The synthesis rate is about 5%/h/70kg and the elimination half-life estimated from changes in ... cology of warfarin can be found in O'Reilly and. Aggeler (1970) ...
Review Article
Clinical Pharmacokinetics II: 483-504 (1986) 0312-5963/86/0011-0483/$11.00/0 © ADIS Press Limited All rights reserved.
Clinical Pharmacokinetics and Pharmacodynamics of Warfarin Understanding the Dose-Effect Relationship
Nicholas H.G. Holford Department of Pharmacology and Clinical Pharmacology, School of Medicine, University of Auckland, Auckland
Summary
The simplest complete system accounting for the time-course of changes in the prothrombin time induced by warfarin requires the combination of 4 independent models: 1. A pharmacokinetic model for the absorption, distribution, and elimination of warfarin. Warfarin is essentially completely absorbed, reaching a maximum plasma concentration between 2 and 6 hours. It distributes into a small volume of distribution (10 L/ 70kg) and is eliminated by hepatic metabolism with a very small clearance (0.2 L/h/70kg). The elimination half-life is about 35 hours. 2. A pharmacodynamic model for the effect of warfarin on the synthesis of clotting factors (prothrombin complex). Prothrombin complex synthesis is inhibited 50% at a warfarin concentration of about 1.5 mg/L. Warfarin concentrations associated with therapeutic anticoagulation are of similar magnitude. 3. A physiological model for the synthesis and degradation of the prothrombin complex. The synthesis rate is about 5%/h/70kg and the elimination half-life estimated from changes in prothrombin time is approximately 17 hours. On average it will take 3 days for the anticoagulant effect of warfarin to reach a stable value when warfarin concentrations are constant. 4. A model for the relationship between the activity of prothrombin complex and the prothrombin time. In general there is a hyperbolic relationship between these quantities. Its exact shape depends upon the method used for measuring the prothrombin time. Attempts to integrate these models into a single system have used essentially the same pharmacokinetic, phYSiological, and prothrombin activity models. Four distinct pharmacodynamic models have been proposed: linear, log-linear, power and Emax. One might be preferred on theoretical grounds (EmaJ but its performance is not clearly different from the others. Empirical methods for warfarin dose prediction as well as those based on the combined pharmacokinetic-pharmacodynamic-physiological-prothrombin system have been proposed. Only one (which was also the first) [Sheiner 1969] has been adequately described and compared with the performance of an unaided physician. The programme compared favourably with decisions made by those physicians normally responsible for adjusting warfarin dose, but was not tested prospectively. A sizeable body of theoretical and experimental observations has contributed to our understanding of the warfarin dose-effect relationship. It remains to be demonstrated that any alternative method is superior to the traditional empirical approach to warfarin dose adjustment.
Pharmacokinetics and Pharmacodynamics of Warfarin
The anticoagulant response to warfarin has been widely studied and is commonly applied in clinical practice. Despite a great deal of detailed knowledge, physicians continue to initiate therapy and individualise subsequent doses in a largely empirical manner without any discernible rational basis. This review will attempt to summarise the relevant facts and opinion which may provide a rational basis for the choice of warfarin dose for anticoagulant therapy. Other helpful reviews of the clinical pharmacology of warfarin can be found in O'Reilly and Aggeler (1970) [comprehensive early analysis of all aspects of oral anticoagulant pharmacology and use], Koch-Weser and Sellers (l971a,b) [drug interactions], Breckenridge (1977), [individual differences in response], Kelly and O'Malley (1979) [pharmacokinetics], Sawyer (1983) [pharmacokinetics and pharmacodynamics], and Wessler and Gitel (1984) [mechanism of action and clinical use].
1. One Drug or Two? Warfarin is administered clinically as a racemic mixture of 2 enantiomers, R- and S-warfarin. The disposition and action of the enantiomers are qualitatively similar but quantitatively quite different. For most purposes the racemic mixture can be considered as a single drug, but it is worth keeping in mind that the object of most studies has been the net result of the administration of 2 distinct entities. In order to focus attention on the factors influencing the clinical use of warfarin, studies following the administration of the racemic mixture have been emphasised in this review.
2. The Dose-Effect Relationship For most drugs the relationship between dose and effect can be conveniently considered in 2 parts: the dose-concentration relationship (pharmacokinetics) and the concentration-effect relationship (pharmacodynamics). However, this simple division is inadequate to describe the pharmacology of warfarin because the clinically observable response, anticoagulation, is not the same as the drug
484
effect, the inhibition of vitamin K reductases and associated decreases in the synthesis of clotting factors. A third step is required to describe the extent and time course of changes in clotting factor concentrations, collectively referred to as the prothrombin complex. This step has been called the physiological effect relationship (Holford & Sheiner 1981). Finally, a link must be established between the readily measured prothrombin time and the activity of the prothrombin complex. This is beset with a wide range of difficulties when results from different laboratories are to be compared (Kirkwood 1983).
