AAPS PharmSci

, Volume 3, Issue 4, pp 30–43 | Cite as

Allometric scaling of xenobiotic clearance: Uncertainty versus universality

  • Teh-Min Hu
  • William L. Hayton


Statistical analysis and Monte Carlo simulation were used to characterize uncertainty in the allometric exponent (b) of xenobiotic clearance (CL). CL values for 115 xenobiotics were from published studies in which at least 3 species were used for the purpose of interspecies comparison of pharmacokinetics. The b value for each xenobiotic was calculated along with its confidence interval (CI). For 24 xenobiotics (21%), there was no correlation between log CL and log body weight. For the other 91 cases, the mean±standard deviation of the b values was 0.74±0.16; range: 0.29 to 1.2. Most (81%) of these individual b values did not differ from either 0.67 or 0.75 at P=0.05. When CL values for the subset of 91 substances were normalized to a common body weight coefficient (a), the b value for the 460 adjusted CL values was 0.74; the 99% CI was 0.71 to 0.76, which excluded 0.67. Monte Carlo simulation indicated that the wide range of observed b values could have resulted from random variability in CL values determined in a limited number of species, even though the underlying b value was 0.75. From the normalized CL values, 4 xenobiotic subgroups were examined: those that were (i) protein, and those that were (ii) eliminated mainly by renal excretion, (iii) by metabolism, or (iv) by renal excretion and metabolism combined. All subgroups except (ii) showed a b value not different from 0.75. The b value for the renal excretion subgroup (21 xenobiotics, 105 CL values) was 0.65, which differed from 0.75 but not from 0.67.


allometric scaling body-weight exponent clearance metabolism metabolic rate pharmacokinetics Monte Carlo simulation power law 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schmidt-Nielsen K. Scaling: Why Is Animal Size So Important? Princeton, NJ: Cambridge University Press, 1983.Google Scholar
  2. 2.
    Calder WA III. Size, Function and Life History. Cambridge, MA: Harvard University Press, 1984.Google Scholar
  3. 3.
    West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science. 1997;276:122–126.PubMedGoogle Scholar
  4. 4.
    West GB, Brown JH, Enquist BJ. The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science. 1999;284:1677–1679.PubMedGoogle Scholar
  5. 5.
    Kleiber M. Body size and metabolism. Hilgardia. 1932;6:315–353.Google Scholar
  6. 6.
    Heusner AA. Energy metabolism and body size. I. Is the 0.75 mass exponent of Kleiber's equation a statistical artifact? Respir Physiol. 1982;48:1–12.PubMedGoogle Scholar
  7. 7.
    Feldman HA, McMahon TA. The 3/4 mass exponent for energy metabolism is not a statistical artifact. Respir Physiol. 1983;52:149–163.PubMedGoogle Scholar
  8. 8.
    Banavar JR, Maritan A, Rinaldo A. Size and form in efficient transportation networks. Nature. 1999;399:130–132.PubMedGoogle Scholar
  9. 9.
    Dodds PS, Rothman DH, Weitz JS. Re-examination of the “3/4-law” of metabolism. J Theor Biol. 2001;209:9–27.PubMedGoogle Scholar
  10. 10.
    Boxenbaum H. Interspecies scaling, allometry, physiological time, and the ground plan of pharmacokinetics. J Pharmacokin Biopharm. 1982;10:201–227.Google Scholar
  11. 11.
    Sawada Y, Hanano M, Sugiyama Y, Iga T. Prediction of disposition of beta-lactam antibiotics in humans from pharmacokinetic parameters in manimals. J Pharmacokin Biopharm 1984;12:241–261.Google Scholar
  12. 12.
    Mordenti J. Man versus beast: Pharmacokinetic scaling in mammals. J Pharm Sci. 1986;75:1028–1040.PubMedGoogle Scholar
  13. 13.
