ANIMAL DRUG SAFETY
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES Lewis W. Dittert College of Pharmacy, University of Kentucky, Lexington, Kentucky The applications of pharmacokinetic modeling to the prediction of tissue residues of drugs in food-producing animals are reviewed. The properties of the one-compartment open model are discussed, and the application of this model to the serum levels, urine outputs, and tissue residues of sulfamethazine and its metabolites in sheep is described. The properties of the two-compartment model are discussed, and the application of this model to the serum levels and urine outputs of dicloxacillin in humans is described. Complexities encountered with drugs such as pentobarbital, the tetracyclines, etidronate, and salicylate are discussed as examples of pharmacokinetic behavior that make both modeling and tissue residue prediction difficult.
INTRODUCTION Pharmacokinetic modeling is the science of describing, in mathematical terms, the time course of drug and metabolite concentrations in body fluids and tissues. Most often the models are based on blood concentration versus time profiles, since it is generally assumed that blood is in equilibrium with all tissues and fluids of the body. The outputs of drug and metabolites in urine and feces are also followed, since these are the major routes of elimination. A pharmacokinetic model is regarded as being accurate and correct if it predicts blood concentrations and urine and fecal outputs of drug and metabolites for as long as these substances can be measured analytically. The model may be tested by comparing its predictions with experimental data when the drug is administered by various routes and on various dosing regimens. Usually, recovery of 95+% of the administered dose(s) as unchanged drug and metabolites in urine and feces and agreement between the recovered amounts and the pharmacokinetic model is considered confirming evidence that the model accounts for the fate of all the administered drug. The objective of pharmacokinetic modeling in food-producing animals is to predict when and if an animal's meat will be contaminated without having to slaughter the animal. Such models are useful in determining withdrawal times for new drugs, dosage forms, or routes of administration. They also provide the theoretical basis for field testing animals by This work was supported in part by Research Grant FDA 74-178, Division of Veterinary Medical Research, Bureau of Veterinary Medicine, Food and Drug Administration, Beltsville, Maryland 20505. Requests for reprints should be sent to Lewis W. Dittert, College of Pharmacy, University of Kentucky, Lexington, Kentucky 40506.
735 Journal of Toxicology and Environmental Health, 2:735-756,1977 Copyright © 1977 by Hemisphere Publishing Corporation
736
L. W. DITTERT
analyzing blood or urine rather than tissues. The approach to modeling for the prediction of tissue residues involves first developing a model using blood, urine, and fecal data, then comparing the model's predictions with tissue residues determined experimentally at various times following dosing. If the model predictions match the experimental data, it can be assumed that the time required for a particular tissue to fall to any given level can be determined by mathematical extrapolation of the model. ONE-COMPARTMENT MODEL The simplest pharmacokinetic model is the one-compartment open model illustrated in Fig. 1. Here, the body is viewed as a single homogeneous box with a fixed volume. Drug entering the systemic circulation by any route is instantaneously distributed throughout the body. Although the absolute concentrations in all body tissues and fluids are not identical, it is assumed that they all rise and fall in parallel as drug is added and eliminated. Overall elimination of drug from the body by urinary excretion and/or metabolism usually obeys first-order kinetics; that is, the rate of elimination is proportional to drug concentration in blood or plasma, as shown by the following equation:
Rearrangement and integration of Eq. (1) gives log Cp = -
^
+ log Cp°
(2)
which says that following an iv dose, a semilog plot of plasma concentrations versus time will be a straight line with a slope of —ke]/2.3. This is a practical definition of a one-compartment drug, and the best way to determine whether a one-compartment model is appropriate for a given drug is to plot iv plasma concentrations against time on semilog paper and see if the plot is a straight line. This approach will also yield values for the two parameters of the model: kei, the overall elimination
D , Drug i n Body
k , el
Eliminated Drug
FIGURE 1. One-compartment open pharmacokinetic model.