3. Concentration - Unbound or Plasma? The study of plasma protein binding of warfarin and its interactions with other drugs has provided an insight into the significance of plasma protein binding for many clinically useful drugs. From the pharmacologist's point of view, plasma protein binding can be considered as the source of an unwanted artefact when convenient methods for measuring plasma concentrations are used. If the concentration of unbound drug, rather than the total plasma concentration (bound plus unbound), was always measured, then our understanding of drug- and disease-induced changes in pharmacokinetics and pharmacodynamics would be greatly simplified. For instance, the painstaking study of the disposition of warfarin (based on total plasma concentrations) in a patient with idiopathic hypoalbuminaemia by Piroli and colleagues (1981) led to the conclusion that an apparent increase in warfarin clearance was the reason for a half-life which was 3 times shorter than normal. In fact, clearance calculated from unbound concentrations was essentially normal and it is the reduction by a factor of 3 in the volume of distribution of unbound drug that best explains the short half-life. Similar conclusions can be drawn from the observations of Fischer et al. (1985) in patients with hypoalbuminaemia associated with the nephrotic syndrome. The
Pharmacokinetics and Pharmacodynamics of Warfarin
explanation for the marked reduction in the volume of distribution is most likely the reduction in extravascular albumin, the principal 'tissue' binding site for warfarin. Mungall et al. (1984b) have pointed out potential methodological difficulties facing investigators of warfarin plasma protein binding. They found a greater than 2-fold discrepancy in the estimated unbound fraction depending on the method used (equilibrium dialysis 0.44%, ultrafiltration 1.01%). However, others using equilibrium dialysis and 14C_ warfarin have obtained very similar values to Mungall's ultrafiltration results (table I). Observations arising from measurements of plasma protein binding and calculation of unbound concentrations are of great theoretical interest. However, systematic differences in measurements of protein binding are magnified when unbound drug parameters such as clearance, volume of distribution and pharmacodynamic sensi-
485
tivity are calculated. For this reason, conclusions about the properties of unbound warfarin are best limited to those drawn from data obtained within a single report. At present, comparisons of results from investigators using different techniques should be avoided. Because drug concentrations are central to our current understanding of pharmacokinetics and pharmacodynamics, all concentrations in this review refer to total concentrations, i.e. bound plus unbound, and will be referred to as plasma concentration even if measured in a serum sample. Errors in interpretation arising from differences in plasma protein binding may be ignored by assuming binding differs only in a random fashion among different groups of subjects. Systematic errors may still be present due to differences in assay specificity but these are similar for both unbound and plasma concentrations, while the sensitivity and precision of plasma concentra-
Table I. Plasma protein binding of warfarin (values mean ± SO)
References
Enantiomer8
Koch-Weser & Sellers (1971a)
R+S
Yacobi et al. (1976)
Population
No. of subjects
Method
Assay
Fraction unbound (%)
3.0
R+S
Patients
30
ED
14C
1.01 ± 0.33
Shepherd et al. (1977)
R+S
Volunteers
26
ED
14C
1.4 ± 0.1
Slattery et al. (1979b)
R+S
Volunteers
10
ED
14C
0.93 ± 0.08
Bjornsson et al. (1979a)
R+S
Volunteers
4
ED
14C
1.58 ± 0.25 0.85 ± 0.2
Piroli et al. (1981)
R+S
Female volunteers
12
ED
14C
Mungall et al. (1984b)
R+S
Patients
19
ED UF
14C
0.44 ± 0.34 1.01 ± 0.69
Chan et al. (1984b)
R S
Patients
36
ED
HPLC
0.54 0.54
a
Administration of racemate - symbols indicate assayed enantiomer.
Abbreviations: ED = equilibrium dialysis; UF = ultrafiltration; HPLC = high pressure liquid chromatography.
Pharmacokinetics and Pharmacodynamics of Warfarin
1600
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1200
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600 400 200 O+--'--~--~'~i--~i---i~/~~~
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4 8 12 24 28 32 Time after dosing (hours)
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486
report described slow absorption, with maximum concentrations being achieved between 3 and 9 hours after a starch base warfarin tablet (O'Reilly et al. 1963). A more recent study observed maximum concentrations between 0.3 and 4 hours for a primary peak and 1 to 8 hours for a secondary peak (fig. 1) [Stirling et al. 1982]. The absolute bioavailability of an aqueous solution of warfarin was nearly 100% (Breckenridge & Orme I973a) and estimates based on the apparent volume of distribution and clearance obtained after oral doses of the tablet form suggest that solid dosage forms of warfarin are also essentially completely bioavailable (table III). 4.2 Distribution
Fig. 1. Time course of plasma warfarin concentrations in normal subjects after 1Smg of warfarin by mouth. Data are presented for 2 different formulations. Warfarin is rapidly absorbed reaching its maximum concentration about 2 hours after administration (Stirling et ai, 1982),
tion measurements can be expected to be superior to unbound concentration measurements.
