Continuous wavelet transform of aortic pressure oscillations in anesthetized dogs: effects of 45 degrees tilting

The time-frequency analysis of signals by means of continuous wavelet transform (CWT) was applied to blood pressure oscillations recorded from the aorta of anesthetized dogs. This method yielded two and three-dimensional representations of either the module or phase in function of time, in contrast with the fast Fourier transform (FFT) which gives the spectrum in the frequency domain. From the CWT of arterial pressure oscillations we obtained visual information on aortic valves closure, heart rate, respiratory rate and smooth muscle contractions in arterial and arteriolar walls (very low frequency component). The objective of this study was to analyze the frequency-time behavior in two and three-dimensional cardiovascular changes during 45 degrees head-up and head-down tilts, compared with zero degree supine position. In eight pentobarbitone anesthetized dogs, the postural changes were repeated for more than ten times in each one. Heart rate variability was derived by applying a new mathematical procedure. We utilized the pronounced changes of heart rate during each respiratory cycle (inspiratory tachycardia and expiratory bradycardia) to establish a correlation with the arterial pressure fluctuations during normal and tilting conditions. Significant differences in heart rate were observed between the 45 degrees head-up and head-down tilts, compared with the supine position. The results show that anesthetized dogs might constitute an appropriate model where to study orthostatic hypotension and microgravity blood shifts

Allometry of ECG waves in mammals

The present allometric study deals with the duration of three electrocardiographic intervals (PQ, QRS, QT) and their relationships with the corresponding cardiac cycle length (R-R interval) in mammals across a wide body mass range. The numerical values of the different ECG intervals were obtained from Grauwiler's (1965) monograph on the subject. Because the corresponding body masses were not given by this author, Heusner's (1991) data on basal metabolic rate as function of body mass were used to establish the most likely body mass figure for each case, based on the taxonomic identity between the corresponding specimens. On the other hand, in a recent study we established the "duality" of physiological times (Günther & Morgado, 1996) and, therefore, we adopted this novel approach to investigate the ECG intervals and their relationships with the R-R interval (heart rate reciprocal). Considering that the anatomy and physiology of auricles and ventricles are different (spheroids versus quasi-cylinders), and that excitation (sino-atrial node and His-Purkinje's system) and contraction processes can be described either by Euclidean or fractal geometries, only a quantitative analysis of the different ECG waves could resolve the dilemma. From the present preliminary study we can conclude that fractal geometry is prevalent with regard to ECG intervals

In memoriam Professor Jaime Talesnik, MD

In memoriam Jaime Talesnik. Born in Santiago, Chile, 18 May 1915; deceased Toronto, Canada, 7 April 1996. Medical studies at University of Chile, 1935-1940. MD, University of Chile, 1941. Assistant Professor of Physiology, Faculty of Biology and Medicine, University of Chile, 1940-45. Rockefeller Research Fellow, Banting-Best Institute, Department of Medical Research, University of Toronto, Canada, 1945-46. Associate Professor of Physiology, Faculty of Medicine, University of Chile, 1947-51. British Council Research Scholar in Pharmacology, National Institute for Medical Research, London, England, 1951-52. Associate Professor of Pathophysiology, Faculty of Medicine, University of Chile, 1952-63. Professor and Chairman, Department of Experimental Medicine, Faculty of Medicine, University of Chile, 1963-67. Visiting Professor, Department of Pharmacology, University of Toronto, Canada, 1967-69. Professor, Department of Pharmacology, University of Toronto, Canada, 1969-81. Professor Emeritus, University of Toronto, Canada, 1981. Member Emeritus, Medical Association of Chile, 1991. Honorary Member, Chilean Society of Physiological Sciences, 1995. Author of textbook of pathophysiology and many articles in scientific journals

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

Allometric algorithms

The aim of the present study is to emphasize the applicability and versatility of the allometric equation in the biological sciences. This equation (Y = a x Mb) was introduced by Huxley (1932) for intra- and interspecific comparisons of morphological, physiological and ecological variables (Y), when they are expressed as functions of body mass (M). The regression analysis of the experimental data, plotted in a double logarithmic scale, yields a straight line, which is equivalent to the logarithmic form of the above mentioned allometric equation [log Y = log(a) + (b) x log(M)]. Only the exponent (b) can be calculated a priori for a given function, based firstly on the corresponding dimensional analysis in accordance with the MLT-system of physics, and secondly on one of the theories of biological similarity, while parameter (a) is of empirical nature. A relevant feature of the allometric equations is that they can be treated algebraically to obtain allometric ratios, mass independent numbers (MIN), and even dimensionless numbers (M0L0T0), which are valid for all organisms pertaining to the same taxonomic classification

