୯!ҥ!Ҭ!೯!ε!Ꮲ!
!
ႝᐒᆶڋπำᏢس!
!
ᅺγፕЎ!
!
аӕᢀෳკکਔ࣬ଯ໘ᓎϩ!
ٰᕝ֤ޑЈޤҬϕբҔ!
Study on Meditation Cardiorespiratory Interactions
Based on Synchrogram and Time-phase Bispectral Analysis
!
ʳ
!!!!!!!!!!!!ࣴ!ز!ғǺጰࡹৱ!
!!!!!!!!!!!!ࡰᏤ௲Ǻᛥٵᅼ!റγ!
!
!
!!!!!!!ύ!!҇!୯!ΐ!Μ!Ϥ!ԃ!Μ!Д!
аӕᢀෳკکਔ࣬ଯ໘ᓎϩ!
ٰᕝ֤ޑЈޤҬϕբҔ!
Study on Meditation Cardiorespiratory Interactions
Based on Synchrogram and Time-phase Bispectral Analysis
ࣴ!ز!ғǺጰࡹৱ!
!
!
!!!!!!!!!StudentǺJeng-En Tsai
ࡰᏤ௲Ǻᛥٵᅼ!റγ!!!!! AdvisorǺDr. Pei-Chen Lo
୯!!ҥ!!Ҭ!!೯!!ε!!Ꮲ!
ႝᐒᆶڋπำᏢس!
ᅺ!γ!ፕ!Ў!
A Thesis
Submitted to Department of Electrical and Control Engineering
College of Electrical and Computer Engineering
National Chiao Tung University
In Partial Fulfillment of the Requirements
For the Degree of
Master
In
Electrical and Control Engineering
October 2007
Hsinchu, Taiwan, Republic of China
аӕᢀෳკکਔ࣬ଯ໘ᓎϩ!
ٰᕝ֤ޑЈޤҬϕբҔ!
ʳ
!ࣴزғǺጰࡹৱ!! !!!!!!ࡰᏤ௲Ǻᛥٵᅼ!റγ!
!
!
୯ҥҬ೯εᏢႝᐒᆶڋπำᏢس!
!
ᄔा!
ҁࣴزޑҞޑӧܭЈޤҬϕբҔวғӧᕝ֤ਔޑ࣬Տӕکߚጕ ܄ҬϕբҔǶӕᢀෳკکਔ࣬ଯ໘ᓎϩπڀϩձҔٰࣴز࣬Տӕک ߚጕ܄ҬϕբҔǶҁࣴزӅԏΑ 16 Տԃស࣬՟ޑڙෳޣǴځύჴᡍಔࣁ 7 ՏڀԖᕝ֤ᡍޣǴԶڋಔ 9 Տڙෳޣ߾คԜᡍǶҗ่݀วǴวғӕ ޑਔࢤኧǵᕴᆢਔ໔کߚጕ܄ҬϕբҔޑਔࢤኧԖᡉቚу!)p ॶϩձࣁ! 0.023-!0.034-!0.038*ǶਥᏵԜ่݀Ǵᕝ֤ਔჹܭЈޤӕຝޑቹៜࢂࡐܴ ᡉӦǶᜢܭӕکߚጕ܄ҬϕբҔ่݀ޑठ܄Ǵךॺวᕝ֤ਔޑ҅࣬ ᜢᡉቚу!)p ॶࣁ 0.011*ǴӢԜෳӧวғߚጕ܄ҬϕբҔਔǴᕝ֤ёૈ ቚуЈޤسϐ໔ޑӕຝǶ!Study on Meditation Cardiorespiratory Interactions
Based on Synchrogram and Time-phase Bispectral Analysis
ʳ
Student : Jeng-En Tsai Advisor :Dr. Pei-Chen Lo
Institute of Electrical and Control Engineering
National Chiao-Tung University
Abstract
The aim of this research was to investigate the phase synchronization and nonlinear coupling while cardiorespiratory interaction occurred during Zen meditation. Synchrogram analysis was applied to the investigation of phase synchronization, and time-phase bispectral analysis was employed in studying the nonlinear coupling. This study included 16 subjects, 7 experimental subjects with Zen-meditation experience and 9 control subjects in the same age range, yet, without any meditation experience. According to our results, number of the synchronous epochs, the total synchronization duration, and the number of the coupling epochs all significantly increased (p=0.023, 0.034, and 0.038, respectively) during meditation. As a result, the effect of meditation on cardiorespiratory synchronization was evident. Regarding the methodological coincidence between synchronization and nonlinear coupling, we found that positive correlation increased significantly (p = 0.011) during meditation. It suggests that under nonlinear coupling, meditation might enhance the phase synchronization between cardiac and respiratory systems.
ᇞ!!!!!!!ᖴ!
