LESSON 2 Basic Pharmacokinetics

OBJECTIVES

After completing Lesson 2, you should be able to: 1. Define the concept of apparent volume of distribution and use an appropriate mathematical equation to calculate this parameter. 2. Identify the components of body fluids that make up extracellular and intracellular fluids and know the percentage of each component. 3. Describe the difference between whole blood, plasma, and serum. 4. Define drug clearance. 5. Describe the difference between first- and zero-order elimination and how each appears graphically.

To examine the concept of volume of distribution further, let’s return to our example of the body as a tank described in Lesson 1. We assumed that no drug was being removed from the tank while we were determining volume. In reality, drug concentration in the body is constantly changing, primarily due to elimination. - utes. This flux makes it more difficult to calculate the volume in which a drug distrib One way to calculate the apparent volume of drug distribution in the body is to measure the plasma concentration immediately after intravenous administra-

intravenous administration (at time zero, t0) is abbreviated as C0 (Figure 2-1). The volumetion before of distribution elimination can has be had calculated a significant using effect. the equation: The concentration just after amount of drug administered (dose) X (mg) volume of distribution = or V(L) = 0

initial drug C 0 (mg/L) concentration (See Equation 1-1.)

C0 can be determined from a direct measurement or estimated by back- extrapolation from concentrations determined at any time after the dose. If two concentrations have been determined, a line containing the two values and extending through the y-axis can be drawn on semilog paper. The point where that line crosses the y-axis gives an estimate of C0. Both the direct measurement and back-extrapolation approaches assume that the drug distributes instantaneously into a single homogeneous compartment. Concepts in Clinical Pharmacokinetics 22

as that is the approximate volume of extracellular that its distribution is limited to extracellular fluid,-

allfluid body in the water body. because If a drug a 70-kg has a personvolume has of distribuapproxi- tion of about 40 L, the drug may× be 60%). distributing If the volume into

probablymately 40 isL ofbeing body concentrated water (70 kg in tissue outside the FIGURE 2-1. of distribution is much greater than 40–50 L, the drug Concentration resulting immediately after an intravenous If a drug distributes extensively into tissues, injection of a drug is referred to as C0. plasma and interstitial fluid. the volume of distribution calculated from plasma concentrations could be much higher than the The volume of distribution is an important actual physiologic volume in which it distributes. parameter for determining proper drug dosing regi- For example, by measuring plasma concentrations, mens. Often referred to as the apparent volume of it appears that digoxin distributes in approximately distribution, it does not have an exact physiologic

to muscle tissue, plasma levels are fairly low relative distribution and aid in determination of dosage to440 concentrations L in an adult. Becausein muscle digoxin tissue. binds For other extensively drugs, requirements.significance, but Generally, it can indicate dosing theis proportional extent of drug to tissue concentrations may not be as high as the the volume of distribution. For example, the larger plasma concentration, so it may appear that these the volume of distribution, the larger a dose must be drugs distribute into a relatively small volume. to achieve a desired target concentration. It is also important to distinguish among blood, To understand how distribution occurs, you plasma, and serum. Blood in combination with formed elements (white cells, and tissues (Figure 2-2 red cells, and platelets). refers to refers the fluid only portion to the inmust an adult have amakes basic up understanding approximately of 60% body of fluids total Plasma ). The fluid portion (water) but not formed elements). When the soluble protein fluid portion of blood (including soluble proteins body weight and is composed of intracellular fluid (35%) and extracellular fluid (25%). Extracellular product is serum (Figure 2-3). fibrinogen is removed from plasma, the remaining vascularfluid is made system. up of These plasma percentages (4%) and interstitialvary somewhat fluid in(21%). a child. Interstitial fluid surrounds cells outside the recognized when considering reported drug concen- trations.These The differences plasma concentration in biologic of fluids a drug must may be If a drug has a volume of distribution of approxi- much less than the whole blood concentration if the mately 15–18 L in a 70-kg person, we might assume drug is preferentially sequestered by red blood cells.

