Linear Analysis Variability of Signal

Transcription

1 Linear Analysis Variability of Signal Albert C. Yang, M.D., Ph.D. Beth Israel Deaconess Medical Center Harvard Medical School, Boston, USA Aug 6, 2018

2 中醫對於脈象變異的觀察 十難 論一脈十變 十難曰 : 一脈為十變者, 何謂也? 然 : 五邪剛柔相逢之意也 假令心脈急甚者, 肝邪干心也 ; 心脈微急者, 膽邪干小腸也 ; 心脈大甚者, 心邪自干心也 ; 心脈微大者, 小腸邪自干小腸也 ; 心脈緩甚者, 脾邪干心也 ; 心脈微緩者, 胃邪干小腸也 ; 心脈濇甚者, 肺邪干心也 ; 心脈微濇者, 大腸邪干小腸也 ; 心脈沉甚者, 腎邪平心也 ; 心脈微沉者, 膀胱邪干小腸也 五藏各有剛柔邪, 故令一脈輒變為十也 難經戰國晚期 99 B.C.

3 Quantitative Measurements of Arterial Blood Pressure 1733 AD - United Kingdom Stephen Hales noted the correlation between the respiratory cycle, blood pressure level, and interbeat intervals, the phenomenon known as normal sinus arrhythmia

4 Electrocardiogram 1912 Invented by Willem Einthoven 1924 Nobel Prize in Medicine

5 What is Heart Rate Variability? Picture from

6 Autonomic Nervous System Parasympathetic modulation Sympathetic modulation

7 Cardiac Transplantation Sands, KEF et al., Circulation 79:76-82, 1989

8 Physiological Origin of Heart Rate Variability Respiratory sinus arrhythmia (seconds) Slower rhythms (minutes) Day-night periodicity (hours)

9 Respiratory Sinus Arrhythmia Increased heart rate during inspiration Reduced heart rate during expiration

10 Slower Rhythms Heart Rate (beat/min) Heart Rate (beat/min) Time (sec) Time (sec) Data from normal control database at Dept. Psychiatry, Taipei Veterans General Hospital

11 Day-Night Periodicity Heart rate, mean blood pressure, and renal sympathetic nerve activity recorded 3 weeks after implantation of catheters and electrodes in a conscious rabbit. Note the strong day-night periodicity in heart rate and mean blood pressure that are accompanied by similar oscillations in sympathetic nerve activity. Malpas SC, Am J Physiol Regul Integr Comp Physiol 286: R1-R12, 2004

12 Why is Heart Rate Variability Useful? Changes in heart rate over time provide a window onto autonomic physiology. Analysis of heart rate variability is a noninvasive method for identifying abnormalities in cardiac autonomic modulation. Heart rate variability in combination with other risk stratifiers improves risk stratification. Goldberger AL, et al. Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci U S A 2002;99 Suppl 1:

13 Quantifying Heart Rate Variability Approach 1: How much variability is there? Time Domain and Geometric Analyses Approach 2: What are the underlying rhythms? Frequency Domain Analysis Approach 3: How much complexity or self-similarity is there? Non-linear Analyses

14 Time Domain and Geometric Analyses

15 Variability: Within the World of Statistics RR Interval (sec) ± 0.06 A Healthy Subject RR Interval (sec) ± 0.01 B Heart Failure Time (sec) Data Source: physionet.org

16 Which Subject is Healthier? 1.00 RR Intervals (sec) A B

17 Definition of Time Domain HRV Measures SDNN SDANN RMSSD pnn50 Standard deviation of normal interbeat intervals standard deviation of the averages of normal interbeat intervals in all five minutes segments of the entire recording Square root of the mean of the squared differences between successive interbeat intervals Percentage of adjacent intervals that varied by greater than 50 ms Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology: Heart rate variability: standards of measurement, physiological interpretation and clinical use. Circulation 1996;93:

18 Geometric Analysis - Poincaré Plot Huikuri, H. V. et al. Circulation 1996;93:

19 Henri Poincaré ( )

20 Poincaré plot Poincaré HRV plot is a graph in which each RR interval is plotted against next RR interval (a type of delay map) Synonyms Scatter plot; scattergram Return map; phase delay map Lorenz plot

21 Poincaré & related plots as nonlinear tools Visualization of higher-dimensional phase spaces in two or three-dimensional sub-spaces uncorrelated noise harmonic oscillation chaotic time series with linear trend time series generated from an AR model Source:

22 RRn+1 (ms) Poincaré HRV plot: normal RRn (ms)

23 Visualization of ectopic beats normal ectopic post-ectopic normal normal beats

24 Poincaré HRV plot: healthy vs. disease Healthy Control mean heart rate : 52 bpm Critically ill Patient mean heart rate : 51 bpm Data Source: Taipei Veterans General Hospital, Taiwan

25 HRV in Different Stages of Cancer Early-detected cancer patient Chemotherapy cancer patient Hospice cancer patient Data Source: Taipei Veterans General Hospital, Taiwan

26 How Aging and Illness May Affect the Geometry of Poincaré HRV plot RRn+1 (ms) Critically ill patient in ICU 25-year-old healthy control Newborn (one day) Prematurely (22 th week) 10-year-old healthy control RRn (ms) Data Source: Taipei Veterans General Hospital, Taiwan

27 Quantitative analysis of Poincaré HRV plots Variable geometries of Poincaré HRV plots Ellipse fitting technique Histogram technique Correlation coefficient

28 Ellipse fitting technique Line-of-identity SD1: dispersion (standard deviation) of points perpendicular to the axis of line-of-identity SD1 SD2 SD2: dispersion (standard deviation) of points along the axis of line-of-identity Huikuri, H. V. et al. Circulation 1996;93:

29 Ellipse fitting technique Risk Stratification in Cardiovascular Disease Stein PK et al. Indian Pacing and Electrophysiology Journal 2005;5:

30 Histogram Technique Brennan M. et al. IEEE Trans Biomed Eng 2001;48:

31 Do Poincaré indices actually measure nonlinear properties of heart rate dynamics? Tulppo MP et al. Am J Physiol 1996;271:H244-H252

32 Do Poincaré indices actually measure nonlinear properties of heart rate dynamics? Ellipse fitting technique SDRR : standard deviation of the RR intervals SDSD: standard deviation of the successive differences of the RR intervals Brennan M. et al. IEEE Trans Biomed Eng 2001;48:

33 Summary Advantages Simple quantitative measure None or very few input parameter Possible insights into short-term variability (in the case of heart rate variability, short-term variability is related to parasympathetic modulation) Limitations Variability statistics is vulnerable to outliers or noisy signal.