{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T04:47:55Z","timestamp":1792298875547,"version":"4.4.0"},"reference-count":24,"publisher":"National Academy of Sciences","issue":"9","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[1998,4,28]]},"abstract":"<jats:p>\n                    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 \u201cempirical mode decomposition method.\u201d 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)\n                    <jats:italic>Introduction to the Theory of Fourier Integrals<\/jats:italic>\n                    (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 extreme-value 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.\n                  <\/jats:p>","DOI":"10.1073\/pnas.95.9.4816","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T10:31:44Z","timestamp":1027679504000},"page":"4816-4821","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":161,"title":["Engineering analysis of biological variables: An example of blood pressure over 1 day"],"prefix":"10.1073","volume":"95","author":[{"given":"Wei","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093-0412; Divisions of Engineering Science and Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125; and Laboratory for Hydrospheric Processes, Ocean and Ice Branch, National Aeronautics and Space Administration Goddard Space Flight Center, Greenbelt, MD 20771"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093-0412; Divisions of Engineering Science and Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125; and Laboratory for Hydrospheric Processes, Ocean and Ice Branch, National Aeronautics and Space Administration Goddard Space Flight Center, Greenbelt, MD 20771"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Norden E.","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093-0412; Divisions of Engineering Science and Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125; and Laboratory for Hydrospheric Processes, Ocean and Ice Branch, National Aeronautics and Space Administration Goddard Space Flight Center, Greenbelt, MD 20771"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan Cheng","family":"Fung","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093-0412; Divisions of Engineering Science and Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125; and Laboratory for Hydrospheric Processes, Ocean and Ice Branch, National Aeronautics and Space Administration Goddard Space Flight Center, Greenbelt, MD 20771"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[1998,4,28]]},"reference":[{"key":"e_1_3_3_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02584301"},{"key":"e_1_3_3_2_2","first-page":"H544","volume":"262","author":"Fung Y C","year":"1992","unstructured":"Y C Fung, S Q Liu Am J Physiol 262, H544\u2013H552 (1992).","journal-title":"Am J Physiol"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(93)90350-N"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1161\/01.RES.65.5.1340"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1991.70.6.2455"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.2895523"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1097\/00000542-198510000-00014"},{"key":"e_1_3_3_8_2","first-page":"736","volume":"37","author":"Wixson S K","year":"1987","unstructured":"S K Wixson, W J White, H C Hughes, C M Lang, W K Marshall Lab Anim Sci 37, 736\u2013742 (1987).","journal-title":"Lab Anim Sci"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1097\/00000542-198111000-00014"},{"key":"e_1_3_3_10_2","volume-title":"Digital Signal Processing","author":"Oppenheim A V","year":"1989","unstructured":"A V Oppenheim, W Schafer Digital Signal Processing (Prentice\u2013Hall, Englewood Cliffs, NJ, 1989)."},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-2213-3"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fl.24.010192.002143"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0265(93)90049-D"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0265(93)90048-C"},{"key":"e_1_3_3_15_2","first-page":"217","volume":"35","author":"Claasn T T","year":"1980","unstructured":"T T Claasn, W F G Mecklenbrauker Philips J Res 35, 217\u2013250, , 276\u2013300, 372\u2013389. 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