FIGURE 2-2. FIGURE 2-3. Fluid distribution in an adult. Relationship of whole blood, plasma, and serum. Lesson 2 | Basic Pharmacokinetics 23

Clinical Correlate Initial Resulting concentration concentration Most drug concentrations are measured using Elimination over time plasma or serum that usually generate similar values. It is more relevant to use plasma or serum than whole blood measurements to Volume from estimate drug concentrations at the site of effect. which drug is However, some drugs, such as antimalarials, are removed over time extensively taken up by red blood cells. In these FIGURE 2-5. situations, whole blood concentrations would be Clearance may be viewed as the volume of plasma from which more relevant, although they are not commonly drug is totally removed over a specified period. used in clinical practice. Drugs can be cleared from the body by many different mechanisms, pathways, or organs, including Clearance hepatic biotransformation and renal and biliary excretion. Total body clearance of a drug is the sum of Another important parameter in pharmacokinetics all the clearances by various mechanisms. is clearance. Clearance is a measure of the removal of drug from the body. Plasma drug concentrations are 2-1 Cl=++ Cl Cl Cl+ Cl affected by the rate at which drug is administered, t rmbother the volume in which it distributes, and its clearance. A drug’s clearance and the volume of distribution where determine its half-life. The concept of half-life and its Cl = total body clearance (from all relevant equations are discussed in Lesson 3. t mechanisms, where t refers to total); Clearance (expressed as volume/time) Cl = renal clearance (through renal describes the removal of drug from a volume of r excretion); plasma in a given unit of time (drug loss from the Cl = clearance by liver metabolism or body). Clearance does not indicate the amount m of drug being removed. It indicates the volume biotransformation; of plasma (or blood) from which the drug is Clb = biliary clearance (through biliary completely removed, or cleared, in a given time excretion); and period. Figures 2-4 and 2-5 represent two ways Clother = clearance by all other routes (gastro- intestinal tract, pulmonary, etc.). amount of drug (the number of dots) decreases but of thinking about drug clearance. In Figure 2-4, the- For an agent removed primarily by the kidneys, tration. Another way of viewing the same decrease renal clearance (Clr) makes up most of the total body fillswould the be same to calculatevolume, resultingthe volume in a thatlower would concen be clearance. For a drug primarily metabolized by the drug-free if the concentration were held constant. liver, hepatic clearance (Clm) is most important. A good way to understand clearance is to consider a single well-perfused organ that elimi- Initial Resulting concentration concentration to as Q (mL/minute) as seen in Figure 2-6, where Elimination nates drug. Blood flow through the organ is referred over time Cin is the drug concentration in the blood entering

the organ and Cout is the drug concentration in the exiting blood. If the organ eliminates some of the drug, C is greater than C . FIGURE 2-4. in out Decrease in drug concentration due to drug clearance. Concepts in Clinical Pharmacokinetics 24

TABLE 2-1. Rating of Extraction Ratios

Extraction Ratio (E ) Rating > 0.7 High 0.3–0.7 Intermediate < 0.3 Low

FIGURE 2-6. Clearance may also be a useful parameter for Model for organ clearance of a drug. constructing dosage recommendations in clinical situations. It is an index of the capacity for drug We can measure an organ’s ability to remove a removal by the body’s organs.

drug by relating Cin and Cout. This extraction ratio (E) is: CC− E = in out Clinical Correlate

Cin Blood flow and the extraction ratio will determine This ratio must be a fraction between zero and one. a drug’s clearance. Propranolol is a drug that is eliminated exclusively by hepatic metabolism. will have an extraction ratio approaching one (i.e., The extraction ratio for propranolol is greater than Organs that are very efficient at eliminating a drug 100% extraction). Table 2-1 is used as a general 0.9, so most of the drug presented to the liver is guide. removed by one pass through the liver. Therefore, The drug clearance of any organ is determined clearance is approximately equal to liver blood flow (Cl = Q × E: when E ~ 1.0, Cl ~ Q). One indication of the high extraction ratio is the by bloodorgan flow clearance and the = bloodextraction flow× ratio:extraction ratio relatively high oral dose of propranolol compared with the intravenous dose; an oral dose is 10–20 or: times the equivalent intravenous dose. The difference reflects the amount of drug removed

CC− by first-pass metabolism after absorption from 2-2 Cl =Q ×=in out or Cl QE organ C organ the gastrointestinal tract and before entry into the in general circulation.