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
737
o o
X O
o o o
(Jo CCO
Too
10.00
20.00
30.00
40.00
50.00
HOURS FIGURE 2. Typical cumulative urine output curve for unchanged drug (sulfamethazine in sheep). From Bourne et al. (1977).
rate constant, and VD, the apparent volume of distribution of the drug in the body. If the drug is eliminated partially or completely unchanged in the urine, kel can also be determined from urine output data. These data are usually expressed as cumulative urine output versus time, as illustrated in Fig. 2. But they can be plotted as a straight line on semilog paper as shown by the following equation (Notari, 1975):
where UM is the final total amount of drug recovered unchanged in urine and Ut is the cumulative amount recovered up to time t. The value ((/„ — Ut) represents the amount remaining to be excreted (ARE) as unchanged drug, and a plot such as that shown in Fig. 3 is sometimes referred to as an "ARE plot." Equation (3) shows that the slope of an ARE plot is —&e)/2.3. Thus, the same kei can be determined from both plasma and urine data, and agreement between plasma and urine data is an essential test of the validity of the model. Figure 3 illustrates a major difficulty with the use of ARE plots. The
738
L. W. DITTERT
> UNCHflNCEO STZ . STZ ( I N F ) ' - S O
lb.00 IS. 00 TIME IN HOURS
5.00
z b . o o a s . oo
FIGURE 3. Typical ARE plot showing the errors introduced when the estimate of U^ is in error by ± 1 SD (sulfathiazole in swine).
solid line represents a calculation of ARE values using the "true" value of U^. The points above and below the line represent ARE values calculated using £/„ + 1 SD and Um — 1 SD, respectively. Thus, the accuracy with which U^ is determined has a great influence on the apparent slope of the ARE plot. This problem is magnified by the fact that accurate experimental determination of £/„ requires complete collection of total voided urine over a prolonged period of time, plus accurate analysis of large volumes of urine containing small amounts of drug. An alternative to the ARE plot is the rate-of-excretion plot shown in Fig. 4. The equation of this plot is (Wagner, 1975) =
-TT
(Dose)]
(4)
where AU/At is the excretion rate in percentage of dose per hour. This plot yields the same value of kei as the ARE plot, and it is independent of the value of 6 L .
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
00
10 00
20,00
739
30.0040.0050.00
HOURS FIGURE 4. Typical rate of excretion plot (sulfamethazine in sheep). From Bourne et al. (1977).
The Ux value is also used to calculate f, the fraction of the absorbed dose eliminated unchanged in urine, as follows:
Dose
= f
(5)
The value of f is important because it represents the fraction of the overall elimination of the drug that is due to urinary clearance. This may be expressed in terms of rate constants as follows:
ku = /fceI
(6)
Thus, if a drug is eliminated partially by metabolism and partially by urinary excretion, the value of f can be used to determine the values of the urinary excretion rate constant, ku) and the metabolism rate constant, km. In this determination, it is assumed that any drug not excreted unchanged in urine has been "metabolized," and this would include drug eliminated unchanged by such nonurinary routes as biliary excretion. If more than one metabolite is formed and excreted in urine, values can be assigned to the individual metabolite formation rate constants by
740
L. W. DITTERT
determining the fraction of the absorbed dose eliminated as each metabolite and applying a calculation similar to Eqs. (5) and (6): (7) b
R
m
= f b
tR\
'm"el
\°>
Here, £/„„, is the final total amount of a specific metabolite recovered in urine and km is the rate constant for formation of that metabolite. Although the kidney is capable of metabolizing drugs and it has been shown that this process can occur simultaneously with elimination of the metabolite (Cabana et al., 1975) in most cases, metabolites are formed elsewhere in the body. This requires modification of the one-compartment model as shown in Fig. 5. This figure shows a metabolite appearing in the plasma, then being excreted into urine. The plasma concentrations achieved by the metabolite depend on the relative values of the formation rate constant, km, and the metabolite excretion rate constant, & mu , as well as on the apparent volume of distribution of the metabolite. In most cases, the metabolite is more polar than the parent drug, causing it to have a smaller VD than that of the parent drug. This tends to increase the metabolite's plasma concentrations. On the other hand, more polar compounds are more rapidly cleared by the kidney, and this tends to make kmu greater than km, causing a decrease in the metabolite's plasma concentrations. It is impossible to predict, for an unknown drug, which of these effects will predominate or whether metabolites can be expected to appear in significant concentrations in plasma. This can lead to meaningless and very confusing results if a nonspecific assay method is used. For example, if a radiolabeled lipophilic drug with a large volume of distribution is metabolized to a relatively polar radioactive metabolite with a small volume of distribribution and the toal radioactivity in plasma is followed, the plasma levels will at first appear to increase rather than decrease following an iv injection. If the initial increasing plasma radioactivity is
u
-•D.
