期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1999
卷号：96
期号：5
页码：1834-1839
DOI：10.1073/pnas.96.5.1834
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension ({Delta}pO2) in the breathing gas. For a step change of {Delta}pO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and {Delta}pO2, which can be written as P(t-t1 | {Delta}pO2). An effective method does not exist to examine the nonlinear function P(t-t1 | {Delta}pO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.