- If an organ is very efficient in removing drug (i.e., The average clearances of some commonly used removingextraction ratiodrug near(i.e., one)extraction but blood ratio flow close is low, to clearzero) drugs are shown in Table 2-3. These values can ance will also be low. Also, if an organ is inefficient in vary considerably between individuals and may be low. See Table 2-2. altered by disease. even if blood flow is high, clearance would again be The equations noted previously are not used routinely in clinical drug monitoring, but they TABLE 2-2. Effect on Clearance - tion of a single well-perfused organ to understand Blood Flow (Q ) Clearance (Cl) clearancedescribe theis concepta noncompartmental of drug clearance. approach; Examina no Extraction Ratio (E ) (L/hour) (L/hour) assumptions about the number of compartments High (0.7–1.0) Low Low have to be made. Therefore, clearance is said to be Low (< 0.3) High Low a model-independent parameter. Clearance also can be related to the model-dependent param- High (0.7–1.0) High High eters volume of distribution and elimination rate Low (< 0.3) Low Low (discussed in Lesson 3). Lesson 2 | Basic Pharmacokinetics 25

TABLE 2-3. Average Clearances of Common Drugs TABLE 2-4. First-Order Elimination Amlodipine 5.9 ± 1.5 mL/min/kg Amount of Drug Time after Drug Amount of Eliminated over Fraction of Drug Ganciclovir 3.4 ± 0.5 mL/min/kg Administration Drug in Body Preceding Hour Eliminated over (hours) (mg) (mg) Preceding Hour Ketorolac 0.50 ± 0.15 mL/min/kg 0 1000 — — Lansoprazole 6.23 ± 1.60 mL/min/kg 1 880 120 0.12 Montelukast 0.70 ± 0.17 mL/min/kg 2 774 106 0.12 Sildenafil 6.0 ± 1.1 mL/min/kg 3 681 93 0.12 Valsartan 0.49 ± 0.09 mL/min/kg 4 599 82 0.12 5 527 72 0.12 Source: Brunton LL, Lazo JS, Parker KL (editors), The 6 464 63 0.12 Pharmacologic Basis of Therapeutics, 11th edition. New York: 7 408 56 0.12 McGraw-Hill; 2006. pp. 1798, 1829, 1839, 1840, 1851, 1872, 1883. The actual amount of drug eliminated is different

First-Order and Zero-Order Elimination amount in the body, but the fraction removed is the for each fixed time period depending on the initial The simplest example of drug elimination in a one- elimination of this drug (like most drugs) occurs by compartment model is a single intravenous bolus same, so this elimination is first order. Because the dose of a drug. decreases as the concentration in plasma decreases. Thea first-order actual fraction process, of thedrug amount eliminated of drug over eliminated any given 1. DistributionIt is first and assumed equilibration that: to all tissues the individual patient’s capacity to eliminate the drug. compartment model applies. time (in this case 12%) depends on the drug itself and and fluids occurs instantaneously so a one- On the other hand, with zero-order elimination, the amount of drug eliminated does not change with 2. Elimination is first order. the amount or concentration of drug in the body, but the fraction removed varies (Figure 2-7). For mustMost be understood. drugs are eliminatedWith first-order by a elimination first-order, example, if 1000 mg of a drug is administered and theprocess, amount and of the drug concept eliminated of first-order in a set elimination amount of the drug follows zero-order elimination, we might time is directly proportional to the amount of drug observe the patterns in Table 2-5. in the body. The amount of drug eliminated over a certain time period increases as the amount of drug in the body increases; likewise, the amount of drug eliminated per unit of time decreases as the amount of drug in the body decreases. although the amount of drug eliminated may change withWith the amount the first-order of drug in the elimination body, the process,fraction of a drug in the body eliminated over a given time remains constant. In practical terms, the fraction or percentage of drug being removed is the same with either high or low drug concentrations. For example, FIGURE 2-7. if 1000 mg of a drug is administered and the drug Zero- versus first-order elimination. The size of the arrow represents the amount of drug eliminated over a unit of time. Percentages are the fraction of the initial drug amount patterns in Table 2-4. remaining in the body. follows first-order elimination, we might observe the Concepts in Clinical Pharmacokinetics 26

