Volumes of Distribution

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Volumes of Distribution J. vet. Pharmacol. Therap. 27, 441–453, 2004. REVIEW Volumes of distribution P. L. TOUTAIN & Toutain, P. L., Bousquet-Me´lou, A. Volumes of distribution. J. vet. Pharmacol. A. BOUSQUET-ME´ LOU Therap. 27, 441–453. Volumes of distribution are proportionality constants between total amount of UMR 181 Physiopathologie et drug in the body and plasma concentrations. As snapshot plasma drug Toxicologie Expe´rimentales INRA/ENVT, Ecole Nationale Ve´te´rinaire de Toulouse, concentrations may be measured in different conditions (at equilibrium, under Toulouse cedex 03, France pseudo-equilibrium condition,…), several volumes of distribution have been defined. The two most relevant are the volume of distribution at equilibrium (Vss), and the volume of distribution during pseudo-equilibrium (Varea). Volumes of distribution are used to compute a loading dose (Vss) or the residual amount of drug in the body knowing plasma concentrations (Varea). Volume of distribution may be interpreted in terms of drug distribution having recourse to physiological models involving drug binding to plasma and tissues. Volumes of distribution should be determined early in drug development programmes and those having a large volume of distribution may be selected to obtain a long terminal half-life even for drugs having a relatively high clearance. 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: [email protected] INTRODUCTION VOLUME OF DISTRIBUTION: A GENERAL DEFINITION Three volumes of distribution (Vd) are classically reported in All the volumes of distribution correspond to the ratio of an the scientific literature: the volume of the central compartment amount (A) of drug in the body at a given time (At), and plasma (Vc), the volume of distribution calculated by the area (blood) concentration at that time (Eqn 1): method (Varea) and the steady-state volume of distribution (Vss). Amount of drug in the body at time t ðAtÞ Vd ¼ ð1Þ Vd is the parameter used to assess the amount of drug in Cplasma at time t the body from the measurement of a snapshot plasma concentration. The main clinical application of Vd is to By definition a Vd should only be regarded as a propor- compute a loading dose (e.g. the first dose of a multiple tionality constant (parameter) between a plasma concentration dosage regimen) in order to immediately reach the target and the corresponding amount of drug in the body. This therapeutic plasma concentration. Frequently, and often proportionality constant having a volume for dimension incorrectly, the numerical value of a Vd is advocated to has been termed volume of distribution. Figure 2 gives a support claims on the extent of drug distribution. It should be pictorial view of the concept of Vd using a flask analogy to the stressed that Vd was not primarily designed to evaluate drug body. distribution in the different physiological spaces, and that a Vd can be much higher than the total body water space (Fig. 1). Nevertheless, a physiological interpretation of Vd is possible DRUG DISTRIBUTION AND VOLUME OF DISTRIBUTION but this requires having recourse to models involving drug binding to plasma and tissues. The evaluation of drug distribution (with its different determi- This review defines each volume of distribution, how to nants) and that of volume of distribution are two different issues. compute them (with particular attention to the most frequent They should be carefully distinguished, even if relationships incorrect computations) and how to interpret and use appropri- between them exist, as expressed by different physiological ately the different Vd. models (vide infra). Figure 3 depicts the principles of drug Ó 2004 Blackwell Publishing Ltd 441 442 P. L. Toutain & A. Bousquet-Me´lou Volume of distribution (mL/kg) 10 10 10 10 10 ² 3 4 5 Flunixin Phenylbutazone Ketoprofen Meclofenamic Naproxen Vedaprofen Carprofen Gentamicin Ibuprofen Ampicillin Eltenac Sulphadiazine Prednisolone Theophilline Diazepam Caffeine Metronidazole Thiopentone Guaphenesin DM60 Meperidine Trimethoprim Methadone Codeine Furosemide Ketamine Dexamethasone Dipyrone Quinidine Isoxsuprine Methylpredisolone Hordenin Pentazocine Heptaminol Clenbuterol Acepromazin Azithromycin Bromhexine Fig. 1. Volume of distribution, Varea (mL/kg), Morphine for a selection of drugs in the horse. repartition between the vascular space (plasma) and extra- of drug in the body and the plasma concentration will have vascular spaces (tissues). different values according to the state of drug disposition. Figure 4 gives the four possibilities, with Vc being the initial volume of distribution, Vss, the appropriate volume of distri- WHY DO SEVERAL VOLUMES OF DISTRIBUTION EXIST? bution when plasma concentrations are measured in steady- state conditions, and Varea or Vz (formerly termed Vdb), the As the plasma concentration can be measured in different appropriate Vd when plasma concentration is measured in situations [just after an intravenous (i.v.) drug administration, pseudo-equilibrium conditions. When plasma concentration is during the phase of drug distribution, during the terminal measured during the drug distribution phase, the ratio of the phase of drug disposition or at equilibrium], several Vd are drug amount over the plasma concentration is not a needed because the proportionality ratio between the amount parameter but a time dependent variable. Ó 2004 Blackwell Publishing Ltd, J. vet. Pharmacol. Therap. 