(1) Universidad de Zaragoza, Spain. (2) Politecnico di Milano, Italy

Transcription

1 Time-frequency phase differences and phase locking to characterize dynamic interactions between cardiovascular signals M. Orini 1,2, R. Bailón 1, L.T. Mainardi 2 and P. Laguna 1 (1) Universidad de Zaragoza, Spain (2) Politecnico di Milano, Italy M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

2 Intro Methods Validations Physiological study Discussion - Introduction - M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

3 Intro Methods Validations Physiological study Discussion Which Interactions? ECG PRESS RESP Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

4 Intro Methods Validations Physiological study Discussion Which Interactions? Baroreflex (feedback baroreceptive path) ECG PRESS SAP RR RESP Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

5 Intro Methods Validations Physiological study Discussion Which Interactions? Baroreflex (feedback baroreceptive path) Mechanical feedforward path ECG PRESS SAP RR RESP Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

6 Intro Methods Validations Physiological study Discussion Which Interactions? Baroreflex (feedback baroreceptive path) Mechanical feedforward path Respiratory sinus arrhythmia (RSA) ECG PRESS SAP RR RESP RESP Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

7 Intro Methods Validations Physiological study Discussion Which Interactions? Baroreflex (feedback baroreceptive path) Mechanical feedforward path Respiratory sinus arrhythmia (RSA) Mechanical influences ECG PRESS SAP RR RESP RESP Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

8 Intro Methods Validations Physiological study Discussion Which estimates? Time-frequency coherence by SPWVD: Strength of the local coupling between two signals Presence of oscillations with same instantaneous frequency M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

9 Intro Methods Validations Physiological study Discussion Which estimates? Time-frequency phase differences / time delay by SPWVD: Changes in the synchronization (latencies) Prevalent direction of the coupling (causality) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

10 Intro Methods Validations Physiological study Discussion Why? Many mechanisms of the cardiovascular control (baroreflex, RSA, origin of Mayer wave ) are still not fully understood and are currently matter of debate [Eckberg & Karemaker, J Appl Phys, 29] Robust and accurate estimates of: Local coupling between cardiovascular signals Latencies of the dynamic interactions between them provide valuable information to improve the understanding of the cardiovascular regulation M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

11 Intro Methods Validations Physiological study Discussion - Methods - M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

12 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

13 SAPV [mmhg] RRV [s] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Obtaining the RR variability and SAP variability signals Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

14 SAPV [mmhg] RRV [s] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Example [2 min] Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

15 SAPV [mmhg] RRV [s] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Example [2 min] RRV and SAPV are locally coupled Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

16 SAPV [mmhg] RRV [s] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Example [2 min] RRV and SAPV are locally coupled Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

17 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate TF resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

18 υ Φ(τ,) (, ) Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Select a kernel giving an appropriate time-frequency (TF) resolution Elliptical exponential kernel defined in the AF domain* τ υ λ τ -> Frequency resolution ν -> Time resolution λ -> Roll-off τ τ * [Costa & B.-Bartels, IEEE JSP 1995] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

19 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

20 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate auto and cross TF spectra Wigner-Ville distribution (WVD) TF resolultion Interference terms Smoothed pseudo Wigner-Ville distribution (SPWVD) Reduce interference terms while maintaining a good TF resolution Kernel design M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

21 [Hz] [Hz] [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate auto and cross TF spectra RRV RRV SAPV.3.1 SAPV CROSS Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

22 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

23 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

24 Freq [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate TF coherence and TF phase difference TF coherence Time [s] TFC = 1 locally coupled TFC = locally uncoupled.4 M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

25 Freq [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate TF coherence and TF phase difference.3 TF phase difference Time [s] TFPD =, no time delay < TFPD < π, x(t) leads y(t) -1 M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

26 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

27 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Localize TF regions where the local coupling is significant TF coherence estimates depend on the degree of filtering Statistical test is used to localize time-frequency regions characterized by a significant level of local coupling Hypothesis testing: H : [x(t),y(t)] are uncorrelated (i) Generate white noises (uncorrelated test signals) (ii) Estimate Γ(t,f) = {γ 1 (t,f),,γ i (t,f), } (iii) Estimate TF-Threshold γ TH (t,f;α) = (1-α)-percentile of Γ(t,f) (iv) Localize the region of rejection of H : Ω = { (t,f) γ(t,f)> γ TH (t,f;α) } M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

28 Freq [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Localize TF regions where the local coupling is significant TF coherence Time [s].4 M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

29 Freq [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Localize TF regions where the local coupling is significant TF coherence Time [s].4 M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

30 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

31 Freq [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Localize specific TF regions for the phase difference and time delay C(t,f).25 Hz.3 TF phase differences 2 s Time [s] -1 M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

