DRUG DISPOSITION

Clin. Pharmacokinet. 21 (2): 95-109. 1991 03 I 2-5963/9 I/ 0008-0095/$07.50/ 0 © Adis International Limited. All rights reserved. CPK1039

Clinical Pharmacokinetics and Kinetic-Dynamic Relationships of Dilevalol and Labetalol Richard Donnelly and Graeme l.A. Macphee University Department of Medicine and Therapeutics. Gardiner Institute. Western Infirmary. Glasgow. and the Department of Geriatric Medicine. Southern General Hospital. Glasgow. Scotland

Contents 95 96 97 97 9 98 99 100 10 I 102 102 102 104 /05 106 106 106

Summary

Summary I. i3-Adrenoceptor Antagonists with Vasodilator Activity 1.1 Labetalol 1.2 Dilevalol 2. Pharmacokinetic Properties of Dilevalol and Labetalol 2. 1 Absorption and Bioavailability 2.2 Metabolism and Excretion 2.3 Special Patient Groups 2.4 Drug Interactions 3. Pharmacokinetic-Pharmacodynamic Relationships 3. 1 Dose-Concentration-Response Relationships 3.2 Drug Concentration-Effect Analysis 4. Clinical Applications of Integrated Pharmacokinetic-Pharmacodynamic Analysis 4.1 Relationship Between Age and Antihypertensive Response 4.2 Relationship Between Smoking and Antihypertensive Response 4.3 Constancy and Predictability of Drug Response 5. Conclusions

Dilevalol and labetalol are examples of a growing number of new i3-blockers which combine nonselective i3-adrenoceptor antagonism with vasodilator activity. Dilevalol is one of the 4 stereoisomers of labetalol, and is estimated to form approximately 25% of the racemic drug. Labetalol itself is an a I -antagonist but dilevalol, which has negligible affinity for a-receptors, exerts its vasodilator effect via i32-agonism. Both drugs are rapidly and completely absorbed in 60 to 90 min and subject to extensive firstpass hepatic metabolism; the average bioavailability after oral administration is around 20 to 35%, and there is wide interindividual variability in plasma drug concentrations and dosage requirements. The volume of distribution of dilevalol (17 to 25 L/ kg) is higher than that reported for labetalol (3 to 16 L/kg), although both drugs are concentrated in the extravascular compartment. Correspondingly, the elimination half-life of dilevalol at steady-state is around 15h compared with 8h for labetalol. There is evidence that the pharmacokinetics of dilevalol change (a reduction in clearance) in translation from single-dose to long term therapy. There is no clinically significant effect of age on the steady-state disposition of either drug and the pharmacokinetics

Clin. Pharmacokinel. 21 (2) 1991

96

of labetalol appear to be unchanged during pregnancy. Although there is a linear relationship between dose and area under the concentration-time curve. early studies found no evidence of a simple relationship between dose or plasma drug concentration and the fall in blood pressure. However. an integrated pharmacokinetic-pharmacodynamic model has been used to correlate concentrations of both drugs wi th reductions in systolic and diastolic blood pressure in individuals. This approach derives a mathematical description of antihypertensive response which integrates pharmacokinetic and pharmacodynamic information and also takes account of placebo effects and changes in drug concentration and blood pressure during the dosage interval. The pharmacokinetic-pharmacodynamic relationships oflabetalol are characterised by a linear model. For example. in a group of healthy volunteers. the 'responsiveness' to labetalol was -0. 19mm Hg/ /lg/L. In contrast. the relationships of dilevalol are best described by a Langmuir maximum effect model, and so individual responses to short and long term treatment have been quantified by the concentration-effect parameters of maximum effect and drug concentration required to produce 50% of this. This integrated method of analysis with dilevalol and labetalol has revealed that (a) drug concentrations are related to the fall in blood pressure in individual subjects; (b) there is no relationship between age and antihypertensive response; and (c) there is a direct correlation for an individual patient between response to the first dose and the response during long term therapy.

