J. vet. Pharmacol. Therap. 27, 427–439, 2004.
`
`REVIEW
`
`Plasma terminal half-life
`
`P. L. TOUTAIN &
`A. BOUSQUET-ME´ LOU
`
`Toutain, P. L., Bousquet-Me´lou, A. Plasma terminal half-life. J. vet. Pharmacol.
`Therap. 27, 427–439.
`
`UMR 181 Physiopathologie et
`Toxicologie Expe´rimentales INRA/ENVT,
`Ecole Nationale Ve´te´rinaire de Toulouse,
`Toulouse cedex 03, France
`
`Terminal plasma half-life is the time required to divide the plasma concentra-
`tion by two after reaching pseudo-equilibrium, and not the time required to
`eliminate half the administered dose. When the process of absorption is not a
`limiting factor, half-life is a hybrid parameter controlled by plasma clearance
`and extent of distribution. In contrast, when the process of absorption is a
`limiting factor, the terminal half-life reflects rate and extent of absorption and
`not the elimination process (flip-flop pharmacokinetics). The terminal half-life is
`especially relevant to multiple dosing regimens, because it controls the degree of
`drug accumulation, concentration fluctuations and the time taken to reach
`equilibrium.
`
`P. L. Toutain, UMR 181 Physiopathologie et Toxicologie Expe´rimentales INRA/
`ENVT, Ecole Nationale Ve´te´rinaire de Toulouse, 23, chemin des Capelles, 31076
`Toulouse cedex 03, France. E-mail: pl.toutain@envt.fr
`
`INTRODUCTION
`
`DEFINITION OF TERMINAL HALF LIFE
`
`The plasma half life (half life of elimination or half life of the
`terminal phase)
`is
`the most
`frequently reported of all
`pharmacokinetic parameters. It has the apparent advantage
`of being a familiar term, immediately comprehensible because
`it is expressed in units of time. This is not the case for body
`clearance (the most
`important pharmacokinetic parameter),
`which is more difficult to conceive because it has the units of
`flow.
`The half life is (apparently) easy to compute and it is often
`the only reported pharmacokinetic parameter in some in vitro
`or in vivo assays. In some circumstances,
`it is generally the
`only parameter which can be computed, e.g.
`for a drug
`metabolite or any analyte disposition when the dose is
`unknown.
`Actually, plasma half life is very often wholly misunderstood
`and many non kineticists continue to mistakenly believe that it
`represents the time required to eliminate half the administered
`dose of a drug.
`In this review, we will re state the definition of terminal half life
`and qualify its pharmacokinetic meaning, which can be very
`different after intravenous (i.v.) and extra vascular administra
`tion. The clinical relevance of terminal half life will also be
`discussed together with its value in the rational selection of dosage
`interval. Finally, some technical issues concerning its estimation
`(sampling time and level of quantification of the analytical
`technique) will be addressed.
`is preferred to
`In this review, the term ‘terminal half life’
`‘elimination half life’, because it does not prejudge the mechan
`ism controlling plasma concentration decay.
`
`Following i.v. administration, the terminal half life is the time
`required for plasma/blood concentration to decrease by 50% after
`pseudo equilibrium of distribution has been reached;
`then,
`terminal half life is computed when the decrease in drug plasma
`concentration is due only to drug elimination, and the term
`‘elimination half life’ is applicable. Therefore, it is not the time
`necessary for the amount of the administered drug to fall by one half.
`The decay of a drug following first order pharmacokinetics
`being exponential, the terminal half life is obtained from Eqn 1:
`t1=2 ¼ 0:693
`ð1Þ
`kz
`
`where 0.693 is the natural logarithm of 2 and kz, the slope of the
`terminal phase.
`Figure 1 shows two drugs having the same terminal half life but
`with very different clearances. In order to express the overall
`persistence of a drug in the body using a time parameter, then the
`mean residence time (MRT), and not the terminal plasma half life,
`should be selected.
`The confusion in the definition of half life is historical. In
`the early stages of pharmacokinetics, analytical performances
`were poor and many drug dispositions were described by a
`single mono exponential phase. In this situation, and only in
`this situation, the half life is also the time it takes to eliminate
`half the administered dose of the drug. It is also relevant to
`note that when the pseudo equilibrium has been reached, the
`disposition curve becomes mono exponential and here also,
`the terminal half time becomes the time taken to eliminate
`half the remaining fraction (not half the administered dose).
