A mathematical description of the functionality of correction factors used in allometry for predicting human drug clearance

The functionality of the correction factors, maximum life-span potential (MLP), and brain weight (BrW) used in allometry is mathematically described. Correction by MLP or BrW is equivalent to a multiplication of some constants by the predicted values in humans from simple allometry, but they have no relationship to measured pharmacokinetic parameters in the animal species. The values of these constants (F-MLP or F-BrW) were calculated for some commonly used combinations of animal species. For all combinations of animal species, the value of F-BrW is always greater than that of F-MLP with a fold-increase of about 1.3 to 1.9. Different combinations of species give different values of F-BrW and F-MLP. In addition, the role of correction factors (MLP and BrW) or the "rule of exponents" (ROE) was evaluated. An intrinsic defect in using correction factors or ROE was revealed; different study designs will produce significantly different prediction results. However, ROE may still serve as a useful practical approach in predicting human CL since it was derived from real observations and has been applied to many examples.