1. {3-Adrenoceptor Antagonists with Vasodilator Activity The first ,B-adrenoceptor antagonist, propranolol, was developed in the early 1970s as a new treatment for angina pectoris. Since then a large number of different ,B-blockers have emerged and the therapeutic indications for ,a-blockade have widened considerably to include hypertension, cardiac arrhythmias, migraine, glaucoma, anxiety, thyrotoxicosis and essential tremor. Potential new applications have received particular attention over the past few years; for example, limitation of infarct size in conjunction with thrombolytic therapy, secondary prevention after myocardial infarction, mild heart failure and hypertrophic obstructive cardiomyopathy. ,B-Blockers are often selected for different clinical conditions on the basis of their ancillary properties. Thus, in the early years, the choice was based on the relative selectivity of a drug for the ,B(- and ,B2-receptor subtypes, membrane stabilising actions, the degree of lipophilicity and the extent of any partial agonist activity. These properties are particularly relevant in some circumstances (e.g. when selecting a drug for thyrotoxicosis or migraine) but they have little or no effect on the therapeutic response in hypertension, although they

may influence the type and degree of adverse effects. ,B-Blockers have formed the mainstay of antihypertensive therapy for many years, but the precise mechanism by which they lower blood pressure is still unresolved. It is clear, however, that they do not ameliorate the increase in peripheral vascular resistance which is now recognised as the main pathophysiological abnormality in essential hypertension. In addition, some ,B-blockers may adversely affect plasma lipids, which is often seen as another relative disadvantage. This contrasts with the profile of some of the newer antihypertensive agents [e.g. calcium antagonists and angiotensin converting enzyme (ACE) inhibitors) which have primary vasodilator activity and neutral metabolic effects. Nevertheless these drugs, too, have their limitations, not least in terms of the associated reflex sympathetic activation, the assorted 'vasodilatory' side effects such as headache and flushing and in some cases a dose-limiting adverse effect of postural hypotension. Third and fourth generation ,B-blockers have been designed to overcome some of the limitations of 'plain' ,B-adrenoceptor antagonists such as propranolol. A number of drugs are now available with new ancillary properties that improve the haemodynamic profile in patients with hypertension by

97

Kinetic-Dynamic Relationships of Dilevalol and Labetalol

combining (j-blockade with vasodilator activity. The combination of a (j-blocker (e.g. propranolol) and a vasodilator (e.g. hydralazine) is of course well established in routine clinical practice, but 'hybrid' (or multifactorial) drugs that combine 2 or more pharmacological actions within a single molecule are likely to avoid many of the disadvantages of fixed-dose combination regimens (Van Zwieten 1990). A number of 'hybrid' (j-blockers with vasodilator activity are now available or in the late stages of clinical development (table I). l.l Labetalol

Labetalol is a competitive antagonist at both aand (j-adrenoceptors. The (j-blockade is nonselective, whereas the a-antagonist effect is highly selective for the al - rather than the a2-adrenoceptor subtype. The ratio of a- to (j-blocking potency of labetalol in humans is estimated to be between I : 3 and I: 7 (Richards et al. 1977). At . lower doses, labetalol has predominantly (j-adrenoceptor-blocking properties and it is only at relatively high doses that a-blockade becomes prominent. Thus, orthostatic hypotension due to a-blockade significantly limits the use of higher doses of labetalol (Dargie et al. 1976). The rationale for the development of labetalol Table I. Some i3-adrenoceptor antagonist drugs with vasodilator activity (for further details see Van Zwieten 1990) Drug Amosulalol Arotinolol Labetalol Dilevalol Medroxalol Carvedilol Celiprolol BW A575C Bevantolol Carteolol Tertalolol a