`
`Ó 2004 Blackwell Publishing Ltd
`
`427
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`very different terminal half lives. The plasma clearance expres
`ses only the ability of the body to eliminate the drug (see
`Toutain & Bousquet Me´lou, 2004a). In contrast, terminal half
`life expresses the overall rate of the actual drug elimination
`process during the terminal phase;
`this overall
`rate of
`elimination depends not only on drug clearance but also on
`the extent of drug distribution.
`Figure 2 provides a pictorial representation of the influence
`of clearance and distribution on terminal half life. More
`formally, Eqn 2 expresses the dependency of the terminal
`half life on the volume of distribution and clearance:
`
`t1=2 ¼ 0:632  Volume of distribution
`
`Plasma clearance
`
`ð2Þ
`
`Equation 2 indicates that a long terminal half life can be
`associated to a large volume of distribution (Vd) or/and
`attributable to a small plasma clearance. During the terminal
`phase, the drug will be eliminated only if it is presented to the
`clearing organs, regardless of the capacity level of these clearing
`organs to eliminate the drug. In mammals, the two most
`important clearing organs are the liver and kidney. In the
`framework of compartmental models, both are located in the
`central compartment and if the drug is present mainly in a
`peripheral compartment, the efficiency of the overall clearance
`process of drug elimination will be low and terminal half life will
`be long.
`
`HOW TO USE TERMINAL SLOPE TO EXPRESS THE
`EFFICIENCY OF DRUG ELIMINATION
`
`A simple way to express the efficiency of drug elimination is to
`consider the numerical value of the slope (kz) of the terminal
`phase. For instance, the terminal half life of phenylbutazone in
`cattle following i.v. administration is about 48 h, which
`corresponds to a terminal slope of 0.0144/h (Toutain et al.,
`1980), a figure not easy to conceptualize. However, if this rate
`constant is multiplied by 100,
`it will mean that during the
`terminal phase of elimination, about 1.44% of the residual
`
`Table 1. Terminal half life vs. plasma clearance for different antibiotics
`in the dog
`
`Parameters
`
`Plasma clearance
`(mL/kg/min)
`Terminal
`half life (min)
`
`Benzyl
`penicillin Gentamicin Oxytetracycline
`
`Tylosin
`
`3.5
`
`30
`
`3.1
`
`75
`
`4.0
`
`360
`
`22
`
`54
`
`Note that for three antibiotics (penicillin, gentamicin and oxytetracy
`cline) the plasma clearances are very similar but the terminal half lives
`are very different, indicating that terminal half life and plasma clearance
`do not convey the same information. The terminal half life is also
`influenced by the extent of drug distribution, so that, for almost the same
`plasma clearance, oxytetracycline having the largest volume of distri
`bution also has the longest half life.
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 427 439
`
`428 P. L. Toutain & A. Bousquet-Me´lou
`
`Curve A : C(t) = 90 e–1t + 10 e–0.1t
`Curve B : C(t) = 50 e–1t + 50 e–0.1t
`1000
`
`B
`
`A
`
`6
`
`12
`Time (h)
`
`18
`
`24
`
`B
`
`A
`
`6
`
`12
`Time (h)
`
`18
`
`24
`
`100
`
`10
`
`1
`
`Concentrations
`
`0.1
`
`0
`
`120
`
`100
`
`80
`
`60
`
`40
`
`20
`
`Concentrations
`
`0
`
`0
`
`Fig. 1. Terminal half life is the time required for the plasma concentration
`to fall by 50% during the terminal phase, and not the time required to
`eliminate half the administered dose. The figure shows two drugs (A and B)
`having exactly the same terminal half life (6.93 h) (see top figure semi
`logarithmic plot), but for which the time required to eliminate half the
`administered dose is very different (6 h for drug B and 2 h for drug A) (see
`bottom figure arithmetic plot). This difference is due to the fact that drug B
`has a lower clearance than drug A (0.182 mL/kg/h vs. 0.526 mL/kg/h),
`and a lower Varea (1.82 mL/kg vs. 5.26 mL/kg). It is only when the pseudo
`equilibrium state has been reached (e.g. 12 h after drug administration),
`that the time required to eliminate half the remaining amount of drug in the
`body becomes equal to the terminal half life.
