J. vet. Pharmacol. Therap. 27, 455–466, 2004.
`
`REVIEW
`
`Bioavailability and its assessment
`
`P. L. TOUTAIN &
`A. BOUSQUET-ME´ LOU
`
`Toutain, P. L., Bousquet-Me´lou, A. Bioavailability and its assessment. J. vet.
`Pharmacol. Therap. 27, 455–466.
`
`UMR 181 Physiopathologie et
`Toxicologie Expe´rimentales INRA/ENVT,
`Ecole Nationale Ve´te´rinaire de Toulouse,
`Toulouse cedex 03, France
`
`Bioavailability is a key pharmacokinetic parameter which expresses the
`proportion of a drug administered by any nonvascular route that gains access
`to the systemic circulation. Presented in this review are the different approaches
`to measurement of bioavailability (absolute and relative), including the case in
`which intravenous administration is impossible. The rate of drug absorption is
`also discussed with special emphasis on the possible difficulties encountered
`using Cmax and Tmax or curve fitting to evaluate the rate of drug absorption.
`
`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
`
`Bioavailability (denoted as F and generally expressed as a
`percentage, F%) quantifies the proportion of a drug which is
`absorbed and available to produce systemic effects. Bioavailabil-
`ity is a fundamental property of a pharmaceutical product for a
`given route of administration. It should be known and shown to
`be reproducible for all drug products intended to produce a
`systemic effect. Bioavailability assessment may also be of value
`for substances locally administered and intended to produce only
`local effect,
`in order to demonstrate the absence of systemic
`exposure and to support claims regarding the absence of
`systemic effect, or possible residues in edible tissues of
`food
`producing species.
`This review will focus on the bioavailability assessment (rate
`and extent) and not on the numerous physicochemical, physio-
`logical and pathological
`factors capable of
`influencing the
`bioavailability of a drug (see Baggot, 2001). The review by
`Cutler (1981) on the several approaches to compute bioavail-
`ability is still authoritative.
`
`DEFINITION OF BIOAVAILABILITY
`
`According to the European Medicines Evaluation Agency (EMEA,
`human guidelines) ‘bioavailability means the rate and extent to
`which the active substance or active moiety is absorbed from a
`pharmaceutical form, and becomes available at the site of action’
`(Anonymous, 2001). As the site of action may not be well
`defined, it is also stated that ‘bioavailability is understood to be
`the extent and the rate at which a substance or its active moiety
`is delivered from a pharmaceutical form, and becomes available
`in the general circulation’.
`
`To become available in the general circulation, drug should
`gain access to arterial blood. However, as arterial (aortic) blood
`is seldom sampled, bioavailability is normally referred to the
`usual site of measurement (venous blood). There are occasions
`when drugs delivered to venous blood are not systemically
`available due to an extensive pulmonary first-pass effect (vide
`infra).
`
`ABSORPTION VS. BIOAVAILABILITY
`
`In a physiological context, the terms absorption and bioavaila-
`bility are neither synonymous nor interchangeable (Chiou,
`2001). Absorption is only one of the steps separating drug
`administration from its delivery to the site of action. From a
`mechanistic point of view, it can be helpful to distinguish the two
`concepts in order to explain the origin of low bioavailability; for
`example, a drug can be 100% absorbed from a given formulation
`(therefore no possible improvement) but have nevertheless a low
`bioavailability due to breakdown after absorption. This is the
`case for prostaglandin (PgF2a), which undergoes a 90% lung
`first-pass effect (Bonnin et al., 1999) (see review on clearance in
`this issue) and for many drugs undergoing variable hepatic first-
`pass effect after oral or intra-peritoneal administration,
`for
`example propranolol in dog (Bai et al., 1985). To ascribe low
`bioavailability to poor absorption (and expecting to improve it
`with a new formulation) when the cause is actually a first-pass
`effect (and not amendable to improvement) can be counterpro-
`ductive during drug development.