! ೭ጇፕЎޑֹԋǴ२ӃाགᖴࡰᏤ௲ᛥٵᅼԴৣޑ௲ᏤǴόᆅӧܭࣴز ޑࣽᏢᡄᒠࡘԵǵፕЎቪբޑ߄ၲǴᗋԖғࢲೀШޑᄊࡋǴᡣךᕇؼӭǶӕ ਔΨाགᖴα၂ہླྀكࢩǵഋ҉ܹԴৣჹܭፕЎගрޑӭࡰᏤکࡌǶ! ! ӧᅺγޑࣴزғఱύǴךाձགᖴၲᏢߏჹܭፕЎޑБӛǵБݤᆶቪ բޑЈࡰᏤǶΨགᖴኾǵਖሎǵᏦ҅ǵࡹᏌǵ۸ǵഩᏢߏǵ◔ຐᏢۊ ӧ೭ࢤਔ໔๏ΑךӭࣴزޑࡌکႴᓰǶᗋԖᖴᖴଆոΚޑৱᄪǵറ๔ǵ ےϘǵߞҦǵ᰾ኾǶќѦǴΨགᖴ cvxpopm ᡣךᏢಞᖱमЎǵᗶࣁჴᡍ࠻ٰ ޑݗǵৎ໋ӧՐஎޑᔅԆǵౚ϶ࠂྍکسਫޑεৎǴᡣךӧࣴزϐᎩૈ ܫيЈǶ! ! നࡕךाགᖴР҆کৎΓॺǴᖴᖴգॺޑᜢЈکЍǴᡣךૈӧؒԖࡕ៝ ϐኁΠֹԋᏢǶ!Contents
ʳ
ʳ ʳύЎᄔा
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁi
Abstract
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁiiᇞᖴ
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁiii
Contentsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ
iv
List of Tables
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁvi
List of Figures
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁvii
1. Introductionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ
1
1.1 Background and Motivationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 1 ʳ ʳ ʳ 1.2 Aims of this Workˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 4ʳ 1.3 Organization of this Thesisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 4ʳ
2. Theories and Methods
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ52.1 Introduction to ECG and Respiratory Signalsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 5ʳ 2.1.1 Introduction to ECGˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 5ʳ 2.1.2 Introduction to Respirationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 7ʳ 2.2 The Synchrogram Methodˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 8ʳ 2.2.1 Theory of Phase Synchronizationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 8ʳ 2.2.2 Instantaneous Phaseˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 10ʳ 2.2.3 Synchrogram Method and Quantificationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 11ʳ 2.3 Time-phase Bispectral Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ14 2.3.1 Classical Bispectral Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ14 2.3.2 Time-phase Bispectral Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ16ʳ
3.1 Experimental Setup and Procedureˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ18 ʳ ʳ ʳ ʳ ʳ ʳ 3.1.1 Measurement of ECG signalˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ20 3.1.2 Measurement of Respiratory Signalˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 21 3.2 Strategies for Synchronization Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 22ʳ 3.3 Strategies for Time-phase Bispectral Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 29
4. Results
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ344.1 Results of Synchronization Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ34 ʳ ʳ ʳ ʳ ʳ 4.1.1 Comparison of Lasting Lengthˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ35 4.1.2 Comparison of Number of Epochsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 36 4.1.3 Comparison of Total Lengthˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ36ʳ 4.2 Results of Time-phase Bispectral Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 39ʳ ʳ ʳ ʳ ʳ ʳ 4.2.1 Comparison of Lasting Lengthˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ39 4.2.2 Comparison of Number of Epochsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 41 4.2.3 Comparison of Total Lengthˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ41 4.3 Correlation between Phase Synchronization and Nonlinear Couplingˁˁˁˁˁˁˁˁˁˁˁ43 4.3.1 Qualitative Observationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ43 4.3.2 Quantitative Analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ45ʳ
5. Conclusion and Discussion
ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ505.1 Conclusion and Discussionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ50 5.2 Future Workˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 52
Referencesˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ53
Appendix A. Detection of ECG R Peak and Respiratory Peak
ˁˁˁˁˁˁˁˁˁˁˁ56A.1 R-Peak Detectionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 56 A.2 Respiratory Peak Detectionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ59
List of Tables
3.1 Subjects of experimental and control groupsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 18 4.1 Mean values of three synchronization parameters analyzed for the
experimental and control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ34 4.2 Mean values of three nonlinear coupling parameters analyzed for the
experimental and control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ39 4.3 Percentage of total time interval of each correlation stateˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ 48
List of Figures
ʳʳ
2.1 The conducting system of heartˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ6 2.2 The typical wave complex of ECGˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ7 2.3 Mechanics of expiration and inspirationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ8 2.4 Derivation of instantaneous phase using method based on marker events. In
this example, the marker events are determined from the wave peaksˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ10 2.5 Illustration of constructing the synchrogramˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ12 2.6 Examples of good synchronization and poor synchronizationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ12 2.7 The process of quantifying the degree of synchronization: an example of
complete n : m synchronizationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ14 3.1 Experimental procedureˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ19 3.2 The physiological signal recording systemˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ20 3.3 (a) Lead҇configuration of bipolar limb leads, (b) Disposable ECG
electrode.ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ21 3.4 Piezo-electric respiratory transducerˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ21 3.5 Respiratory signalˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ22 3.6 Flow chart of synchronization analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ23 3.7 The synchrograms of an experimental subject during meditation: (a) n : 1
synchrogram (b) n : 2 synchrogram (c) n : 3 synchrogramˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ24 3.8 Instantaneous frequency of heart beating and respiration: (a) Respiratory
signal, (b) fr: instantaneous frequency of respiration, (c) ECG signal, (d)
Instantaneous frequency of heart beating, (e) fh: instantaneous frequency of
3.9 (a) Time-varying sequence of fh, (b) time-varying sequence of fr , and (c)
the sequence of frequency ratio fh fr of an experimental subject during meditationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ25 3.10 Synchronization degrees for all possible (n,m) pairs for an experimental
subject during meditation. The right color bar denotes the scale mapping for color representationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ27 3.11 (a) Time-varying synchronization degree, ( )
2
max tk
J
, and (b) corresponding n/m ratio that the maximum synchronization degree was detected at the given time2 k
t (subject: a meditator during meditation)ˁˁˁˁˁˁˁˁˁ27 3.12 Synchronization durationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ28 3.13 Histogram of Jmean( )t for (a) experimental group, and (b) control groupˁˁˁˁˁˁ28 3.14 Flow chart of time-phase bispectral analysisˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ29 3.15 (a) One-minute cross-bispectrum for an experimental subject during
meditation, (b) its contour illustration, and (c) the zoom-in of contour illustrationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ31 3.16 The curves of (a) normalized biamplitude, Anormalized(m), (b) biphase,
) (m
I
, (c) constant degree of biphase,J
I(m), and (d) coupling degree, )(m
O
, of an experimental subject during meditationˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ32 3.17 The histogram ofO
mean(t) for (a) experimental group and (b)control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ33 4.1 Histograms of lasting length of synchronization for (a) experimental group,
and (b) control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ35 4.2 Mean values of lasting length of synchronization for both groups in
different recording sessionsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ36 4.3 Variations of mean number of synchronization epochs for both groups in
different recording sessionsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ37 4.4 Mean values of the total synchronization length for both groups in
different recording sessionsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ37 4.5 Average length of synchronization for different (n/m) ratios in (a)
experimental group and (b) control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ38 4.6 Histograms of lasting length of nonlinear coupling for (a) experimental
group and (b) control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ40 4.7 Mean values of lasting length of nonlinear coupling for both groups in
different recording sessionsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ41 4.8 Variations of mean number of nonlinear coupling epochs for both groups
in different recording sessionsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ42 4.9 Mean values of total length of nonlinear coupling for both groups in
different recording sessionsˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ42 4.10 Instantaneous degree of (blue) the phase synchronization and (red) the
nonlinear coupling (subjects : (a) experimental subject 0928, (b) experimental subject 1003, (c) control subject 0411, and (d) control subject 0727)ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ44 4.11 Time course of correlation coefficient between the phase synchronization
and the nonlinear coupling (subjects : (a) experimental subject 0928, (b) experimental subject 1003, (c) control subject 0411, and (d) control subject 0727)ˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ46 4.12 Histograms of correlation coefficient between the phase synchronization
and the nonlinear coupling for (a) experimental group and (b) control groupˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ48 4.13 Histograms of lasting length of the segment identified to be (a) the
A.1 Flow chart of R peak detectionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ56 A.2 The raw ECG and preprocessed ECGˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ58 A.3 R peak detection by thresholdˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ58 A.4 Flow chart of Respiratory peak detectionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ59 A.5 The raw and preprocessed respiratory signalˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ60 A.6 Parameters for respiratory signal peak detectionˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁˁ60
Chapter 1
Introduction
1.1 Background and Motivation
The interaction between human cardiac and respiratory systems has been widely studied for many decades. It has been found that these two systems do not act independently; instead, they are coupled by some mechanisms. One well-known phenomenon of cardiorespiratory interaction is the frequency modulation of heart rate by respiration, which is known as respiratory sinus arrhythmia (RSA) [1]. RSA portrays the heart rate variability in synchrony with respiration, that is, the heart rate increases during inspiration and decreases during expiration. With RSA, human pulmonary air exchange can be more efficient [2]. In addition to modulation, other cardiorespiratory interaction such as synchronization has been observed, and the nature of interaction like nonlinear coupling was proposed in recent years [3-10].
