  The quarter power allometric scaling of mammalian metabolic rate is largely
regarded as a universal law of biology. However, it is well known that cell
cultures do not obey this law. The current thinking is that were in-vitro
cultures to obey quarter power scaling, they would have more predictive power
and could for instance provide a viable substitute for animals in research.
About two decades ago, West and coworkers established a model which predicts
that metabolic rate follows a quarter power relationship with the mass of an
organism, based on the premise that tissues are supplied nutrients through a
fractal distribution network. This paper outlines a theoretical and
computational framework for establishing quarter power scaling in-vitro,
starting where fractal distribution ends. Allometric scaling in non-vascular
spherical tissue constructs was assessed using models of Michaelis Menten
oxygen consumption and diffusion. The results demonstrate that physiological
scaling is maintained when about 5 to 60% of the construct is exposed to oxygen
concentrations less than the Michaelis Menten constant. In these conditions the
Thiele modulus is between 8 and 80, with a significant concentration gradient
in the sphere. The results have important implications for the design of
downscaled in-vitro systems with physiological relevance.
