug is given by the oral route, it must first pass through the portal circulation. Certain drugs are extensively metabolized (extracted) during this "first pass" through the liver. This may significantly reduce "F" or systemic bioavailability. Other drugs escape total degradation during the first pass through the liver, but are continuously cleared by hepatic drug metabolism on subsequent passes through the liver. Clearance depends on the functional capacity of the liver enzymes to degrade a drug and on hepatic blood flow. Quantitative estimation of this clearance is difficult, but has been determined experimentally for a number of

TABLE 2. SIX SIMPLE PHARMACOKINETIC FORMULAE To Calculate

Use

Concentration (C)*

C=V V

Dose (D)*

D= F

Clearance (CL)

CL =

F

0.7 V 1/2

Steady-State Concentration (Css) Css = FR CL7 Time to Reach Tss (Tss) Tss = 4-5 x t 1/2 Dose to Achieve Css (Ro) Ro = CssCL F

*Assumes no prior drug administration

drugs. It can vary from one individual to another, and may be affected by environmental factors. Average values for the clearance of drugs dependent upon the liver for elimination can also be found in Appendix II of Goodman and Gilman.6 It should be noted that the metabolism of some drugs is "capacity limited"; the enzymes responsible for their metabolism are saturable. For these drugs the clearance is "dose dependent," ie, the apparent clearance may diminish as the dose increases.7 An example of a drug where this concept is important is phenytoin (Dilantin). On the average, the body can metabolize phenytoin at a maximum of about 8.5 mg/kg of body weight per day (Vmax) and the plasma concentration at which half of this maximum occurs is about 8.5 ,4g/mL (km), below the usual lower limits of the therapeutic range (10-20).7 An unusual consequence of capacitylimited metabolism is that steady-state drug concentrations may rise out of proportion to increases in the dose (eg, doubling the phenytoin dosage may triple the serum concentration).

EFFECT OF PROTEIN BINDING Many drugs bind to circulating protein. Acidic drugs usually bind to albumin and basic drugs to

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TABLE 3. CALCULATION OF CREATININE CLEARANCE

(1) Usual method

CLCr = p-Cr x Urine Flow (mLlmin)* PCr (2) Cockcroft and Gault Method5 CLCr

CLCr =

(140-age)

x

Wt

(kg)

PCr x 72 kg

For women, multiply above by 0.85 Wt is lean body mass or ideal body weight

*UCr is the concentration of creatinine in the urine in mg/100 mL.

PCr is the concentration of creatinine in the plasma in the same units

cc-acid glycoprotein (orosomucin). The degree of protein binding can have a major effect on pharmacokinetics and pharmacodynamics as it is the "free" drug or unbound fraction of the drug that is available for disposition and determines pharmacodynamics. At present most laboratories measure only total drug concentration. Hence the clinician must understand what factors affect protein binding to properly assess the -significance of a specific drug concentration. Protein binding can be affected by physiological factors (age, sex, pregnancy, genetic variability) and various disease states (liver, renal, cardiac). For a detailed discussion on the effect of these factors, the reader is referred to Mungall. For our purposes here we would like to point out how variations in protein binding can affect the pharmacokinetic parameters discussed above, namely, volume of distribution and clearance. A decrease in plasma-protein binding may cause an increase in volume of distribution as there will be a greater amount of drug distributed extravascularly. However, a decrease in protein binding may also increase the clearance of a drug. This latter statement requires clarification. For certain drugs (eg, phenytoin and warfarin) clearance through the liver is dependent upon the drug's circulating free fraction and on the ability of the liver to metabolize the free drug. On the other hand, other drugs (eg, propranolol, organic nitrates, and morphine) are highly extracted by the liver regardless of protein binding. Such drugs undergo a considerable "first-pass" effect; they have a high extraction ratio (E). Therefore, degree of protein bind478

ing is irrelevant for these drugs. With regard to renal clearance and protein binding, it is only the free fraction that is fitered through the glomerulus, but elimination is complicated by tubular secretion and reabsorption. Hence, the effect of alterations in protein binding on renal clearance are difficult to predict.