Synchronization is a particular phenomenon that occurs due to interaction of two or more self-sustained oscillators [3]. This concept is widely used in various fields of science and engineering [11] and is interpreted in different ways when applied to different problems. In our study, we focused on the phase synchronization phenomenon in cardiorespiratory system. Details and definitions are described in Chapter 2.
In 1998, Schäfer et al. [4] applied the concept of phase synchronization of chaotic oscillators [12] to the development of a technique called ‘synchrogram’ to analyze irregular, non-stationary bivariate data. Based on this method, they found cardiorespiratory synchronization of several locking ratios (ratios of heartbeat
frequencies to respiratory frequencies) occurring in young healthy athletes at rest. This overthrew the widely accepted knowledge that cardiac and respiratory rhythms in humans were unsynchronized. Afterward several researches followed the synchrogram method and presented the phenomenon of cardiorespiratory phase synchronization on different subjects. Duration and frequency ratio are parameters of phase synchronization that have ever been investigated in these researches. Regarding the duration, long synchronous episodes were observed in young healthy athletes (about 1000 seconds) [3] and heart transplant patients (several hundreds of seconds) [5], while short episodes were observed in non-athlete normal subjects (less than 2 minutes) [6]. And there was no synchronous event detected in a critically ill patient in coma [7]. Bartsch et al. [8] showed that the occurrence of synchronization was significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and reduced during REM sleep. In the aspect of frequency ratio, a research on anaesthetized rats found that the frequency ratio upon phase synchronization would transit as the depth of anesthesia changed [9]. In spite of increasing researches devoted to this phenomenon in recent years, the mechanisms and meanings of cardiorespiratory phase synchronization are still not well understood. As a consequence, more researches are still needed to explore this emerging topic.
In addition to synchronization, the nature of coupling between cardiac and respiratory systems has been investigated. Bispectral analysis has been appealing to researchers during the last few years, particularly in investigating the presence of quadratic coupling in interacting harmonic oscillators [13]. For simplification, most studies consider biological systems to be stationary. In practical situations, however, interaction among subsystems often results in time-varying characteristics such as frequency and coupling strength. Hence, bispectral analysis based on time averaging for stationary signals is no longer sufficient. Time evolution of the bispectral
estimates is needed. In 2003, Jamšek et al. [14] proposed the time-phase bispectral analysis that introduced time dependence to the bispectral analysis of univariate data. In 2004, the method was used to detect the coupling phenomenon between cardiac and respiratory systems, and several episodes were detected (smaller than 2 minutes) [10].
As CAM (complementary and alternative medicine) becomes more popular in the West, scientific researches have been extensively carried out to justify the therapeutic effects of CAM and its benefits to human health. Among a large variety of approaches in CAM, meditation has been one of the most widely acceptable practices due to its substantial effectiveness and safety. It thus drew more attention from such professional areas as medicine, clinics, sciences, engineering, sociology, etc. According to numerous research reports since 1960’s, meditation has been proved to benefit human health in various aspects. During meditation, the human body can be optimized by tuning up the brain-nervous system, cardiovascular system, respiratory system, etc. The phenomena and intrinsic mechanisms of such tune-up processes not only are of great interest but play an important role of exploring an optimal solution to human health maintenance.
For most meditation techniques, respiration is an important skill that ensures a good-quality meditation. Via specific respiration technique, human cardiovascular system may be influenced through cardiorespiratory interactions. There have been several researches aimed to investigate the cardiorespiratory interactions in different meditation schemes. In 1999, Peng et al. [15] observed very prominent low-frequency (~0.1Hz) oscillations in heart rate during specific forms of Chinese Chi and Kundalini yoga meditation in healthy young adults. In their later research [16], same phenomenon was also observed in two forms of meditations with different respiration techniques. In 2005, the RSA resulted from cardiorespiratory interactions was
investigated during Zen meditation. They concluded that low-frequency breathing could lead to in-phase RSA [17]. These researches showed that cardiorespiratory interactions during meditation were of unusual different features. However, except for RSA phenomenon, very few researches are performed to study the synchronization and nonlinear coupling of cardiorespiratory systems during meditation.
1.2 Aims of this Work
Our lab has been investigating the Zen-meditation EEG (electroencephalograph) since 1999. In recent years, we began studying the cardiovascular system-related physiological signals as well because they might be appropriate indicators for meditation effects on stress manipulation. This study was thus focused on ECG (electrocardiograph) and respiratory signals and aimed to investigate the phase synchronization and nonlinear coupling while cardiorespiratory interaction occurred during Zen meditation. Synchrogram was employed in the phase synchronization study, while time-phase bispectral analysis was used to quantify the nonlinear coupling. Moreover, we investigated the correlation between these two attributes.
1.3 Organization of this Thesis
This thesis is composed of five chapters. Chapter 1 describes the background, motivation, and main aim of this study. In Chapter 2, an introduction to ECG and respiratory signal is given, and the theories of synchrogram analysis and time-phase bispectral analysis are presented. In Chapter 3, the experimental setup and protocol are presented. Then the procedures for phase synchronization and nonlinear coupling analysis are illustrated. Chapter 4 reports and discusses the results. The last chapter makes a summary of this research and brings forward some issues for future study.
Chapter 2
Theories and Methods
Physiological signals play an important role in clinical diagnosis, and provide scientific indicators for the health of human body. Many physiological signals can be measured non-invasively and processed completely in digital form, for example, EEG (electroencephalograph), EMG (electromyograph), ECG (electrocardiograph), and respiratory signals. Since we mainly focused on the ECG and respiratory signals, Section 2.1 firstly gives a background introduction to these two signals. Section 2.2 describes the synchrogram method used to analyze the phase synchronization. Finally, to study the nonlinear coupling phenomenon, Section 2.3 presents the approach for time-phase bispectral analysis.
