Biomaterial Database

Nonlinear parameters estimation from sequential short time data series. 2001

M Smietanowski

Department of Experimental and Clinical Physiology, Medical Academy, Warsaw, Poland. creamsky@mercury.ci.uw.edu.pl

Procedures of nonlinear parameter estimation require large samples of data. In stationary physiological situations, usually short time series are available. The method of dynamics-dependent windowing and data aggregation procedure are proposed. This technique was tested on chaotic signal generated by Lorenz model and applied to investigate beat-to-beat control of the cardiovascular system in 10 healthy volunteers. Nonivasively recorded blood pressure, respiratory activity and blood oxygen saturation were digitized and saved for further off-line analysis. The experimental procedure consisted of 10 min control--C, 20 voluntary apneas 1 min each-A, interapnea 20 periods of 1 min spontaneous breathing--B, and 10 min free-breathing recovery--R. Respiration signal served as a reference for apnea and interapnea free-breathing identification period. Correlation dimension-CD, according to Grassberger and Procaccia, and recurrence plot strategy, according to Webber and Zbilut, were applied to check dynamical properties of the signals. Results of numerical experiment on Lorenz model, original and transformed by segmentation and aggregation, support our assumption of similarity of their dynamics. Error in CD and recurrence parameters estimation strongly depended on segment length and was about 5% for 600 to 1,200 data points. However, even for segments of 75 to 100 samples, it did not exceed 10% for all, but one, periodic testing signal. Segmentation and aggregation applied to interbeat interval (IBI) and total peripheral resistance (TPR) data showed that CD and recurrence variables estimated separately for apneic and interapneic period and those calculated for mixed (apneic and interapneic) intervals were different. Average CD and recurrence parameters of IBI and TPR for 10 subjects during apnea and interapnea intervals were significantly different than during control and recovery. The lowest CD (mean +/- S.D.) of 6.38 +/- 0.4, 5.62 +/- 0.2 and %recurrence 10.35 +/- 0.8, 6.62 +/- 0.6 (highest ratio 4.95 +/- 0.2, 5.13 +/- 0.3) were observed in apnea for IBI and TPR, respectively. Low values of the estimates computed for mixed periods may suggest the influence of slowly varying, quasiperiodic driving force due to experimental procedure regime. Signal dynamics-dependent windowing and data aggregation regardless of the sequence of data could be a practical solution for nonlinear analysis of very short repeatable time series.

UI	MeSH Term	Description	Entries
D008955	Models, Cardiovascular	Theoretical representations that simulate the behavior or activity of the cardiovascular system, processes, or phenomena; includes the use of mathematical equations, computers and other electronic equipment.	Cardiovascular Model,Cardiovascular Models,Model, Cardiovascular
D012119	Respiration	The act of breathing with the LUNGS, consisting of INHALATION, or the taking into the lungs of the ambient air, and of EXHALATION, or the expelling of the modified air which contains more CARBON DIOXIDE than the air taken in (Blakiston's Gould Medical Dictionary, 4th ed.). This does not include tissue respiration (	Breathing
D001794	Blood Pressure	PRESSURE of the BLOOD on the ARTERIES and other BLOOD VESSELS.	Systolic Pressure,Diastolic Pressure,Pulse Pressure,Pressure, Blood,Pressure, Diastolic,Pressure, Pulse,Pressure, Systolic,Pressures, Systolic
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000328	Adult	A person having attained full growth or maturity. Adults are of 19 through 44 years of age. For a person between 19 and 24 years of age, YOUNG ADULT is available.	Adults
D000465	Algorithms	A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.	Algorithm
D001049	Apnea	A transient absence of spontaneous respiration.	Apneas
D001341	Autonomic Nervous System	The ENTERIC NERVOUS SYSTEM; PARASYMPATHETIC NERVOUS SYSTEM; and SYMPATHETIC NERVOUS SYSTEM taken together. Generally speaking, the autonomic nervous system regulates the internal environment during both peaceful activity and physical or emotional stress. Autonomic activity is controlled and integrated by the CENTRAL NERVOUS SYSTEM, especially the HYPOTHALAMUS and the SOLITARY NUCLEUS, which receive information relayed from VISCERAL AFFERENTS.	Vegetative Nervous System,Visceral Nervous System,Autonomic Nervous Systems,Nervous System, Autonomic,Nervous System, Vegetative,Nervous System, Visceral,Nervous Systems, Autonomic,Nervous Systems, Vegetative,Nervous Systems, Visceral,System, Autonomic Nervous,System, Vegetative Nervous,System, Visceral Nervous,Systems, Autonomic Nervous,Systems, Vegetative Nervous,Systems, Visceral Nervous,Vegetative Nervous Systems,Visceral Nervous Systems
D012815	Signal Processing, Computer-Assisted	Computer-assisted processing of electric, ultrasonic, or electronic signals to interpret function and activity.	Digital Signal Processing,Signal Interpretation, Computer-Assisted,Signal Processing, Digital,Computer-Assisted Signal Interpretation,Computer-Assisted Signal Interpretations,Computer-Assisted Signal Processing,Interpretation, Computer-Assisted Signal,Interpretations, Computer-Assisted Signal,Signal Interpretation, Computer Assisted,Signal Interpretations, Computer-Assisted,Signal Processing, Computer Assisted
D017711	Nonlinear Dynamics	The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.	Chaos Theory,Models, Nonlinear,Non-linear Dynamics,Non-linear Models,Chaos Theories,Dynamics, Non-linear,Dynamics, Nonlinear,Model, Non-linear,Model, Nonlinear,Models, Non-linear,Non linear Dynamics,Non linear Models,Non-linear Dynamic,Non-linear Model,Nonlinear Dynamic,Nonlinear Model,Nonlinear Models,Theories, Chaos,Theory, Chaos