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.

Fig. 9.2 Allometric relationship between body weight and systemic clearance of fluconazole.

Thus everything occurs more rapidly in the rat than in man and "physiological time" is shorter (on a chronological scale) the smaller the species. Hence physiological processes that are dependent upon time become disproportionately more rapid in smaller species. This is illustrated by the allometric analysis of creatinine clearance (a measure of glomerular filtration rate) which shows an allometric exponent of 0.69. A similar allometric exponent is obtained for the clearance of fluconazole (Figure 9.2), a compound that is almost exclusively cleared by the kidneys. Hence whilst weight normalized clearance may decrease from 4 mL min-1 kg-1 in mouse to 0.3 mL min-1 kg-1 in man, an allometric relationship is observed across the different species with an exponent of 0.73. This value for the exponent is in keeping with the general observation for small organic molecules where successful predictions are associated with an exponent value of about 0.75 [8]. Thus clearance of fluconazole remains relatively constant across species with respect to "physiological time", as renal clearance remains a constant fraction of the glomerular filtration rate (GFR) at about 20% [9].

As with the allometric relationship with volume of distribution, fluconazole exhibits only low plasma protein binding and for compounds which exhibit variation in protein binding across species, allometry should be based upon clearance of unbound drug. Amongst other drugs cleared by the kidneys which show an allometric relationship, the a1-adrenoceptor antagonist, metazosin, is notable in that the allometric exponent for clearance is 0.28 [12]. Together with the unusual allometric exponent of 0.6 for volume of distribution this clearly suggests some abnormality in the disposition of this compound which has not yet been explained.

When clearance is dependent upon metabolism, species-specific differences in the enzymes of metabolism can clearly prevent any such allometric relationship. An example of this is the absence of a close homologue of the human CYP2C9 enzyme in the dog, hence its inability to hydroxylate drugs such as tolbutamide and tienilic acid [13]. This said, many compounds cleared by metabolism do exhibit allometric relationships (e.g. N-nitrosodimethylamine, [14]). In an extensive analysis of the allometric relationship between clearance in the rat and man for 54 extensively cleared drugs, the mean allometric exponent value was 0.66 [15]. This analysis also confirmed the improved correlation when unbound plasma clearance was considered.

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