2.1 Introduction to ECG and Respiratory Signals
2.1.1 Introduction to ECG
Heart can beat by itself at a regular rhythm due to a specialized conducting system. The system comprises four parts, as shown in Fig. 2.1, SA node (sinoatrial node), AV node (atrioventricular node), Bundle of His, and Purkinje fibers. The SA node is the heart pacemaker that controls the beat rate of heart. Depolarization waves are generated by SA node and spread out to atria, AV node, and ventricles. When depolarization waves propagate to atria, atria contract resulting in emergence of “P” wave in ECG. These waves afterwards spread to AV node that connects with Bundle of His. Purkinje fibers are the extended parts of Bundle of His. The networking of
Purkinje fibers appears to be a threadlike net on subendocardial surface. Therefore, through Bundle of His, depolarization waves spread to entire ventricles and make two ventricles contract at the same time. In sum, the sequence of heart pumping is: SA node Ш atria Ш AV node Ш Bundle of His Ш Purkinje fibers Ш ventricles [18].
The depolarization waves not only spread throughout the whole heart, but also induce the electrical current change that can be non-invasively recorded on the body surface as the ECG signal. Without stimulation, the heart cells are in the quiescent state (approximate -80 mV) with negative potential (so-called polarization). Once being stimulated, they bear positive potential and the systole reaction is induced. Hence, ECG reflects the potential variation of rhythmic activity of the heart.
The typical wave complex of ECG is shown in Fig. 2.2. The physiological meaning of each ECG complex pattern is described below:
P wave: The wave is due to the depolarization of atria. Atria contract at this time. Fig. 2.1 The conducting system of heart [18].
Q wave: The wave is caused by the depolarization of ventricles, and the R wave follows. Atria expand at this time.
R wave: The period of the depolarization of ventricles. Atria expand gradually, and ventricles start to contract at this time.
S wave: The period of the depolarization of ventricles. Atria completely expand, and ventricles completely contract.
T wave: This wave is due to the repolarization of ventricles. Ventricles expand gradually.
2.1.2 Introduction to Respiration
The respiration is responsible for bringing oxygen into the body and removing carbon dioxide out of the body. The mechanics of respiration involve muscles that change the volume of the thoracic cavity to generate inspiration and expiration. Two sets of muscles involved are the diaphragm and the intercostal muscles. The diaphragm is the wall separating the abdomen from the thoracic cavity that can move up and down. The intercostal muscles surround the thoracic cavity and are responsible for moving the rib cage in and out. As shown in Fig. 2.3, inspiration results from
contraction of the diaphragm (downward movement) and intercostal muscles (rib cage swings up and outward). Hence, the enlarged cavity housing the lungs has a pressure reduction of -3mm Hg with respect to the pressure outside the body, and the lung expands because of the difference of pressure. On the contrary, expiration results from the opposite mechanism. Using suitable instruments, the behavior of respiration can be recorded and transduced to an electrical signal [19].
2.2 The Synchrogram Method
2.2.1 Theory of Phase Synchronization
The phenomenon of synchronization is considered as an adjustment of rhythms, via specific manner of interaction, among distinctive self-sustained oscillators [3]. Such an interaction can lead to the locking of their phases, whereas their amplitudes may remain uncorrelated. Various definitions of synchronization have been proposed that require further description for each model-oriented, specific problem. In classical
sense of periodic self-sustained oscillators, synchronization is usually defined as locking (entrainment) of the phases,
(2.1) where n and m are integers, I1 and I2 are phases of two oscillators, and
M
n m, is the generalized phase difference. Note that the values of I1 and I2 are not bounded in [0, 2S]. According to equation (2.1), oscillator 1 completes m cycles while oscillator 2 completes n cycles, and it is said to be a synchronization of m cycles of oscillator 1 with n cycles of oscillator 2. For generalization, a weaker condition for phase locking was proposed, as shown in equation (2.2) below, that can be feasible for nonlinear oscillators. In such cases, the n : m phase locking manifests as a variation G ofM
n m, around a horizontal plateau.(2.2) In case of cardiorespiratory coupling, synchronization is usually influenced by the noise that originates not only from measurement and external disturbance but also from other subsystems taking part in the cardiovascular control [21]. Weak noise can lead
M
n m, into fluctuation in a random way around a constant value, and strong noise may cause phase slips. As a consequence, the phenomenon of synchronization cannot be interpreted in a unique way, but be treated in a statistical sense. Follow the basic work of Stratonovich [22], phase locking in noisy systems is understood as the appearance of a peak in the distribution of the cyclic relative phase <n m, , and can be interpreted as the existence of a dominated stable value of phase difference between the two oscillators.(2.3) where ‘mod’ is an operator converting the value of
M
n m, into the range [0, 2S] by, 1- 2 const n m n m
M
I
I
, |M
n m - const |G
, , mod 2 n mM
n mS
<subtracting 2
S
k ( k is an integer) such that 0d <n m, < 2S
.2.2.2 Instantaneous Phase
Analysis of the synchronization between nonlinear oscillators requires quantification of the instantaneous phases of oscillators. In this thesis, we employed the method based on marker events to characterize the cyclic patterns of oscillators [23]. An example is illustrated in Fig. 2.4. The marker events are determined from the wave peaks. Then the instantaneous phase at any time t can be derived by the linear interpolation equation below,
(2.4)
where t is the time of the kk th marker event. The instantaneous phase of kth marker event is 2 kS ˁʳ ʳ Time 2Ӹk ( )t I (Rad) tk-1 tk tk+1 tk+2 2Ӹ(k-1) 2Ӹ(k+1) 2Ӹ(k+2)
Fig. 2.4 Derivation of instantaneous phase using method based on marker events. In this example, the marker events are determined from the wave peaks.
1 1 - ( ) 2 2 , - k k k k k t t t k t t t t t
I
S
S
d] 2 mod ) ( [ 2 1 ) ( 2 2 1 t m tk k m
I
S
S
\
2.2.3 Synchrogram Method and Quantification
The synchrogram method [3] was used to analyze the phase synchronization of two interacting self-oscillatory systems. The method is feasible for such cases like pseudo-periodic ECG with particular rhythmic events (R peak) occurring at given time instants. To plot the synchrogram, we need to determine the normalized relative
phase )(
2 k m t
\
of oscillator 1 at specific time instants that specific events of oscillator 2 occur. As described in equation (2.5), ( )2 k m t
\
is obtained by wrapped phaseI
1 modulo 2S
m (i.e., m consecutive cycles are viewed as one longer cycle), and is observed at time2 k
t when the marker events of oscillator 2 occur. Then the
values of ( ) 2 k m t
\
at time 2 kt are marked by dots along the vertical axis and the
synchrogram is completed.