`In the context of bioavailability measurement (not interpret-
`ation), the terms of absorption and bioavailability are often used
`interchangeably (e.g. in Gibaldi & Perrier, 1982; Rowland &
`Tozer, 1995) despite the above considerations. Unless stated
`
`Ó 2004 Blackwell Publishing Ltd
`
`455
`
`Grün. Exhibit 1080
`Grünenthal v. Antecip
`PGR2017-00022
`
`

`

`variability in drug exposure because of the different factors
`influencing the bioavailability. In contrast, when the mean
`bioavailability is
`low (e.g. 10%), a large inter-individual
`variability will be expected, with some subjects having a very
`low (e.g. 5%), and with others having a higher bioavailability
`(e.g. 20%), thus leading to exposures varying from 1 to 4, i.e. by
`400% (and consequently, a lack of reproducibility of
`this
`formulation in terms of clinical efficacy).
`Fig. 1 shows the relationship between absolute bioavailability
`and inter-individual variability for a set of drugs in man
`(Hellriegel et al., 1996). In veterinary medicine, similar obser-
`vations can be made, e.g. in the horse, the bioavailability of
`rifampicin when the drug is administered 1 h before feeding is
`68 ± 26% (coefficient of variation ¼ 38%), whereas when the
`same drug is administered 1 h after feeding, the bioavailability is
`26 ± 17%, i.e. with a coefficient of variation of 67% (Baggot,
`2001). In pigs, the mean absolute bioavailability of chlortetra-
`cycline administered by the oral route in fasted animals is low
`(19%) and variable, ranging from 9 to 30% (Kilroy et al., 1990),
`which is not satisfactory in terms of
`the prudent use of
`antibiotics. Indeed, the emergence of resistance is often because
`of an underexposure of small animal population subgroups
`despite an appropriate average dose.
`Whenever bioavailability is low, drug companies may attempt
`to increase the dose to achieve an appropriate drug exposure.
`However, it may not be recognized that the dose is generally
`increased more than proportionally to the mean bioavailability
`factor in order to ensure drug efficacy in animals having the
`lowest bioavailability. For instance,
`for a hypothetical drug
`having a mean bioavailability of 33% (with some subjects
`having 20% bioavailability, and others 50%) and for which an
`
`125
`
`100
`
`75
`
`50
`
`25
`
`CV (%)
`
`0
`
`0
`
`25
`
`50
`
`100
`
`125
`
`150
`
`75
`F %
`
`Fig. 1. Relationship between bioavailability (F%) and inter-subject
`variability (CV) in man (Hellriegel et al., 1996). Data correspond to 100
`different drugs.
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 455–466
`
`456 P. L. Toutain & A. Bousquet-Me´lou
`
`otherwise, the word absorption in this review should also be
`understood to be synonymous with bioavailability.
`
`ABSOLUTE VS. RELATIVE BIOAVAILABILITY
`
`the
`the actual percentage of
`Absolute bioavailability is
`administered dose (from 0 to 100%), which reaches the general
`circulation. Estimation involves comparing drug exposure fol-
`lowing extravascular (e.v.) administration of the tested dosage
`form with that of an intravenous administration (i.v.), assumed
`to be 100% available.
`Relative bioavailability involves comparison of two formula-
`tions (or two routes of administration of the same formulation)
`without reference to an i.v. administration.
`It should be
`emphasized that interpretation of a relative bioavailability trial
`can be of
`limited value if the absolute bioavailability of the
`reference formulation is not known. Indeed, improving by 100%
`the bioavailability of a given reference formulation (e.g. either by
`manipulating the food regimen in the case of oral administration
`or modifying the formulation) has different meanings if the
`reference formulation is 5 or 50% bioavailable. In the former
`case, the improvement lacks interest, whereas in the latter it is
`very significant!
`
`BIOAVAILABILITY VS. BIOEQUIVALENCE
`
`Although bioavailability is used as an endpoint in bioequivalence
`trials, bioavailability and bioequivalence trials are conceptually
`different. A bioequivalence trial aims to establish the therapeutic
`equivalence of two formulations (or two routes of administra-
`tion). It is not concerned with documenting the physiological
`factors capable of influencing systemic exposure of the drug. In a
`bioequivalence trial, animals are only biological
`test-tubes,
`required for an in vivo quality control for different formulations
`(Toutain & Koritz, 1997). In contrast, in a bioavailability trial, it
`is the animal physiology and possibly pathology (age, sex, food
`intake, disease state and severity, etc.) which are of primary
`interest.
