Scaling of pharmacokinetics in peds

From: "Bonate, Peter" - pbonate@ilexonc.com Subject:[NMusers] Scaling of pharmacokinetics in peds Date: 12/17/2003 12:27 PM Hello everyone. I know we have have this conversation in the past. I am modeling some pharmacokinetic data in kids. I think it was pretty much agreed in those earlier discussions that weight should be built into the structural model a priori. Everyone also pretty much also agreed that weight should go on CL and Q with fixed power 0.7 and weight on volume terms with fixed power 1.0. So here is my question. Clearance for the drug I am modeling is dose-dependent. I wanted to get some opinions on what I am doing. Without any immediate knowledge I am assuming that Km does not change with weight, but Vmax does. So what do you think, should the power term on Vmax be estimated or treated as fixed at 0.7? I am treating it as estimable. If it is anywhere near 0.7, I will make it fixed to 0.7. Any thoughts? Does this seem reasonable. Thanks, Pete Peter L. Bonate, PhD, FCP Director, Pharmacokinetics ILEX Oncology, Inc 4545 Horizon Hill Blvd San Antonio, TX 78229 phone: 210-949-8662 fax: 210-949-8219 email: pbonate@ilexonc.com

From: Paul Hutson - prhutson@pharmacy.wisc.edu Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/17/2003 1:40 PM Peter: Seems reasonable, but it seems to me that the variability (or consistency) of the power term would be somewhat apparent if you were to plot (ln Vmax) vs (ln wt). Good luck. Paul

From: Nick Holford - n.holford@auckland.ac.nz Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/17/2003 3:22 PM Peter, I don't know who is the advocate for an allometric exponent of 0.7 for clearance. I do not wish to be counted among the "everyone [who] pretty much agreed" to a value of .7 Here (again) are some references for theory and experiment in support of a value of 0.75. Peters R. The ecological implications of body size. Cambridge: Cambridge University Press; 1983. West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science 1997;276:122-26. West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 1999;284(5420):1677-9. Anderson BJ, van Lingen RA, Hansen TG, Lin YC, Holford NHG. Acetaminophen developmental pharmacokinetics in premature neonates and infants: a pooled population analysis. Anesthesiology 2002;96(6):1336-45. This is a useful page explaining some background to allometric ideas: http://www.anaesthetist.com/physiol/basics/scaling/Kleiber.htm At any given conc then CL is Vmax CL = ---------- Km + Conc It can be allometrically scaled as follows: VmaxStd CLStd*Fsize = (---------)*Fize Km + Conc where Fsize=(WT/WTstd)**0.75 No allometric scaling would be expected a priori on Km. So I think it might be reasonable to restate this expression as: VmaxStd*Fsize CLStd*Fsize = ------------- Km + Conc i.e. apply the allometric scaling directly to Vmax alone. Note, factors other than size (such as age) may be associated with between subject differences in Km. It is important to recognize that size scaling is not the only factor that explains between and within species differences. These other factors may sometimes obscure the view of what the emperor is wearing Bonate PL, Howard D. Prospective allometric scaling: does the emperor have clothes? J Clin Pharmacol 2000;40(6):665-70; discussion 671-6. Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: Nick Holford - n.holford@auckland.ac.nz Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/19/2003 3:00 AM Paul, Fine in theory but in practice I expect it would require a wide range of weights plus doses and intensive sampling to expect to be able to distinguish any departure from the theoretical expectation of 0.75 for the allometric exponent. Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: Paul Hutson - prhutson@pharmacy.wisc.edu Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/19/2003 10:25 AM Another beautiful theory brutalized by a vicious gang of facts.

From: Jenny Yuehling Chien - CHIEN_JENNY_YUEHLING@lilly.com Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/19/2003 10:27 AM Nick and Pete, another good reference to support 0.75 for clearance: Hu and Hayton, Allometric scaling of xenobiotic clearance: uncertainty vs universality. AAPS PharmSci 2001; 3(4) article 29. The treatment of Km will depend on the source of nonlinearity. If source of nonlinearity is metabolism-based, tons of literature exist on ontogeny of drug metabolizing enzymes to support no scaling on Km, I would agree the effect of weight would only be on Vmax. If source of nonlinearity is due to other biological factors, you will need to know the impact of age-related physiological changes on the empirical "Km," in that case, I imagine simple scaling on Km would not make any sense either. Jenny Chien, PhD research scientist Global PK/PD & TS Lilly Research Laboratories Lilly Corporate Center Indianapolis, IN 46285

From: Nick Holford - n.holford@auckland.ac.nz Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/20/2003 7:36 PM Jenny, Thanks for the additional reference which I had not seen before. This is an excellent source for experimental confirmation of allometric scaling, in particular an exponent of 0.75 for metabolic clearance. I was surprised, as were the authors, that an exponent closer to 0.67 was observed for renal clearance. This would be a good area for future allometric/physiological research to try to understand why this might be and why measures of renal functon (e.g. GFR) seem to scale with an exponent of 0.75. You bring up a good point about age and Km. I agree with you that any such relationship can only be considered empirical and does not have any theoretical backing like allometric scaling can provide. I mentioned age and Km as an example because it is one of the results from a very early population analysis of the pharmacokinetics of phenytoin by Ted Grasela et al. I am not sure of the reference. I think it was in JPB but cannot locate it via PubMed. I think of Km as an enzyme molecule property and would not expect this to change by simply increasing the number of molecules as body mass increases. Estimates of Km in vivo are more complex and hard to estimate. I expect they could be 'contaminated' by size if blood flow is an important determinant of clearance. Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: Jenny Yuehling Chien - CHIEN_JENNY_YUEHLING@lilly.com Subject: Re: [NMusers] Scaling of pharmacokinetics in peds Date: 12/23/2003 3:57 PM Nick, There are 2 papers on phenytoin, Ted can probably verify that: - steady-state pharmacokinetics of phenytoin from routinelycollected patient data. Clinical Pharmacokinetics. 8(4):355-64, 1983. - phenytoin pharmacokinetics: inappropriate data analysis. American Journal of Hospital Pharmacy. 39(1):41-3, 1982 You must be thinking of the first paper with an age effect on Km. jenny Jenny Chien, PhD research scientist Global PK/PD & TS Lilly Research Laboratories Lilly Corporate Center Indianapolis, IN 46285 _______________________________________________________