(2.5)
As an illustration, the synchrogram with m = 2 is shown in Fig. 2.5. It presents n dots within m consecutive cycles of oscillator 1.
In the ideal case of n : m synchronization, phase
I
1 within m cycles of oscillator 1 that grows from 0 to 2S
m presents the same value at time2 k t and tkn 2 , i.e., ) ( ) ( 2 2 m k n k m t
\
t\
. For example, ( ) ( 3) 2 2 m k k m t\
t\
for the case of goodsynchronization illustrated in Fig. 2.6. In consequence, the synchrogram will manifest
n horizontal lines. An advantage of this graphic tool is that only one integer of
parameter m has to be chosen, and then several synchronous events with different integers of parameter n can be derived within one plot. Namely, various n : m synchronization conditions can be scrutinized based on a fixed valued of m, and the transitions between them can be traced.
Next, we develop the scheme for quantifying the synchronization phenomenon in addition to the graphical illustration by synchrogram. The examples of two different degrees of synchronization are presented in Fig. 2.6. High degree of n : m
0
m
Time Good synchronization Poor synchronization
Fig. 2.6 Examples of good synchronization and poor synchronization. ) ( 2 k m t
\
n horizontal lines 0 1 Time 2 m Oscillator 1 Oscillator 2Fig. 2.5 Illustration of constructing the synchrogram. ) ( 2 k m t
\
2 k t m cycles n cycles Marker events of oscillator 2synchronization (good synchronization) indicates that the values of ( )
2 k m t
\
aredistributed regularly at the n specific values in the normalized range [0, m]. On the contrary, low degree of n : m synchronization (poor synchronization) is reflected by the random distribution of values of ( )
2 k m t
\
.Note that high degree of n : m synchronization introduces n horizontal lines within m adjacent cycles of oscillator 1. The scheme of quantification can be designed by examining how regular the distribution of values of ( )
2 k m t
\
is in the synchrogram. According to this concept, we first transform ( )2 k m t
\
to ( ) 2 ,m k n t < using equation (2.6). Then the degreeJ
n m, of n : m synchronization can be evaluated by equation (2.7) [24].(2.6)
(2.7)
where N represents the number of marker events of oscillator 2 in a given window length. The value of
J
n m, ranges from 0 to 1, whereJ
n,m 1 indicates the case of complete synchronization, andJ
n,m 0 reveals the fact of complete desynchronization.An example of complete n : m synchronization is shown in Fig. 2.7. The synchrogram illustrates n horizontal lines within the normalized range [0, m], with equidistance d between adjacent lines. The bottom line begins with ( )
2 k m t
\
= d1. By equation (2.6), n horizontal lines are mapped to a constant value n,m(tk ) 2 d1/d2
S
< , and 0d ( ) 2 ,m k n t< < 2S . According to equation (2.7), degree of synchronization is
^
t n m`
m tk m k m n [ ( ) ]mod 2 ) ( 2 2 , < S \ ]} ) ( [ sin 1 { } ] ) ( [ cos 1 { 2 , 2 , , 2 2 2 2¦
¦
< < k k m n k k m n m n t N t NJ
,
n m
J
= 1, reflecting the occurrence of complete synchronization.2.3 Time-phase Bispectral Analysis
2.3.1 Classical Bispectral Analysis
Bispectral analysis belongs to a group of techniques based on high-order statistics (HOS) that can be used to analyze non-Gaussian signals, to obtain phase information, to suppress Gaussian noise of unknown spectral form, and to detect and characterize signal nonlinearities [13]. Besides, bispectral analysis is also a tool to observe the property of nonlinear (quadratic) phase coupling between oscillators.
The bispectrum involves third-order statistics. Its spectral estimation mainly adopts the direct, conventional Fourier transformation applied to the third-order moments. In the case of third-order statistics, the third-order moments are equivalent to third-order cumulants. From the above, classical way of estimating the bispectrum
0 m Time d1 d1+d d1+2d d1+(n-1)d 0 Time 2Ӹd1/d 2Ӹ ӫn ,m ) ( 2 k m t
\
) ( 2 ,m k n t <Fig. 2.7 The process of quantifying the degree of synchronization: an example of complete n : m synchronization.
ˆ ( , )
B k l is to evaluate the average of estimated third-order moments M k l ,ˆ ( , )3i
(2.8)
where M k lˆ ( , ) 3i is the triple product of discrete Fourier transforms (DFTs) at discrete frequencies k, l, and k + l,
(2.9)
where Xi(.) is the discrete Fourier transform of signal x[n]. The signal is divided into
K segments to obtain the statistical stability of the estimates.
Bispectrum B k l is a complex function, characterized by its magnitude ˆ ( , )
function A and phase function
I
, also known as biamplitude and biphase, respectively.(2.10) Bispectrum ˆ ( , )B k l quantifies the quadratic coupling between two underlying
oscillatory components of a signal. That is, the relation among the oscillations at two basic frequencies k and l, and a harmonic component at the frequency k + l is
examined. The set of three frequencies is known as a triplet (k, l, k + l). Strong coupling implies that the oscillatory components at k and l may have a common generator, and such components may synthesize a new component at the combinatorial frequency k + l if a quadratic nonlinearity is presented.
To observe the coupling information between two signals x[n] and y[n], the cross bispectrum Bxyx(k,l) is adopt. The coupling information among X at frequency k, Y at
frequency l, and X at frequency k + l can be examined. As shown below, cross bispectrum is estimated by 3 1 1 ˆ( , ) K ˆi( , ) i B k l M k l K
¦
* 3 ˆ ( , ) ( ) ( )i i i i( ), 1,..., M k l X k X l X kl i k ˆ ( , ) ( , ) ˆ( , ) | ˆ( , ) | j B k l ( , ) j k l B k l B k l e A k l e I(2.11)
2.3.2 Time-phase Bispectral Analysis
The classical bispectral analysis is appropriate for studying stationary signals. In practical systems, interactions among subsystems often result in time variability of their characteristic frequencies. Accordingly, time-phase bispectral analysis that encompasses time dependence within the bispectral analysis was proposed [14].
In analogy with the short-time Fourier transform, the M-point DFT of signal x(n) at time m is calculated by employing a moving window w(nm),
(2.12)
where k is the discrete frequency and n is the discrete time. Following equations (2.8), (2.9), and (2.11) while substituting
^
X(k,m),Y(l,m), X*(kl,m)`
for^
X(k),Y(l), X*(kl)`
and letting i 1, the time-phase cross-bispectral analysis ofsignal x and y is
(2.13)
Similar to equation (2.10), the biamplitude and biphase functions can be obtained by the following equations.