RELATIONSHIP BETWEEN PHARMACOKINETICS AND EFFECT KINETICS The discussion above states little about a drug's effect on the body, which, after all, is what we are really interested in. It should be intuitively obvious that pharmacokinetics will influence effect kinetics. This relationship has been described by many different models.1 A therapeutic range ("window") has been determined for a number of commonly usedsdrugs, which makes it possible to develop rational dosage regimens. The therapeutic ranges for several of these drugs are given in Table 4.7 The clinical usefulness of determining serumdrug concentrations has been discussed by Koch-Weser.8 Two main reasons for obtaining drug-level information in a patient are (1) to determine the level in relation to the known minimum effective concentration and the maximum safe concentration for clinical correlation; and (2) for use in clinical pharmacokinetic calculations to assist in the development of a rational drug regimen. Clinical in-



TABLE 4. THERAPEUTIC RANGES FOR SOME COMMONLY USED DRUGS

Drug

Units

Digoxin

Gentamicin,

ng/mL mg/L

Tobramycin Lidocaine Phenobarbital Phenytoin *Procainamide Quinidine Salicylic acid Theophylline

mg/L mg/L mg/L mg/L mg/L mg/L mg/L

Minimum Effective Concentration (MEC) 0.8 2 2 15 10 4 2 150 5

Maximum safe Concentration (MSC) 1.6 10 5 40 20 8 5 300 20

*Procainamide is converted into N-acetyl procainamide (NAPA) The sum of procainamide and NAPA concentrations from 5 to 30 mg/L is therapeutic

stances of these indications include: 1. At the outset of inpatient therapy where the level resulting from outpatient therapy is uncertain. 2. Toxicity is suspected. 3. In evaluating a state of apparent therapeutic failure from a conventional dosing regimen of the drug. 4. There is a narrow therapeutic window, eg, digoxin. 5. Oral bioavailability is uncertain, eg, in the elderly (see below). 6. Poor compliance is suspected. 7. A drug interaction is suspected, eg, digoxin and quinidine. 8. Maintenance therapy to prevent a pathologic event when no other indicator of drug effect is available, eg, anti-seizure therapy. For a drug level to be meaningful, it must be drawn after the drug has been completely absorbed from the oral or intramuscular route, and after the drug has had an opportunity to distribute to its site of action. In addition, it should be remembered that the steady concentration will not be reached until four to five half-lives have passed. A good example is digoxin administered on a daily schedule; the absorption and distribution phases may take 6 to 12 hours to complete. Hence for a

meaningful interpretation, the level should be drawn at least midway through the elimination phase (about six hours prior to the next dose). If the level is drawn just prior to the next dose, one obtains a "trough" level; while a level drawn 6 to 12 hours after dosing would be a "peak" level. In the case of digoxin, the "swing" between peak and trough would be expected to be minimal, as the drug is given at intervals that are less than the drug's half-life (42 + 19 hours). A trough level, however, will be most helpful in determining whether or not the level is still within the therapeutic window when the drug is given at intervals greater than its half-life. An example of this is a slow-release theophylline formulation. In the case of aminoglycoside therapy, intermittent infusions are given at time intervals that exceed the drug's half-life, resulting in wide swings of the drug level. Here the therapeutic effect is related to the peak concentration, and the toxicity is related to the trough concentration. Hence, it is common to draw both peak and trough levels during a dosing interval. Of course the blood level attained at steadystate during a continuous intravenous infusion is expected to be constant; only one blood level need be obtained. Finally, the recording of the time of the sample in relation to the dose is always essential. If levels are drawn during an infusion, blood


479


should be drawn from the opposite extremity.

DOSING IN CHILDREN AND THE ELDERLY Dosing in children and in the elderly requires special pharmacokinetic and pharmacodynamic considerations. In the neonate, for example, there is decreased acid secretion in the stomach. Hence, there may be a decreased bioavailability of drugs like phenobarbital, but an increase in the availability of the acid-labile penicillins. A decreased gastric-emptying time may increase the bioavailability of some drugs (erythromycin, penicillins) because of a longer contact time with the gastric mucosa. Total body water is large (85 percent of body weight in premature infants, 70 percent in full term infants, compared to 60 percent in the adult) and hence water-soluble drugs (sulfa drugs, penicillin, cephalosporins, and aminoglycosides) will distribute throughout a greater volume of distribution and require a larger loading dose. Protein binding is decreased in the newborn because of a decreased concentration of albumin and a decreased capacity of fetal albumin to bind drugs. Hence, the free fraction of certain acidic drugs (salicylates, ampicillin, and sulfa drugs) is large with a resultant increase in their effect. Metabolic pathways have not fully matured in very young children. Such drugs as acetaminophen, lidocaine, phenobarbital, and phenytoin are cleared more slowly. On the other hand, certain drugs may undergo high rates of metabolism in childhood due to a large liver volume compared to the rest of the body; hence the clearance of theophylline, carbamazepine, and sulfonamides may be increased compared to adults. Finally, the glomerular filtration rate is only about 10 mL/min/m2 in the newborn, doubling in 14 days and reaching adult levels in two to four months. Drugs excreted primarily through the kidney (eg, certain antibiotics) will have a longer half-life (lower clearance) in the newborn. In the elderly, drugs absorbed by active transport (eg, calcium ions, ferrous ions, and thiamine) may have lower bioavailability. Increased stomach pH, decreased gastric motility and emptying time may have a variable effect on bioavail480

