West, G. B. / Brown, J. H. / Enquist, B. J. A General Model for the Origin of Allometric Scaling Laws in Biology 1997 Science , Vol. 276 p. 122-126 presents a general model of allometric scaling.

Radius r is linear, and has a scale factor beta in their derivation. The number of tubes per level, proportional to a level’s volume, has scale factor n. Since beta multiplies one dimensional r and n multiplies three dimensional volume, in effect, beta should equal n^(-1/3).

But notes WBE, in the middle column of p. 124, that beta = N^(-1/3) gives the wrong answer. They resolve this N^(-1/3) problem by showing that in pulsatile flow N^(-1 /2) instead.

Chaui-Berlinck, José Guilherme A critical understanding of the fractal model of metabolic scaling 2006-08 Journal of Experimental Biology , Vol. 209, No. 16 p. 3045-3054 doubts that pulsatile flow succeeds. Savage, Van M. / Enquist, Brian J. / West, Geoffrey B. Comment on `A critical understanding of the fractal model of metabolic scaling' 2007-11 Journal of Experimental Biology , Vol. 210, No. 21 p. 3873-3874 in turn doubts Chaui-Berlinck’s 2006 critical doubts.

WBE 1997 supports their use of pulsatile flow in a long footnote which seems to be critically important for the success of the pulsatile flow argument, footnote 20, in their article. Which leads to the question: How do the calculations and references in footnote 20 explain the role of pulsatile flow in the WBE derivation? And are the arguments in footnote 20 successful?