    Mahmood I, Balian JD. Interspecies scaling: Prediction clearance of drugs in humans. Three different approaches. Xenobiotica. 1996;26:887–895.PubMedGoogle Scholar
  14. 14.
    Feng MR, Lou X, Brown RR, Hutchaleelaha A. Allometric pharmacokinetic scaling: Towards the prediction of human oral pharmacokinetics. Pharm Res. 2000;17:410–418.PubMedGoogle Scholar
  15. 15.
    Mahmood I. Interspecies scaling of renally secreted drugs. Life Sci. 1998;63:2365–2371.PubMedGoogle Scholar
  16. 16.
    McGovren SP, Williams MG, Stewart JC. Interspecies comparison of acivicin pharmacokinetics. Drug Metab Dispo. 1988;16:18–22.Google Scholar
  17. 17.
    Brazzell RK, Park YH, Wooldridge CB, et al. Interspecies comparison of the pharmacokinetics of aldose reductase inhibitors. Drug Metab Dispos. 1990;18:435–440.PubMedGoogle Scholar
  18. 18.
    Bjorkman S, Redke F. Clearance of fentanyl, alfentanil, methohexitone, thiopentone and ketamine in relation to estimated hepatic blood flow in several animal species: Application to prediction of clearance in man. J Pharm Pharmacol. 2000;52:1065–1074.PubMedGoogle Scholar
  19. 19.
    Cherkofsky SC. 1-Aminocyclopropanecarboxylic acid: Mouse to man interspecies pharmacokinetic comparisons and allometric relationships. J Pharm Sci. 1995;84:1231–1235.PubMedGoogle Scholar
  20. 20.
    Robbie G, Chiou WL. Elucidation of human amphotericin B pharmacokinetics: Identification of a new potential factor affecting interspecies pharmacokinetic scaling. Pharm Res. 1998;15:1630–1636.PubMedGoogle Scholar
  21. 21.
    Paxton JW, Kim SN, Whitfield LR. Pharmacokinetic and toxicity scaling of the antitumor agents amsacrine and CI-921, a new analogue, in mice, rats, rabbits, dogs, and humans. Cancer Res. 1990;50:2692–2697.PubMedGoogle Scholar
  22. 22.
    GreneLerouge NAM, Bazin-Redureau MI, Debray M, Schermann JM. Interspecies scaling of clearance and volume of distribution for digoxin-specific Fab. Toxicol Appl Pharmacol. 1996;138:84–89.Google Scholar
  23. 23.
    Lave T, Dupin S, Schmidt C, Chou RC, Jaeck D, Coassolo PH. Integration of in vitro data into allometric scaling to predict hepatic metabolic clearance in man: Application to 10 extensively metabolized drugs. J Pharm Sci. 1997;86:584–590.PubMedGoogle Scholar
  24. 24.
    Bazin-Redureau M, Pepin S, Hong G, Debray M, Scherrmann JM. Interspecies scaling of clearance and volume of distribution for horse antivenom F(ab′)2. Toxicol Appl Pharmacol. 1998;150:295–300.PubMedGoogle Scholar
  25. 25.
    Lashev LD, Pashov DA, Marinkov TN. Interspecies differences in the pharmacokinetics of kanamycin and apramycin. Vet Res Comm. 1992;16:293–300.Google Scholar
  26. 26.
    Patel BA, Boudinot FD, Schinazi RF, Gallo JM, Chu CK. Comparative pharmacokinetics and interspecies scaling of 3′-azido-3′-deoxy-thymidine (AZT) in several mammalian species. J Pharmacobio-Dyn. 1990;13:206–211.PubMedGoogle Scholar
  27. 27.
    Kurihara A, Naganuma H, Hisaoka M, Tokiwa H, Kawahara Y. Prediction of human pharmacokinetics of panipenem-betamipron, a new carbapenem, from animal data. Antimicrob Ag Chemother. 1992;36:1810–1816.Google Scholar
  28. 28.