`
`IT IS A MISCONCEPTION THAT A LOW
`BIOAVAILABILITY CAN ALWAYS BE COMPENSATED BY
`INCREASING THE RECOMMENDED DOSE
`
`It is frequently stated that ‘the absolute bioavailability of this
`drug/product is of no consequence (e.g. a pour-on for cattle),
`because the dose has been sufficiently increased to guarantee
`clinical efficacy’. This statement is questionable in general terms,
`as it is a primary objective of all rational drug development
`programmes to market drug products having the highest
`possible systemic bioavailability.
`More specially, a low bioavailability can be a major source of
`therapeutic variability. If the mean bioavailability in a group of
`animals is 100%, there is no possibility of
`inter-individual
`
`

`

`Bioavailability and its assessment 457
`
`RATE OF BIOAVAILABILITY
`
`Not only extent, but also rate of absorption needs to be known,
`because both determine the shape of the plasma concentration
`vs. time curve and may influence the drug effect (e.g. concen-
`tration vs. time dependent antibiotic, duration of protection for
`an avermectin, etc.). Similarly, the toxic- or side-effect can be
`markedly different when absorption rates for new formulations
`differ widely (Fig. 3). It is also essential to know the rate of
`availability when a drug is presented as a specific formulation,
`intended to precisely control the rate of drug delivery (e.g.
`modified released products such as rumen retention device,
`vaginal sponge, etc.).
`
`ABSOLUTE BIOAVAILABILITY BY THE I.V. ROUTE IS
`NOT ALWAYS 100%
`
`By assumption, a drug administered by the i.v. route has 100%
`bioavailability. This is true only if the active substance reaches
`arterial blood without loss. Drugs are generally administered by
`the i.v. route and have first to cross the pulmonary circulation
`before gaining access to arterial blood. Lungs can be the site of
`an extensive first-pass effect and reduce drug availability. This is
`the case for prostaglandins or some amines (see our companion
`paper on plasma clearance in this issue, Toutain & Bousquet-
`Me´lou 2004, pp. 415–425).
`After the i.v. administration of a pro-drug, bioavailability can
`be <100%. For example, methylprednisolone (a corticosteroid) is
`
`Undesired concentrations
`
`Therapeutic concentrations
`
`C
`
`A
`
`B
`
`Concentrations (mg/L)
`
`0
`
`6
`
`12
`Time (h)
`
`18
`
`24
`
`Fig. 3. Drug effect and the rate of drug absorption. For three formula-
`tions (A, B and C) having the same bioavailability (same AUC), effect
`(therapeutic and undesired) differs depending on rate of absorption. For
`formulation A, the rate constant of absorption is high and the peak
`plasma concentration is above the safe concentration. In contrast, for
`formulation C, the rate of absorption is too low to allow plasma
`concentration to reach effective plasma concentrations (e.g. for a time-
`dependent antibiotic). Only formulation B gives a plasma concentration
`profile within the therapeutic window.
`
`exposure corresponding to 100% bioavailability is required, the
`dose should be multiplied by 5 (not by 3) to guarantee that the
`subjects with the lowest bioavailability are fully exposed. By
`doing this, the subjects having an initial bioavailability of 50%
`are unnecessarily overexposed by a factor of 2.5! If such an
`overexposure is considered to be detrimental on safety or other
`grounds, the dose can only be doubled. Then, it will be the
`subjects with the poorest availability who will be underexposed,
`with a possible reduction of clinical efficacy or worse, by creating
`a situation favouring the emergence of resistance (antibiotic and
`antiparasitic drugs). Finally, for a drug having both a narrow
`therapeutic window and a poor bioavailability, it is possible to
`encounter a situation for which no dose is able to expose
`adequately all the animals within a population (Fig. 2).
