Volume Terms in

Keyphrases 0 Volume terms-pharmacokinetic definitions 0 lXd Distribution volume terms-comparison 0 Steady-state distribution terms-use, limitations .WE Model 1

Sir: where :

T = the amount of in the tissue (peripheral) com- Volume terms, designated by a V, are used in phar- partment (including the reference region) at any time, macokinetics and biopharmaceutics for three purposes. t. First, a volume constant might be used to describe the P = the amount of the drug in the central compartment lincluding the reference region) at time. t. actual size of a body region as recently used in de- the arnoht of drug eliiinated by all processes of scribing thiopental pharmacokinetics (1). Under these metabolism and , assumed to take place V exclusively in the central compartment, up to time, t. conditions the value of is given some physiological the volumes of distribution (as defined above) of the meaning. The second use for the term V is as a volume central and tissue compartments, respectively. of distribution. The concept of the volume of distribu- the amount of drug in the reference region of the central compartment at time, 1. tion was introduced by Dominguez (2) and was defined the amount of drug in an assumed reference region of by him as the hypothetical “volume of body fluid dis- the tissue compartment at time, 1. solving the substance at the same concentration as the the actual volume of the reference region in the central compartment. This volume has a physiological plasma.” Presently the volume of distribution is taken to significance as defined above. refer to the volume of a particular compartment if we the volume of the hypothesized reference region in the tissue compartment. This would be the actual volume were to assume that all of the substance or drug con- in the tissue compartment, throughout which the tained within the compartment were actually distributed concentration of the reference region is constant. at a uniform concentration which is equal to that concen- first-order rate constants of distribution. the sum of the simultaneous processes of metabolism tration measured in a particular reference region (3). and excretion all assumed to be first-order. Although the volume of distribution may not have any primed terms indicate amounts or concentrations implication as to the actual distribution of the substance, taken at the time when the amount of drug in the tissue compartment is at a maximum. it is a valuable constant which allows one to calculate concentrations. the total amount of substance or drug in a compart- ment, if one is able to measure the concentration in a instantaneously. The volume of distribution steady reference region such as the plasma. state as defined above may be expressed as: The third use of the term V is employed with reference to the volume of an unsampled compartment. This use of V may be restricted to describing a volume or volume of distribution for a single compartment within a model, such as VT in Model I, or it may be used Equation 1 is only the definition of The equation, to describe a summed volume or a volume of dis- however, gives us no useful information about a drug tribution for a number of compartments, at least one and its distribution within the body. Therefore, it is of which has not been sampled. Riggs (3) has intro- necessary to understand how V,,, is related to other duced the use of an overall volume of distribution pharmacokinetic parameters. The volume of distribu- term, and has labeled it the volume of distribution tion steady state is derived in the following manner. steady state (VdsJ.This volume term is defined specif- When the amount of drug in the tissue compartment ically with respect to the two-compartment open model reaches a maximum, the rate of transfer from the cen- (see Model 1). The volume of distribution steady state tral to the tissue compartment must be exactly equal to equals the total quantity of drug in the body divided by the rate of transfer from the tissue to the central com- the concentration in the reference region of the central partment as shown in Eq. 2. compartment, these measurements taken at the time when the tissue compartment contains the maximum kid’‘ = k21T’ (Eq. 2) amount of drug (see Eq. 1). The purpose of this com- munication is to define the conditions where the terms Substituting volumes of distribution and reference Vdsa and VT may be useful in the pharmacokinetic compartment concentrations for amount terms, Eq. 2 analysis. becomes : The two-compartmental open system (Model I) will be defined using the terminology of Riegelman et al. (6), with the additional schematic representation of reference regions within each compartment. Rearranging Eq. 3 and realizing that the ratio of con- Model I clearly indicates that within the kinetic centrations in the reference compartments at time t’ description utilized, the central compartment includes equals the ratio of concentrations we would expect those portions of the intercellular fluids and tissues to find at equilibrium for a two-compartment closed which appear to come into equilibrium with the blood model, we may substitute the partition coefficient for

Vol. 58, No. 5, Mag 1969 IJ 639