32 Freq [Hz] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Localize specific TF regions for the phase difference and time delay C(t,f).25 Hz.3 TF phase differences 2 s Time [s] -1 M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

33 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

34 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Select a kernel giving an appropriate time-frequency (TF) resolution Estimate auto and cross TF spectra Estimate instantaneous frequencies Estimate TF coherence and TF phase difference Localize TF regions where the local coupling is significant Localize specific TF regions for the phase difference and time delay Estimate phase differences by averaging in the specific TF regions Estimate time-delay by converting radians into seconds M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

35 Intro Methods Validations Physiological study Discussion Time-frequency phase locking Time-frequency phase difference quantifies the changes in the synchronization between two oscillations Time-frequency phase locking measures the degree of similarity of these changes across subjects M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

36 Intro Methods Validations Physiological study Discussion - Validation - M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

37 ΔPhase RRV2 RRV1 [rad] [s] [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences RRV1 : signal from a head-up tilt table Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

38 ΔPhase RRV2 RRV1 [rad] [s] [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences RRV1 : signal from a head-up tilt table RRV2 = RRV1 * exp(i* ΔPhase) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

39 Δphase [rad] X2 [s] X1 [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences X1 = RRV1 + noise1 X2 = RRV2 + noise M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

40 Δphase [rad] X2 [s] X1 [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences X1 = RRV1 + noise1 X2 = RRV2 + noise2 5 couples [X1,X2] for each one of the 14 RRV signals Θ est = (Θ LF + Θ HF )/ M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

41 ΔPhase [rad] ΔPhase [rad] Error [rad] Error [rad] ΔPhase [rad] ΔPhase [rad] Error [rad] Error [rad] Intro Methods Validations Physiological study Discussion Simulation study Phase differences Comparison between: Cross time-frequency analysis Straightforward method Case 1 Case Case 2 Case M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC Time [s] SNR [db] Time [s] SNR [db]

42 ΔPhase [rad] ΔPhase [rad] Error [rad] Error [rad] ΔPhase [rad] ΔPhase [rad] Error [rad] Error [rad] Intro Methods Validations Physiological study Discussion Simulation study Phase differences Comparison between: Cross time-frequency analysis Straightforward method Case 1 Case Phase differences are estimated by integrating the difference between instantaneous frequencies Case 2 Case M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC Time [s] SNR [db] Time [s] SNR [db]

43 ΔPhase [rad] ΔPhase [rad] Error [rad] Error [rad] ΔPhase [rad] ΔPhase [rad] Error [rad] Error [rad] Intro Methods Validations Physiological study Discussion Simulation study Phase differences Comparison between: Cross time-frequency analysis Straightforward method Case 1 Case Case 2 Case M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC Time [s] SNR [db] Time [s] SNR [db]

44 Intro Methods Validations Physiological study Discussion - Physiological study- M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

45 SP [mmhg] HR [bpm] Intro Methods Validations Physiological study Discussion Experimental Procedure Tilt table test : orthostatic stress -> sympathetic activation Supine Head-up Supine [4 min] [5 min] [4 min] healthy subjects Age: 28.2±2.7 -ECG: BiopacMP15 (1KHz) -RESP: BiopacMP15 (15Hz) -PRESS: Finometer (25Hz) Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

46 Intro Methods Validations Physiological study Discussion Experimental Procedure Baroreflex (feedback baroreceptive path) Mechanical feedforward path Respiratory sinus arrhythmia (RSA) Mechanical influences ECG PRESS SAP RR RESP RESP Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

47 Freq [Hz] Freq [Hz] Intro Methods Validations Physiological study Discussion.3 Results [1 subject] TF Coherence TF phase differences M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

48 θ LF [rad] θ HF [rad] Freq [Hz] Freq [Hz] Intro Methods Validations Physiological study Discussion.3 Results [1 subject] TF Coherence TF phase differences Time [s] 1 Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

49 θ LF [rad] θ HF [rad] θ LF [rad] θ HF [rad] Freq [Hz] Freq [Hz] Intro Methods Validations Physiological study Discussion.3 Results [14 subjects] TF Coherence TF phase differences Time [s] Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

50 θ LF [rad] θ HF [rad] Intro Methods Validations Physiological study Discussion Results [14 subjects] Time [s] Time [s] Early Supine Head-up tilt Later Supine θ LF (t) -.61±.1 rad -.56±.9 rad -.56±.14 rad ΔT LF (t) -.89±.15 s -.9±.22 s.91±.3 s θ HF (t).29±.18 rad -.2±.14 rad.15±.17 rad ΔT HF (t).23±.11 s -.13±.1 s.12±.12 s M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

51 Ψ(t) Freq [Hz] Intro Methods Validations Physiological study Discussion.4 Results [14 subjects] TF phase locking Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

