Wavelet and Fourier analysis of ventricular and main arteries pulsations in anesthetized dogs

The purpose of this study was to characterize time-frequency behavior using the Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) to analyze ventricular and arterial pressure signals from anesthetized mongrel dogs. Both ventricular and arterial pressure pulsations were recorded using catheter-tip manometers and the CWT was applied to these signals to obtain module coefficients, associated contours, and the 3-D representation of these modules. FFT was applied to obtain the Fourier spectrum. The mathematical analysis of the cardiovascular pressure pulsations permitted the identification of the evolution of the frequency components for the aortic and pulmonary valve functions as well as the intra-ventricular and respiratory influences on the cardiovascular dynamics. The CWT is a very sensitive and reliable procedure for determining the three-dimensional (time-frequency-amplitude) of the oscillatory phenomena during each cardiac cycle, providing more, although complementary, information than the spectral analysis obtained with the FFT. Thanks to the FFT, exact values in Hz could be found for the different events produced in each cycle, and thus the information provided by CWT could be related to the information provided by FFT. The combination of both mathematical methodologies permitted identification of each component of the analyzed signals. The 3D representation allowed an easy comparison of the relative importance of the complex magnitudes in frequency for the different components of the pulsatile waves.

Homeostasis and Heterostasis: from invariant to dimensionless numbers

In the present paper we have examined the applicability of dimensionless and invariant numbers (DN & IN) to the analysis of the cardiovascular system of mammals, whose functions were measured at standard metabolic conditions. The calculated IN did not change when we compared these figures with those obtained in dogs while they were submitted to graded exercise on a treadmill. In both instances, rest and exercise, the constancy of the IN prevailed, in accordance with Cannon's principle of "homeostasis" (1929). On the contrary, when dogs were examined during a standardized hypovolemic shock, we observed a breakdown of the IN, and the resulting DN evolved as a reliable index of the condition of "heterostasis" as defined by H. Selye. The robustness of the homeostatic regulations is based on high-gain integral feedback mechanisms, while "heterostasis" could be associated with low-gain integral feedback processes, when organisms are submitted to unitary step disturbances or to changes of the set-point at the entrance of the feedback loop

Pressure oscillations in anesthetized dogs and its conversion into quasi-periodic orbits

Using a basic representation of dynamic systems, arterial blood pressure pulsations is converted into quasi-perioic orbits with the purpose of transforming a periodic phenomena into a cyclical on by plotting the pressure p(t) versus its first derivative dp/dt. This elementary mathematical procedure made it possible to evaluate the variability of the systemic arterial pressure pulsations, both systolic and diastolic, as well as the slope variability, can be distinguished in the carachrotic phase. One corresponds to the open aortic valves, and the other is associated with the closed valves. Furthermore, through the first derivative of pressure oscillations we were able to identify small changes in arterial pressure, which appeared when the sampling rate at least 150 samples per second. Since the time variable was converted into a parameter, the result was a synoptic or holistic approach, which is a considerable improvement for the visual analysis of cardiovascular phenomena. This simplified mathematical procedure can be easily implemented on a personal computer in real time and applied to all rhythmic phenomena in Physiology and Pathology.