Duality in physiological time: Euclidean and fractal

The aim of the present study was to differentiate two modalities of intrinsic time scales: i- the geometric or Euclidean modality, which is based on the constant speed of mass transport or of wave transmission in cylindrical structures (arteries, veins, nerves), whose allometric exponent (TE = aMb) is b = 0.33, where M is body mass (kg) and a the mass coefficient; ii- the fractal time scale (TF), which is characteristic of organs with self-similar branching structures and with volume-specific flows, whose allometric exponent is b = 0.25. The proposed dichotomy could be confirmed by means of the statistical analysis of empirical allometric exponents (b). Our findings demonstrate the need to separate the chronology of bulk transport at long distances (inter-organic) which follows an Euclidean geometry (cylinders), from the fractal time scale, which operates at short distances (intra-organic) and is represented by a self-similar branching system which determines both the morphometric and physiometric characteristics within each organ.