(2.14)
(2.15)
When two frequency components k and l of, respectively, X and Y signals are coupled, the last term in (2.15) becomes
I
x(kl m, ) ( , )I
x k mI
y( , )l m , resulting- 1 - 2 / 0 1 ( , ) ( ) ( - ) M j nk M n X k m x n w n m e M S
¦
ˆ ( , , ) ( , , )ˆ
( , , ) |
ˆ
( , , ) |
j Bxyx k l m( , , )
j xyx k l mxyx xyx xyx
B
k l m
B
k l m e
A
k l m e
I * 1 1 ˆ ( , ) K ( ) ( ) ( ) xyx i i i i B k l X k Y l X k l K¦
* ˆ ( , , ) ( , ) ( , ) ( , ) xyx B k l m X k m Y l m X kl m ( , , ) ( , ) ( , ) - ( , ) xyx k l m x k m y l m x k l mI
I
I
I
2 2 ]} ) , , ( [ sin 1 { ]} ) , , ( [ cos 1 {
¦
¦
m xyx m xyx k l m N m l k N I I JIin the biphase value of either 0 or 2S radian. Because dependent frequency components in a system may have phase difference, phase-coupling estimation requires less strict conditions and is able to reflect the existence of phase coupling in a wider sense. In addition, biamplitude function can be used to infer the relative strength of interaction between spectral components. As a consequence, the degree of coupling is determined by the magnitude of biamplitude and the observation of constant biphase. The degree of constant biphase
J
I (a constant) can be quantified by equation (2.16) below [24].(2.16)
where N represents the number of points in a given window length, and
J
I is a valuebetween 0 and 1. Biphase degree
J
I 1 indicates a complete constant biphase, and0 I
Chapter 3
Experiment and Signal Analysis
In this chapter, the setup and procedure of experiments are first introduced. Next, implementation strategies and parameters are presented, particularly for applying the synchrogram analysis and time-phase bispectral analysis to ECG and respiratory signals
3.1 Experimental Setup and Procedure
This study involved two groups of subjects, the experimental group including subjects with Zen-meditation experience and the control group including subjects without any meditation experience. Background of subjects in each group is listed in Table 3.1.
Table 3.1 Subjects of experimental and control groups
Experimental group Control group
Number of subjects 7 9
Sex (male : female) 5 : 2 8 : 1
Age (years) 26.4 ̈́ 2.5 25.3 ̈́ 3.3
Meditation experience (years) 5.9 ̈́ 2.6
The experimental procedure of this study is illustrated in Fig. 3.1. Because the human cardiac function can be regulated by autonomic nervous system (ANS), the
experiments were conducted during the same period (3:00pm to 5:00pm) to ensure the approximately same state of ANS of all subjects. The experiments comprised two sessions. During Session 1, subjects of both groups rested, in a ~70̓ head-up back-tilt position with eyes closed, for 10 minutes. During Session 2, subjects of control group continued resting for 20 minutes; on the other hand, experimental subjects began meditation for 20 minutes. Experimental subjects, following their routine meditation habit, meditated with either full-lotus or half-lotus posture, with eyes closed. During meditation, practitioners concentrated their mind on “Zen Chakra” that was an energy point inside the third ventricle of human brain. All subjects breathed spontaneously in both sessions.
As shown in Fig. 3.2, ECG and respiratory signals were measured using PowerLab biosignal recording system (ADInstruments, Sydney, Australia) and then displayed and saved on a personal computer using the software Chart4 (ADInstruments, Bella Vista, Australia).
Experimental Group
Rest MeditationControl Group
Session 1 10 minutes Session 2 20 minutes Rest Rest3.1.1 Measurement of ECG signal
The ECG signal was recorded using Lead҇of standard bipolar limb leads [25], as shown in Fig. 3.3 (a). Electrode site on the left (right) arm was connected to the amplifier’s positive (negative) input, with the ground on the inside of left ankle. The disposable ECG electrodes (Medi-Trace 200 Foam Electrodes, Kendall, Chicopee, MA, USA) as shown in Fig. 3.3 (b) were applied in this study. The ECG was pre-filtered by a 0.3-200 Hz bandpass filter and digitized by a sampling rate of 1000 Hz. Physiological signal recording system (PowerLab) USB port Personal Computer (Chart4 software)
Fig. 3.2 The physiological signal recording system.
Physiological signal
3.1.2 Measurement of Respiratory Signal
Respiratory signal was recorded using a piezo-electric transducer (Model 1132 Pneumotrace II (R), UFI, Morro Bay, CA, USA) as shown in Fig. 3.4, that was wrapped around the belly passing the navel. The respiratory signal was pre-filtered by a lowpass filter with cutoff frequency of 5 Hz and digitized at the sampling rate of 1000 Hz. An example of respiratory signal is shown in Fig. 3.5. Note that the amplitude increases during inspiration and decreases during expiration.
Fig. 3.3 (a) Lead҇configuration of bipolar limb leads, (b) Disposable ECG electrode.
(a) (b)
3.2 Strategies for Synchronization Analysis
The flow chart of synchronization analysis is shown in Fig. 3.6. The pre-processing stage was aimed to detect the R peaks of ECG and all the inspiration-phase peaks of respiratory signal. Then the instantaneous phases and frequencies were derived so that the synchrogram was ready to be constructed. At last, the synchronization length was quantified to evaluate the degree of synchronization for further comparison and interpretation.
Step 1. Pre-processing
Power spectrums of QRS complexes and respiratory signals are approximately 10-30 Hz and 0.2-0.3 Hz [21, 26, 27]. Accordingly, in pre-processing stage, we applied Matlab’s built-in polyphase filter implementation, including anti-aliasing (lowpass) FIR filter, to down-sample the raw ECG and respiratory signals, respectively, to the rate of 200 samples and 20 samples per second. Then the algorithms described in Appendix A were applied to the detection of R peaks of ECG and inspiration-phase peaks of respiratory signal.
Time (second) Inspiration Expiration
Fig. 3.5 Respiratory signal.
0 2 4 6 8 10 12 14 16 18 20 -2 -1 0 1 2 3 Amplitud e
Step 2. Formulate Synchrogram
After peak detection, time positions of respiratory peaks were extracted as the marker events. Note that two adjacent marker events are considered as one complete cycle and a phase increase of 2S was assumed. Then, following equations (2.4)-(2.5), the normalized relative phase of respiratory signal could be determined.
