Jafferson K L da Silva et al 2007 J. Phys. A: Math. Theor. 40 F953 doi:10.1088/1751-8113/40/44/F01
Jafferson K L da Silva, Lauro A Barbosa1 and Paulo Roberto Silva
Show affiliationsA general simple theory for the interspecific allometric scaling is developed in the d + 1-dimensional space (d biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the metabolic states in such a way that the mass and energy d + 1-densities are size-invariant quantities (independent of body mass). The different metabolic states (basal and maximum) are described by considering that the biological lengths and the physiological time are related by different transport processes of energy and mass. In the basal metabolism, transportation occurs by ballistic and diffusion processes. In d = 3, the 3/4 law occurs if the ballistic movement is the dominant process, while the 2/3 law appears when both transport processes are equivalent. Accelerated movement during the biological time is related to the maximum aerobic sustained metabolism, which is characterized by the scaling exponent 2d/(2d + 1) (6/7 in d = 3). The results are in good agreement with empirical data and a verifiable empirical prediction about the aorta blood velocity in maximum metabolic rate conditions is made.
87.10.-e General theory and mathematical aspects
87.19.R- Mechanical and electrical properties of tissues and organs
92C35 Physiological flow (See also 76Z05)
Issue 44 (2 November 2007)
Received 7 September 2007
Published 16 October 2007
Jafferson K L da Silva et al 2007 J. Phys. A: Math. Theor. 40 F953
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