Understanding allometry

On 21-May-16 00:42, Steven L Shafer <sshafer_at_stanford.edu> wrote: > Nick: > > You say below: > > "Theory based allometry predicts an exponent of 3/4 for many functional processes e.g. basal metabolism, cardiac output, lung volume flow (West et al 1997). It is not restricted to metabolism." > > The article you cite by West is an excellent treatise on the subject of scaling across species. There are numerous other papers that provide theoretical foundations for allometric scaling across species (e.g., Darveau, Nature, 2002; West, J Exp Biol. 2005). The allometric theory accounts for differences in rate-related functions across species that span many orders of magnitude in body mass. I am not aware of any theory that supports scaling by weight to the 3/4 power WITHIN A SPECIES. NH: Unfortunately, you repeat a common misunderstanding of allometric theory that it is somehow only applicable across species. Allometric theory as originally proposed by West is based only on body mass (West, Brown et al. 1997). Allometric theory does not require consideration of species or any other covariate. This is the first commandment of allometry (Holford 2008). If you read the work by West et al. you will find that there is nothing in the theory that prevents its use for within species scaling using mass. Therefore the theory of West supports the use of the 3/4 exponent within species. SS: > Similarly, I am unaware of unambiguous data strongly supporting allometric scaling across the typical range of human weights. NH: I recommend that you read the paper by McCune et al. that formally tests the allometric theory prediction of an exponent of 3/4 for clearance based on a large study of busulfan across the human size range (McCune, Bemer et al. 2014). The theory was tested explicitly and no evidence found to reject the value of 3/4. Work with a drug where your expertise is renowned ( https://www.youtube.com/watch?v=gD7BZIl2uzc) has clearly demonstrated the benefit of allometric theory across humans from infants to adults. Eleveld showed the fit was improved using theory based allometric scaling (Eleveld, Proost et al. 2014)Schuttler also demonstrated an improved fit with an estimated exponent for clearance 0.75 which is consistent with the theoretical value of 3/4 (Schuttler and Ihmsen 2000). In the spirit of modern scientific philosophy are you aware of unambiguous data (and analysis) that falsifies the theory of allometry ( https://en.wikipedia.org/wiki/Karl_Popper)? SS: > > As applied to human pharmacokinetics, I do not believe any theory supports allometric scaling. NH: As noted above there is nothing in the theory of allometry proposed by West that would mean it is not applicable to humans. If you do not want to believe this theory then that is your personal choice, as it would be for any religious belief, and I will not attempt to change your religion. SS: > You can see this if you consider the ends of the spectrum. Small size is associated with children. They are not a separate species, but are humans undergoing metabolic maturation. NH: I have personally been a strong advocate on considering all humans, regardless of age, as being a single species and have sought integrated explanations of human clinical pharmacology. If you were aware of the paediatric pharmacokinetic literature then you would know of many publications supporting the use of a combination of theory based allometry for size plus empirical maturation models for age (see this review (Holford, Heo et al. 2013)). SS: > I am not aware of any allometric theory that accounts for metabolic maturation with age. NH: From the first commandment it necessarily follows that changes associated with age are not predictable from the allometric theory of West et al. There is no age related theory to predict quantitative changes. However, plausible biological understanding of maturation means that clearance will be zero (or at least very small) at conception and will approach a maximum when it will be indistinguishable from the mature adult value. So at least at the extremes there is a biological and quantitative prediction of maturation. Joining these extremes requires an empirical approach. A monotonic sigmoid emax function has been suggested (Tod, Jullien et al. 2008)and widely applied (Holford, Heo et al. 2013). A more complex function may be needed but this will need to be driven first by data not by theory. SS: > Similarly, very large size is associated with morbid obesity. I am not aware of any allometric theory that suggests that clearance in morbid obesity is best estimated using allometric principles. Between these extremes, scaling by weight is not very different than scaling by weight to the three quarters power. NH: Body composition contributes to body mass. Theory based allometry does not specify how differences in body composition affect allometric size. It is plausible however to propose that the size that is the driving force behind allometric theory may not be determined simply by total body weight. Application of theory based allometry in conjunction with fat free mass can be used to determine a normal fat mass (NFM) (Anderson and Holford 2009). The NFM concept has been used to account for body composition differences determining allometric size. NFM is not predicted from allometric theory but is a biologically plausible extension of the theory of allometric size based on mass. NFM has been used to show that total body mass rather than fat free mass provides a better description of propofol pharmacokinetics in the obese (Cortinez, Anderson et al. 2010). It has also be used to show that fat free mass is a better predictor of dexmedetomidine but obesity is associated with reduced clearance independently of allometric size based on fat free mass (Cortinez, Anderson et al. 2015). This demonstrates how the