To construct the cardiorespiratory synchrogram, we sketched the normalized relative phase ( )
2 k m t
\
of respiratory signal at time2 k
t identified as the appearances
of R peaks of ECG. In this research, we observed the cardiorespiratory synchronization within 3 respiratory cycles. Therefore, only three synchrograms need to be plotted for each subject, i.e. n : 1, n : 2, and n : 3 synchrograms.
As an example, Fig. 3.7 displays three synchrograms derived for an experimental subject during meditation. Apparently, synchronization is evidently observed within
Pre-processing
Formulate Synchrogram
Quantify the Synchronization Degree and Length ECG and Respiratory Signals
Fig. 3.6 Flow chart of synchronization analysis.
the range of 12-18 minutes, according to the piecewise, nearly parallel behaviors of
n’s curves in synchrograms.
Step 3. Calculate Frequency Ratio
fh frin Each Respiratory Cycle
The instantaneous frequency of heart beating fh was calculated by inversing the
time interval between two adjacent R peaks of ECG signal, while that of the respiration fr was the reciprocal of the time interval between two respiratory peaks.
Each computed value was placed in the mid point of two adjacent peaks (see Fig. 3.8 (b) and (d)). To calculate instantaneous frequency ratio fh fr within each respiratory cycle, the instantaneous frequency of heart beating at the mid point of two adjacent respiratory peaks was estimated by linear interpolation (refer to Fig. 3.8 (e)). As an illustrating example, Fig. 3.9 displays the sequence of instantaneous frequency ratio fh fr of an experimental subject during meditation.
(a)
Fig. 3.7 The synchrograms of an experimental subject during meditation: (a) n : 1 synchrogram (b) n : 2 synchrogram (c) n : 3 synchrogram. (b) (c) Time (minute) Respiratory cycle 0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 0 2 4 6 8 10 12 14 16 18 20 0 1 2 Respiratory cycle Respiratory cycle
Time (a)
Interval between R peaks
Interpolated frequency of heart beating
Fig. 3.8 Instantaneous frequency of heart beating and respiration: (a) Respiratory signal, (b) fr: instantaneous frequency of respiration, (c)
ECG signal, (d) Instantaneous frequency of heart beating, (e) fh:
instantaneous frequency of heart beating within a respiratory cycle. (b) (c) (d) (e) r
f
hf
Time (minute) 0 2 4 6 8 10 12 14 16 18 20 1.2 1.3 1.4 0 2 4 6 8 10 12 14 16 18 20 0.25 0.3 0.35 0.4 0 2 4 6 8 10 12 14 16 18 20 4 5 6 (a) (c) Instantaneous frequency ( H z) Frequency RatioFig. 3.9 (a) Time-varying sequence of fh, (b) time-varying sequence of fr ,
and (c) the sequence of frequency ratio fh fr of an experimental subject during meditation.
(b) Instantaneous frequency (
H
Step 4. Quantify the Synchronization Degree
To evaluate the synchronization degree, the following procedure was proposed: (1) The maximum and minimum values of frequency ratio, min[fh/fr] and
max[fh/fr], were derived.
(2) According to the maximum and minimum ratio, we determined all possible pairs of (n,m)’s such that n/m satisfied: min[fh/fr]d n/m d max[fh/fr]. Note that
all pairs (n/m)’s, after being reduced, were considered to be the same if they resulted in the same ratio. For example, only pair (4,1) was kept for the ratios of 4:1 and 8:2.
(3) Following equations (2.6)-(2.7), synchronization degree, ( )
2
,m k
n t
J
, ofqualified (n,m) pairs could be calculated with a window centered at time
2 k
t .
In this study, we employed the window length of 60 consecutive R peaks, with the moving step size of one R peak.
As an illustration, Fig. 3.10 demonstrates the time-varying synchronization degrees for all possible (n,m) pairs for an experimental subject during meditation. Based on this figure, significant synchronization is observed for the frequency ratio of 4:1, 7:2, and 11:3, respectively, in the time interval 12-18, 6-7, and 18-20 minute.
(4) The synchronization degree at a given time
2 k
t =Tsd was determined by
finding the maximum value along the vertical line defined by ( )
2
,m k sd
n t T
J
.The result was denoted by ( )
2
max tk Tsd
J
.As an example, the sequence ( )
2
max tk
J
of an experimental subject during meditation is shown in Fig. 3.11.Step 5. Quantify the Synchronization Duration
To evaluate the effective duration of synchronization, we first determined a threshold of synchronization degree, D . As shown in Fig. 3.12, synchronization duration measured the total duration in time with the degree of synchronization no
Fig. 3.11 (a) Time-varying synchronization degree, ( )
2
max tk
J
, and (b)corresponding n/m ratio that the maximum synchronization degree was detected at the given time
2 k t (subject: a meditator during meditation). Time (minute) n /m ratio Synchronization d egree 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 1 2 4 6 8 10 12 14 16 18 20 3 4 5 6 (a) (b) Time (minute)
Fig. 3.10 Synchronization degrees for all possible (n,m) pairs for an
experimental subject during meditation. The right color bar denotes the scale mapping for color representation.
Time (minute) n /m ratio Synchronization d egree 2 4 6 8 10 12 14 16 18 20 3 4 5 6 0.2 0.4 0.6 0.8
less than
D
.To systematically determine the value of D , the following procedure was proposed:
(1) The values of ( )
2
max tk
J
were averaged every minute and the mean values were denoted asJ
mean( )t .(2) The histograms of
J
mean( )t were illustrated in Fig. 3.13 for both the experimental group (Fig. 3.13 (a)) and control group (Fig. 3.13 (b)).(3) We found that the largest value of the histogram occurred at
J
mean( )t =0.2. Therefore, the threshold was determined to be D = 0.2.˛˼̆̇̂˺̅˴̀ʳ̂˹ʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳ˹̂̅ʳʳ˸̋̃˸̅˼̀˸́̇˴˿ʳ˺̅̂̈̃ ˃ʸ ˅˃ʸ ˇ˃ʸ ˉ˃ʸ ˃ˁ˄ ˃ˁ˅ ˃ˁˆ ˃ˁˇ ˃ˁˈ ˃ˁˉ ˃ˁˊ ˃ˁˋ ˃ˁˌ ˄ ˖ ̂̈́̇ ʳʻ ʸ ʼ ˦˸̆̆˼̂́ʳ˄ ˦˸̆̆˼̂́ʳ˅ ˛˼̆̇̂˺̅˴̀ʳ̂˹ʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳ˹̂̅ʳ˶̂́̇̅̂˿ʳ˺̅̂̈̃ ˃ʸ ˅˃ʸ ˇ˃ʸ ˉ˃ʸ ˃ˁ˄ ˃ˁ˅ ˃ˁˆ ˃ˁˇ ˃ˁˈ ˃ˁˉ ˃ˁˊ ˃ˁˋ ˃ˁˌ ˄ ˖ ̂̈́̇ ʳʻ ʸ ʼ ˦˸̆̆˼̂́ʳ˄ ˦˸̆̆˼̂́ʳ˅ (a) (b) mean(t) J mean(t) J Jmean(t) mean(t) J
Fig. 3.13 Histogram of
J
mean( )t for (a) experimental group, and (b) control group. ) ( 2 ,m k n t J 0 1 2 k t D duration3.3 Strategies for Time-phase Bispectral Analysis
Time-phase bispectral analysis was proposed to investigate the phenomena of phase coupling between ECG and respiratory signals. The flow chart of time-phase bispectral analysis is shown in Fig. 3.14.