`A poor (oral) bioavailability is also a risk factor for possible
`interaction. Indeed, for a drug having a low bioavailability, there is
`room for increasing exposure and a possibility of leading to over-
`exposure, as exemplified in man with felodipine. Felodipine is an
`anti-arrhythmic drug which has a low (approximately 15%) and
`erratic bioavailability because of a gut first-pass effect (metabolism
`by intestinal CYP3A4). Ingestion of grapefruit (which inhibits
`intestinal CYP450) can greatly increase the systemic exposure to
`felodipine (from 1 to 12 times between individuals) (Bailey et al.,
`2000). In veterinary medicine, oral bioavailability of endectocides
`is relatively low,
`leading to a possible interaction with food
`components as shown between moxidectin and quercetin, a
`natural flavonoid occurring in plants, and which is a modulator of
`P-glycoprotein (Dupuy et al., 2003).
`Finally,
`in order to document exposure variability and to
`anticipate possible under or over exposure, the measurement of
`absolute bioavailability is mandatory for any new drug formu-
`lation. Thus,
`that no serious drug development should be
`performed without intravenous data information.
`
`AUC
`
`Overexposure of some
`animals (side effects)
`
`Undesired
`exposure
`
`Therapeutic
`exposure
`
`Doses
`
`1
`
`3
`
`Underexposure
`of some animals
`(therapeutic failure, resistance)
`2
`
`Fig. 2. Low bioavailability and the impossibility of establishing a safe and
`efficacious dosage regimen for all animals. The figure shows, diagram-
`matically, the circumstance for which a drug formulation having a low
`and variable bioavailability cannot be administered at the same
`efficacious dosage in all animals due to a relatively narrow therapeutic
`window. With dose 1, all animals fail to achieve effective therapeutic
`exposure. Increasing the dose threefold guarantees that all animals now
`have an exposure above the therapeutic threshold, but animals with the
`highest bioavailability are now above the undesired threshold. Finally,
`increasing the dose by twofold guarantees that no animal undergoes
`undesired exposure, but the animals having the lowest bioavailability are
`under-exposed.
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 455–466
`
`

`

`Dose ¼ Body clearance  AUC:
`
`ð2Þ
`
`Equation 1 is the reduced form of the following equation:
`
`F% ¼ AUCe:v:  Cle:v:  Dosei:v:
`ð3Þ
`AUCi:v:  Cli:v:  Dosee:v:
`and Eqn 3 reduces to Eqn 1 if Cli.v. ¼ Cle.v., i.e. if the body
`clearance is a dose and time invariable parameter (linear phar-
`macokinetics).
`Generally, bioavailability is measured experimentally using a
`crossover study design and it is necessary to check for a possible
`carry-over effect, i.e. a differential residual effect of the first period
`over the second one. For example, hepatic enzymatic inhibition
`(or induction) after the first administration can modify the
`clearance during the second period. Therefore, the washout
`period should be long enough, not only to guarantee the absence
`of residual drug plasma concentration but also the lack of residual
`drug effect on clearance (induction/inhibition). This nonlinearity
`due to time dependency is also called nonstationarity.
`The presence of a significant (differential) carry-over effect can
`be detected by properly analysing the design (by testing the
`sequence effect), but if an unbalanced design has been carried
`out (i.e. by performing i.v. route of administration for all animals
`in the first period, and e.v. in the second period), an equal carry-
`over will be obtained, which can be totally confounded with a
`period effect
`leading to a possibly large overestimation (or
`underestimation) of bioavailability. With this type of design, a
`bioavailability higher than 100% can be computed.
`For random inter-occasion clearance variability, it has been
`suggested to correct the computed bioavailability factor by the
`terminal half-life (Wagner, 1967) using the following equation:
` t1=2; i:v:
`F% ¼ AUCe:v:
` 100:
`ð4Þ
`AUCi:v:
`t1=2; e:v:
`
`The logic for the so-called half-life correction is rooted in the
`relationship between t1/2 and clearance from the following
`equation:
`
`t1=2 ¼ 0:693  Vd
`
`Clearance
`
`:
`
`ð5Þ
`
`Assuming that Vd is invariable, t1/2 can be incorporated as a
`surrogate of clearance in Eqn 3.