U
mu FIGURE 5. One-compartment open pharmacokinetic model with appearance of a metabolite in plasma.
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
0.00
10.00
20.00
TIME
30.00
741
U0.00
50.00
(HOURS)
FIGURE 6. Sulfamethazine in plasma (o) and rate of excretion of sulfamethazine in urine (A) following an iv bolus dose in young ewe lambs.
overlooked or ignored and the later declining plasma radioactivity is treated kinetically, the estimated half-life will correspond to the kmu value rather than the true k^ value. Thus, total radioactivity in plasma can not be used to determine the pharmacokinetic model of a drug or to study the bioavailabilities of dosage forms. For similar reasons, nonspecific studies of total radioactivity levels in tissues following feeding of a radiolabeled drug may yield misleading results. Bevill and co-workers (Bevill et al., 1977; Bourne et al., 1977) have studied the pharmacokinetics of sulfamethazine in sheep and correlated the plasma concentrations and urine outputs with tissue residues. This work provides an excellent example of the application of the above principles. Figure 6 shows semilog plots of sulfamethazine in plasma and of rate of excretion of unchanged sulfamethazine in urine following an iv bolus dose of 107.5 mg/kg in 13 young ewe lambs. The plasma data fit a straight line on the semilog plot, showing that sulfamethazine can be adequately described by a one-compartment model. The urine line is
L. W. DITTERT
742
TABLE 1. Metabolic Pattern of Sulfamethazine in Sheep, Intravenous Administration Recovery in urine (% of dose)
Substance Sulfamethazine Acetyl Hydroxy Polar
*mu(hr-')
*m(hr-')
19 9 16 23
AB = ^HB = kpQ = ^misc = fe
SMZ = 0.0189 0.0088 ^AU = 1.02 0.0159 = 0.37 0.0223 kpfj = 0.42 0.0319
*el = 0.098
parallel to the plasma line, and both sets of data yield a half-life of 7.1 hr (*e, = 0.098 h r ' 1 ) . Urine outputs of the acetyl, hydroxy, and polar metabolites were followed in addition to unchanged sulfamethazine. The final total amounts of the metabolites recovered in urine, in terms of percentage of administered dose, are given in Table 1. The urinary excretion rate constant for sulfamethazine (kSMZ), calculated with Eqs. (5) and (6), and the formation rate constants for the metabolites (/?AB> ^HB> a p d ^PB)> calculated with Eqs. (7) and (8), are also shown in Table 1. The complete pharmacokinetic model for sulfamethazine and its metabolites is shown in Fig. 7. Five of the rate constants—that is, kSMZ, ^AB> ^HB> ^PB> a n d ^misc~ w e r e estimated as described above. The metabolite excretion rate constants, & A U , kHU, and & P U , were estimated by iterative digital computation using the SAAM-23 program (Berman and Weiss, 1968). Table 1 shows that the values of the metabolite excretion rate constants are between 20 and 100 times the values of the corresponding metabolite formation rate constants. This means that (1) the estimates of the excretion rate constants are probably not very accurate, but this is of little consequence, and (2) the concentrations of metabolites in the blood are expected to be very low, probably undetectable.
SMZ
SMZ
*-SMZT,
•-Polar
U
Misc. FIGURE 7. Complete pharmacokinetic following iv administration.
model for sulfamethazine and its metabolites in lambs
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
743
The final fit of the complete model to plasma and urine data is shown in Figs. 6 and 8. In these figures, the lines were generated by a computer programmed with the model shown in Fig. 7 and the rate constants shown in Table 1. The points are averaged experimental data, and the agreement between the theoretical lines and the experimental data points is excellent. From these results it can be concluded that the pharmacokinetics of sulfamethazine in sheep following iv administration has been completely described from a classical point of view, but the question of what the model means with regard to tissue residues remains to be answered. The correlation between the pharmacokinetic model and sulfamethazine residues in tissues was studied by slaughtering the sheep in pairs at 6, 12, 24, 36, 48, 60, and 84 hr following drug administration and analyzing kidney, liver, heart, skeletal muscle, and fat for drug residues (Bevill et al., 1977). Concentrations as high as 124 ppm and as low as 0.02 ppm were detected. The results of the residue analyses (Fig. 9) show that all tissues fall in parallel with plasma (dashed line) through approximately three logarithmic decades. This experimentally confirms the onecompartment nature of sulfamethazine pharmacokinetics and supports the argument that drug concentrations in plasma reflect drug residues in tissues. Figure 10 shows the correlation between muscle residues and plasma concentrations of sulfamethazine, and Fig. 11 shows the correlation between muscle residues and urine data (amount remaining to be excreted).
