From: Nick Holford <>

Subject: Pharmacokinetics, allometry and flat earth theories
Date: Thu, 04 Oct 2001 14:33:02 +1200


Thank you for supplying references for this BSA formula (and to Paul Hutson who also sent the Mosteller reference).

Mosteller (1987) describes the formula originally proposed by Gehan & George (1970). He points out (Mosteller 1988) that it is one of a family of formulae for BSA:

BSA = k x Ht**a x Wt**b

with the allometric constraint:
a + 3b = 2

This family includes the original du Bois and du Bois formula:

BSA = k x Ht**0.725 x Wt**0.425

Gehan & George's formula:

BSA = k x Ht**0.5 x Wt**0.5

and the simple allometric formula which only requires weight:

BSA = k x Ht**0 x Wt**(2/3)

But what relevance do these formulae have for pharmacokinetics? Is their any scientifically valid reason to believe that surface area is a rational covariate for predicting individual differences in pharmacokinetic parameters? I would answer that there is not. I know of no drug whose elimination (clearance) is predominantly via the skin nor a drug whose distribution (volume) is determined by skin. An old idea was that heat loss is proportional to BSA and thus metabolic rate would be proportional to BSA and therefore one might expect drug metabolism and thus clearance to be proportional to BSA. However, allometric theory and experiment have discredited the surface area theory for metabolic rate (See Peters (1983)).

The best theoretical allometric model (West et al. 1997,1999) for functional properties such as metabolic rate, glomerular filtration rate and clearance is:

CL= CLstd x (Wt/Wtstd)**(3/4)

and for structural properties, blood volume and drug volume of distribution it is:

V = Vstd x (Wt/Wtstd)**1

These models have been shown to be superior to surface area formulae and to be applicable to drugs across the human size range (Holford 1996, Anderson et al. 1997). An interesting discussion of allometric basic ideas and controversies can be found here

Allometric scaling for metabolic rate using the 3/4 power formula has been empirically validated across 15 orders of magnitude (unicellular organisms to elephants, Peters (1983)). I know of no other biological phenomenon that has been tested over such a range. Anyone who does not consider these models to account for differences in body size is ignorant of science and biology. Deliberately applying BSA to clearance and volume of distribution in the face of these facts is comparable to believing the earth is flat.

It should be noted that body weight in these formulae assumes 'normal' body composition. Further adjustments for the prediction of body size differences clearance and volume in obese or very skinny people will usually require the use of other covariate information e.g. height, skin thickness, to predict the weight with 'normal' body composition. Additional adjustments may be required to account for developmental changes in very young children (Anderson et al. 2000).

Anderson BJ, McKee D, Holford NHG. Size, myths and the clinical pharmacokinetics of analgesia in paediatric patients. Clinical Pharmacokinetics 1997;33:313-327

Anderson BJ, Woolard G, Holford NHG. A model for size and age changes in the pharmacokinetics of paracetamol in neonates, infants and children. Br J Clin Pharmacol. 2000; 50:125-134

Holford NHG. A size standard for pharmacokinetics. Clinical Pharmacokinetics 1996;30:329-332

Gehan EA, George SL. Estimation of human body surface area from height and weight. Cancer Chemother Rep 1970;54:225-35.

Mosteller RD. More on simplified calculation of body-surface area. New England Journal of Medicine 1988;318:1130

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

Kazimierz wrote:
> Dear Professor Holford,
> I have used this formula for modelling Vd of Ganciclovir in
> newborns and infants
> (Kozlowski KH et al. PAGE2001) and have >10years
> experiences.
> BSA(m2)=(HT(cm)*WGT(kg))**0.5/60
> it uses geometric mean of HT and WGT
> Alternative option for inches also exists.
> References:
> Mosteller RD.N.Engl.J.Med. 317(17), 1098, 1987 - original
> Lam TK et. al.: -//- 318(17), 1130, 1988
> Clin Pharmacol. Ther. 69, 145-57, 2001 - application for PK
> Sincerely Kazimierz H. Kozlowski, Warsaw, Poland

Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand tel:+64(9)373-7599x6730 fax:373-7556


From: Paul Hutson <>
Subject: Re: Pharmacokinetics, allometry and flat earth theories
Date: Thu, 04 Oct 2001 09:55:57 -0500

At 02:33 PM 10/4/2001 +1200, Nick Holford wrote:
> Deliberately applying BSA to clearance and volume of distribution in the
> face of these facts is comparable to believing the earth is flat.

I agree with Nick (nice review), and our fits of chemotherapy PK data do
not support the use of BSA over other scaling (including the topotecan
data for which I inquired earlier this week). Ratain and others have
argued before against the willy-nilly use of BSA for scaling cytotoxic
treatment doses, but it has become almost a sacred cow in oncology. Part
of the reason is likely that clinicians are not familiar with using a
factor of ^0.75 in calculations: they are dosing using BSA slide rules,
nomograms, or four function calculators.

Since it is in oncology and pediatrics where this scaling is seen most
often, it is my opinion that the following should be addressed in reports
of investigative PK for new drugs:
1. Does a scaling factor of wt, wt^0.75, or BSA significantly improve fit?

2. Is the improvement in minimization function significant wrt interpatient
variability. That is, is there a significant improvement in the ability to
predict clearance (and resulting AUC) based upon increasingly complex
factors (eg, wt vs "ideal" or "lean" wt vs wt^0.75 vs BSA) compared to the
remaining variability (ETAs, if you will).

3. If indeed the wt^0.75 or wt^x scaling is the most general in our fits,
we need to report it as such, and not yield to manuscript reviewer's
arguments that it is awkward.

We may not be able to change the FDA-approved labeling of extant drugs
dosed by BSA, but we can promote the accurate representation of new products.

Paul Hutson, Pharm.D.
Associate Professor (CHS)
UW School of Pharmacy
NOTE NEW ADDRESS effective 6/2001
777 Highland Avenue
Madison, WI 53705-2222
Tel: (608) 263-2496
FAX: (608) 265-5421
Pager: (608) 265-7000, #7856


From: "Piotrovskij, Vladimir [JanBe]" <>
Subject: RE: Pharmacokinetics, allometry and flat earth theories
Date: Mon, 15 Oct 2001 10:15:08 +0200

I totally agree with Nick and Paul that using BSA for dose scaling has no
scientific rationale. Though I am not sure using a factor of WT^0.75 in dose
calculation is really necessary in adult population, BSA scaling should be
certainly avoided as it may result in wrong individual dose prescription.

Best regards,

Vladimir Piotrovsky, Ph.D.
Research Fellow
Advanced Modelling and Simulations
Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463)
Janssen Research Foundation
B-2340 Beerse