Step 1. Pre-processing
Fundamental frequencies of ECG and respiratory signals are approximately 1.2 Hz and 0.3 Hz [21]. Accordingly, raw ECG and respiratory signals originally recorded with sampling rate of 1000 Hz were downsampled to 10 Hz using Matlab’s built-in polyphase filter implementation, including anti-aliasing, lowpass FIR filter with cutoff frequency 5 Hz. Then Chebyshev I IIR highpass filter with cutoff frequency 0.04 Hz was used to remove the baseline drift.
Pre-processing
Estimate Cross-Bispectrum (window size: 1min, step size: 1sec)
Calculate Biamplitude and Biphase at bifrequency ( f ,e f )r
ECG and Respiratory Signals
Fig. 3.14 Flow chart of time-phase bispectral analysis. Quantify the Coupling Degree and Length
Step 2. Estimate Cross-Bispectrum
By equation (2.13), the cross-bispectrum ˆBxyx( , , )k l m ʳ was estimated. Here, k represents the frequency of ECG signal, l represents the frequency of respiratory signal, and m represents the time. The length of time window was selected to be 10 times of the period of slower signal, i.e. respiratory signal, to get reliable FFT (fast Fourier Transform) result. The slowest frequency of respiratory signals in our study was about 0.2 Hz (period: 5 sec per breath). We thus selected the window length to be 1 minute. To observe the time-varying behavior in more details, the moving step was selected to be 1 second.
Step 3. Calculate Biamplitude and Biphase at Bifrequency (
fe,
fr)
Using equation (2.14), biamplitude and biphase were evaluated at bifrequency ( f ,e f ) for each window frame. The bifrequency (r f ,e f ) of each window was r
determined by the maximum-power frequencies of ECG and respiratory signals respectively. Fig. 3.15 displays the example of one-minute cross-bispectrum for an experimental subject during meditation.
Step 4. Quantify the Coupling Degree
The coupling degree is determined by(3.1) where Anormalized (m) is the normalized biamplitude for a given window, that is derived
by first dividing the biamplitude by total power of cross-bispectrum in 0d f ,e fr d
fs/2 and then normalizing the results of all subjects to the range [0 1]. The
J
I(m), denoting the constant degree of biphase, can be calculated by equation (2.16) for a given window centered at time m. Fig. 3.16 illustrates the analyzing procedure for investigating the coupling degree of an experimental subject during meditation.) ( ) ( ) (m Anormalized m
J
I mO
u0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 4 6 8 10 12 14 x 10-6 (a) (b) (c) Amplitude ECG frequency (Hz) Respiratory frequency (Hz) Amplitude ECG frequency (Hz) Respiratory frequency (Hz) ECG frequency (Hz) Respiratory frequency (Hz) fe fr
Fig. 3.15 (a) One-minute cross-bispectrum for an experimental subject during meditation, (b) its contour illustration, and (c) the zoom-in of contour illustration.
Step 5. Quantify the Coupling Length
Coupling length provides an index of characterizing the duration of significance of phase coupling during the entire process. To quantify the coupling length, a threshold D needs to be determined first. To determine an appropriate value of D , the following procedure was proposed:
(1) A new sequence
O
mean(t) containing the results of moving average ofO
(m)was obtained using a window size of one minute without overlap.
(2) The histogram of
O
mean(t) was derived. Fig. 3.17 illustrates the histograms for experimental group (Fig. 3.17 (a)) and control group (Fig. 3.17 (b)).(3) Maximum of the histogram (here, 0.2) indicates the majority of phase-coupling distribution. Accordingly, we selected D = 0.2 for this specific case. 2 4 6 8 10 12 14 16 18 20 0 0.5 1 2 4 6 8 10 12 14 16 18 20 -2 0 2 2 4 6 8 10 12 14 16 18 20 0 0.5 1 2 4 6 8 10 12 14 16 18 20 0 0.5 1 (a) (b) (c) (d) Time (minute) Rad Am p litude
Fig. 3.16 The curves of (a) normalized biamplitude, Anormalized(m), (b) biphase,
) (m
I
, (c) constant degree of biphase,J
I(m), and (d) coupling degree,O
(m), of an experimental subject during meditation.Degree
˛˼̆̇̂˺̅˴̀ʳ̂˹ʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳ˹̂̅ʳ˸̋̃˸̅˼̀˸́̇˴˿ʳ˺̅̂̈̃ ˃ʸ ˅˃ʸ ˇ˃ʸ ˉ˃ʸ ˃ ˃ˁ˄ ˃ˁ˅ ˃ˁˆ ˃ˁˇ ˃ˁˈ ˃ˁˉ ˃ˁˊ ˃ˁˋ ˃ˁˌ ˄ ˖ ̂̈́̇ ʳʻ ʸ ʼ ˦˸̆̆˼̂́ʳ˄ ˦˸̆̆˼̂́ʳ˅ ˛˼̆̇̂˺̅˴̀ʳ̂˹ʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳʳ˹̂̅ʳ˶̂́̇̅̂˿ʳ˺̅̂̈̃ ˃ʸ ˅˃ʸ ˇ˃ʸ ˉ˃ʸ ˃ ˃ˁ˄ ˃ˁ˅ ˃ˁˆ ˃ˁˇ ˃ˁˈ ˃ˁˉ ˃ˁˊ ˃ˁˋ ˃ˁˌ ˄ ˖ ̂̈́̇ ʻʸ ʼ ˦˸̆̆˼̂́ʳ˄ ˦˸̆̆˼̂́ʳ˅ (a) (b) mean(t)
O
O
mean(t) mean(t)O
O
mean(t)Fig. 3.17 The histogram of