    Mehta SC, Lu DR. Interspecies pharmacokinetic scaling of BSH in mice, rats, rabbits, and humans. Biopharm Drug Dispos. 1995;16:735–744.PubMedGoogle Scholar
  29. 29.
    Bonati M, Latini R, Tognoni G. Interspecies comparison of in vivo caffeine pharmacokinetics in man, monkey, rabbit, rat, and mouse. Drug Metab Rev. 1984-85;15:1355–1383.PubMedGoogle Scholar
  30. 30.
    Kaye B, Brearley CJ, Cussans NJ, Herron M, Humphrey MJ, Mollatt AR. Formation and pharmacokinetics of the active drug candoxatrilat in mouse, rat, rabbit, dog and man following administration of the produg candoxatril. Xenobiotica. 1997;27:1091–1102.PubMedGoogle Scholar
  31. 31.
    Mordenti J, Chen SA, Moore JA, Ferraiolo BL, Green JD. Interspecies scaling of clearance and volume of distribution data for five therapeutic proteins. Pharm Res. 1991;8:1351–1359.PubMedGoogle Scholar
  32. 32.
    Sawada Y, Hanano M, Sugiyama Y, Iga T. Prediction of the disposition of β-lactam antibiotics in humans from pharmacokinetic parameters in animals. J Pharmacokinet Biopharm. 1984;12:241–261.PubMedGoogle Scholar
  33. 33.
    Matsushita H, Suzuki H, Sugiyama Y, et al. Prediction of the pharmacokinetics of cefodizime and cefotetan in humans from pharmacokinetic parameters in animals. J Pharmacobio-Dyn. 1990;13:602–611.PubMedGoogle Scholar
  34. 34.
    Mordenti J. Pharmacokinetic scale-up: Accurate prediction of human pharmacokinetic profiles from animal data. J Pharm Sci. 1985;74:1097–1099.PubMedGoogle Scholar
  35. 35.
    Feng MR, Loo J, Wright J. Disposition of the antipsychotic agent CI-1007 in rats, monkeys, dogs, and human cytochrome p450 2D6 extensive metabolizers: Species comparison and allometric scaling. Drug Metab Dispos. 1998;26:982–988.PubMedGoogle Scholar
  36. 36.
    Hildebrand M. Inter-species extrapolation of pharmacokinetic data of three prostacyclin-mimetics. Prostaglandins. 1994;48:297–312.PubMedGoogle Scholar
  37. 37.
    Ericsson H, Tholander B, Bjorkman JA, Nordlander M, Regardh CG. Pharmacokinetics of new calcium channel antagonist clevidipine in the rat, rabbit, and dog and pharmacokinetic/pharmacodynamic relationship in anesthetized dogs. Drug Metab Dispo. 1999;27:558–564.Google Scholar
  38. 38.
    Sangalli L, Bortolotti A, Jiritano L, Bonati M. Cyclosporine pharmacokinetics in rats and interspecies comparison in dogs, rabbits, rats, and humans. Drug Metab Dispo. 1998;16:749–753.Google Scholar
  39. 39.
    Kim SH, Kim WB, Lee MG. Interspecies pharmacokinetic scaling of a new carbapenem, DA-1131, in mice, rats, rabbits and dogs, and prediction of human pharmacokinetics. Biopharm Drug Dispos. 1998;19:231–235.PubMedGoogle Scholar
  40. 40.
    Klotz U, Antonin K-H, Bieck PR. Pharmacokinetics and plasma binding of diazepam in man, dog, rabbit, guinea pig and rat. J Pharmacol Exp Ther. 1976;199:67–73.PubMedGoogle Scholar
  41. 41.
    Kaul S, Daudekar KA, Schilling BE, Barbhaiya RH. Toxicokinetics of 2′,3′-deoxythymidine, stavudine (D4T). Drug Metab Dispos. 1999;27:1–12.PubMedGoogle Scholar
  42. 42.