TABLE 2-5. Zero-Order Elimination Clinical Correlate Fraction of Amount of Drug Drug Elimi- Most antimicrobial agents (e.g., Time after Drug Eliminated over nated over Administration Amount of Drug Preceding Hour Preceding aminoglycosides, cephalosporins, and (hours) in Body (mg) (mg) Hour vancomycin) display first-order elimination when administered in usual doses. The 0 1000 — — pharmacokinetic parameters for these drugs are 1 850 150 0.15 not affected by the size of the dose given. As 2 700 150 0.18 the dose and drug concentrations increase, the 3 550 150 0.21 amount of drug eliminated per hour increases 4 400 150 0.27 while the fraction of drug removed remains the 5 250 150 0.38 same. Some drugs (e.g., phenytoin), when given in high doses, display zero-order elimination. Zero- order elimination occurs when the body’s ability order elimination, let’s return to our simple to eliminate a drug has reached its maximum one-compartment,Now that we have intravenous examined bolus zero- andsituation. first- capability (i.e., all transporters are being used). If the plasma drug concentration is continuously As the dose and drug concentrations increase, measured and plotted against time after admin- the amount of drug eliminated per hour does istration of an intravenous dose of a drug with not increase, and the fraction of drug removed - declines. tion curve shown in Figure 2-8 would result. To first-orderpredict concentrations elimination, at thetimes plasma when we concentra did not collect samples, we must linearize the plot by using semilog paper (Figure 2-9).

FIGURE 2-8. FIGURE 2-9. Plasma drug concentration versus time after an intravenous As in Figure 2-8, but with a log scale y-axis. (bolus) drug dose, assuming a one-compartment model with first-order elimination (linear y-scale). Lesson 2 | Basic Pharmacokinetics 27

natural log of plasma concentration versus time plotFor is a astraight drug withline. first-orderConversely, elimination,plots with zero- the order elimination would be as shown in Figure A 2-10. Note that for a drug with zero-order elimina- tion, the plot of the plasma concentration versus

semilog paper (representing the natural log of plasmatime is linearconcentration (plot A in versus Figure time) 2-10), it whereas is a curve on

a plasma drug concentration versus time plot is linear,(bottom it plotgenerally in Figure can 2-10).be assumed If the naturalthat the log drug of B follows first-order elimination.

FIGURE 2-10. Plasma drug concentrations versus time after an intravenous (bolus) drug dose, assuming a one-compartment model with zero-order elimination (A, linear plot; B, log plot). Concepts in Clinical Pharmacokinetics 28 REVIEW QUESTIONS

Plasma divided by initial drug concentration: blood, including soluble proteins but not 2-1. The volume of distribution equals ______2-5. refers only to the fluid portion of A. clearance formed elements. B. initial drug concentration A. True C. half-life B. False D. dose

A. concentration/half-life. 2-6. The units for clearance are: to a patient, and the following concentrations B. dose/volume. 2-2. A dose of 1000 mg of a drug is administered result at the indicated times below. Assume a C. half-life/dose. one-compartment model. D. volume/time. Plasma Concentration Time after Dose (mg/L) (hours) 100 2 by the kidneys, liver, and other routes of 2-7. elimination.Total body clearance is the sum of clearance 67 4 A. True 45 6 B. False An estimate of the volume of distribution would be: A. 10 L. 2-8. two-compartmentTo determine drug model. clearance, we must first determine whether a drug best fits a one- or A. True C. 6.7 L. B. 22.2 L. B. False D. 5 L. - tion, the amount of drug eliminated per unit apparent volume of distribution is probably: 2-9. time:With a drug that follows first-order elimina 2-3. If a drug is poorly distributed to tissues, its A. large. A. remains constant while the fraction of B. small. drug eliminated decreases. B. decreases while the fraction of drug eliminated remains constant. rank them from the lowest volume to the 2-4. highest,For the in body a typical fluid 70-kg compartments person. below, - ANSWERS