SMZ IN EWES LINERR MODEL METfiBOLITES IN URINE
en o O
z UJ
£g kJ_:
10.00
20.00 30.00 U0.00 TIME IN HOURS
SO. 00
FIGURE 8. Cumulative urinary excretion of sulfamethazine (o) and its polar (x), hydroxy (+), and acetyl (*) metabolites in lambs following iv administration.
vj ^ * .
o
20.00 30.00 HOURS
FIGURE 9. Sulfamethazine concentrations in kidney (^), heart (Z), liver (X), loin muscle ( A ) , leg muscle (+), shoulder muscle (o), body fat (X), and omental fat (o) of lambs following iv administration. The dashed line shows the slope of the plasma concentration curve. From Bourne et al. (1977).
•4.00
8.00
12.00
16.00
20.00
PLflSMR CONC. (MG/100ML) FIGURE 10. Average sulfamethazine concentration in muscle tissue versus sulfamethazine concentration in plasma at various times following iv administration to lambs. From Bourne et al. (1977).
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
745
Siso (no
10.00
20.00
30.00
10.00
50.00
DOSE TO BE EXCRETED IV.) FIGURE 11. Average sulfamethazine concentration in muscle tissue versus percentage of dose remaining to be excreted in urine (unchanged) at various times following iv administration to lambs. From Bourne et al. (1977).
It can be concluded that a pharmacokinetic model for sulfamethazine, developed using a classical approach, accurately reflects and predicts tissue residues of the drug. TWO-COMPARTMENT MODEL Although the classical two-compartment pharmacokinetic model (Fig. 12) is mathematically more complex than the one-compartment model, Drug In Tissues
k
Unabsorbed Drug
12f | k 21 Drug in Blood (V p )
kei
Eliminated Drug
FIGURE 12. Two-compartment open pharmacokinetic model.
L. W. DITTERT
746
there is often little practical difference between them. Usually, tissue distribution is much more rapid than absorption or elimination. As a result, evidence of the tissue distribution process may only be seen following iv injection; after tissue distribution equilibrium has been achieved, the drug behaves as a one-compartment drug. Also, for extravascular administration the tissues are essentially at equilibrium with the blood throughout the absorption process, and again the drug behaves as a one-compartment drug. The penicillins are examples of classical two-compartment drugs. Dicloxacillin administered iv (Dittert et al., 1969) gives the typical two-compartment plasma concentration versus time plot shown in Fig. 13. From these data, the parameters of the model (Fig. 12) can be determined, and the model can be used to generate plasma concentrations and urine outputs that fit the experimental data points, as shown in Fig. 14. The model will also generate the amount (fraction of the dose) of dicloxacillin in the tissue compartment, as shown in Fig. 15. After tissue distribution equilibrium has been achieved, drug in tissue falls in parallel with drug in plasma. This is the same behavior observed for onecompartment drugs; therefore, after distribution equilibrium, dicloxacillin is, for practical purposes, a one-compartment drug. Figure 16 shows a semilog plot of dicloxacillin plasma concentrations following an im injection (Doluisio et al., 1970). This figure suggests that
.60 3 Q: LU
10 < X
o o Q
0
1
2
3 HOURS
FIGURE 13. Average plasma concentrations of dicloxacillin versus time showing the twocompartment nature of the drug in humans following iv administration. From Dittert et al. (1970).
FIGURE 14. Average plasma concentrations and cumulative urine outputs of dicloxacillin following iv administration to humans. The points are experimental data. The lines were generated by an analog computer programmed with the dicloxacillin two-compartment model. From Dittert et al. (1970).