    Sanwald-Ducray P, Dow J. Prediction of the pharmacokinetic parameters of reduced-dolasetron in man using in vitro-in vivo and interspecies allometric scaling. Xenobiotica. 1997;27:189–201.PubMedGoogle Scholar
  43. 43.
    Kawakami J, Yamamoto K, Sawada Y, Iga T. Prediction of brain delivery of ofloxacin, a new quinolone, in the human from animal data. J Pharmacokinet Biopharm. 1994;22:207–227.PubMedGoogle Scholar
  44. 44.
    Tsunekawa Y, Hasegawa T, Nadai M, Takagi K, Nabeshima T. Interspecies differences and scaling for the pharmacokinetics of xanthine derivatives. J Pharm Pharmacol. 1992;44:594–599.PubMedGoogle Scholar
  45. 45.
    Bregante MA, Saez P, Aramayona JJ, et al. Comparative pharmacokinetics of enrofloxacin in mice, rats, rabbits, sheep, and cows. Am J Vet Res. 1999;60:1111–1116.PubMedGoogle Scholar
  46. 46.
    Duthu GS. Interspecies correlation of the pharmacokinetics of erythromycin, oleandomycin, and tylosin. J Pharm Sci. 1995;74:943–946.Google Scholar
  47. 47.
    Efthymiopoulos C, Battaglia R, Strolin Benedetti M. Animal pharmacokinetics and interspecies scaling of FCE 22101, a penem antibiotic. J Antimicrob Chemother. 1991;27:517–526.PubMedGoogle Scholar
  48. 48.
    Jezequel SG. Fluconazole: Interspecies scaling and allometric relationships of pharmacokinetic properties. J Pharm Pharmacol. 1994;46:196–199.PubMedGoogle Scholar
  49. 49.
    Segre G, Bianchi E, Zanolo G. Pharmacokinetics of flunoxaprofen in rats, dogs, and monkeys. J Pharm Sci. 1988;77:670–673.PubMedGoogle Scholar
  50. 50.
    Khor SP, Amyx H, Davis ST, Nelson D, Baccanari DP, Spector T. Dihydropyrimidine dehydrogenase inactivation and 5-fluorouracil pharmacokinetics: Allometric scaling of animal data, pharmacokinetics and toxicodynamics of 5-fluorouracil in humans. Cancer Chemother Pharmacol. 1997;39:233–238.PubMedGoogle Scholar
  51. 51.
    Clark B, Smith DA. Metabolism and excretion of a chromone carboxylic acid (FPL 52757) in various animal species. Xenobiotica. 1982;12:147–153.PubMedGoogle Scholar
  52. 52.
    Nakajima Y, Hattori K, Shinsei M, et al. Physiologically-based pharmacokinetic analysis of grepafloxacin. Biol Pharm Bull. 2000;23:1077–1083.PubMedGoogle Scholar
  53. 53.
    Baggot JD. Application of interspecies scaling to the bispyridinium oxime HI-6. Am J Vet Res. 1994;55:689–691.PubMedGoogle Scholar
  54. 54.
    Lave T, Levet-Trafit B, Schmitt-Hoffmann AH, et al. Interspecies scaling of interferon disposition and comparison of allometric scaling with concentration-time transformations. J Pharm Sci. 1995;84:1285–1290.PubMedGoogle Scholar
  55. 55.
    Sakai T, Hamada T, Awata N, Watanabe J. Pharmacokinetics of an antiallergic agent, 1-(2-ethoxyethyl)-2-(hexahydro-4-methyl-1H-1,4-diazepin-1-yl)-1H-benzimidazole difumarate (KG-2413) after oral administration: Interspecies differences in rats, guinea pigs and dogs. J Pharmacobio-Dyn. 1989;12:530–536.PubMedGoogle Scholar
  56. 56.