`
`PHARMACOKINETIC MEANING OF HALF LIFE
`
`to
`for a non pharmacokineticist
`sometimes difficult
`is
`It
`understand the difference between information conveyed by
`plasma clearance and terminal half life. Table 1 gives an
`example of antibiotics having the same clearance in dog but
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`standing that, under equilibrium conditions, the AUC over the
`dosing interval is equal to the total AUC (i.e. from 0 to ¥) after a
`single dose administration. On the other hand,
`if doses are
`administered in the post distributive phase (i.e. when the decay
`is again monoexponential), Eqn 5 is also applicable, if most of
`the drug is eliminated during the elimination phase.
`
`ACCUMULATION AND DELAY TO REACH STEADY
`STATE IN PERIPHERAL COMPARTMENTS
`
`Most drugs display multiphasic pharmacokinetic profiles, which
`suggests the existence of both a central and several peripheral
`compartments. For these drugs, it is relevant to examine the
`degree of drug accumulation, not only in plasma but also in the
`peripheral compartment (possible location of the biophase, level
`of drug residues, etc.). Figure 9 illustrates the example of a
`hypothetical drug obeying a tri compartmental model and
`having a terminal half life of 48 h. The drug is administered
`once daily. Figure 9 shows that drug accumulation in the
`shallow and deep compartments is very different. In the deep
`compartment, drug accumulation is large and progressive. In
`contrast,
`in the shallow compartment, a pseudo plateau is
`reached much sooner. If the site of action is in rapid equilibrium
`with plasma, pharmacological (or toxicological) effects can be
`immediately equivalent to those characterizing the steady state
`conditions.
`In contrast,
`if
`the effect
`site is
`in the deep
`compartment, there is a time development of effects, which
`progressively increases with successive drug administrations.
`This example illustrates the general rule that delay to reach
`steady state conditions in the deepest tissue compartment is
`controlled by the terminal half life, and that
`the rate of
`accumulation is associated with the rate constant of redistribu
`tion from the deep compartment to the central compartment
`when this rate constant is a major determinant of the terminal
`half life.
`
`Plasma terminal half-life 433
`
`TERMINAL HALF LIFE AND THE RATIONAL SELECTION
`OF A DOSING INTERVAL
`
`The dosing interval is often selected for practical convenience
`(SID, BID, etc.). For many drugs and formulations it is necessary
`to control not only the dose but also the dosing interval, in order
`to optimize efficacy and/or
`to minimize side effects. The
`relationship between terminal half life and dosing interval
`determines
`the amplitude of fluctuations
`in drug plasma
`concentrations during the dosing intervals (Fig. 7). If the dosing
`interval is large relative to terminal half life, there will be wide
`fluctuations in concentrations with possible side effects (Cmax too
`high), or lack of efficacy (Cmin too low). The particular drugs for
`such considerations are those having a narrow therapeutic index
`(anti arrhythmic, anti epileptic, etc.), a poor selectivity (Cox1 vs.
`Cox2 inhibitory effect for NSAID), or which should be main
`tained above some threshold value (anti arrhythmic drugs, time
`dependent antibiotics, etc.).
`In the case of digoxin in the dog, it has been proposed that
`plasma concentrations should exceed 2 ng/mL for therapeutic
`effects and that the probability of adverse effects increase when
`concentrations exceed 2.5 ng/mL. Therefore, an appropriate
`dosage regimen must guarantee that digoxin plasma concentra
`tions fluctuate within this narrow therapeutic window. First, the
`daily dose can be selected to obtain an average steady state
`concentration within the therapeutic window [see the relation
`between dose, clearance and average steady state concentration
`(Toutain & Bousquet Me´lou, 2004a)]. Secondly, calculating the
`ratio of the upper and lower required concentrations (2.5/2) we
`obtain the value 1.25, which can be compared to the
`fluctuations of digoxin plasma concentrations at steady state
`given by the P/T ratio (Eqn 6). This P/T ratio must be smaller
`than 1.25, and using Eqn 6 or Table 2, it can be calculated that
`this fluctuation is obtained for a s/t1/2 ratio of 0.25. Finally,
`because digoxin t1/2 in dog being 40 48 h, the corresponding
`dosing interval is 10 12 h. This is the reason why the dosage
`
`Dose 100
`
`Shallow
`(2)
`
`0.137/h
`
`0.518/h
`
`1
`Vc = 1
`
`0.0869/h
`
`0.0479/h
`
`Deep
`(3)
`
`160
`
`140
`
`120
`
`100
`
`80
`
`60
`
`40
`
`20
`
`0
`
`Concentrations(mg/L)
`
`Fig. 9. Terminal half life and accumulation of
`drug in peripheral compartment vs. central
`compartment. A tri compartmental model
`was simulated to show that the degree of drug
`accumulation for daily administration of a
`fixed dose can be very different in central (1),
`shallow (2) and deep (3) peripheral compart
`ments. This can be of clinical relevance with
`regard to location of the biophase. If the
`biophase is located in a shallow (2) compart
`ment, the ‘steady state’ condition for efficacy
`is obtained almost immediately, whereas
`when the biophase is in the deep (3) com
`partment, the effect would develop progres
`sively over several days. This situation can
`also apply to residues in edible tissues.