Mechanism of vasodilating activity aI-Antagonist and a2-antagonist aI-Antagonist

was the knowledge that blockade of I adrenoceptor type causes a reflex stimulation of the other - i.e. a-mediated vasoconstriction is a reflex response to (j-blockade in the heart and, correspondingly, (jmediated tachycardia follows peripheral a-blockade. Since both these compensatory responses tend to counteract the fall in blood pressure, a relatively weak blockade of both receptor types should produce a useful antihypertensive effect with minimal disturbance of counter-regulatory mechanisms. In practice, labetalol is an effective antihypertensive agent. Several studies have reported clinically useful reductions in blood pressure during short and long term treatment (Lund-Johansen 1983; Mehta et al. 1983; Omvik & Lund-Johansen 1982). In comparative studies, the antihypertensive effect oflabetalol is similar to that of propranolol (Kubik & Coote 1984; Weber et al. 1984); however, unlike ordinary (j-blockers, labetalol has little or no effect on heart rate and is associated with a 15 to 20% reduction in peripheral vascular resistance (Fagard et al. 1982). Although a-adrenoceptor blockade may wane during long term therapy (Lund-Johansen 1983) the vasodilator effect oflabetalol is sustained and there is a significant reduction in both systemic and renal vascular resistance (Heck et al. 1981; Larsen & Pedersen 1980; Malini et al. 1983). Labetalol is often used in pregnancy-induced hypertension. While there are significant reductions in maternal blood pressure with minimal change in heart rate, the drug has no effect on fetal heart rate or uteroplacental blood flow (Lunell et al. I 982a,b). 1.2 Dilevalol

al-

i32-Agonist al-Antagonist8 aI-Antagonist i32-Agonista ACE inhibition Direct vasodilator Nonselective i3-agonist Unknown (selective renal vasodilator)

May not be the sole mechanism.

Abbreviation: ACE = angiotensin converting enzyme.

Dilevalol is one of the 4 optical isomers of labetalol and is estimated to form approximately 25% of racemic labetalol. Dilevalol (the R-R stereoisomer) is a nonselective (j-adrenoceptor antagonist with vasodilating properties that are mediated by selective (j2-receptor agonist activity (Brittain et al. 1982; Gold et al. 1982). Dilevalol has negligible affinity for a-adrenoceptors, whereas most of the antagonist activity oflabetalol is attributable to the S-R stereoisomer (Brittain et al. 1982). The main

Clin. Pharmacokinet. 21 (2) 1991

98

advantage of dilevalol over labetalol is the capacity to lower peripheral vascular resistance via a fhagonist effect rather than a-blockade, and thus to avoid the troublesome adverse effect of postural hypotension at higher doses. Dilevalol is a much more potent (j-adrenoceptor antagonist than labetalol. For example, in healthy volunteers, the former is twice as effective at the same dose in attenuating isoprenaline (isoproterenol)-induced increases in heart rate (EI-Ackad et al. 1984). The haemodynamic profile of dilevalol is characterised by reductions in peripheral vascular resistance (Maclennan et al. 1989) and blood pressure (Fogari et al. 1988; Strom et al. 1989) with little or no overall effect on heart rate (Clifton et al. 1988; Fujimura et al. 1989a). The antihypertensive effect is sustained for 24h (Dahlof et al. 1989; Kinhal et al. 1989; Silagy et al. 1990) and appears to be comparable with that of established treatments (Fogari et al. 1988; McGrath et al. 1990; Materson et al. 1988; Rodriguez-Saavedra et al. 1989). Dilevalol reduces or has no effect on renal vascular resistance (Baba et al. 1988; Clifton et al. 1989; Cook et at. 1988). The antihypertensive effect of ordinary (j-blocking drugs such as propranolol and atenolol is largely due to a reduction in cardiac output. In contrast, the blood pressure-lowering effect of dilevalol is due principally to the fall in peripheral vascular resistance (Strom et al. 1989). Heart rate and cardiac output at rest are usually unchanged with dilevalol, and this is likely to be due to a reflex positive chronotropic effect in response to the fall in vascular resistance.

2. Pharmacokinetic Properties of Dilevalol and Labetalol The pharmacokinetics of labetalol have been studied extensively after single and multiple doses both in healthy volunteers and in various patient groups (Goa et al. 1989). However, in all of these studies the analytical technique of the fluorimetric or high performance liquid chromatography (HPLC) assays that were used did not separate its 4 stereoisomers. Thus, the 'overall' pharmacokin-