IOO
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES Lewis W. Dittert College of Pharmacy, University of Kentucky, Lexington, Kentucky The applications of pharmacokinetic modeling to the prediction of tissue residues of drugs in food-producing animals are reviewed. The properties of the one-compartment open model are discussed, and the application of this model to the serum levels, urine outputs, and tissue residues of sulfamethazine and its metabolites in sheep is described. The properties of the two-compartment model are discussed, and the application of this model to the serum levels and urine outputs of dicloxacillin in humans is described. Complexities encountered with drugs such as pentobarbital, the tetracyclines, etidronate, and salicylate are discussed as examples of pharmacokinetic behavior that make both modeling and tissue residue prediction difficult.
INTRODUCTION Pharmacokinetic modeling is the science of describing, in mathematical terms, the time course of drug and metabolite concentrations in body fluids and tissues. Most often the models are based on blood concentration versus time profiles, since it is generally assumed that blood is in equilibrium with all tissues and fluids of the body. The outputs of drug and metabolites in urine and feces are also followed, since these are the major routes of elimination. A pharmacokinetic model is regarded as being accurate and correct if it predicts blood concentrations and urine and fecal outputs of drug and metabolites for as long as these substances can be measured analytically. The model may be tested by comparing its predictions with experimental data when the drug is administered by various routes and on various dosing regimens. Usually, recovery of 95+% of the administered dose(s) as unchanged drug and metabolites in urine and feces and agreement between the recovered amounts and the pharmacokinetic model is considered confirming evidence that the model accounts for the fate of all the administered drug. The objective of pharmacokinetic modeling in food-producing animals is to predict when and if an animal's meat will be contaminated without having to slaughter the animal. Such models are useful in determining withdrawal times for new drugs, dosage forms, or routes of administration. They also provide the theoretical basis for field testing animals by This work was supported in part by Research Grant FDA 74-178, Division of Veterinary Medical Research, Bureau of Veterinary Medicine, Food and Drug Administration, Beltsville, Maryland 20505. Requests for reprints should be sent to Lewis W. Dittert, College of Pharmacy, University of Kentucky, Lexington, Kentucky 40506.
735 Journal of Toxicology and Environmental Health, 2:735-756,1977 Copyright © 1977 by Hemisphere Publishing Corporation
736
L. W. DITTERT
analyzing blood or urine rather than tissues. The approach to modeling for the prediction of tissue residues involves first developing a model using blood, urine, and fecal data, then comparing the model's predictions with tissue residues determined experimentally at various times following dosing. If the model predictions match the experimental data, it can be assumed that the time required for a particular tissue to fall to any given level can be determined by mathematical extrapolation of the model. ONE-COMPARTMENT MODEL The simplest pharmacokinetic model is the one-compartment open model illustrated in Fig. 1. Here, the body is viewed as a single homogeneous box with a fixed volume. Drug entering the systemic circulation by any route is instantaneously distributed throughout the body. Although the absolute concentrations in all body tissues and fluids are not identical, it is assumed that they all rise and fall in parallel as drug is added and eliminated. Overall elimination of drug from the body by urinary excretion and/or metabolism usually obeys first-order kinetics; that is, the rate of elimination is proportional to drug concentration in blood or plasma, as shown by the following equation:
Rearrangement and integration of Eq. (1) gives log Cp = -
^
+ log Cp°
(2)
which says that following an iv dose, a semilog plot of plasma concentrations versus time will be a straight line with a slope of —ke]/2.3. This is a practical definition of a one-compartment drug, and the best way to determine whether a one-compartment model is appropriate for a given drug is to plot iv plasma concentrations against time on semilog paper and see if the plot is a straight line. This approach will also yield values for the two parameters of the model: kei, the overall elimination
D , Drug i n Body
k , el
Eliminated Drug
FIGURE 1. One-compartment open pharmacokinetic model.