Alexander Lipschutz (1883-1980). A biographical synopsis

Alexander Lipschütz was born in Riga, Latvia, in 1883. He obtained his M.D. from the University of Göttingen, Germany, in 1901. He conducted research at the Universities of Zürich, Bonn, Göttingen, Bern and Vienna. He was full Professor of Physiology at the Universities of Dorpart (1919-1926), in Tartu, Estonia, and Concepción (1927-1936), in Chile. Later, he became the first Director of the Institute of Experimental Medicine, of the Chilean National Health Service. He authored 22 books and a large number of scietific papers, mostly on Endocrinology and Oncology. He directed 16 medical theses at the University of Concepcion and 81 at the University of Chile. He was awardet with the first Chilean National Prize in Science (1969). He died in Santiago, Chile, in 1980

Oxidative metabolism and body weight: inactive, active, and mitochondrial volumes

In homeotherms, the standardized (basal) metabolic rate should not be expressed per kilogram of body weight (specific metabolic rate), nor per unit of body surface (square meters of body-ambient interface), since both mitochondrial thermogenesis and heat-loss mechanisms (radiation, conduction, convection, evaporation) are not uniform processes. On the contrary, each organism is an heterogeneous bioreactor, which is composed at least of two compartments: 1) a metabolically active volume (aV), where oxidative phosphorylation takes place; and 2) a metabolically inactive volume (iV), where oxygen consumption is negligible. The ratio (aV/iV) is not invariant, since iV increases disproportionately with the scaling up of body size, and as shown by us, when the three main components of iV, i.e., skeleton, fat deposits, and blood volume, are added together, a similar disproportionality is found. The aV was determined by subtracting the iV from the total volume (V) of an organism, or by estimating the volume occupied by all mitochondria, or mitochondrial volume (mtV). For this purpose two procedures are discussed: 1) the stereological or morphometric method; and 2) the oxygen consumption per unit time or physiometric method. The latter procedure is based on the equivalence between an VO2 = 3 ml O2.min-1 and a mtV of 1 ml, whose oxidative phosphorylation yields an approximate power output of 1 watt. The correspondence between oxygen consumption, heat production, and electron flux at the respiratory chain of the mitochondrial cristae, is discussed. From a physical point of view, the metabolic rate is a ®power® function (P = M L2T-3), where M = mass, L = length, and T = time. The dimensional analysis and the statistical treatment of the corresponding numerical values of more than 200 allometric equations yields the 3/4 power, law established by Kleiber (1961), for the relationship between basal metabolism and body weight. Instead of expressing the metabolic rate per unit body weight (kg-1) or per unit body surface (m-2) structural and functional criteria should be taken into account as, for instance, the distinction between iV and aV, and particularly by emphasizing the paramount importance of the mtV where oxidative phosphorylation takes place. An allometric equation relating mtV and body weight (W) could be tentatively established for interspecies comparisons

Wavelet analysis of arterial pressure and blood velocity pulsations in the aorta of anesthetized dogs

The arterial pressure and blood velocity pulsations were recorded from the aorta of anesthetized dogs by means of micro-tip pressure and velocity transducers. Wavelet transforms (Wt) were obtained by converting the analog signals into digital samples at the rate of 42.7 per second, which were subsequently subjected to an algorithm of WT. An iterative rarefaction (2(0) to 2(-4) resolutions) of the number of samples was followed by a substraction of the high frequency components (wavelet coefficients) from the corresponding resolutions. Analyses of the arterial pulsations revealed that the second WT always yielded four types of systolic apexes, which were apparently devoid of physiological meaning, since they were inherent to the ®triangulation phase® of the WT algorithm. In addition, the third WT occasionally revealed slow amplitude modulations, which could not be identified in the original recordings and whose significance deserves further investigation. This is also valid for the wavelet coefficients, whose biological meaning is still obscure. In summary, the WT operates as a low pass filter, which brings to light the lower frequency components of arterial pulsations and which finally yields the mean values of both arterial pressure and blood velocities

Biological similarity theories: a comparison with the empirical allometric equations

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