Use of intrinsic modes in biology: Examples of indicial response of pulmonary blood pressure to 6 step hypoxia (nonstationaryystochastic processyFourier spectrumyHilbert spectrumynonlinear oscillations)

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero ‘‘local mean,’’ and a final nonoscillatory mode. With this device, we obtain a set of ‘‘mean trends,’’ each of which represents a ‘‘mean’’ in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of ‘‘indicial response function’’ is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions. One often studies a biological system by changing one variable as a step function of time and recording the changes of other variables that are sometimes oscillatory, stochastic, and nonstationary. The question is how to analyze such stochastic data to obtain crystal clear results describing the effects of that step change of one variable on the other measured variables. For example, in ref. 1, we have shown that the pulmonary blood pressure in a rat in a presumably constant environment is stochastic. Now, let us consider the pulmonary blood pressure in response to step change of oxygen concentration in the gas that an animal breathes. The general feature of the results of such an experiment is shown in Fig. 1A. The upper, oscillatory trace shows a 36-h record of the pulmonary blood pressure in the arterial trunk of a rat breathing normal air at sea level for 6 h, breathing a gas with 10% oxygen at sea level for the next 24 h, and returning to normal air (20.9% oxygen) for 6 h. The lower, smooth line shows the history of oxygen concentration as a function of two steps. One can see certain trends of change of the pulmonary blood pressure in the record, but we need a definitive way to handle this overwhelmingly complex data to reveal the underlying physiological variations. Fourier analysis does not work for such nonstationary signals. The intrinsic mode method (1, 2), however, applies naturally to the present situation. The present article shows how it works and what physiological responses it reveals. Pulmonary hypoxic hypertension has been studied by many authors (3–25). Tissue changes and cellular aspects are discussed in refs. 3–12. Molecular aspects are discussed in refs. 13–19. Our own preliminary results on the arterial tissue remodeling and change of mechanical properties caused by the altered mechanical stresses are presented in refs. 20–25. A method of analysis of the blood pressure to derive the indicial response function is not available. In this paper, we use a rational approach to deduce the indicial response of the pulmonary blood pressure to 6 step hypoxia.