Huang, WeiYong and Shen, Zheng and Huang, Norden E. and Fung, Yuan Cheng (1999) Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia. Proceedings of the National Academy of Sciences of the United States of America, 96 (5). pp. 18341839. ISSN 00278424. http://resolver.caltech.edu/CaltechAUTHORS:HUApnas99

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Abstract
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 pO(2)) in the breathing gas. For a step change of Delta pO(2), beginning at time t(1), the pulmonary blood pressure is a nonlinear function of time and Delta pO(2), which can be written as P(tt(1)\Delta oO(2)). An effective method does not exist to examine the nonlinear function P(tt(1)ΔpO(2)). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the kegs. 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.
Item Type:  Article  

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Additional Information:  © 1999 by the National Academy of Sciences. Contributed by Yuan Cheng Fung, December 21, 1998. This work was supported by National Heart, Lung, and Blood Institute Grant HL 43026; American Heart Association, California Affiliate, Postdoctoral Fellowship 96–95 (to W.H.); National Science Foundation Grant CM9615897 and National Aeronautics and Space Administration Grant NAG 5–5149 (to Z.S.); and National Aeronautics and Space Administration Grant RTOP 622–4711–20 (to N.E.H.). The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.  
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Subject Keywords:  degree of nonlinearity; Fourier spectrum; Hilbert spectrum; nonlinear relationships  
Record Number:  CaltechAUTHORS:HUApnas99  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:HUApnas99  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  12079  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  24 Oct 2008 06:16  
Last Modified:  26 Dec 2012 10:26 
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