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
737
o o
X O
o o o
(Jo CCO
Too
10.00
20.00
30.00
40.00
50.00
HOURS FIGURE 2. Typical cumulative urine output curve for unchanged drug (sulfamethazine in sheep). From Bourne et al. (1977).
rate constant, and VD, the apparent volume of distribution of the drug in the body. If the drug is eliminated partially or completely unchanged in the urine, kel can also be determined from urine output data. These data are usually expressed as cumulative urine output versus time, as illustrated in Fig. 2. But they can be plotted as a straight line on semilog paper as shown by the following equation (Notari, 1975):
where UM is the final total amount of drug recovered unchanged in urine and Ut is the cumulative amount recovered up to time t. The value ((/„ — Ut) represents the amount remaining to be excreted (ARE) as unchanged drug, and a plot such as that shown in Fig. 3 is sometimes referred to as an "ARE plot." Equation (3) shows that the slope of an ARE plot is —&e)/2.3. Thus, the same kei can be determined from both plasma and urine data, and agreement between plasma and urine data is an essential test of the validity of the model. Figure 3 illustrates a major difficulty with the use of ARE plots. The
738
L. W. DITTERT
> UNCHflNCEO STZ . STZ ( I N F ) ' - S O
lb.00 IS. 00 TIME IN HOURS
5.00
z b . o o a s . oo
FIGURE 3. Typical ARE plot showing the errors introduced when the estimate of U^ is in error by ± 1 SD (sulfathiazole in swine).
solid line represents a calculation of ARE values using the "true" value of U^. The points above and below the line represent ARE values calculated using £/„ + 1 SD and Um — 1 SD, respectively. Thus, the accuracy with which U^ is determined has a great influence on the apparent slope of the ARE plot. This problem is magnified by the fact that accurate experimental determination of £/„ requires complete collection of total voided urine over a prolonged period of time, plus accurate analysis of large volumes of urine containing small amounts of drug. An alternative to the ARE plot is the rate-of-excretion plot shown in Fig. 4. The equation of this plot is (Wagner, 1975) =
-TT
(Dose)]
(4)
where AU/At is the excretion rate in percentage of dose per hour. This plot yields the same value of kei as the ARE plot, and it is independent of the value of 6 L .
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
00
10 00
20,00
739
30.0040.0050.00
HOURS FIGURE 4. Typical rate of excretion plot (sulfamethazine in sheep). From Bourne et al. (1977).
The Ux value is also used to calculate f, the fraction of the absorbed dose eliminated unchanged in urine, as follows:
Dose
= f
(5)
The value of f is important because it represents the fraction of the overall elimination of the drug that is due to urinary clearance. This may be expressed in terms of rate constants as follows:
ku = /fceI
(6)
Thus, if a drug is eliminated partially by metabolism and partially by urinary excretion, the value of f can be used to determine the values of the urinary excretion rate constant, ku) and the metabolism rate constant, km. In this determination, it is assumed that any drug not excreted unchanged in urine has been "metabolized," and this would include drug eliminated unchanged by such nonurinary routes as biliary excretion. If more than one metabolite is formed and excreted in urine, values can be assigned to the individual metabolite formation rate constants by
740
L. W. DITTERT
determining the fraction of the absorbed dose eliminated as each metabolite and applying a calculation similar to Eqs. (5) and (6): (7) b
R
m
= f b
tR\
'm"el
\°>
Here, £/„„, is the final total amount of a specific metabolite recovered in urine and km is the rate constant for formation of that metabolite. Although the kidney is capable of metabolizing drugs and it has been shown that this process can occur simultaneously with elimination of the metabolite (Cabana et al., 1975) in most cases, metabolites are formed elsewhere in the body. This requires modification of the one-compartment model as shown in Fig. 5. This figure shows a metabolite appearing in the plasma, then being excreted into urine. The plasma concentrations achieved by the metabolite depend on the relative values of the formation rate constant, km, and the metabolite excretion rate constant, & mu , as well as on the apparent volume of distribution of the metabolite. In most cases, the metabolite is more polar than the parent drug, causing it to have a smaller VD than that of the parent drug. This tends to increase the metabolite's plasma concentrations. On the other hand, more polar compounds are more rapidly cleared by the kidney, and this tends to make kmu greater than km, causing a decrease in the metabolite's plasma concentrations. It is impossible to predict, for an unknown drug, which of these effects will predominate or whether metabolites can be expected to appear in significant concentrations in plasma. This can lead to meaningless and very confusing results if a nonspecific assay method is used. For example, if a radiolabeled lipophilic drug with a large volume of distribution is metabolized to a relatively polar radioactive metabolite with a small volume of distribribution and the toal radioactivity in plasma is followed, the plasma levels will at first appear to increase rather than decrease following an iv injection. If the initial increasing plasma radioactivity is
u
-•D.