`This correction should be used cautiously and accepted only
`if it results in a substantial decrease in the variability of the
`results, or in order to avoid a mean bioavailability higher than
`100%. Indeed, the estimation of terminal half-life (contrary to
`body clearance) is not very robust. In addition, if the terminal
`half-life does not represent the drug elimination but rather
`drug absorption (flip-flop), the correction becomes totally illicit
`and its unjustified use may lead to markedly underestimated
`F%. For the same objective, an equation correction can be
`made using renal clearance, which could be independently
`evaluated during a bioavailability trial. According to Karlsson
`and Sheiner (1994), the best way to handle random inter-
`occasion clearance variability is to analyse all the subjects
`simultaneously with a nonlinear mixed effect model.
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 455–466
`
`458 P. L. Toutain & A. Bousquet-Me´lou
`
`a poorly hydrosoluble drug. In order to administer it by the i.v.
`route, a hydrosoluble ester has been synthesized (methylpredni-
`solone sodium succinate or SolumedrolÒ). This is a pro-drug of
`methylprednisolone, and the ester must be hydrolysed to release
`its active moiety (i.e. methylprednisolone). In the dog, it was
`shown that the i.v. bioavailability of methylprednisolone from its
`succinic ester was only 40% (Toutain et al., 1986) (Fig. 4). Other
`examples of pro-drugs are inactive esters of macrolides, antibi-
`otics such as pivampicillin and chloramphenicol succinate and
`antiviral pro-drugs.
`
`THE MEASUREMENT OF ABSOLUTE BIOAVAILABILITY
`
`There are many methods used to evaluate the extent of systemic
`availability, the most classical one consisting of comparing
`plasma exposure (AUC) after an i.v. and an e.v. administration.
`Classically, the bioavailability factor is obtained by the following
`equation:
`
`F% ¼ AUCe:v:
`AUCi:v:
`
` Dosei:v:
`Dosee:v:
`
` 100:
`
`ð1Þ
`
`In Eqn 1, AUC is the area under the plasma (total or free) drug
`concentration or total blood concentration–time curve and
`Dosei.v. and Dosee.v. are the doses actually administered to
`evaluate F%.
`There is a compelling assumption underlying Eqn 1: the i.v.
`and the e.v. clearances must be equal. Indeed, according to the
`mass balance consideration, what is actually measured when
`using Eqn 1, is the ratio of the bioavailable doses after an e.v. and
`an i.v. administration; the bioavailable dose actually corresponds
`to the dose eliminated from plasma, as given by the general
`relationship:
`
`MP after IV administration of MP
`
`MP after administration of MPS
`
`MPS
`
`0 60 120
`
`240
`
`360
`
`480 min
`
`105
`
`104
`
`103
`
`10 2
`
`10
`
`Plasma concentration (ng / mL)
`
`Fig. 4. Absolute bioavailability of methylprednisolone in the dog.
`Methylprednisolone (MP) is a nonhydrosoluble steroid which can be
`administered by the i.v. route using a hydrosoluble salt of a succinate
`ester (methylprednisolone sodium succinate, MPS). After i.v. adminis-
`tration of MPS, its concentration decreases rapidly providing the active
`moiety, i.e. MP. Using this MP plasma concentration profile to estimate
`the MP bioavailability of another formulation would lead to gross
`overestimation of the true MP bioavailability, because only 44% of the
`administered MPS was transformed into MP. The true bioavailability of
`an MP formulation should be obtained by administering MP itself via the
`i.v. route (Toutain et al., 1986).