etic parameters of labetalol are derived from the simultaneous administration and subsequent measurement in plasma of 4 stereoisomers that may differ significantly in their individual pharmaco~ kinetic profiles. Such stereoselective drug metabolism and disposition is well recognised with other drugs (Ariens & Wuis 1987; Williams & Lee 1985). 2.1 Absorption and Bioavailability Following oral administration, both drugs are rapidly and completely absorbed, with peak plasma drug concentrations (C max ) occurring within 60 to 90 min. Both have high hepatic clearance and a significant first-pass effect, which results in a low bioavailability after oral administration (Kramer et al. 1988; McNeil & Louis 1984). The average bioavailability is around 20 to 3S% (table II). As with many drugs that are subject to extensive firstpass extraction, clinical studies have shown large inter- and intraindividual differences in bioavailability and plasma concentration. For example, in 12 patients with hypertension the oral bioavailability of labetalol ranged from 11 to 86% (McNeil et al. 1979). Similarly, there can be as much as a 2- or 3-fold difference between individuals in the Cmax and the area under the concentration-time curve (AUC) ofdilevalol (Macphee et al. 1991; Tenero et al. 1989). Dilevalol is extensively distributed into tissues, with an apparent volume of distribution (Vd) of 16.6 to 24.6 L/kg reported following a single SOmg intravenous dose (Kramer et al. 1988; Tenero et al. 1989). This value exceeds the range of 2.S to IS.7 L/kg reported for racemic labetalol (Goa et al. 1989). Both drugs are thus concentrated in the extravascular compartment, although there is a paucity of information about their relative distribution in different human tissues; however, since neither drug is particularly lipid soluble, it is probable that very little crosses the blood-brain barrier (Martin et al. 1976). Approximately SO% of labetalol and 7S% of dilevalol is bound to plasma proteins in humans (table II).

99

Kinetic-Dynamic Relationships of Dilevalol and Labetalol

Table II. Approximate mean values (and reported range) for the pharmacokinetic parameters of labetalol and dilevalol Drug

Labetalol Dilevalol

(%)

Vd (L/kg)

35 (10-80)

9 (2-16)

25

20 (16-25)

(10-22)

F

(10-33)

CL (L/h)

fb (%)

8 (3-11)

132 (84-234)

50 (45-55)

15

96 ( 54-150)

75 (73-77)

tll2#

(h)

Abbreviations: F = bioavailability; Vd = apparent volume of distribution; tV2# fb fraction of drug bound to protein.

=

2.2 Metabolism and Excretion Less than 5% of an oral dose of labetalol and 1.5% of dilevalol is excreted unchanged in the urine (Kramer et al. 1988; Martin et al. 1976), indicating that both drugs are eliminated principally by metabolic degradation, predominantly in the liver and possibly also in the intestinal wall. The biotransformation oflabetalol yields an unidentified conjugate as the major metabolite and an O-phenyl-glucuronide derivative (Goa et al. 1989). Both these metabolites are inactive and excreted in urine (60%) and faeces (20%). In contrast, dilevalol is metabolised almost entirely by glucuronidation. Various glucuronide conjugates of dilevalol are excreted in the urine and faeces (Chrisp & Goa 1990). Removal of labetalol from the systemic circulation is rapid but the elimination half-life (t'h,,) varies between individuals: reported values range from around 3 to 8h following an oral or intravenous dose to normotensive volunteers or patients with hypertension (table II) [Abernethy et al. 1985; Elliott et al. 1984]. The t'h" at steady-state is around 8h. The t'hiJ of dilevalol may be slightly longer than that for labetalol (table II) and, in addition, there is evidence of a change in its pharmacokinetics in translation from single-dose to steady-state therapy. In particular, there appears to be a reduction in drug clearance after long term administration. For example, in 18 patients with essential hypertension t'hiJ increased from 7.8h after a single oral dose of dilevalol 200mg to 11.7h after treatment with di-

= elimination

half-life; CL

= total

plasma clearance;

levalol 200mg once daily for 4 weeks (Macphee et al. 1991). This increase was accompanied by a 35% increase in mean (± SD) AUC from 261 ± 103 to 352 ± 152 ,ug/L.h, respectively. Similar reductions in the clearance of dilevalol have been noted in healthy volunteers (Fujimura et al. 1989a) and after 8 days' treatment in elderly patients with hypertension (Fujimura et al. 1989b). An overview of all the published data demonstrates a consistent trend towards higher estimates of t'hiJ and AUC at steady-state compared with single-dose administration (Chrisp & Goa 1990). The explanation for this apparent change in the pharmacokinetics of dilevalol is not entirely clear. Similar reductions in clearance with translation from short to long term therapy have been reported with other drugs that undergo high presystemic elimination, for example propranolol (Evans & Shand 1973) and the calcium antagonist verapamil (Freedman et al. 1981), and these differences have been attributed to saturation of the hepatic metabolic enzyme activity at steady-state (Bach et al. 1986). The same mechanism has been proposed for dilevalol (Macphee et al. 1991); an alternative explanation involves changes in hepatic blood flow. The clearance of dilevalol and labetalol is dependent on hepatocellular function (Homeida et al. 1978) and liver blood flow (Daneshmend et al. 1982; Kotegawa et al. 1990). Indeed, many drugs that are largely metabolised in the liver exhibit flowdependent pharmacokinetics (George 1979). Some vasodilator drugs in particular (e.g. verapamil and hydralazine) increase liver and splanchnic blood flow in the short term, and this may contribute to

