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Despite the fact that the concept of sheet-flow in the pulmonary microcirculation of mammals was introduced more than three decades ago, the capillary circulatory model still prevails in the physiological literature. Since cardiac output is identical in the systemic and in pulmonary circulations, it is noteworthy that in the former, the resulting arterial pressure is five times higher than that of the latter, which means that the corresponding microcirculations must be radically different. The present study addresses this problem from both morphological and physiological perspectives.

A wide spectrum of cyclic functions in terrestrial mammals of different size, from the 3-gram shrew to the 3-ton elephant, yields an allometric exponent around 0.25, which is correlated--as a kind of common denominator--with the specific metabolic rate. Furthermore, the applicability of these empirical findings could be extrapolated to chronological events in the sub-cellular realm. On the other hand, the succession of growth periods (T98%) until sexual maturity is reached also follows the 1/4 power rule. By means of Verhulst's logistic equation, it has been possible to simulate three different biological conditions, which means that by modifying the numerical value of only one parameter, revertible physiological and pathological states can be obtained, as for instance isostasis, homeostasis and heterostasis.

In contrast with classical physics, particularly with Sir Isaac Newton, where time is a continuous function, generally valid, eternally and evenly flowing as an absolute time dimension, in the biological sciences, time is in essence of cyclical nature (physiological periodicities), where future passes to past through an infinitely thin boundary, the present. In addition, the duration of the present (DP) leads to the so-called 'granulation of time' in living beings, so that by the fusion of two successive pictures of the world, which are not entirely similar, they attain the perception of 'movement,' both in the real world as well as in the sham-movement in the mass media (TV).

The applicability of dimensional analysis (DA) is discussed in relation to the metabolic scaling laws. The evolution of different theories of biological similarity has shown that the calculated reduced exponents (b) of Huxley's allometric equation are closely correlated with the numerical values obtained from the statistical analysis of empirical data. Body mass and body weight are not equivalent as biological reference systems, since in accordance to Newton's second law, the former has a dimension of a mass, while the latter should be dimensionally considered as a force (W = MLT-2). This distinction affects the coefficients of the mass exponent (alpha). This difference is of paramount importance in microgravity conditions (spaceflight) and of buoyancy during the fetal life in mammals. Furthermore, the coefficients (beta) of the length dimension, and (gamma) of the time dimension do not vary when mass or weight are utilized as reference systems. Consequently, the "specific metabolic time," that results from the ratio of basal oxygen consumption and body mass or body weight yields the "biological meaning" of the time dimension, which is of fractal nature.

From four empirical allometric equations concerning the dynamics of the respiratory functions of mammals, it has been possible to obtain an invariant and dimensionless number after applying Buckingham's pi-theorem. In the present study, this invariant number (IN(R)), whose origin was interspecies comparisons in mammals of different sizes, was assayed with the aim to compare in a quantitative manner the possible difference between newborn and adult mammals. The results were compared with the predicted values from two theories of biological similarity, one mass-dependent, valid for newborns, and the other, weight-dependent, valid for adult mammals. Finally, we utilized Stahl's residual mass exponents (RME) to test the validity of the empirical and theoretical approaches.

Twelve biological variables were submitted to dimensional analysis in accordance with the MLT-system of physics (M, mass; L, length; T, time). Each of these variables has a characteristic numerical value for the exponents alpha for mass, beta for length, and gamma for time. By means of Newton's reduction coefficient (chi), the three dimensions (MLT) can be expressed as power functions of body mass (Mb); the exponent (b) is the result of the combination of the three dimensional exponents (alpha, beta, gamma). By linear regression analysis of 203 allometric exponents (betaE) obtained from the literature, the following equation was found for the regression exponent (bR) (equation: see text). The estimated numerical coefficients (ki) for the three exponents (alpha, beta, gamma) of the basic dimensions (MLT) do not agree with those of the prevailing theories of biological similarity.

The aim of the present study was to submit Huxley's allometric equation (Y = aMb) to a dimensional analysis; in this equation Y is any biological variable, a is the mass-coefficient, M represents body mass, and b the mass-exponent. The dimensions of each of its components is thoroughly analyzed by means of the MLT-system of physics, as is the dimensionality of the whole equation. The relationship between the dimensional analysis and the postulates of some theories of biological similarity is discussed. In conclusion, parameter a of the allometric equation is always dimensionless, while the physical dimensions of the dependent variable Y can be defined by means of the power function Mb.

Scale dependent variables in animals of different sizes can be studied by means of dimensional analysis and biological similarity criteria. The aim of this report is to demonstrate a transport similarity at the cellular level, based on two postulates derived from Fick's law of diffusion; the constancy of the "concentration gradient" between two compartments separated by a membrane; and the invariance of the "diffusion coefficient" of a given substance in homologous cells. A general equation for a transport similarity was deduced from these two postulates and it was then possible to calculate the corresponding "reduced exponents" as functions of body weight, which, in turn, can be compared with the empirical allometric exponents of Huxley's power equation. The biological meaning of the theoretically predicted reduced exponents of the transport similarity are discussed and the predicted values are compared with the experimental findings.

The dimensional analysis of physics, based on the MLT-system (M = mass, L = length, T = time), can be applied to the living world, from mycoplasmas (10(-13) g) to the blue whales (10(8) g). Body mass (M), or body weight (W), are utilized as convenient reference systems, since they represent the integrated masses of all elementary particles--at the atomic level--which conform an organism. A triad of biological similarities (mechanical, biological, transport) have been previously described. Each similarity was based on two postulates, of which the first was common to all three, i.e., the constancy of body density; whereas the second postulates were specific for each of the three theories. In this study a physical foundation for these second postulates, based on three universal constants of nature, is presented, these are: 1) the acceleration of gravity (g = LT-2); 2) the velocity of light (c = LT-1); and 3) the mass-specific quantum (h/m = L2T-1). The realm of each of these biological similarities is the following: 1) the gravitational or mechanical similarity (where g = constant), deals mainly with the relationship between a whole organism and its environment, particularly with locomotion. The acceleration of gravity (g) is also one of the determining factors of the "potential" energy (E = m.g.H), where m is the mass, and H is the height above the reference level; 2) the electrodynamic similarity (formerly biological similarity), (c = constant), is able to quantitatively define the internal organization of an organism from both a morphological and a physiological point of view.(ABSTRACT TRUNCATED AT 250 WORDS)