`
`

`

`MEASUREMENT OF ABSOLUTE BIOAVAILABILITY
`WHEN PLASMA DRUG CONCENTRATIONS ARE NOT
`DIRECTLY MEASURABLE
`
`EVALUATION OF BIOAVAILABILITY WHEN TERMINAL
`HALF-LIFE IS VERY PROLONGED AND LIMITS THE USE
`OF A CROSS-OVER DESIGN
`
`Bioavailability and its assessment 459
`
`In some instances, the measurement of plasma concentration of
`the administered drug is impossible, either because an appropriate
`analytical technique is not available, or more often because the
`drug is rapidly transformed into an active metabolite (e.g. 4-
`methylaminoantipyrine or 4-MMA from dipyrone). In these
`conditions, the drug absolute bioavailability can be evaluated by
`measuring the AUC of its metabolite using the following equation:
`
`F% ¼ AUC metabolite
`e:v:; parent drug
`AUC metabolite
`i:v:; parent drug
`
` 100:
`
`ð6Þ
`
`The condition for using Eqn 6 is that the metabolite must not
`be formed at the administration site or by a first-pass effect. In
`the same circumstance (no first-pass effect) a nonspecific assay
`(e.g. radioactivity), measuring both the drug and its metabo-
`lite(s), can be used to determine bioavailability. However, a
`nonspecific assay cannot be used for nonlinear systems.
`If a drug is metabolized solely by the liver and subjected to a
`significant hepatic first-pass effect, then Eqn 1 will be appropriate
`to measure the absolute bioavailability of an oral formulation,
`whereas Eqn 6 will give the fraction of the dose actually absorbed
`after the oral administration (for more information see Weiss,
`1990).
`
`MEASUREMENT OF BIOAVAILABILITY USING URINARY
`CONCENTRATIONS
`
`Absolute bioavailability can be assessed by measuring the
`amount of drug excreted in urine (or any other biological fluid
`or excreta) using the following equation:
`
`F% ¼ X1
`X1
`
`u; e:v:
`
`u; i:v:
`
` Dosei:v:
`Dosee:v:
`
` 100;
`
`ð7Þ
`
`where X1
`u is the total amount of drug eliminated in urine (or
`other biological fluid).
`The assumption underlying Eqn 7 is that the ratio of renal
`clearance and total clearance is the same for the i.v. and e.v.
`administrations. The main limit of the urinary approach is the
`need to collect urine (or faeces, milk, etc.) until almost all the
`drug has been excreted. The use of partial urine collection is
`theoretically possible but requires several assumptions not
`always easy to check. Urinary metabolite, provided that it is
`not formed by a first-pass effect, can be used for absolute
`bioavailability measurement:
`
`F% ¼ X1; metabolite
`X1; metabolite
`
`u; e:v:; parent drug
`
`u; i:v:; parent drug
`
` Dosei:v:
`Dosee:v:
`
` 100:
`
`ð8Þ
`
`For some drugs having a long terminal half-life (e.g. avermec-
`tins, moxidectin, salicylanilides, etc.) the absolute bioavailability
`is seldom measured, because trials involving two (long) periods
`separated by a washout period of 10 times the terminal half-life
`are considered as prohibitive. In addition, nothing guarantees
`the invariance of the plasma clearance over such a prolonged
`period of time, especially in growing animals, thus making
`invalid the use of Eqn 1.
`A possible solution to this problem is to consider the
`estimation of bioavailability by a semi-simultaneous drug
`administration such as
`that described by Karlsson and
`Bredberg (1990). The principle of
`this method comprises
`administering one of the two doses (i.v. then e.v., or e.v. then
`i.v.) at an optimal
`interval and fitting simultaneously the
`entire curve obtained with an appropriate model,
`including
`and estimating the rate constant of absorption, lag, and the
`bioavailability factor.
`It was shown that the precision of the method was influenced
`by the dose rate, the order of administration, the e.v. vs. i.v. dose
`ratio, the duration of the sampling, and the interval between the
`doses. This approach deserves to be encouraged in veterinary
`medicine as a screening method, when intra-animal variability is
`expected (e.g.
`time-dependent variation of clearance during
`growth), or to reduce the total number of blood samplings. The
`most appropriate design can be determined by Monte Carlo
`simulations. The relative bioavailability of two e.v. formulations
`can also be documented using this approach.
