West and Brown has done some work on this which seemed pretty solid to me when I read it a few months ago. The basic idea is that biological systems are designed in a fractal way which messes up the dimensional analysis.

From the abstract of http://jeb.biologists.org/cgi/content/abstract/208/9/1575:

We have proposed a set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which we assume have invariant terminal units, are space-filling and are optimised by the process of natural selection. We show how these general constraints explain quarter power scaling and lead to a quantitative, predictive theory that captures many of the essential features of diverse biological systems. Examples considered include animal circulatory systems, plant vascular systems, growth, mitochondrial densities, and the concept of a universal molecular clock. Temperature considerations, dimensionality and the role of invariants are discussed. Criticisms and controversies associated with this approach are also addressed.

A Science article of theirs containing similar ideas: http://www.sciencemag.org/cgi/content/abstract/sci;284/5420/1677

Edit: A recent Nature article showing that there is systematic deviations from the power law, somewhat explainable with a modified version of the model of West and Brown:

http://www.nature.com/nature/journal/v464/n7289/abs/nature08920.html

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