1. University of Zaragoza, CIBER-BBN, Spain 2. University of Pisa, Italy 3. Harvard Medical School, USA Tetra-variate point-process model for the continuous characterization of cardiovascular-respiratory dynamics during passive postural changes Michele Orini 1 Gaetano Valenza 2 Luca Citi 3 Riccardo Barbieri 3

Introduction …

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Heart rate/contractility Cardiac output Peripheral resistance Arterial stiffness Arterial blood pressure Cardiovascular system: variables Sympathetic/ Parasympathetic Nervous System Respiration 1/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Baroreflex Negative feedback that buffers short term changes in arterial pressure by modifying heart rate and peripheral resistance Clinical relevance: Total cardiac mortality, autonomic dysfunction Cardiovascular system: mechanisms 2/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Clinical relevance: Total cardiac mortality, autonomic dysfunction Afferent flow Cardiovascular system: mechanisms Baroreflex Negative feedback that buffers short term changes in arterial pressure by modifying heart rate and peripheral resistance 2/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Clinical relevance: Total cardiac mortality, autonomic dysfunction Afferent flow Parasympathetic Cardiovascular system: mechanisms Baroreflex Negative feedback that buffers short term changes in arterial pressure by modifying heart rate and peripheral resistance 2/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Clinical relevance: Total cardiac mortality, autonomic dysfunction Afferent flow Parasympathetic Sympathetic Cardiovascular system: mechanisms Baroreflex Negative feedback that buffers short term changes in arterial pressure by modifying heart rate and peripheral resistance 2/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Clinical relevance: Total cardiac mortality, autonomic dysfunction Afferent flow Parasympathetic Sympathetic Cardiovascular system: mechanisms Baroreflex Negative feedback that buffers short term changes in arterial pressure by modifying heart rate and peripheral resistance 2/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Respiratory sinus arrhythmia: HRV in synchrony with respiration Cardiovascular system: mechanisms 3/23 ECG Respiration

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Time ECG AP RESP Non-invasive measurements 1 s Cardiovascular system: dynamic interactions 4/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Time ECG AP RESP Non-invasive measurements 1 s Cardiovascular system: dynamic interactions 4/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Time RRI SAP RESP Non-invasive measurements 1 s Cardiovascular system: dynamic interactions 4/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Time RRI SAP RESP Non-invasive measurements 1 s Cardiovascular system: dynamic interactions 5/23 The assessment of dynamic interactions between cardiovascular signals, both in health and disease, is of primarily importance to improve our understanding and early detection of CV dysfunctions

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Propose a model for a comprehensive characterization of cardiovascular functioning Multivariate : heart rate, pressure, respiration, vasculature Non-stationary : track fast changes Dynamic Interactions : quantify coupling & causality Accurate : goodness-of-fit Objective 6/23 Tetra-variate non-stationary point process

Methods …

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Point processes Point-Process: Interbeat Interval Probability Model What is it: Point processes are used to mathematically model physical systems that produce a stochastic set of localized events in time or space. When to use: If data are better described as events than as a continuous series. Examples: Spike Trains, Heart Beats, Earthquake sites and times 7/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Point processes Barbieri R, Matten EC, Alabi AA, Brown EN. A point process model of human heart rate intervals: new definitions of heart rate and heart rate variability. American Journal of Physiology: Heart and Circulatory Physiology, 288: H , Barbieri R., Brown EN. Analysis of heart dynamics by point process adaptive filtering. IEEE Transactions on Biomedical Engineering, 53(1), 4-12, Point-Process: Interbeat Interval Probability Model What is it: Point processes are used to mathematically model physical systems that produce a stochastic set of localized events in time or space. When to use: If data are better described as events than as a continuous series. Examples: Spike Trains, Heart Beats, Earthquake sites and times HRV: Efficient continuous/instantaneous estimates of HRV (at each moment in time without interpolation), with measures Goodness-of-Fit 7/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Point processes The IGD is the distribution of the inter-event-intervals of an integrate-and-fire model driven by a white Gaussian noise and a positive drift Physiological reasons The Inverse Gaussian distribution (IGD) Point-Process: Interbeat Interval Probability Model 8/23 Time Beats