`
`MEASUREMENT OF AN ABSOLUTE BIOAVAILABILITY
`WHEN AN I.V. ADMINISTRATION IS NOT POSSIBLE
`
`Sometimes, it is difficult or impossible to administer a drug by
`the i.v. route, but an indirect evaluation of
`the absolute
`bioavailability is still possible if a fraction of
`the dose is
`eliminated by the kidney (or any other accessible body fluid),
`and if there is a sufficiently large variability in renal clearance
`among the different subjects under investigation (Hinderling &
`Shi, 1995).
`The principle of
`administration:
`
`this method is as follows; after an i.v.
`
`Dose
`AUCi:v:
`
`¼ Cltot ¼ ClR þ ClnR;
`
`ð9Þ
`
`is the body (plasma) clearance, ClR is the renal
`where Cltot
`clearance and ClnR, the non-renal clearance. After an e.v.
`administration, the following relationship holds:
`¼ 1
`¼ Cltot
`ClR þ ClnR
`F
`F
`F
`
`Dose
`AUCe:v:
`
`;
`
`ð10Þ
`
`Equation 8 can be used to assess the relative bioavailability of
`two formulations administered by the same route regardless of
`the presence of a first-pass effect.
`
`where F is the bioavailability factor to be estimated. Assuming
`that ClnR/F is a constant and ClR is a variable, Eqn 10 is the
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 455–466
`
`

`

`WHY MAY A BIOAVAILABILITY HIGHER THAN 100%
`BE COMPUTED?
`
`Bioavailabilities higher than 100% are regularly reported, which
`is conceptually impossible. The reasons for this are numerous,
`including experimental errors and nonfulfilment of the assump-
`tion for computation of absolute bioavailability (Martinez,
`1998). Table 1 gives the main reasons for obtaining a bioavail-
`ability higher than 100%.
`
`RELATIVE BIOAVAILABILITY BETWEEN TWO
`FORMULATIONS OR TWO E.V. ROUTES OF
`ADMINISTRATION
`
`Relative bioavailability can be measured by comparing the AUC
`of the two tested formulations at the same dose levels using the
`following equation:
`
`F% ¼ AUCtest
`AUCreference
`
` 100:
`
`ð13Þ
`
`Relative bioavailability can also be evaluated under steady-
`state conditions (Fig. 6), because the total AUC over a dosing
`interval at steady-state (i.e. AUCs) is equal to the total AUC0–¥
`after a single dose administration.
`Therefore, under steady-state conditions (obtained for exam-
`ple with formulation A), AUCs,A is measured; then formulation
`B is immediately administered (i.e. without any washout
`period), and when a new steady-state is obtained with
`formulation B (i.e. after a delay of 4–5 times the terminal
`half-life), AUCs,B is then measured. This method is useful for
`drugs having a long terminal half-life, and for which a
`conventional cross-over design cannot be extended over several
`months because of the requirement for a washout period of
`approximately 10 times the terminal half-life. Another advant-
`age of this method is that fewer data points are required to
`characterize the AUC over the dosing interval as the time
`course of drug concentration at equilibrium is more stable than
`after a single dose administration. The condition required to use
`this method is that all the bioavailable amounts of the two
`tested formulations have been absorbed during the dosing
`interval, i.e. that absorption does not continue after the end of
`the dosage interval. Urinary excretion data can be used in the
`same way. Urinary excretion data can be used at steady-state
`using the following equation:
`
`F% ¼ XSS
`XSS
`u; reference
`
`u; test
`
` 100;
`
`ð14Þ
`
`where XSS
`u denotes the amount of drug excreted in the urine over
`a dosing interval at steady-state. Equation 14 is used for the
`same dosage regimen for both formulations. The advantage of
`this approach is the duration of the collecting period (corres-
`ponding to the dosage interval), which can be much shorter than
`after a single dose administration. The condition to apply Eqn 14
`is to have reached an initial steady-state with the reference
`
`Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 455–466
`
`460 P. L. Toutain & A. Bousquet-Me´lou
`line (y ¼ mx + c) which can be
`equation of a straight
`visualized by plotting Dose/AUCe.v. against ClR; the slope is 1/
`F and the intercept ClnR/F. These two parameters of the line
`are obtained by curve fitting (Fig. 5). The conditions for this
`approach are twofold: the drug must be cleared mainly by the
`renal route (or any other measurable route), and patients
`under investigation should display a large inter-individual
`variability in their renal clearance (see Hinderling, 2003 for
`application of the method).