100

the apparent increase in drug clearance (i.e. lower AUq after the first dose compared with long term administration (Meredith et al. 1985, 1986). Dilevalol may have similar effects on visceral perfusion, although this has not been adequately studied. Furthermore, such changes in hepatic blood flow may also account for a number of pharmacokinetic interactions with vasodilators: for example, those between hydralazine and propranolol (Schneck & Vary 1984) and between verapamil and prazosin (Elliott et al. 1988). Thus, an alternative explanation for the apparent change in the pharmacokinetics of dilevalol is that its short term vasodilator effect may be associated with a transient increase in hepatic blood flow which enhances drug elimination and gives rise to a lower AUC following the first dose, compared with steady-state therapy. 2.3 Special Patient Groups It is well established that, even among healthy volunteers, there are large interindividual differences in the bioavailability and plasma drug concentrations of both labetalol and dilevalol (Chrisp & Goa 1990; McNeil et al. 1979). Accordingly, in routine clinical practice there are likely to be significant differences between patients in their dosage requirements. Therefore, in order to optimise treatment, it is important to establish which factors may contribute to the pharmacokinetic variability. There is still a paucity of information about the pharmacokinetic variability of dilevalol and labetalol, although isolated small studies have characterised the drug disposition in selected patient groups.

2.3.1 The Elderly Increasing age is associated with a decline in hepatic blood flow (Woodhouse & Wynne 1988) and a reduction in functional hepatic mass (Wynne & James 1990) which may affect the pharmacokinetics of drugs that are eliminated primarily by the liver. One small study has reported a direct correlation between age and the bioavailability of labet-

Clin. Pharmacokinet. 21 (2) 1991

alol in 10 patients with hypertension, age range 28 to 75 years (Kelly et al. 1982), but this was not confirmed in a much larger study comparing groups of young and elderly hypertensive patients (Abernethy et al. 1985). Nevertheless, these authors did report a 2-fold increase in the C max of labetalol in older patients following a single oral dose and a reduction in systemic clearance with a prolonged tlh/1 following a 50mg intravenous dose (Abernethy et al. 1985). A combined analysis from 4 singledose and 3 multiple-dose studies suggested that age may account for around 20% of the variability in the oral clearance of labetalol after single-dose administration; however, there was no evidence of an age-related effect on the pharmacokinetics during long term administration (Rocci et al. 1989). Similarly, there is no evidence of a significant agerelated effect on the pharmacokinetics of dilevalol (Macphee et al. 1991) [fig. I]. Fujimura et al. (l989b) did suggest that the AUC and tlh/1 of dilevalol may be increased after a single oral dose in elderly hypertensive patients, but this comparison was made with younger patients from a different study (Fujimura et al. J989a). The absence of any significant age-related effect on the pharmacokinetics of labetalol and dilevalol is entirely consistent with the general view that age has no effect on the clearance of drugs which are metabolised by glucuronidation (Montamat et al. 1990).