    Lave T, Saner A, Coassolo P, Brandt R, Schmitt-Hoffman AH, Chou RC. Animal pharmacokinetics and interspecies scaling from animals to man of lamifiban, a new platelet aggregation inhibitor. J Pharm Pharmacol. 1996;48:573–577.PubMedGoogle Scholar
  57. 57.
    Richter WF, Gallati H, Schiller CD. Animal pharmacokinetics of the tumor necrosis factor receptor-immunoglobulin fusion protein lenercept and their extrapolation to humans. Drug Metab Dispos. 1999;27:21–25.PubMedGoogle Scholar
  58. 58.
    Lapka R, Rejholec V, Sechser T, Peterkova M, Smid M. Interspecies pharmacokinetic scaling of metazosin, a novel alpha-adrenergic antagonist. Biopharm Drug Dispo. 1989;10:581–589.Google Scholar
  59. 59.
    Ahr H-J, Boberg M, Brendel E, Krause HP, Steinke W. Pharmacokinetics of miglitol: Absorption, distribution, metabolism, and excretion following administration to rats, dogs, and man. Arzneim Forsch. 1997;47:734–745.Google Scholar
  60. 60.
    Siefert HM, Domdey-Bette A, Henninger K, Hucke F, Kohlsdorfer C, Stass HH. Pharmacokinetics of the 8-methoxyquinolone, moxifloxacin: A comparison in humans and other mammalian species. J Antimicrob Chemother. 1999;43(Suppl. B):69–76.PubMedGoogle Scholar
  61. 61.
    Lave T, Portmann R, Schenker G, et al. Interspecies pharmacokinetic comparisons and allometric scaling of napsagatran, a low molecular weigrobin inhibitor. J Pharm Pharmacol. 1999;51:85–91.PubMedGoogle Scholar
  62. 62.
    Higuchi S, Shiobara Y. Comparative pharmacokinetics of nicardipine hydrochloride, a new vasodilator, in various species. Xenobiotica. 1980;10:447–454.PubMedGoogle Scholar
  63. 63.
    Mitsuhashi Y, Sugiyama Y, Ozawa S, et al. Prediction of ACNU plasma concentration-time profiles in humans by animal scale-up. Cancer Chemother Pharmacol. 1990;27:20–26.PubMedGoogle Scholar
  64. 64.
    Yoshimura M, Kojima J, Ito T, Suzuki J. Pharmacokinetics of nipradilol (K-351), a new antihypertensive agent. I. Studies on interspecies variation in laboratory animals. J Pharmacobio-Dyn. 1985;8:738–750.PubMedGoogle Scholar
  65. 65.
    Gombar CT, Harrington GW, Polypiw HM Jr, et al. Interspecies scaling of the pharmacokinetics of Nnitrosodimethylamine. Cancer Res. 1990;50:4366–4370.PubMedGoogle Scholar
  66. 66.
    Mukai H, Watanabe S, Tsuchida K, Morino A. Pharmacokinetics of NS-49, a phenethylamine class α1A-adrenoceptor agonist, at therapeutic doses in several animal species and interspecies scaling of its pharmacokinetic parameters. Int J Pharm. 1999;186:215–222.PubMedGoogle Scholar
  67. 67.
    Owens SM, Hardwick WC, Blackall D. Phencyclidine pharmacokinetic scaling among species. J Pharmacol Exp Ther. 1987;242:96–101.PubMedGoogle Scholar
  68. 68.
    Ishigami M, Saburomaru K, Niino K, et al. Pharmacokinetics of procaterol in the rat, rabbit, and beagle dog. Arzneim Forsch. 1979;29:266–270.Google Scholar
  69. 69.
    Khor AP, McCarthy K, DuPont M, Murray K, Timony G. Pharmacokinetics, pharmacodynamics, allometry, and dose selection of rPSGL-Ig for phase I trial. J Pharmacol Exp Ther. 2000;293:618–624.PubMedGoogle Scholar
  70. 70.
