TY - JOUR
T1 - Engineering analysis of biological variables
T2 - An example of blood pressure over 1 day
AU - Huang, Wei
AU - Shen, Zheng
AU - Huang, Norden E.
AU - Fung, Yuan Cheng
PY - 1998/4/28
Y1 - 1998/4/28
N2 - 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 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.
AB - 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 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.
KW - Fourier spectrum
KW - Gumbel extreme-value statistics
KW - Hilbert spectrum
KW - Pulmonary artery
UR - http://www.scopus.com/inward/record.url?scp=0032574709&partnerID=8YFLogxK
U2 - 10.1073/pnas.95.9.4816
DO - 10.1073/pnas.95.9.4816
M3 - 期刊論文
C2 - 9560185
AN - SCOPUS:0032574709
SN - 0027-8424
VL - 95
SP - 4816
EP - 4821
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 9
ER -