2.3.2 Hepatic Impairment The bioavailability oflabetalol is almost doubled in patients with hepatic cirrhosis: 63% compared with 33% in age-matched controls (Homeida et al. 1978). Changes in liver blood flow, independent of hepatocellular function, also affect the disposition of labetalol (Daneshmend et al. 1982). No comparable data are available for dilevalol. 2.3.3 Renal Impairment As a general rule, it is often assumed that impaired renal function has little or no effect on the pharmacokinetics of drugs that are eliminated by the liver. However, a number of recent examples illustrate that uraemia may have a marked effect

101

Kinetic-Dynamic Relationships of Dilevalol and Labetalol

80

~ 0> .=,

60

c: .2

'§

C Q) (J

40

c: 0

(J

"0

(ij

>

~

is 20

O+-~-.----~---.----~--~~--~--~ -2

2

6

10

14

18

22

26

Time (h)

Fig. 1. The plasma concentration-time profiles for dilevalol in 6 young (&),6 middle-aged (0) and 6 elderly (0) hypertensive patients following a single oral dose of dilevalol 200 mg (after Macphee et al. 1991).

on hepatic metabolic enzyme activity (Ahmed et al. 1991; Macdonald et al. 1991). In particular, the pharmacokinetics of hepatically eliminated drugs may be 'normal' in patients undergoing dialysis (Paton et al. 1985) but significantly altered in patients with chronic renal failure who are not receiving dialysis (Ahmed et al. 1991; Macdonald et al. 1991). Renal failure is reported to have no effect on the pharmacokinetics of labetalol (Wood et al. 1982), but these data were obtained from dialysis patients and the effects of moderate renal impairment on labetalol disposition have not been clearly evaluated. Auer et al. (1988) report a significant change in the pharmacokinetics of dilevalol in both dialysed and nondialysed patients. The tlh~ increased from 12h in a control group to 19.3 and 29.5h, respectively, in the 2 categories of renal disease. It is unlikely that such a large difference could be due to loss of renal elimination, as suggested by Chrisp and Goa (1990). Instead, it probably reflects the impact of renal failure on hepatic drug metabolism. In a different study, severe renal impairment had no significant effect on the elimin-

ation of dilevalol although small increases in AUC were detected (Vandenburg et al. 1990). 2.3.4 Pregnancy

Pregnancy is associated with a number of physiological changes that may influence drug disposition: for example, serum proteins undergo substantial changes in concentration, body water and body fat increase, renal plasma flow almost doubles and liver metabolism also increases (Davis et al. 1973). Labetalol has been widely used in pregnancy-induced hypertension. There was no difference in its pharmacokinetics between the 3rd trimester of pregnancy and 4 months post partum in a small group of women (Rubin et al. 1983). Thus, in contrast to some drugs whose pharmacokinetics change in pregnancy (e.g. phenytoin and carbamazepine), the disposition of labetalol appears to be unaffected by the assorted physiological changes that occur. 2.4 Drug Interactions Daneshmend and Roberts (1984) have shown that cimetidine causes a 56% increase in the systemic bioavailability of labetalol, presumably by

102

decreasing the intrinsic hepatic clearance and firstpass extraction. This interaction is somewhat surprising because cimetidine does not usually alter the disposition of drugs that are eliminated primarily by conjugative metabolism (Abernethy et al. 1983). A similar, though much less marked (11 %) interaction is seen with dilevalol (Tenero et al. 1989), thus raising the possibility that cimetidine may have different effects on the 4 stereoisomers. This would not be without precedent: for example, the interaction between cimetidine and propranolol is also stereoselective (Donn et al. 1985).

3. Pharmacokinetic-Pharmacodynamic Relationships 3.1 Dose-Concentration-Response Relationships In general, there is a linear relationship between dose and plasma drug concentration for both labetalol and dilevalol (Kramer et al. 1989; McNeil & Louis 1984), although such correlations for groups of subjects may be partly obscured by the large interindividual differences in pharmacokinetic parameters. Figure 2 shows the correlation between steady-state AVC and dosage following 5 days' treatment with dilevalol 200, 400 or 800mg in 15 hypertensive patients (Kramer et al. 1989); the large standard deviations highlight the wide variability between subjects. Despite the reasonably linear relationship between drug dose and plasma concentration, clinical studies have found notorious difficulty in identifying a corresponding relationship between dose (or concentration) and blood pressure reduction. {3Blockers in general are often said to have 'shallow' or 'flat' dose-response curves (Hansson et al. 1974) and from a superficial analysis of mean data many authors have concluded that no predictable drug concentration-effect relationship exists (Chrisp & Goa 1990; Lund-Johansen & Bakke 1979). Thus, although there is some evidence of dose-related reductions in blood pressure with dilevalol (Given et al. 1989), the overall findings have been inconsistent and a clear pharmacokinetic-pharmacodynamic relationship has not been established (Given

Clin. Pharmacokinet. 21 (2) 1991

3.0

I

2.5

2.0

2

1.5

...J

0;

.s

1.0

U'" =>

«

0.5

!

