Dimensional analysis and theory of biological similarity

From this review we conclude the following: 1) The body weight of an organism is an adequate reference index for the correlation of morphological and physiological characteristics. In comparative physiology, body weight can be recommended as a unifying frame of reference, particularly if the ponderal scale includes several decades, in order to apply logarithmic scales for the variables involved. (See article). 2) The statistical analysis of the experimental data can be represented conveniently by means of the logarithmic equivalent of Huxley's allometric equation (y = a-Wb), which is the most simple and at the same time the most versatile mathematical expression for intra- or interspecies comparisons. The exponents (b) for the allometric equations can be predicted for all biological variables definable in terms of the MLT system of physics (M = mass, L = length, T = time) or of a four-dimensional system MLTt where t = temperature. 3) By means of dimensional analysis and the theory of biological similarity a range of similarity criteria can be established: a) mechanical or dynamic similarity, b) kinematic or biological similarity; and c) hydrodynamic or transport similarity. Most functions obey the so-called biological (kinematic) similarity, particularly when the concept of operational time is introduced into Lambert-Teissier's original theory. 4) A satisfactory correlation (r = 0.99) for 80 empirical allometric exponents (b) describing morphological and physiological characteristics of living beings was found. These results are discussed in relation to Rosen's optimality principles in biology. 5) Organisms should be considered as mixed regimes. This means that no single similarity criterion can predict the allometric exponent (b) of all functions that dimensionally belong to MLT or MLTt systems, despite the fact that in the great majority of cases kinematic similarity will satisfactorily predict the reduced exponent (b). Nevertheless, in some instances mechanical (dynamic) similarity must be applied, and in other circumstances hydrodynamic (transport) similarity. 6) Cellular or molecular levels are not in the domain of the present theory, since neither cell dimensions nor molecular processes (viz., blood viscosity, diffusion capacity) can be predicted by biological similarity criteria.