    Mordenti J, Osaka G, Garcia K, Thomsen K, Licko V, Meng G. Pharmacokinetics and interspecies scaling of recombinant human factor VIII. Toxicol Appl Pharmacol. 1996;136:75–78.PubMedGoogle Scholar
  71. 71.
    Coassolo P, Fischli W, Clozel J-P, Chou RC. Pharmacokinetics of remikiren, a potent orally active inhibitor of human renin, in rat, dog, and primates. Xenobiotica. 1996;26:333–345.PubMedGoogle Scholar
  72. 72.
    Widman M, Nilsson LB, Bryske B, Lundstrom J. Disposition of remoxipride in different species. Arzneim Forsch. 1993;43:287–297.Google Scholar
  73. 73.
    Lashev L, Pashov D, Kanelov I. Species specific pharmacokinetics of rolitetracycline. J Vet Med A. 1995;42:201–208.Google Scholar
  74. 74.
    Herault JP, Donat F, Barzu T, et al. Pharmacokinetic study of three synthetic AT-binding pentasaccharides in various animal species-extrapolation to humans. Blood Coagul Fibrinol. 1997;8:161–167.Google Scholar
  75. 75.
    Ward KW, Azzarano LM, Bondinell WE, et al. Preclinical pharmacokinetics and interspecies scaling of a novel vitronectin receptor antagonist. Drug Metab Dispos. 1999;27:1232–1241.PubMedGoogle Scholar
  76. 76.
    Lin C, Gupta S, Loebenberg D, Cayen MN. Pharmacokinetics of an everninomicin (SCH 27899) in mice, rats, rabbits, and cynomolgus monkeys following intravenous administration. Antimicrob Ag Chemother. 2000;44:916–919.Google Scholar
  77. 77.
    Chung M, Radwanski E, Loebenberg D, et al. Interspecies pharmacokinetic scaling of Sch 34343. J Antimicrob Chemother. 1985;15(Suppl. C):227–233.PubMedGoogle Scholar
  78. 78.
    Hinderling PH, Dilea C, Koziol T, Millington G. Comparative kinetics of sematilide in four species. Drug Metab Dispo. 1993;21:662–669.Google Scholar
  79. 79.
    Walker DK, Ackland MJ, James GC, et al. Pharmacokinetics and metabolism of sildenafil in mouse, rat, rabbit, dog, and man. Xenobiotica. 1999;29:297–310.PubMedGoogle Scholar
  80. 80.
    Brocks DR, Freed MI, Martin DE, et al. Interspecies pharmacokinetics of a novel hematoregulatory peptide (SK&F 107647) in rats, dogs, and oncologic patients. Pharm Res. 1996;13:794–797.PubMedGoogle Scholar
  81. 81.
    Cosson VF, Fuseau E, Efthymiopoulos C, Bye A. Mixed effect modeling of sumatriptan pharmacokinetics during drug development. I: Interspecies allometric scaling. J Pharmacokin Biopharm. 1997;25:149–167.Google Scholar
  82. 82.
    Leusch A, Troger W, Greischel A, Roth W. Pharmacokinetics of the M1-agonist talsaclidine in mouse, rat, rabbit, and monkey, and extrapolation to man. Xenobiotica. 2000;30:797–813.PubMedGoogle Scholar
  83. 83.
    van Hoogdalem EJ, Soeishi Y, Matsushima H, Higuchi S. Disposition of the selective α1A-adrenoceptor antagonist tamsulosin in humans: Comparison with data from interspecies scaling. J Pharm Sci. 1997;86:1156–1161.PubMedGoogle Scholar
  84. 84.
    Cruze CA, Kelm GR, Meredith MP. Interspecies scaling of tebufelone pharmacokinetic data and application to preclinical toxicology. Pharm Res. 1995;12:895–901.PubMedGoogle Scholar
  85. 85.