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Point processes Point-Process: Interbeat Interval Probability Model 9/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Point processes Point-Process: Goodness of Fit Conditional Intensity Function Rescaled Time Series z n are independent random variables in [0,1] (time-rescaling theorem) Q-Q plot: The closer a model’s Q-Q plot is to the 45° line, the more accurately the model describes the data Model’s Quintiles Empirical Quintiles 95% confidence interval 10/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Point processes Conditional Intensity Function Rescaled Time Series z n are independent random variables in [0,1] (time-rescaling theorem) Autocorrelation of z n to test statistical independence Time Lag Correlation 95% confidence interval Point-Process: Goodness of Fit 11/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis Tetra-variate model 12/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis Tetra-variate model 12/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis Tetra-variate model 12/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis RRI PTT RSPSAP Tetra-variate model RSP → RRI : Respiratory sinus arrythmia RSP → SAP : Mechanical influence of respiration SAP → RRI : Baroreflex RRI → SAP : Direct mechanical effect PTT (~pulse wave velocity) represents the vasculature Probability density functions:  RRI, PTT : Inverse Gaussian  RSP, SAP : Gaussian 13/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis RRI PTT RSPSAP Tetra-variate model PTT can be modeled as a point process triggered by another point process, the RRI Orini et al. EMBC conf, 2012 Probability density functions:  RRI, PTT : Inverse Gaussian  RSP, SAP : Gaussian RSP → RRI : Respiratory sinus arrythmia RSP → SAP : Mechanical influence of respiration SAP → RRI : Baroreflex RRI → SAP : Direct mechanical effect PTT (~pulse wave velocity) represents the vasculature 14/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Dynamic interactions characterization Transfer Function Spectra Directed Coherence Indices of Interaction 15/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Dynamic interactions characterization (1) RRI (2) PTT (4) RSP (3) SAP Directed Coherence : causal index Indices of Interaction 16/23 Example: RSP→PTT

Results …

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results Tilt table test : orthostatic stress -> sympathetic activation 0:004:00 4:18 9:18 9:36 13:36 SUPINE (T es ) HEAD-UP (T ht ) SUPINE (T es ) 17 healthy subjects Age: 28.2±2.7 ECG: 1000 Hz RESPIRATION (band): 150Hz ARTERIAL PRESSURE: Finometer (250Hz) Experimental procedure 17/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results Time [s] [s] [mmHg] [au] Inverse Gaussian Gaussian Results : mean parameter 18/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RRIPTT RRIPTT RRI SAPRRI SAPRRI SAP PTT SAPPTT SAP Pow |H| Time [s] Results : median trends Low-frequency band 20/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RRIPTT RRIPTT RRI SAPRRI SAPRRI SAP PTT SAPPTT SAP Pow |H| Time [s] Results : median trends Low-frequency band 20/23 Low contribution RRI→PTT PTT add valuable information for an accurate characterization of cardiovascular regulation

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RRIPTT RRIPTT SAPRRI SAPRRI SAPPTT SAPPTT Pow |H| Time [s] Results : median trends Low-frequency band 20/23 PTTRRI SAP PTTSAP Low contribution RRI→PTT PTT add valuable information for an accurate characterization of cardiovascular regulation Head-up tilt: baroreflex sensitivity ↓ mechanical effect ↑

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RRIPTT RRIPTT SAPRRI SAPRRI SAPPTT SAPPTT Pow |H| Time [s] Results : median trends Low-frequency band 20/23 PTTRRI SAP PTTSAP Low contribution RRI→PTT PTT add valuable information for an accurate characterization of cardiovascular regulation Head-up tilt: baroreflex sensitivity ↓ mechanical effect ↑ Autonomic-mediated changes faster than vasculature-mediated ones

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RSPRRI RSPRRI RSP PTT RSPPTT RSP SAP RSPSAP RSP Pow |H| Time [s] Results : median trends Respiratory-frequency band 21/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RSPRRI RSPRRI RSP PTT RSPPTT RSP SAP RSPSAP RSP Pow |H| Time [s] Respiration can be considered a critical external input which drives respiratory- related oscillations in other CV variables Results : median trends Respiratory-frequency band 21/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results RSPRRI RSPRRI RSPPTT RSPPTT RSPSAP RSPSAP Pow |H| Time [s] Respiration can be considered a critical external input which drives respiratory- related oscillations in other CV variables Head-up tilt provoked a decrease in RSA Results : median trends Respiratory-frequency band 21/23 RRIRSP PTTRSP SAPRSP

