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function and units used, b is approximately 0.60.8 for rates, flows, and clearances, 1.0 for volumes and organ sizes, and 0.25 for cycles and times. Thus metabolic rate can be calculated from 7.0·W0.75, liver blood flow from 37·W0.85, blood weight from 0.055·W0.99, and respiratory rate from 0.019·W0.26. Since the blood flows and the weights of the liver and kidney, the two major organs of elimination, can be similarly allometrically scaled, it follows that the same formula could, in principle, be used for extrapolation of the clearance of chemicals between species. This method works well for drugs that are poorly metabolized and those that are extensively renally cleared since renal clearance is primarily dependent on renal blood flow, which is allometrically scaled. |
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Indeed, it has been shown from a survey of the published literature on more than 20 drugs that the exponent b was 0.69 for clearance, 0.89 for volume, and 0.24 for half-life [48]. However, there was a large range of values ranging from 0.920.28 for clearance and, because of this unpredictability for certain compounds, allometric scaling has not gained wide acceptance. For some drugs, particularly those that are extensively metabolized but have a low hepatic clearance, such as phenytoin, antipyrine, or caffeine [49], where simple scaling provides poor prediction for man, an allometric correction using maximum life potential (MLP) has been used to improve the accuracy. Although the allometric approach using body weight alone is valid for many physiological functions, it is poorly predictive of longevity or maximum life potential in man. Using a derived equation based on body weight alone, humans should only live for 26.6 years, clearly an underestimate. In fact, Sacher [50] has shown that a better measure of life span can be calculated using not only body weight but also brain weight (Equation 7), and with this correction the MLP for man becomes 113 years [51]. |
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MLP = 185.4 · BW0.636 · W-0.225 (7) |
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Simplistically, it has been suggested that these differences in longevity can be explained by the assumption that in any one species there is a predetermined or fixed amount of total body metabolic potential and once this is used up, the animal dies [52]. Boxenbaum [53] has extrapolated this concept to include intrinsic hepatic metabolism, suggesting that there is a certain quantity of hepatic pharmacokinetic stuff per unit of body weight available in a lifetime that can be related to the MLP by the following formula: |
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where CL is the unbound clearance, and c is a constant for each compound. Thus, the longer the animal lives, the slower this stuff is used up. Examination of the data available from 13 disparate compounds, where at least 4 species have been investigated, the MLP correction has produced good results with an exponent b equal to unity [48]. Thus, this would suggest that the relative |
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