Engineering analysis of biological variables: An example of blood pressure over 1 day

Abstract

Almost all variables in biology are nonstationarily stochastic. For these variables, the conventional tools leave us a feeling that some valuable information is thrown away and that a complex phenomenon is presented imprecisely. Here, we apply recent advances initially made in the study of ocean waves to study the blood pressure waves in the lung. We note first that, in a long wave train, the handling of the local mean is of predominant importance. It is shown that a signal can be described by a sum of a series of intrinsic mode functions, each of which has zero local mean at all times. The process of deriving this series is called the ''empirical mode decomposition method.'' Conventionally, Fourier analysis represents the data by sine and cosine functions, but no instantaneous frequency can be defined. In the new way, the data are represented by intrinsic mode functions, to which Hilbert transform can be used. Titchmarsh [Titchmarsh, E. C. (1948) Introduction to the Theory of Fourier Integrals (Oxford Univ. Press, Oxford)] has shown that a signal and i times its Hilbert transform together define a complex variable. From that complex variable, the instantaneous frequency, instantaneous amplitude, Hilbert spectrum, and marginal Hilbert spectrum have been defined. In addition, the Gumbel extremevalue statistics are applied. We present all of these features of the blood pressure records here for the reader to see how they look. In the future, we have to learn how these features change with disease or interventions.We recorded the blood pressure in the pulmonary arterial trunk (between the pulmonic valve and the bifurcation point of the right and left pulmonary arteries). The recording was done continuously with an implanted catheter as a part of a research plan to study the remodeling of the three layers of vascular tissues of the arterial wall in response to changes of stresses in the tissues (1-6). Pulmonary arteries were chosen as an object of tissue engineering research because blood pressure in pulmonary arteries can be changed quickly and noninvasively by changing the oxygen concentration in the gas that the animal breathes. Blood pressure is a major parameter related to the stress distribution in the blood vessel wall. The present article is focused on the analysis of the blood pressure records of a normal rat breathing normal atmosphere at sea level. Fig. 1A shows a record over a 24-h period. Fig. 1 B and C show segments recorded at an expanded time scale. It is seen that the amplitude and frequency are variable. The changes are nonstationary, and definitions are needed to know what the heart rate, the mean blood pressure, and the amplitude of pressure oscillations are. Our objective is to see how these quantities can be characterized mathematically. MATERIALS AND EXPERIMENTAL METHODSFor the purpose of long term recording of blood pressure, a catheter must be implanted into an artery. The Riva-Rocci cuff inflation method of blood pressure measurement based on Korotkoff sounds cannot provide the desi...

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