ability. For example, certain drugs which are unstable in acid pH may have increased bioavailability (penicillin, levodopa). Older people have a decreased lean body mass. This may reduce distribution volume and cause high initial peak levels of some drugs (eg, digoxin).' Decreased albumin leads to decreased drug binding and an increased free fraction of the drug. Because of decreased cardiac output, leading to decreased hepatic blood flow, and other factors, older people have drug-metabolism rates in the liver that are one-half or two-thirds those of young adults; therefore, dosages of drugs metabolized in the liver should be reduced accordingly. Renal function declines with advancing age. The creatinine clearance decreases by about 1 mL/min each year after the age of 40. (Note, however, that serum creatinine may not rise because there is also a decreased creatinine-formation rate due to decreased muscle mass.) Pharmacodynamics may change in the elderly due to poorly understood changes in sensitivity to certain drugs. For example, the aged are more sensitive to the benzodiazepines and warfarin, but more resistant to the ,-blocking effects of propranolol.

PRACTICAL APPLICATION Following are some examples of simple pharmacokinetic calculations using the principles discussed above. Specific drugs and clinical situations are used for these illustrations. Problem 1. A 35-year-old man, weighing 60 kg was given 80 mg of tobramycin. What is the expected plasma concentration? V for tobramycin is 0.25 L/kg.6 Solution.

c _ FD x 80mg C- 0.25 L/kg x 60 kg

C =5.3 mg/L Problem 2. In the patient above, it is determined



that a more appropriate C peak from bacterial sensitivity testing is 8 mg/L. What dosage of tobramycin would be required to achieve this C peak assuming no recent tobramycin therapy?

Calculation of new dose rate of aminophylline (80 percent theophylline): Ro= CssCL F

Solution:

15 mg/L x 2.33 L/h 1 x 0.8

D= C xF V

=43.7 mg/h or about 45 mg/h

8 mg/L x 0.25 L/kg x 60 kg

Calculate half-life: - 120 mg t 1/2

Problem 3. A 25-year-old, 70-kg man enters the emergency room with an acute attack of asthma. He has not been taking any medication and is a nonsmoker. (1) What IV loading dose of aminophylline (80 percent theophylline) should he receive to achieve a 15 mg/L plasma theophylline concentration? (2) The physician empirically treats him with a maintenance dose of 1 mg/kg/h of aminophylline (equals 0.8 mg/kg/h of theophylline) hoping to maintain his plasma concentration at 15 mg/L; 45 hours later a plasma level is taken and reported to be 24 mg/L. How would the physician alter the infusion rate to maintain a steady state concentration of 12 mg/L? (3) How long did it take to reach steady state in this patient? V for theophylline is 0.5 L/kg. Assume ideal and actual body weight to be identical in this case. Solution: Cv (1) D = CF 15 mg/L x 0.5 L/kg x 70 kg 1 x 0.8 - 656 mg or about 650 mg.

Calculate clearance as, C 1 _FRo Css 1 x 0.8 mg/kg/h x 70 kg 24 mg/L - 2.33 L/h

0.7V CL

0.7 x 0.5 L/kg x 70kg 2.33 L/h 11 0.52hoursorabout 11 hours Note that you would have to wait 11 hours for the plasma concentration to fall to 12 mg/L before starting the new infusion rate. Tss = 4-5 x t 1/2 = 4-5 x 11 hours = 44-55 hours

Hence, one can be confident that the plasma concentration drawn at 45 hours was at steadystate.