A. Plasma < extracellular fluid < intracel Incorrect answers lular fluid < total body water plasma < total body water 2-1. A, B, C. B. Extracellular fluid < intracellular fluid < the correct answer from the units in D. theCORRECT numerator ANSWER. and denominator.You can determine They plasma < total body water C. Intracellular fluid < extracellular fluid < should cancel to yield a volume unit. D. Total body water < plasma < intracel- Grams divided by grams per liter would leave you with liter as the unit. The lular fluid < extracellular fluid Lesson 2 | Basic Pharmacokinetics 29

volume is therefore determined from the dose, or amount of drug given, and the resulting initial concentration. 2-4. A. CORRECT ANSWER. See Figure 2-2. Plasma would be 2.8 L, extracellular Incorrect answer fluid would be 18 L, intracellular fluid 100 mg/L as the initial concentration. would be 25 L, and total body water B, C, D. Incorrect answers 2-2. A. . You may have used would be 42 L. B. Incorrect answer incorrect initial concentration. . You may have used an B. Incorrect answer 2-5. A. CORRECT ANSWER concentration, plot the given plasma Incorrect answers. The units for clear- C. concentrationCORRECT ANSWER. and Totime find values the initial on ance are volume/time. 2-6. A, B, C. semilog paper, connect the points, and read the value of the y-axis (concentra- tion) when x (time) = 0. This should be D. CORRECT ANSWER - ance can be determined as the sum of volume of distribution using the equa- 2-7. A. individualCORRECT clearances ANSWER. from Total all body organs clear or tion150 mg/L.volume You of can distribution then determine = dose/ the routes of elimination. initial concentration. B. Incorrect answer D. Incorrect answer Incorrect answer an incorrect initial concentration, or you may have used. You linear may graph have paper used 2-8. A. to specify a model to determine drug instead of semilog paper. B. clearance.CORRECT ANSWER. It is not necessary Incorrect answer. Drug concentrations Incorrect answer are generally measured in plasma. When 2-3. A. drug distributes poorly into tissues, 2-9. A. elimination, the amount of drug elimi- the plasma level will be increased. B. natedCORRECT in any ANSWER. time period With is determined first-order - by the amount of drug present at the bution = dose/initial concentration, as start. Although the amount of drug elim- Examiningthe initial concentrationthe equation volume increases, of distri the inated in successive time periods may volume will decrease. decrease, the fraction of the initial drug that is eliminated remains constant.

B. CORRECT ANSWER Concepts in Clinical Pharmacokinetics 30

Discussion Points

D1. D3. and plasma concentrations are then deter- have a volume of distribution for a drug of Drugmined Y as is follows:given by an intravenous injection 700Explain L. how a person who weighs 70 kg can

Concentration D4. For drug X, individual organ clearances have Time after Injection (hours) (mg/L) been determined as follows: 0 12 Renal clearance 180 mL/minute 1 9.8 2 7.9 Hepatic clearance 22 mL/minute 3 6.4 Pulmonary clearance 5.2 mL/minute 4 5.2 How would you describe the clearance of 5 4.2 drug X? 6 3.4 7 2.8 8 2.2

order process? Defend your answer. Is this drug eliminated by a first- or zero- D2. Which of the following patient scenarios is associated with a smaller volume of distri- bution?

A. Dose = 500 mg and initial serum concen-

- tration is 40 mg/L tration is 1.5 mg/L B. Dose = 20 mg and initial serum concen