`If
`it
`is known that a drug is exclusively (or almost
`exclusively) eliminated by an experimentally accessible route
`of elimination (urine, faeces), as is the case for eprinomectin,
`which is almost totally eliminated unchanged by faeces in
`cattle, absolute bioavailability can be obtained without i.v.
`administration by collecting all the effluents (mass balance
`principle). However, for a long acting drug (e.g. avermectins),
`collecting all the faeces can be cumbersome. An alternative
`and less demanding method would involve measuring,
`for
`some limited periods of time (e.g. 24 h), the faecal clearance
`(Clfaeces) using the following equation:
`Clfaeces ¼ Amount exerted in faeces over a given period of time
`:
`Plasma AUC over the same period of time
`ð11Þ
`
`Simultaneously, the total plasma AUC0–¥ should be evaluated
`(this is easier to determine than to collect all the faeces over
`several weeks), and the absolute bioavailability can then be
`computed using the following equation:
`
`F% ¼ AUC01  Clfaeces
`
`Administered dose
`
`:
`
`ð12Þ
`
`to the total body
`is assumed to be equal
`Here Clfaeces
`clearance, and consequently the quantity eliminated via faeces
`(Clfaeces · AUC0–¥) is equal to the bioavailable dose.
`
` = slope
`
`1 F
`
`Dose
`AUCe.v.
`
`Cl R
`
`Cl nr
`
`1 F
`
`Intercept =
`
`Fig. 5. Evaluation of absolute bioavailability when intravenous (i.v.)
`administration is not possible. When i.v. administration is not possible
`but urine sample collection is possible (or any other matrix as faeces,
`etc.), then absolute bioavailability can be measured. The absolute
`clearance of the excretory pathway should be evaluated and the inter-
`individual variability of this absolute clearance should be large enough to
`use a regression approach in order to compute bioavailability. Bioavail-
`ability is estimated by the slope of the straight line between the measured
`absolute (renal) clearance and the apparent extra-vascular (Dose/AUC)
`clearance (see text for further explanation).
`
`

`

`Bioavailability and its assessment 461
`
`Table 1. Selected factors leading to a bioavailability higher than 100%
`
`1. Experimental errors during the in-life phase of the experiment
`Dose administered by the e.v. route is too high (gross error, different salts or esters without correction for the molecular weight, inappropriate scoring
`of tablets etc.)
`Dose administered by i.v. route is too low or not available [gross error, physical interaction with the injecting material (e.g. lidocaine), drug is not
`stable in solution (e.g. peptide during infusion). In vivo precipitation of an extemporaneous solution, a different salt or ester without correction for the
`molecular weight, incomplete transformation of an ester pro-drug to its active moiety (see Fig. 4)]
`Exchange of drug between animals raised in groups (licking in cattle, coprophagy in dogs, etc.)
`2. Experimental errors during sampling, preparation and conservation of samples
`Sampling in the jugular vein homolateral to an ear-implant in cattle
`Contamination of the extra-vascular samples when working with a pour-on formulation
`Nonstability of the drug in the i.v. samples: photodegradation (carprofen), delay to centrifugation and freezing for longer period compared with e.v.
`samples
`Insufficient samples during the initial phase after the i.v. bolus administration or the upswing of the curve after an i.v. infusion (see Fig. 7).
`3. Analytical technique
`For safety reasons, the administered dose using i.v. route is lower than for extra-vascular route, and the LOQ of the analytical phase is too high and
`fails to detect a part of the i.v. AUC
`Non-enantioselective analytical technique for a racemate having an enantioselective disposition (e.g. possible presystemic chiral inversion in the
`digestive tract favouring the enantiomer having the lowest clearance)
`Enantioselective analytical technique for a racemate having an enantioselective disposition (e.g. presystemic chiral inversion of ibuprofen in the
`digestive tract of rabbit increases the S(+) from the R()) ibuprofen (Doki et al., 2003)
`Bacteriolo