Comment. Clearance of theophylline may be decreased by liver, lung, and heart disease, and increased by smoking and certain drugs, eg, phenobarbital and phenytoin administration. The effect of these factors on clearance can be estimated quantitatively.9 Half-life from which clearance can be determined may also be estimated by giving a single dose of the drug and plotting two subsequent plasma concentrations on semilog graph paper.

(2) Problem 4. A 65-year-old woman enters the hospital with nausea and palpitations. She has been taking digoxin 0.25 mg/d regularly. Her electrocardiogram shows atrial tachycardia with 2:1 block. A digitalis level 12 hours from her last dose is 3.0 ng/mL. (1) What is her digoxin clear-


481


ance? (2) What dose rate is required to maintain a serum concentration of 1.0 ng/mL. Oral bioavailability of digoxin is 70 percent. Solution.

CLC= RoxF Css

maintain Cs,, and other useful pharmacological data. In Part 2 of this series, the authors will consider pharmacokinetic problems related to specific drugs in greater detail.

(1)

0.25 mg/d x 0.7 3.0 ng/mL

Acknowledgments This work was supported in part by the Uniformed Services University of the Health Sciences and the Development Grant for Clinical Pharmacology Units from the Pharmaceutical Manufacturers Association Foundation.

17.5 x 104 ng/d 3.0 ng/mL = 5.8 x 104 mL/d or 58.3 L/d Note: 1 ng = 10-9 g = 10-6i mg

Ro= Css Fx CL (2) Ro= 1.0 ng/mL x 5.8 x 104 mL/d

~~~0.7

=8.3 x 104 ng/d = 0.083 mg/d or about 0.25 mg every three days

Comment. This example indicates that the elderly may have an impaired clearance of digoxin that is often due to age-related reduction in its renal clearance.

Literature Cited 1. Holford NHG, Sheiner LB. Understanding the doseeffect relationship. Clin Pharmacokinet 1981; 6:429-453. 2. Koch-Weser J. Bioavailability of drugs. N Engl J Med 1974; 291:233-237. 3. Atkinson AJ Jr, Kushner W. Clinical pharmacokinetics. Ann Rev Pharmacol Toxicol 1979; 19:105-127. 4. Mungall DR (ed). Applied Clinical Pharmacokinetics. New York: Raven Press, 1983, pp 1-48. 5. Cockroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron 1976; 16:31-41. 6. Benet LZ, Sheiner LB. Design and optimization of dosage regimens. Pharmacokinetic data. In: Goodman LS, Gilman A (eds). The Pharmacological Basis of Therapeutics, ed 6. London: Macmillan, 1980, pp 1675-1737. 7. Medical Knowledge Self-Assessment Program VI. Syllabus Part I. Clinical Pharmacology Section. Published by the American College of Physicians, 1982, pp 85-94. 8. Koch-Weser J. Serum drug concentrations in clinical perspective. Ther Drug Monit 1981; 3:3-16. 9. Powell JR, Vozeh S, Hopewell P. Theophylline disposition in acutely ill hospitalized patients: The effect of smoking, heart failure, severe airway obstruction, and pneumonia. Am Rev Respir Dis 1978; 118:229-238.

CONCLUSIONS Calculating a dosage regimen using pharmacokinetic principles need not be difficult. All that one needs is a basic understanding of the terms that define the behavior of a drug when it enters the body. These are bioavailability (F), volume of distribution (V), and clearance (CL). By the appropriate manipulation of these terms, one can easily calculate a loading dose (D), peakplasma concentration (C peak), steady-state plasma concentration (C,,), the dosage rate (Ro) to 482

Suggested Reading Bochner F. Handbook of Clinical Pharmacology. Bos-

ton: Little, Brown, 1978. Evans WE, Schentag JJ, Jusko WJ (eds). Applied Pharmacokinetics: Principles of Therapeutic Drug Monitoring. San Francisco: Applied Therapeutics, 1980. Gibaldi M. Pharmacokinetics in clinical practice. 1. Concepts. JAMA 1976; 235:1864-1867. Gibaldi M. Pharmacokinetics in clinical practice. 2. Applications. JAMA 1976; 235:1987-1992. Peck CC. Bedside Clinical Pharmacokinetics: Simple Techniques for Individualizing Drug Therapy. Rockville, Maryland: Pharmacometrics Press, 1984.
