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plasma and as the make-up of tissues is similar across species the ratio will remain relatively constant. Any species-specific differences in plasma protein binding can be overcome by considering volume of distribution of unbound drug. Due to its unique dependence amongst pharmacokinetic parameters, on body weight, the allometric exponent (a in Eq. 9.1) for volume of distribution is generally around 0.9 to 1.0 . The antifungal agent, fluconazole provides an excellent example of the allometric relationship between body weight and volume of distribution . This compound has low plasma protein binding capacity (12%) across species and therefore this does not need to be considered in the comparison. As can be seen from Figure 9.1 when values for volume of distribution (not weight normalized) are plotted against body weight (BW) on a log-log axis a linear relationship with high correlation is observed (r2 = 0.99).
The value of 0.98 for the allometric exponent is so close to unity as to make the volume of distribution directly proportional to body weight, i.e. weight normalized volume is an invariant parameter (see Table 9.1). The mean value for the volume of distribution in the eight species is 0.82 ± 0.21 L kg-1.
In cases where plasma protein binding varies across the species, allometric scaling should be based upon the volume of distribution of unbound drug. The considerably
Tab. 9.1 Comparison of absolute and weight normalised values for the volume of distribution of fluconazole in various species.
Species Vd(L) Vd(L kg-1)
Mouse 0.02 1.00
Rat 0.08 0.80
Guinea pig 0.3 0.75
Cat 1.2 0.50
Rabbit 2.6 0.87
Dog 9.1 0.69
Pig 22 1.10
Man 49 0.70
126 | 9 Inter-Species Scaling
lower free fraction (10- to 20-fold) of zamifenacin in human compared to animal plasma results in decreased volume (weight normalized) of total drug, although the volume of unbound drug remains constant. This is a major factor in the markedly higher Cmax (of total drug) value after oral dosing in man compared to animal species . This is not always the case for acidic drugs which are restricted to the blood compartment (typically with a volume of distribution of less than 0.1 L kg-1) as changes in protein binding will not alter the volume of distribution of total drug.
An extensive retrospective analysis  examined various scaling approaches to the prediction of clinical pharmacokinetic parameters. In this analysis the most successful predictions of volume of distribution were achieved by calculating unbound fraction in tissues fu) of animals and assuming this would be similar in man. Volume of distribution was then calculated using measured plasma protein binding values and standard values for physiological parameters such as extracellular fluid and plasma volumes. The equation used was as follows:
Vd(human) = Vp + (/^(human) • Ve) + (/b(human) • R • Vp) + Vr • (/^(human)//^) (9.2)
This incorporates volumes of the various fluid compartments, plasma (Vp), extracellular fluid (Ve), and remainder (Vr) in addition to extracellular protein-bound drug determined by the ratio of binding proteins in extracellular fluid relative to plasma (R). The predicted volume of distribution calculated by this method had an averagefold error of 1.56, with 88 % of compounds (n = 16) predicted within two-fold of the actual value. This method was slightly more reliable than allometric scaling of the volume of distribution of unbound drug which provided an average-fold error of 1.83, with 77 % of compounds (n = 13) predicted within two-fold of the actual value. Both methods were significantly better than allometric scaled values without consideration of protein binding differences which only predicted 53 % of compounds (n = 15) within two-fold of the actual value (average-fold error = 2.78).
An allometric relationship for clearance is less obvious. However, in many cases the clearance process will be of similar affinity across species, this is particularly so for renal clearance where the processes of filtration and tubular reabsorption are common. In such instances the allometric relationship will be dependent upon organ blood flow. In general when clearance is expressed in units of volume per unit time per unit of body weight (e.g. mL min-1 kg-1), other mammalian species appear to eliminate drugs more rapidly than man. This is largely a result of the organs of elimination representing a smaller proportion of the body weight as the overall size of the mammal increases. For example the liver of a rat represents approximately 4.5 % total body weight, compared to approximately 2 % for man. The blood flowing to the organ (in this case the liver) is thus reduced when expressed as flow per unit of total body weight from about 100 mL min-1 kg-1 in the rat to about 25 mL min-1 kg-1 in man. When considered another way this means each microlitre of blood in the rat passes though the liver every minute, whereas the equivalent time in man is 2.5 min.