U
mu FIGURE 5. One-compartment open pharmacokinetic model with appearance of a metabolite in plasma.
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
0.00
10.00
20.00
TIME
30.00
741
U0.00
50.00
(HOURS)
FIGURE 6. Sulfamethazine in plasma (o) and rate of excretion of sulfamethazine in urine (A) following an iv bolus dose in young ewe lambs.
overlooked or ignored and the later declining plasma radioactivity is treated kinetically, the estimated half-life will correspond to the kmu value rather than the true k^ value. Thus, total radioactivity in plasma can not be used to determine the pharmacokinetic model of a drug or to study the bioavailabilities of dosage forms. For similar reasons, nonspecific studies of total radioactivity levels in tissues following feeding of a radiolabeled drug may yield misleading results. Bevill and co-workers (Bevill et al., 1977; Bourne et al., 1977) have studied the pharmacokinetics of sulfamethazine in sheep and correlated the plasma concentrations and urine outputs with tissue residues. This work provides an excellent example of the application of the above principles. Figure 6 shows semilog plots of sulfamethazine in plasma and of rate of excretion of unchanged sulfamethazine in urine following an iv bolus dose of 107.5 mg/kg in 13 young ewe lambs. The plasma data fit a straight line on the semilog plot, showing that sulfamethazine can be adequately described by a one-compartment model. The urine line is
L. W. DITTERT
742
TABLE 1. Metabolic Pattern of Sulfamethazine in Sheep, Intravenous Administration Recovery in urine (% of dose)
Substance Sulfamethazine Acetyl Hydroxy Polar
*mu(hr-')
*m(hr-')
19 9 16 23
AB = ^HB = kpQ = ^misc = fe
SMZ = 0.0189 0.0088 ^AU = 1.02 0.0159 = 0.37 0.0223 kpfj = 0.42 0.0319
*el = 0.098
parallel to the plasma line, and both sets of data yield a half-life of 7.1 hr (*e, = 0.098 h r ' 1 ) . Urine outputs of the acetyl, hydroxy, and polar metabolites were followed in addition to unchanged sulfamethazine. The final total amounts of the metabolites recovered in urine, in terms of percentage of administered dose, are given in Table 1. The urinary excretion rate constant for sulfamethazine (kSMZ), calculated with Eqs. (5) and (6), and the formation rate constants for the metabolites (/?AB> ^HB> a p d ^PB)> calculated with Eqs. (7) and (8), are also shown in Table 1. The complete pharmacokinetic model for sulfamethazine and its metabolites is shown in Fig. 7. Five of the rate constants—that is, kSMZ, ^AB> ^HB> ^PB> a n d ^misc~ w e r e estimated as described above. The metabolite excretion rate constants, & A U , kHU, and & P U , were estimated by iterative digital computation using the SAAM-23 program (Berman and Weiss, 1968). Table 1 shows that the values of the metabolite excretion rate constants are between 20 and 100 times the values of the corresponding metabolite formation rate constants. This means that (1) the estimates of the excretion rate constants are probably not very accurate, but this is of little consequence, and (2) the concentrations of metabolites in the blood are expected to be very low, probably undetectable.
SMZ
SMZ
*-SMZT,
•-Polar
U
Misc. FIGURE 7. Complete pharmacokinetic following iv administration.
model for sulfamethazine and its metabolites in lambs
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
743
The final fit of the complete model to plasma and urine data is shown in Figs. 6 and 8. In these figures, the lines were generated by a computer programmed with the model shown in Fig. 7 and the rate constants shown in Table 1. The points are averaged experimental data, and the agreement between the theoretical lines and the experimental data points is excellent. From these results it can be concluded that the pharmacokinetics of sulfamethazine in sheep following iv administration has been completely described from a classical point of view, but the question of what the model means with regard to tissue residues remains to be answered. The correlation between the pharmacokinetic model and sulfamethazine residues in tissues was studied by slaughtering the sheep in pairs at 6, 12, 24, 36, 48, 60, and 84 hr following drug administration and analyzing kidney, liver, heart, skeletal muscle, and fat for drug residues (Bevill et al., 1977). Concentrations as high as 124 ppm and as low as 0.02 ppm were detected. The results of the residue analyses (Fig. 9) show that all tissues fall in parallel with plasma (dashed line) through approximately three logarithmic decades. This experimentally confirms the onecompartment nature of sulfamethazine pharmacokinetics and supports the argument that drug concentrations in plasma reflect drug residues in tissues. Figure 10 shows the correlation between muscle residues and plasma concentrations of sulfamethazine, and Fig. 11 shows the correlation between muscle residues and urine data (amount remaining to be excreted).