I

0 200

400

600

800

Dose (mg/day) Fig. 2. Area under the drug concentration-time curve at steady-state (AVess) versus daily dose after once-daily administration of dilevalol 200, 400 and 800mg to 15 hypertensive patients. Data shown are mean ± SD (after Kramer et al. 1989).

et al. 1989; Lund-Johansen & Bakke 1979; McNeil & Louis 1984). These largely negative findings have come from studies which have invariably sought correlations between dose (or plasma concentration) and effect data for groups of subjects rather than for individuals. Because of the wide interindividual variability in both pharmacokinetic and pharmacodynamic responses, no consistent drug concentrationeffect relationship can be identified when group data are analysed (e.g. for labetalol, fig. 3). It is well recognised with a variety of antihypertensive agents that drug concentrations in plasma are related to the fall in blood pressure in individuals (Donnelly et al. 1989, 1991), and this approach has recently been applied to dilevalol (Macphee et al. 1991) and labetalol (Elliott et al. 1984; Rubin et al. 1983) using an integrated pharmacokinetic-pharmacodynamic model. 3.2 Drug Concentration - Effect Analysis Mathematical modelling of the inter-relationship between the effect of a drug and its concentration in plasma has been variously called 'con-

Kinetic-Dynamic Relationships of Dilevalol and Labetalol

centration-effect analysis' or 'pharmacodynamic modelling'. The detailed methodology and the numerous potential applications of concentration-effect analysis have been reviewed extensively elsewhere (Holford & Sheiner 1981), and in recent years this integrated approach has been extended to characterise relationships between drug concentration and hypotensive response in individual subjects (Donnelly et al. 1991). The fundamental feature of this mathematical approach to integrating pharmacokinetic and pharmacodynamic time profiles is that the conventional compartmental pharmacokinetic model is extended to incorporate an additional 'effect' compartment, which is constrained to be small enough so as not to perturb the pharmacokinetic parameters defined by the original model (fig. 4). The measured effect (i.e. the placebo-subtracted reduction in blood pressure) is then related to the drug concentration in the effect compartment at each time point during a dosage interval. In standard pharmacological experiments the concentration-effect relationship is usually de-

•

2.5

•

•

2.0

1.5

:2 -l

Ci

1.0

U ::J 4:

0.5

S

• • •

• •

• •

•

•

oL---r---.---r---r-~r--50 100 150 200 250 AUCsp (mm Hg . h)

Fig. 3. Relationship between the area under the plasma concentration-time curve (AUe) and the area under the mean blood pressure fall versus time curve (AUeBP) after administration of a single dose of labetalol IOOmg to 12 subjects. Generally. concentration-effect relationships can be identified more easily in individual subjects (after McNeil & Louis 1984).

103

Elfect

r-- -~---

-,

I I

Em ••

I I

--I Linear: E

= mCe +

I

Em ••. Ce Nonlinear: E =

Fig. 4. The standard pharmacokinetic model with central (e) and peripheral (P) compartments is extended to incorporate an additional effect compartment (E). In clinical studies. the most appropriate model to characterise the pharmacokincticpharmacodynamic relationship depends on the portion of the concentration-response curve covered. Thus. with labetalol a linear model produced the best fit. whereas data for dilevalol were characterised more appropriately by a Langmuir Em_x model. Abbrel'ial ions: kcq = first-order rate constant; for equations. see text (for further details of concentration-effect analysis. see Holford & Sheiner 1981).

picted by a plot of effect against the logarithm of drug concentration, when it typically takes the form of a sigmoid maximum effect (Emax) curve. Thus, there is a clearly defined relationship between concentration and effect, but the magnitude of any change in response is related not only to the magnitude of the change in concentration but also to the portion of the concentration-response curve covered for that drug (fig. 4). Once the pharmacokinetic data for an individual subject have been modelled, the pharmacodynamic profile is then related to the drug concentration in the effect compartment by means of either a linear or a nonlinear function (Holford & Sheiner 1981):