complexities of biology can be better understood based on a plausible theory of allometry. The theory may not be perfect but it is compatible with a very large number of observation studies in many domains. Investigation of other phenomena such as maturation and obesity is aided by building on allometric theory. SS: > > Of course, I will defer to data. Can you point me to human PK examples where allometric scaling of weight to the three quarters power reliably provides substantially better fits to the data than scaling by weight alone? NH: In addition to the large study of busulfan PK mentioned previously (McCune, Bemer et al. 2014)I suggest you look at the prediction of morphine clearance across the human size and age range using theory based allometry with maturation. Prediction of clearance in a large external data set was clearly better than other approaches including empirical allometry (Holford, Ma et al. 2012). Other published examples can be found in this review (Holford, Heo et al. 2013). SS: > I can point to many examples where it makes no difference. I can also point to many examples where investigators simply use allometric scaling without first seeing if allometric scaling was supported by the data. NH: This is often the case when sample sizes are small, weight distribution is narrow and power is small (Anderson and Holford 2008). A pragmatic approach given the challenges of falsifying allometric theory with small data sets is to assume it is useful. It is certainly better than using empirical allometry or ignoring size altogether. SS: > However, I know of only one or two examples where models were estimated with and without allometric scaling, and the allometric scaling worked better than the simpler non-scaled model. If allometric scaling for human pharmacokinetics was “true” on first principles, as your comments imply, then the literature should abound with unequivocal examples. NH: If you know of examples of suitably powered studies which can also show they have accounted for other mass correlated factors that would confound the estimation of a true allometric exponent then I would be glad to know the details. If you read the literature carefully and exclude those that are underpowered to truly detect the difference between an exponent of 3/4 and say an exponent of 1 or an exponent of 2/3 and have accounted for all other factors, such as maturation, that are necessarily correlated with mass then you will not find many examples. I am not aware of any that are inconsistent with allometric theory. SS: > > Thanks, > > Steve > -- > Steven L. Shafer, MD > Professor of Anesthesiology, Perioperative and Pain Medicine, Stanford University > Adjunct Associate Professor of Bioengineering and Therapeutic Sciences, UCSF > > ######################################################################## > > PharmPK Home Page https://www.pharmpk.com/ > Information about PK/PD Jobs can be found at https://www.pharmpk.com/pkjob.html > More information about my eBooks, including Basic Pharmacokinetics and Pharmacy Math, and now iOS and tvOS apps can be found at https://www.pharmpk.com/MyeBooks.html > Thank you, David Bourne, PharmPK Moderator > > To unsubscribe from the PHARMPK list, click the following link: > http://lists.ucdenver.edu/scripts/wa.exe?SUBED1=PHARMPK&A=1 Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of size and maturity in pharmacokinetics." _Annu Rev Pharmacol Toxicol_ *48*: 303-332. Anderson, B. J. and N. H. G. Holford (2009). "Mechanistic basis of using body size and maturation to predict clearance in humans." _Drug Metab Pharmacokinet_ *24*(1): 25-36. Cortinez, L. I., B. J. Anderson, N. H. Holford, V. Puga, N. de la Fuente, H. Auad, S. Solari, F. A. Allende and M. Ibacache (2015). "Dexmedetomidine pharmacokinetics in the obese." _Eur J Clin Pharmacol_ *doi:10.1007/s00228-015-1948-2*. Cortinez, L. I., B. J. Anderson, A. Penna, L. Olivares, H. R. Munoz, N. H. Holford, M. M. Struys and P. Sepulveda (2010). "Influence of obesity on propofol pharmacokinetics: derivation of a pharmacokinetic model." _Br J Anaesth_ *105*(4): 448-456. Eleveld, D. J., J. H. Proost, L. I. Cortinez, A. R. Absalom and M. M. Struys (2014). "A general purpose pharmacokinetic model for propofol." _Anesthesia and analgesia_ *118*(6): 1221-1237. Holford, N. (2008). "Re: [NMusers] Scaling for pediatric study planning." http://www.cognigencorp.com/nonmem/current/2008-September/0182.html. Holford, N., Y. A. Heo and B. Anderson (2013). "A pharmacokinetic standard for babies and adults." _J Pharm Sci_ *102*(9): 2941-2952. Holford, N. H., S. C. Ma and B. J. Anderson (2012). "Prediction of morphine dose in humans." _Paediatr Anaesth_ *22*(3): 209-222. McCune, J. S., M. J. Bemer, J. S. Barrett, K. Scott Baker, A. S. Gamis and N. H. G. Holford (2014). "Busulfan in Infant to Adult Hematopoietic Cell Transplant Recipients: A Population Pharmacokinetic Model for Initial and Bayesian Dose Personalization." _Clinical Cancer Research_ *20*(3): 754-763. Schuttler, J. and H. Ihmsen (2000). "Population pharmacokinetics of propofol: a multicenter study." _Anesthesiology_ *92*(3): 727-738. Tod, M., V. Jullien and G. Pons (2008). "Facilitation of drug evaluation in children by population methods and modelling." _Clin Pharmacokinet_ *47*(4): 231-243. West, G. B., J. H. Brown and B. J. Enquist (1997). "A general model for the origin of allometric scaling laws in biology." _Science_ *276*: 122-126. -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand office:+64(9)923-6730 mobile:NZ+64(21)46 23 53 FR+33(6)62 32 46 72 email:n.holford_at_auckland.ac.nz http://holford.fmhs.auckland.ac.nz/ "Declarative languages are a form of dementia -- they have no memory of events" Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34. Holford N. Clinical pharmacology = disease progression + drug action. Br J Clin Pharmacol. 2015;79(1):18-27.