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Discussion Limitations 22/23 Linear structure of the model No a-priori information → many parameters → slower tracking Pulse transit time estimation No statistical analysis to assess the strength of the coupling

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Discussion Summary & Conclusions 23/23 Propose a model for a comprehensive characterization of cardiovascular functioning Multivariate : Variables: HR, SAP, ILV, PTT Mechanisms: Baroreflex, direct effect of RRI on SAP, RSA, mechanical effect of RESP on SAP, interactions between PTT and other variables to take into account the vasculature Non-stationary : 120-s window with forgetting factor Characterization of Dynamic Interactions Accurate : satisfactory goodness-of-fit

1. University of Zaragoza, CIBER-BBN, Spain 2. University of Pisa, Italy 3. Harvard Medical School, USA Tetra-variate point-process model for the continuous characterization of cardiovascular-respiratory dynamics during passive postural changes Michele Orini 1 Gaetano Valenza 2 Luca Citi 3 Riccardo Barbieri 3

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Physiological aspects Heart rate variability (HRV) Important information about the autonomic control of the circulation LFHF Clinical relevance: miocardial infarction risk of sudden cardiac death. Unclear aspects: Physiological interpretation Origin of LF and HF components HF [ Hz] (T=1/F resp ) Parasympathetic LF [ Hz] (T=10 s) Sympathetic & Parasympathetic Spectral analysis

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Results Results : goodness-of-fit Example (1 subject) good fit Model’s Quintiles Empirical Quintiles Time lag Auto-corr Statistical results (all subject) satisfactory goodness-of-fit 19/23

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis x1x1 x2x2 x3x3 w 1 (t)w 2 (t) w 3 (t) Multivariate autoregressive models (MVAR)

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis x1x1 x2x2 x3x3 w 1 (t)w 2 (t) w 3 (t) Multivariate autoregressive models (MVAR)

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis Spectral analysis Spectra do not provide directional information x1x1 x2x2 x3x3 w 1 (t)w 2 (t) w 3 (t)

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis x1x1 x2x2 x3x3 w 1 (t)w 2 (t) Coherence Coherence does not provide directional information w 3 (t)

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Multivariate analysis x1x1 x2x2 x3x3 w 2 (t) Directed Coherence w 1 (t) w 3 (t)

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Dynamic interactions characterization RRI RSPSAP Tetra-variate model Characterization of autonomic response to tilt-table-test PTT (~pulse wave velocity) represents the vasculature RSP → RRI : Respiratory sinus arrythmia SAP → RRI : Baroreflex RRI → SAP : Direct mechanical effect Probability density functions:  RRI, PTT : Inverse Gaussian  RSP, SAP : Gaussian

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Dynamic interactions characterization RRI PTT RSPSAP Tetra-variate model Characterization of autonomic response to tilt-table-test PTT (~pulse wave velocity) represents the vasculature RSP → RRI : Respiratory sinus arrythmia SAP → RRI : Baroreflex RRI → SAP : Direct mechanical effect Probability density functions:  RRI, PTT : Inverse Gaussian  RSP, SAP : Gaussian

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Dynamic interactions characterization RRI PTT RSPSAP Tetra-variate model Characterization of autonomic response to tilt-table-test PTT (~pulse wave velocity) represents the vasculature RSP → RRI : Respiratory sinus arrythmia SAP → RRI : Baroreflex RRI → SAP : Direct mechanical effect Probability density functions:  RRI, PTT : Inverse Gaussian  RSP, SAP : Gaussian

M. Orini – Tetravariate point-process model for the characterization of cardiovascular-respiratory dynamics – Krakow, 11/09/12 Background Heart rate variability (HRV) Important information about the autonomic control of the circulation LFHF Clinical relevance: miocardial infarction risk of sudden cardiac death. Unclear aspects: Physiological interpretation Origin of LF and HF components HF [ Hz] (T=1/F resp ) Parasympathetic LF [ Hz] (T=10 s) Sympathetic & Parasympathetic Spectral analysis Cardiovascular system: variables 2/23