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 427 439
`
`0.0558/h
`
`3
`
`1 2
`
`0
`
`48
`
`96
`
`144
`
`240
`192
`Time (h)
`
`288
`
`336
`
`384
`
`432
`
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`Plasma terminal half-life 437
`
`Curve A : C(t) = 1000 e–1t + 500 e–0.1t + 1e–0.01t
`
`Curve B : C(t) = 1000 e–1t + 500 e–0.1t + 100 e–0.01t
`
`B
`
`Therapeutically relevant LOQ
`
`Therapeutically irrelevant LOQ
`
`A
`
`104
`
`103
`
`10²
`
`10
`
`1
`
`10–1
`
`10–2
`
`Concentrations
`
`0
`
`48
`
`96
`
`144
`
`192
`Time
`
`240
`
`288
`
`336
`
`384
`
`Fig. 16. Clinical meaning of a terminal phase. The continual improve
`ment of analytical techniques can lead to the detection of a very late
`terminal phase (e.g. for ivermectin) without clinical meaning. The
`questions are (a) when to stop sampling and (b) what is the appropriate
`level of quantification (LOQ) for an analytical technique. If the
`pharmacokinetic study is performed to address the question of drug
`efficacy, the range of efficacious concentrations should be considered. If
`there is evidence that the total exposure (as evaluated by the area under
`the plasma concentration time curve or AUC) is relevant in terms of drug
`efficacy, the different AUC associated with the different phases can be
`determined by integrating the equation describing drug disposition (i.e.
`Y1/k1, AUC2
`Y2/k2 and
`for a tri exponential curve AUC1
`Y3/k3) with Y1, Y2, Y3: the intercepts, and k1,k2, and k3: the
`AUC3
`slopes of the different phases. Two curves (drug A and drug B) were
`simulated with exactly the same terminal slopes (0.01/h) but with
`100) for
`1) for drug A and high (Y3
`different intercepts [low (Y3
`drug B]. By integrating the equation describing these 2 curves
`respectively, it can be computed that the terminal phase (half time of
`69.3 h) accounts for only 1.6% of the total exposure (AUC) for drug A,
`whereas for drug B, the corresponding value is of 62.5%. For drug B, it is
`likely to be necessary to determine the last terminal phase (i.e. to carry
`out the study with an analytical technique having a LOQ of about 1),
`whereas for drug A, the last terminal phase can be considered as a very
`late terminal phase without clinical meaning, and it is not necessary to
`improve the analytical technique, i.e. to have a LOQ < 1 to detect the
`late terminal phase. However, this very late terminal phase may be very
`significant in terms of residues (e.g. for aminoglycosides).
`
`robust pharmacokinetic parameter, the ratio between the values
`obtained with LOQ of 1 and 0.1 being of 1.51, whereas the
`terminal half life was 10 times longer for a LOQ of 0.1.
`Twenty years ago, we published pharmacokinetic parameters
`for dexamethasone (DXM) in horses using a HPLC technique with
`a LOQ of 2 3 ng/mL. We reported a plasma clearance of 12.8 mL/
`kg/min and a short terminal half life of 53 min (Toutain et al.,
`1984). More recently, Cunningham et al. (1996), using an
`improved analytical technique (LOQ ¼ 200 pg/mL) reported that
`the plasma clearance of DXM in horse was 8 mL/kg/min, i.e. not
`markedly different from that in our earlier study, whereas the
`reported terminal half life was three times longer (158 min)
`because a supplementary phase was detected.