4. Pharmacokinetics 4.1 Absorption Warfarin is essentially completely absorbed after oral administration with the peak concentration occurring between 2 and 6 hours (table II). An early
Warfarin distributes into a relatively small apparent volume of distribution of about 10 Lj70kg [table III]. A distribution phase lasting 6 to 12 hours is distinguishable after rapid intravenous injection or oral administration of an aqueous solution (Breckenridge & Orme 1973a; O'Reilly et al. 1963). For most purposes a I-compartment model suffices to describe the disposition of warfarin after oral dosing. Using this type of model, and assuming complete bioavailability, estimates of the volume of distribution of the R- and S-enantiomers are similar to each other and to that of the racemate (Banfield et al. 1983; Breckenridge et al. 1974; Hignite et al. 1980).
Table II. Pharmacokinetic absorption parameters of racemic warfarin (mean ± SO) in volunteers References
Preparation
No. of patients
Assaya
O'Reilly et al. (1963)
Tablet (starch base)
14
SP
Breckenridge & Orme (1973)
Solution
8
TLC
93 ± 8
0.6 ± 0.2
Stirling et al. (1982)
Marevan® (old) tablet Marevan® (new) tablet
8
HPLC
98 ± 18a
2.0 ± 1.4
8
HPLC
94 ± 1Sa
1.7 ± 1.1
a
F(%)
Tmax (h)
6.3 ± 3.0
Estimated by comparison of AUC-oral with AUC-iv reported by Breckenridge & Orme (1973).
Abbreviations: SP = spectrophotometry; TLC = thin layer chromatography, HPLC = high pressure liquid chromatography; Tmax =
time to peak plasma concentration; F = bioavailability.
Table III. Pharmacokinetic parameters of racemic warfarin (mean ± SO)
~
II>
References
No. of subjects
Enantiomer"
Population
O'Reilly et a!. (1963)
R+S
Volunteers
6
SP
O'Reilly et a!. (1971)
R+S
Volunteers
6
Breckenridge & Orme (1973a)
R+S
Volunteers
Lewis et a!. (1974)
R+S
Bjornsson et a!. (1979a)
Vd (LJ10kg)
a
CL (L/h/70kg)
(h)
8.4 ± 2.3b. 0
0.1830 ± 0.911"
38.3 ± 13.6
SP
7.8 ± 1.10
0.181 ± 0.084
35.6 ± 12.2
4
TLC
13.0 ± 8.8
0.480 ± 0.224d
21.7d ± 12.0
Volunteers
4
TLC
7.8 ± 1.2b. o. d
0.127 ± 0.0070."
42.5 ± 7.0"
R+S
Volunteers
4
HPLC
9.1 ± 1.6b. 0
0.245 ± 0.076b
29.3 ± 7.9
Slattery et al. (1979a)
R+S
Volunteers
10
HPLC
7.6 ± 1.5b
0.132 ± 0.031b
34.7 ± 7.0
~ II>
O'Reilly et a!. (1980)
R+S
Volunteers
6
HPLC + MS
8.2 ± 0.4b. 0
0.167 ± 0.009 b. 0
37.2 ± 3.2
l'j'
Piroli et a!. (1981)
R+S
Male volunteers
12
HPLC
10.5 ± 1.4"
0.196 ± 0.028b. 0
37.3 ± 3.5
Piroli et al. (1981)
R+S
Female volunteers
12
HPLC
12.6 ± 3.5b. 0
0.238 ± 0.035b. 0
35.5 ± 4.0
Volunteers
8
Stirling et a!. (1982)
Assay
t"." (h)
0.31 ± 0.2
8 PI"" Ej"
~ l'j'
'"
II>
::I Co "tl
R+S
§ ~
0
Co
8
'"0.-., ~
t ::I
R+S
Volunteers
Mungall et a!. (1983)
R+S
Patients
Wingard et a!. (1978)
R+S
Volunteers
10
Hotraphinyo et a!. (1978)
30
HPLC
13.2 ± 2.7b
0.292 ± 0.058b."
31.6 ± 4.3"
SP
9.2 ± 2.2b
0.141 ± 0.036b
47.9 ± 9.8
7.9 ± 3.5
0.093 ± 0.026'
163 SP
0.129 ± 0.020b. 0
R+S
Patients
39
GC
0.203 ± 0.112b
Routledge et a!. (1979b)
R+S
Patients
15
TLC
0.281 ± 0.079 b
Fischer et al. (1985)
R+S
Volunteers
11
Hignite et al. (1980)
~~
Volunteers Volunteers
5 5
HPLC HPLC
Hignite et a!. (1980)
~~ ~~
Volunteers
5
GC-MS
Patients
36
HPLC
~~
Volunteers
8
HPLC
Toon et a!. (1986)
II>
::r
Holford (1986)
Chan et al. (1984)
t'12,8
0.196b
37.0
0.139 ± 0.052b.o 0.232 ± 0.123b.0
47.8 ± 8.7 30.9 ± 10.8
9.5 ± 2.4b. 0 9.2 ± 2.5b. 0 0.158 ± 0.0500 0.325 ± 0.1540 13.3 ± 2.7b 13.9 ± 3.7b
0.233 ± O.043b 0.333 ± 0.085b (continued on next page)
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Pharmacokinetics and Pharmacodynamics of Warfarin
488
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