QSPR models for the prediction of apparent volume of distribution

Abstract

An estimate of volume of distribution (V_d) is of paramount importance both in drug choice as well as maintenance and loading dose calculations in therapeutics. It can also be used in the prediction of drug biological half life. This study employs quantitative structure–pharmacokinetic relationship (QSPR) techniques for the prediction of volume of distribution. Values of V_d for 129 drugs were collated from the literature. Structural descriptors consisted of partitioning, quantum mechanical, molecular mechanical, and connectivity parameters calculated by specialized software and pK_a values obtained from ACD labs/log D database. Genetic algorithm and stepwise regression analyses were used for variable selection and model development. Models were validated using a leave-many-out procedure. QSPR analyses resulted in a number of significant models for acidic and basic drugs separately, and for all the drugs. Validation studies showed that mean fold error of predictions for the selected models were between 1.79 and 2.17. Although separate QSPR models for acids and bases resulted in lower prediction errors than models for all the drugs, the external validation study showed a limited applicability for the equation obtained for acids. Therefore, the universal model that requires only calculated structural descriptors was recommended. The QSPR model is able to predict the volume of distribution of drugs belonging to different chemical classes with a prediction error similar to that of the other more complicated prediction methods including the commonly practiced interspecies scaling. The structural descriptors in the model can be interpreted based on the known mechanisms of distribution and the molecular structures of the drugs.

Introduction

The concentration of drug in the plasma or tissues depends on the amount of drug systemically absorbed and the volume in which the drug is distributed as well as the clearance. The apparent volume of distribution in the body, V_d, is a key pharmacokinetic parameter which determines the extent of drug distribution. It is simply a proportionality constant which relates the amount of drug in the body and/or compartments of the body to its plasma concentration. Therefore, despite the fact that V_d has no physical or anatomical meaning, it represents a measure of the relative partitioning of drug between plasma (the central compartment) and the tissues. An estimate of V_d is of paramount importance both in drug choice as well as maintenance and loading dose calculations in therapeutics. Moreover, V_d, in conjunction with clearance, are the two pharmacokinetic parameters determining the drug biological half life. A number of different V_d terms have been defined in the literature. Eq. (1) represents the V_d of the central compartment as the dose taken divided by the plasma concentration of the drug at time zero (C₀) (Shargel and Yu, 1999).

$$V_{\text{d}}=\frac{\text{Dose}}{C_0}$$

Two different terms have been used to describe the volume of distribution for drugs that follow multiple exponential decay. The first, designated $V_{{\text{d}}_{\text{area}}}$, is calculated as the ratio of clearance to the rate of decline of concentration during the elimination phase of the logarithmic concentration versus time curve:

$$V_{{\text{d}}_{\text{area}}}=\frac{\text{Dose}}{k\text{AUC}}$$

The second volume term is the volume of distribution at steady state ($V_{{\text{d}}_{\text{ss}}}$) which represents the volume in which a drug would appear to be distributed during steady state if the drug existed throughout that volume at the same concentration as that in the measured fluid (plasma or blood). It should be mentioned that when using pharmacokinetics to make drug dosing decisions, the difference between $V_{{\text{d}}_{\text{area}}}$ and $V_{{\text{d}}_{\text{ss}}}$ is not usually clinically significant (Wilkinson, 2001).

The volume of distribution in man is traditionally predicted from in vivo data in preclinical animals with appropriate scaling to man (Smith et al., 2001). This can be based on allometric scaling using the body weight (BW) of the species as is represented by Eq. (3).

$$V_{\text{d}}=a\text{B}{\text{W}}^b$$

where a and b are regression coefficients, and b is ca. 0.9–1.0. In cases where plasma protein binding varies across the species, allometric scaling should be based upon the volume of distribution corrected for the extent of protein binding (V_d of unbound drug). The more successful animal scaling prediction methods include the scaling of fractal volume of distribution (Karalis et al., 2001) and a method based on the incorporation of unbound fraction of drug in tissues of animals as well as human plasma protein binding values for the estimation of V_d in human taking into account physiological parameters such as extracellular fluid and plasma volumes (Obach et al., 1997).

Quantitative structure–pharmacokinetic relationships (QSPRs) offer a convenient alternative to animal scaling (Van de Waterbeemd, 2005). This is particularly of interest in view of the need for high-throughput in vitro screening of absorption, distribution, metabolism, and excretion (ADME) in earlier stages of drug development process. Previous QSPR studies have focused on classification into different ratings of volume of distribution (Hirono et al., 1994) as well as regression models for congeneric series of molecules (Gobburu and Shelver, 1995, Turner et al., 2003), and structurally unrelated drugs (Ritschel et al., 1995, Karalis et al., 2002, Lombardo et al., 2004, Ghafourian et al., 2004). In a previous study we developed QSPR models for the prediction of V_d of structurally unrelated drugs (Ghafourian et al., 2004). In this investigation, a larger numbers of drug V_d values have been collated from the literature and a wider range of structural descriptors have been incorporated. The special emphasis of the present investigation is on the interpretability of the models and rigorous leave-many-out validation process. The large number of compounds used in the study as well as the fact that they cover a wide range of chemical and pharmacological classes can add to the significance and consistency of the models. Predictions have been made based on different QSPR models for acidic drugs and basic drugs separately, as well as for all the drugs together. A comparison with previous QSPR, and other prediction methods, is made.