`The steady improvement in sensitivity of analytical tech
`niques raises the question of relevance of detection of a
`
`LOD2 (or MRL2)
`
`LOD1 (or MRL1)
`
`Multiple doses
`
`Single dose
`
`10²
`
`10
`
`1
`
`0.1
`
`10–1
`
`10–2
`
`10–3
`
`Concentrations
`
`0
`
`100
`
`200
`
`300
`
`400
`
`500
`
`600
`
`Delay 1
`
`Delay 2
`
`700
`Time
`
`Fig. 15. Significance of a very late terminal phase for doping control or
`for withdrawal time. Doping (medication) controls are generally carried
`out with analytical techniques having a low level of detection (LOD1), i.e.
`they are able to detect urine or plasma concentrations having no
`therapeutic impact but requiring a more or less prolonged delay after a
`drug treatment. This delay, required to achieve a ‘negative’ finding, can
`be much more prolonged after a multiple dosing regimen (delay 2) than
`after a single dose administration (delay 1). This is because a very late
`terminal phase (not detected after a single administration) gives
`concentrations above the LOD1 after a multiple dose administration due
`to accumulation specially linked to this very late phase. In contrast, with
`a higher LOD (LOD2) the delay to become ‘negative’ after a single dose or
`a multiple dose administration will be similar. The same phenomenon
`may explain that the withdrawal period, dictated by the time to fall below
`the MRL can be very different after a single and a multiple dose
`administration with regard to the value of MRL (MRL1 vs. MRL2). It is
`noteworthy that in this example, there is no therapeutically relevant
`accumulation in plasma concentration during the treatment itself but it
`is only the remnant amount of drug during the terminal phase which is
`consistently higher after a repeated dosing regimen. This situation is
`observed with phenylbutazone but not with meloxicam in horse.
`
`The practical consequence is that for a slowly absorbed drug
`(low Ka1), some formulations can lead to a flip flop phenomenon
`because Ka2 is low or null (good bioavailability), whereas some
`other formulations do not display a flip flop phenomenon, not
`because they are rapidly absorbed but because Ka2 is large,
`because their bioavailability is low (Fig. 13).
`slope in
`More generally,
`interpretation of
`the terminal
`presence of a flip flop system should be undertaken in terms of
`Ka1 and Ka2, i.e. in terms of bioavailability factors and not in
`terms of clearance and volume of distribution.
`
`A RELEVANT TERMINAL HALF LIFE AND THE
`MEANING OF A VERY LATE TERMINAL HALF LIFE
`
`Terminal half life is the parameter most sensitive to performance of
`the analytical technique, especially the level of quantification
`(LOQ). Figure 14 shows,
`for a hypothetical drug, values of
`terminal half life for different levels of LOQ. Using the same
`equation, different kinetic parameters were calculated for a LOQ of
`1 or 0.1 ng/mL. It can be seen that the body clearance is the most
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 427 439
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`Another point which can strongly influence half life estima
`tion is the use (or not) of an appropriate weighting factor when
`fitting data using non linear regression analysis. It is acknow
`ledged that one of the main factors of variation in half lives
`reported in the literature derives not from biological factors but
`from the selection of the weighting scheme. As an example,
`Fig. 17 provides raw data for which fitting with or without a
`weighting factor leads to very different terminal half lives.
`More generally, if a terminal half life is first roughly approxi
`mated by visual inspection, computer programs using non linear
`regression and an appropriate weighting scheme can then
`improve the isolation and estimation of terminal half life.
`After computation, of half life for each individual animal, the
`results are generally reported as mean ± SD or SE. For terminal
`half life, it is recommended that harmonic mean is used rather
`than arithmetic mean, and it is appropriate to compute standard
`error using a jackknife technique (Lam et al., 1985).
`
`CONCLUSION
`
`Terminal half life is the most frequently reported pharmacoki
`netic parameter, but it is commonly misinterpreted. It is the least
`robustly estimated and its interpretation can be totally flawed if a
`flip flop situation is not recognized. The clinical utility of terminal
`half life is mainly to select an appropriate dosage regimen
`interval.
`
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`
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`
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`Pharmaceutical Sciences, 75, 251 255.
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`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 427 439
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`Page 13 of 13
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`YEDA EXHIBIT NO. 2052
`MYLAN PHARM. v YEDA
`IPR2015-00644