104

Clin. Pharmacokinet. 21 (2) 1991

Linear Model' E = mCe + i Nonlinear Model E = (EmaxCe)/(Ce5o

(Eq. 1)

+ Ce)

(Eq. 2)

On theoretical grounds, the relationship between drug concentration and the corresponding antihypertensive response should be described most accurately by an Emax equation (equation 2), where Emax is the theoretical maximum possible effect and Ce50 is the drug concentration required to produce 50% of Emax. In clinical studies, however, where data points are usually collected over a restricted portion of the concentration-response curve, the pharmacokinetic-pharmacodynamic relationships are often adequately described by the simpler linear model (equation 1) where E is the measured effect, m is the slope of the relationship, Ce is the drug concentration in the effect compartment and i is the intercept (fig. 4). The linear model has the practical advantage that the slope of the relationship (m) represents the effect per unit change in drug concentration and therefore characterises antihypertensive 'responsiveness' in that individual patient (in mm Hg per ~g/L).

The first-order rate constant (ke q ) derived from the concentration-effect analysis (fig. 4) provides an index of the degree of temporal dissociation between the profiles of effect and plasma drug concentration, i.e. the time lag or phase discrepancy, and is expressed in units of h-'. 3.2.1 Labetalol It has been shown both in normotensive males

and in women with pregnancy-induced hypertension that, with an integrated pharmacokineticpharmacodynamic model, labetalol concentrations are directly correlated with placebo-corrected reductions in blood pressure in individual subjects (Elliott et al. 1984; Rubin et al. 1983). In both studies the relationships were best described using the linear model. Accordingly, for each individual, the integrated response was quantified by the parameter 'm' in mm Hg/~g/L (table III). In pregnant women the concentration-effect relationships were

characterised separately for changes in both systolic and diastolic blood pressure, and in both the supine and erect positions (Rubin et al. 1983). 3.2.2 Dilevalol Concentration-effect relationships with dilevalol have been characterised in 18 patients with hypertension after single-dose and long term (4 weeks) treatment (Macphee et al. 1991). In contrast to labetalol, the pharmacokinetic-pharmacodynamic relations of dilevalol were best described in all individuals by the Emax model. Thus, the antihypertensive 'responsiveness' was characterised for each subject by the parameters Emax (in mm Hg) and Ce50 (in ~g/L) [table III]. That an Emax model was more appropriate for dilevalol is in contrast with many other antihypertensive agents (apart from angiotensin converting enzyme inhibitors) which are usually fitted to a linear function (Donnelly et al. 1991), and this may partly explain why fj-blockers have traditionally been thought to have 'flat' dose-response curves. Thus, it seems likely that previous studies may have used relatively high doses of fj-antagonists that produce drug concentrations and effects towards the upper plateau of an Emax curve. An evaluation of much lower doses should therefore reveal a steeper dose-response relationship.

4. Clinical Applications of Integrated Pharmacokinetic-Pharmacodynamic Analysis It is now established that, within individual subjects, drug concentrations of labetalol and dilevalol- and many other antihypertensive agentsbear a consistent and predictable relationship to the pharmacodynamic effects on blood pressure. Indeed, that the prevailing drug concentration in plasma is probably the most important determinant of blood pressure response has previously been underestimated (Donnelly et al. 1991). Developments in pharmacokinetic and pharmacodynamic analysis now permit a more integrated approach to the description of antihypertensive drug response. As a result, there is now scope

Kinetic-Dynamic Relationships of Dilevalol and Labetalol

105

Table III. Mean (± SO) concentration-effect parameters for labetalol and dilevalol in 3 studies using this integrated approach to characterise antihypertensive responsiveness in individual subjects Orug

Oesign

Subjects

Model

Responsiveness M (mm Hgfl'gfL)

Labetalol Elliott et al.

IV (SO)

Linear

-0.19 ± 0.05

IV (SO)

Linear

-0.44 ± 0.26

(1983)

Healthy volunteers Patients with preeclampsia

Dilevalol Macphee et al. (1991)

Patients with hypertension

PO (ST, LT)

Nonlinear

(1984) Rubin et al.

Abbreviations: M

= slope

Caso v