27, 441–453 Volumes of distribution 443 Therefore, V can be viewed as the apparent volume from Dose = 10 mg c which drug elimination occurs because kidney and liver, the two main clearing organs, belong to the central compartment (Fig. 6). Concentration = 10 mg/L Concentration = 2 mg/L Immediately after i.v. bolus administration, the drug begins to be distributed and eliminated. If the distribution is instantane- ous, after the drug administration, the body is reducible to a homogenous pool (compartment) and Vc remains the single Vd. However, for the vast majority of drugs, there is a non- instantaneous distribution phase during which the drug plasma concentration decreases more rapidly than the total amount of drug actually present in the body. During the distribution phase, the decrease of plasma concentration is largely due to the partitioning of the drug in the body, and not to the drug elimination. Therefore, according to the definition of a Vd VD = 1 L VD = 5 L (Eqn 1), the latter increases progressively until it reaches an Fig. 2. A simplistic system to introduce the concept of volume of asymptotic value when the pseudo-equilibrium of distribution is distribution. The same amount of drug (10 mg) is dissolved in the same achieved. This asymptotic value is termed Varea. Thus, Vd during volume of water (1 L). For the left beaker the water concentration is the distribution phase can be viewed as a time-dependent 10 lg/mL and when applying Eqn 1 in the text, the computed apparent variable that expands from V immediately after the bolus drug volume of distribution of the drug in the left beaker is 1 L (which c administration until it reaches the maximal value of V corresponds to the actual volume of water in the beaker). In the right area beaker, there is charcoal that can fix part of the drug, which is divided (Fig. 7). between water and charcoal. The water concentration is here of only When the distribution pseudo-equilibrium is reached, the net 2 lg/mL and applying Eqn 1 of the text gives an apparent volume of exchange (balance) between plasma (central compartment) and distribution of 5 L, i.e. five times the actual volume of water. the tissues (peripheral compartments) is null, and the decrease of plasma concentration is now only because of irreversible drug THE INITIAL (VC)ANDTHETERMINAL(VAREA OR VZ) elimination, which is proportional to the body (total) clearance VOLUMES OF DISTRIBUTION AFTER INTRAVENOUS (Eqn 4): BOLUS DRUG ADMINISTRATION Rate of drug elimination ¼ Cltot  Cplasma ð4Þ Just after an i.v. drug administration, plasma concentration is where Cltot is the plasma clearance. The relationship between plasma concentration and the maximal (C0). Before any drug elimination or distribution, the amount of drug in the body is by definition equal to the amount of drug in the body during the elimination phase is given by Eqn 5: administered dose, and the plasma concentration is C0. Applying the definition of a Vd (Eqn 1), the initial volume of distribution Amount of drug in the body during the terminal phase (Vc) is (Eqn 2): V ¼ area Plasma concentration during the terminal phase Dose Vc ¼ ð2Þ ð5Þ C0 The amount of drug present in the body at a given time t Equation 2 assumes that C corresponds to an initial plasma 0 during the elimination phase is equal to the amount of drug concentration resulting from a total drug mixing in blood before which remains to be eliminated, i.e. (Eqn 6): any drug elimination or distribution, which is generally an Z 1 unrealistic assumption. Practically speaking, C0 is estimated by Amount of drug in the body at time ti ¼ Cl  CðtÞdt ð6Þ extrapolation to time zero of the drug disposition curve (Fig. 5 ti gives an example of the determination of C0 for the evaluation of plasma volume using Evans blue). where ti is a time during the elimination phase. Integration of In the framework of a compartmental analysis, the initial this equation gives Eqn 7: volume of distribution is termed volume of the central compart- Amount of drug at time t ¼ Cl ½AUC ð7Þ ment and is obtained by mean of Eqn 3: i ðti1Þ where AUC is the area under the plasma concentration vs. Dose (ti–¥) Vc ¼ ð3Þ Pn time curve between ti and infinity. Yi i¼1 During the terminal phase the plasma concentration decays according to a mono-exponential curve which can be described where Yi are intercepts of the different phases of the kinetic by a mono-exponential equation (Eqn 8) : disposition obtained by fitting the plasma drug concentration vs.
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