SMZ IN EWES LINERR MODEL METfiBOLITES IN URINE
en o O
z UJ
£g kJ_:
10.00
20.00 30.00 U0.00 TIME IN HOURS
SO. 00
FIGURE 8. Cumulative urinary excretion of sulfamethazine (o) and its polar (x), hydroxy (+), and acetyl (*) metabolites in lambs following iv administration.
vj ^ * .
o
20.00 30.00 HOURS
FIGURE 9. Sulfamethazine concentrations in kidney (^), heart (Z), liver (X), loin muscle ( A ) , leg muscle (+), shoulder muscle (o), body fat (X), and omental fat (o) of lambs following iv administration. The dashed line shows the slope of the plasma concentration curve. From Bourne et al. (1977).
•4.00
8.00
12.00
16.00
20.00
PLflSMR CONC. (MG/100ML) FIGURE 10. Average sulfamethazine concentration in muscle tissue versus sulfamethazine concentration in plasma at various times following iv administration to lambs. From Bourne et al. (1977).
PHARMACOKINETIC PREDICTION OF TISSUE RESIDUES
745
Siso (no
10.00
20.00
30.00
10.00
50.00
DOSE TO BE EXCRETED IV.) FIGURE 11. Average sulfamethazine concentration in muscle tissue versus percentage of dose remaining to be excreted in urine (unchanged) at various times following iv administration to lambs. From Bourne et al. (1977).
It can be concluded that a pharmacokinetic model for sulfamethazine, developed using a classical approach, accurately reflects and predicts tissue residues of the drug. TWO-COMPARTMENT MODEL Although the classical two-compartment pharmacokinetic model (Fig. 12) is mathematically more complex than the one-compartment model, Drug In Tissues
k
Unabsorbed Drug
12f | k 21 Drug in Blood (V p )
kei
Eliminated Drug
FIGURE 12. Two-compartment open pharmacokinetic model.
L. W. DITTERT
746
there is often little practical difference between them. Usually, tissue distribution is much more rapid than absorption or elimination. As a result, evidence of the tissue distribution process may only be seen following iv injection; after tissue distribution equilibrium has been achieved, the drug behaves as a one-compartment drug. Also, for extravascular administration the tissues are essentially at equilibrium with the blood throughout the absorption process, and again the drug behaves as a one-compartment drug. The penicillins are examples of classical two-compartment drugs. Dicloxacillin administered iv (Dittert et al., 1969) gives the typical two-compartment plasma concentration versus time plot shown in Fig. 13. From these data, the parameters of the model (Fig. 12) can be determined, and the model can be used to generate plasma concentrations and urine outputs that fit the experimental data points, as shown in Fig. 14. The model will also generate the amount (fraction of the dose) of dicloxacillin in the tissue compartment, as shown in Fig. 15. After tissue distribution equilibrium has been achieved, drug in tissue falls in parallel with drug in plasma. This is the same behavior observed for onecompartment drugs; therefore, after distribution equilibrium, dicloxacillin is, for practical purposes, a one-compartment drug. Figure 16 shows a semilog plot of dicloxacillin plasma concentrations following an im injection (Doluisio et al., 1970). This figure suggests that
.60 3 Q: LU
10 < X
o o Q
0
1
2
3 HOURS
FIGURE 13. Average plasma concentrations of dicloxacillin versus time showing the twocompartment nature of the drug in humans following iv administration. From Dittert et al. (1970).
FIGURE 14. Average plasma concentrations and cumulative urine outputs of dicloxacillin following iv administration to humans. The points are experimental data. The lines were generated by an analog computer programmed with the dicloxacillin two-compartment model. From Dittert et al. (1970).
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