    Gaspari F, Bonati M. Interspecies metabolism and pharmacokinetic scaling of theophylline disposition. Drug Metab Rev. 1990;22:179–207.PubMedGoogle Scholar
  86. 86.
    Davi H, Tronquet C, Calx J, et al. Disposition of tiludronate (Skelid) in animals. Xenobiotica. 1999;29:1017–1031.PubMedGoogle Scholar
  87. 87.
    Pahlman I, Kankaanranta S, Palmer L. Pharmacokinetics of tolterodine, a muscarinic receptor antagonist, in mouse, rat and dog. Arzneim Forsch. 2001;51:134–144.Google Scholar
  88. 88.
    Tanaka E, Ishikawa A, Horie T. In vivo and in vitro trimethadione oxidation activity of the liver from various animal species including mouse, hamster, rat, rabbit, dog, monkey and human. Human Exp Toxicol. 1999;18:12–16.Google Scholar
  89. 89.
    Izumi T, Enomoto S, Hosiyama K, et al. Prediction of the human pharmacokinetics of troglitazone, a new and extensively metabolized antidiabetic agent, after oral administration, with an animal scale-up approach. J Pharmacol Exp Ther. 1996;277:1630–1641.PubMedGoogle Scholar
  90. 90.
    Grindel JM, O'Neil PG, Yorgey KA, et al. The metabolism of zomepirac sodium I. Disposition in laboratory animals and man. Drug Metab Dispo. 1980;8:343–348.Google Scholar
  91. 91.
    Singer MA, Morton AR. Mouse to elephant: Biological scaling and Kt/V. Am J Kidney Dis. 2000;35:306–309.PubMedGoogle Scholar
  92. 92.
    Singer MA. Of mice and men and elephants: Metabolic rate sets glomerular filtration rate. Am J Kidney Dis. 2001;37:164–178.PubMedGoogle Scholar
  93. 93.
    Edwards NA. Scaling of renal functions in mammals. Comp Biochem Physiol. 1975;52A:63–66.Google Scholar
  94. 94.
    Hayton WL. Maturation and growth of renal function: Dosing renally cleared drugs in children. AAPS PharmSci. 2000;2(1), article 3.Google Scholar
  95. 95.
    Adolph EF. Quantitative relations in the physiological constituents of mammals. Science. 1949;109:579–585.PubMedGoogle Scholar
  96. 96.
    Rubner M. Über den einfluss der körpergrösse auf stoff und kraftwechsel. Z Biol. 1883;19:535–562.Google Scholar
  97. 97.
    Heusner A. Energy metabolism and body size. II. Dimensional analysis and energetic non-similarity. Resp Physiol. 1982;48:13–25.Google Scholar
  98. 98.
    West GB. The origin of universal scaling laws in biology. Physica A. 1999;263:104–113.Google Scholar
  99. 99.
    Murray CD. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc Natl Acad Sci U S A. 1926;12:207–214.PubMedCentralPubMedGoogle Scholar
  100. 100.
    Cohn DL. Optimal systems: I. The vascular system. Bull Math Biophys. 1954;16:59–74.Google Scholar
  101. 101.
    Cohn DL. Optimal systems: II. The vascular system. Bull Math Biophys. 1955;17:219–227.Google Scholar
  102. 102.
    Bonate PL, Howard D. Prospective allometic scaling: Does the emperor have clothes? J Clin Pharmacol. 2000;40:665–670.PubMedGoogle Scholar
  103. 103.
    Mahmood I. Critique of prospective allometric scaling: Does the emperor have clothes? J Clin Pharmacol. 2000;40:671–674.Google Scholar

Copyright information

© American Association of Pharmaceutical Scientists 2001

Authors and Affiliations

  1. 1.Division of Pharmaceutics, College of PharmacyThe Ohio State UniversityColumbus

Personalised recommendations