52 Intro Methods Validations Physiological study Discussion - Discussion - M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

53 Intro Methods Validations Physiological study Discussion Methodology SUMMARY A framework to estimate the dynamic interactions between cardiovascular signals by cross TF analysis is presented Robust and reliable: median error <.1 rad for SNR error variability between -1 % for SNR 2- db Outperform straightforward technique Advantages: Fine TF resolution of the SPWVD (12 sec,.4 Hz) Statistical assessment of the level of TF coherence Localization of specific TF regions where indices are estimated M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

54 Intro Methods Validations Physiological study Discussion Physiological study SUMMARY RRV and SAPV: Highly non stationary during tilt table test High inter-subject variability Locally coupled in both LF and HF In healthy subjects, during tilt table test In LF, θ LF (t) and time delay did not change (9 ms) In HF, θ HF (t) changed.5 rad and time delay 36 ms Phase locking is about.73 rad. It decreased just after headup tilt and it was restored in 2 minutes M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

55 Intro Methods Validations Physiological study Discussion Interpretation What next From the characterization of the interactions to the physiological mechanisms that causes these changes. M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

56 Intro Methods Validations Physiological study Discussion Interpretation What next From the characterization of the interactions to the physiological mechanisms that causes these changes. Other applications Estimation of the respiratory rate from PPG [Orini et al., CinC conf. 211] Characterization of dynamic cardio-respiratory interactions [Orini et al., CMNE conf. 211] Estimation of the degree of similarity between non stationary signals [Gil et al.,physio Meas, 21] Estimation of Baroreflex sensistivity including the assessment of causality [ ] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

57 Time-frequency phase differences and phase locking to characterize dynamic interactions between cardiovascular signals M. Orini 1,2, R. Bailón 1, L.T. Mainardi 2 and P. Laguna 1 (1) Universidad de Zaragoza, Spain (2) Politecnico di Milano, Italy M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

58 Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Series from ECG and systolic arterial pressure signal t E n-1 t P n-1 t P t E n t P n t E n+1 t P n+2 n+1 t E n+2 R-R series RR n = {t E n, t E n+1-t E n} SAP series SAP n = {t P n, SAP n } M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

59 Intro Methods Validations Physiological study Discussion Which estimates? Time-frequency coherence by SPWVD: Strength of the local coupling between two signals Presence of oscillations with same instantaneous frequency M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

60 Intro Methods Validations Physiological study Discussion Which estimates? Time-frequency phase differences / time delay by SPWVD: Changes in the synchronization (latencies) Prevalent direction of the coupling (causality) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

61 SAP [mmhg] RR [s] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals RR and SAP signals by interpolating (fs = 4Hz) Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

62 SAP [mmhg] RR [s] Intro Methods Validations Physiological study Discussion Cross time-frequency analysis Estimate the RRV and SAPV signals Eliminating very slow variations Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

63 Intro Methods Validations Physiological study Discussion Time-frequency analysis Wigner-Ville distribution (WVD) TF resolultion Interference terms Smoothed pseudo Wigner-Ville distribution (SPWVD) Reduce interference terms while maintaining a good TF resolution Kernel design M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

64 Freq Freq Intro Methods Validations Physiological study Discussion Time-frequency analysis Signal + noise WVD: W(t,f) 75 SPWVD: S(t,f) 25 Time -75 Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

65 Freq Freq Intro Methods Validations Physiological study Discussion Time-frequency analysis Signal + noise WVD: W(t,f) 75 SPWVD: S(t,f) 25 Time -75 Time M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

66 [Hz] [Hz] [Hz] [Hz] [Hz] Intro Methods Validations Physiological study Discussion RRV RRV SAPV Cross time-frequency analysis.3.1 Supine Tilt Supine SAPV CROSS TFC PhDiff Time [s] M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC

67 ΔPhase RRV2 RRV1 [rad] [s] [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences RRV1 : signal from a head-up tilt table RRV2 = RRV1 * exp(i* ΔPhase) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

68 ΔPhase RRV2 RRV1 [rad] [s] [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences RRV1 : signal from a head-up tilt table RRV2 = RRV1 * exp(i* ΔPhase) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

69 ΔPhase RRV2 - RRV1 [rad] [s] [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences RRV1 : signal from a head-up tilt table RRV2 = RRV1 * exp(i* ΔPhase) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211

70 ΔPhase RRV2 RRV1 [rad] [s] [s] Intro Methods Validations Physiological study Discussion Simulation study Phase differences RRV1 : signal from a head-up tilt table RRV2 = RRV1 * exp(i* ΔPhase) M. Orini Characterization of cardiovascular interactions by cross TF analysis Boston, EMBC211