1. University of Zaragoza, CIBER-BBN, Spain 2. University of Pisa, Italy 3. Harvard Medical School,...

1. University of Zaragoza, CIBER-BBN, Spain2. 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 Orini1 Gaetano Valenza2 Luca Citi3

Riccardo Barbieri3

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: variablesSympathetic/

Parasympathetic Nervous System

Respiration

1/23


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


Background


Afferent flow

Cardiovascular system: mechanismsBaroreflex Negative feedback that buffers short term changes in arterial

pressure by modifying heart rate and peripheral resistance

2/23


Background


Afferent flowParasympathetic



2/23


Background


Afferent flowParasympatheticSympathetic



2/23


Background

Respiratory sinus arrhythmia: HRV in synchrony with respiration

Cardiovascular system: mechanisms

3/23

ECG

Resp

iratio

n


Background

Time

ECG

APRE

SP

Non-invasive measurements

1 s

Cardiovascular system: dynamic interactions

4/23


Background

Time

RRI

SAP

RESP


1 s


4/23


Background

Time

RRI

SAP

RESP


1 s


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


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 …


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


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: H424-435, 2005.Barbieri R., Brown EN. Analysis of heart dynamics by point process adaptive filtering. IEEE Transactions on Biomedical Engineering, 53(1), 4-12, 2006.

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


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

=1=2=5

8/23

Time

Time

Beats


Point processes

Point-Process: Interbeat Interval Probability ModelProbability of observing the next beat (t > follows an Inverse Gaussian distribution of mean and shape parameter

is a linear function of P past heart period→ History dependent Inverse Gaussian

→ Maximization of local likelihood (right censoring)

9/23


Point processes

Point-Process: Goodness of Fit

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Conditional Intensity Function Rescaled Time Series

zn 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

Empi

rical

Qui

ntile

s

95% confidence interval

10/23


Point processes

0 5 10 15 20

-0.2

-0.1

0

0.1

0.2

Conditional Intensity Function Rescaled Time Series

zn are independent random variables in [0,1]

(time-rescaling theorem)

Autocorrelation of zn to test statistical independence

Time Lag

Corr

elati

on

95% confidence interval

Point-Process: Goodness of Fit

11/23


Multivariate analysis

Registro-01M ECG

Tetra-variate model

12/23



Registro-01M ECG

Tetra-variate model

𝒘𝒏𝑹𝑹𝑰

𝒘𝒏𝑷𝑻𝑻

𝒙𝒏𝑹𝑺𝑷

×

×𝒙𝒏𝑺𝑨𝑷

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Registro-01M ECG

Tetra-variate model

𝒘𝒏𝑹𝑹𝑰

𝒘𝒏𝑷𝑻𝑻

𝒙𝒏𝑹𝑺𝑷

×

×𝒙𝒏𝑺𝑨𝑷

𝒙𝒏+𝟏𝑹𝑺𝑷

×𝒘𝒏+𝟏

𝑹𝑹𝑰

×𝒙𝒏+𝟏𝑺𝑨𝑷

𝒘𝒏+𝟏𝑷𝑻𝑻

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RRI PTT

RSP SAP

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



RRI PTT

RSP SAP

Tetra-variate model

PTT can be modeled as a point process triggered by another point

process, the RRIOrini et al. EMBC conf, 2012


• 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


Dynamic interactions characterization

Transfer Function

Spectra

Directed Coherence

Indices of Interaction

15/23



(1)RRI

(2)PTT

(4)RSP

(3) SAP

when xj xi when there is at least one pathway (direct or indirect) from xj to xi

𝑆 𝑖𝑖=∑𝑚=1

𝑀

¿𝛾𝑖 𝑚𝐷𝐶∨2𝑆𝑖𝑖

: part of due to xm

Directed Coherence : causal index

Indices of Interaction

16/23

Example: RSP→PTT

Results …


Results

Tilt table test : orthostatic stress -> sympathetic activation

0:00 4:004:18

9:189:36

13:36SUPINE (Tes) HEAD-UP (Tht) SUPINE (Tes)

17 healthy subjects Age: 28.2±2.7• ECG: 1000 Hz• RESPIRATION (band): 150Hz• ARTERIAL PRESSURE: Finometer (250Hz)

Experimental procedure

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Results

0.25

0.3

0.6

0.8

100

150

0 100 200 300 400 500 600 700 800-2

0

2

Time [s]

𝜇𝑅𝑅𝐼 (𝑡)

𝜇𝑃𝑇𝑇 (𝑡)

𝜇𝑆𝐴𝑃 (𝑡)

𝜇𝑅𝑆𝑃 (𝑡)

[s]

[s]

[mm

Hg]

[au]

Inverse Gaussian

Inverse Gaussian

Gaussian

Gaussian

Results : mean parameter

18/23


Results

0.2

0.8

DC

med

(t)

0.2

0.8

0.2

0.8

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RRI PTT

RRI PTT

PTT RRI

SAP RRI

SAP RRI

RRI SAP

SAP PTT

SAP PTT

PTT SAP

Pow

|H|

||

Time [s] Time [s] Time [s]

Results : median trends

Low-frequency band

20/23


Results

0.2

0.8

DC

med

(t)

0.2

0.8

0.2

0.8

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RRI PTT

RRI PTT

PTT RRI

SAP RRI

SAP RRI

RRI SAP

SAP PTT

SAP PTT

PTT SAP

Pow

|H|

||



Low-frequency band

20/23

Low contribution RRI→PTT PTT add valuable

information for an accurate characterization of

cardiovascular regulation


Results

0.2

0.8

DC

med

(t)

0.2

0.8

0.2

0.8

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RRI PTT

RRI PTT

SAP RRI

SAP RRI

SAP PTT

SAP PTT

Pow

|H|

||



Low-frequency band

20/23

PTT RRI RRI SAP PTT SAP




Head-up tilt: baroreflex sensitivity ↓

mechanical effect ↑


Results

0.2

0.8

DC

med

(t)

0.2

0.8

0.2

0.8

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RRI PTT

RRI PTT

SAP RRI

SAP RRI

SAP PTT

SAP PTT

Pow

|H|

||



Low-frequency band

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PTT RRI RRI SAP PTT SAP




Head-up tilt: baroreflex sensitivity ↓

mechanical effect ↑

Autonomic-mediated changes faster than

vasculature-mediated ones


Results

0.2

1

0.2

1

0.2

1

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RSP RRI

RSP RRI

RRI RSP

RSP PTT

RSP PTT

PTT RSP

RSP SAP

RSP SAP

SAP RSP

Pow

|H|

||



Respiratory-frequency band

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Results

0.2

1

0.2

1

0.2

1

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RSP RRI

RSP RRI

RRI RSP

RSP PTT

RSP PTT

PTT RSP

RSP SAP

RSP SAP

SAP RSP

Pow

|H|

||


Respiration can be considered a critical external input which

drives respiratory-related oscillations in

other CV variables



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Results

0.2

1

0.2

1

0.2

1

0 258 558 780 0 258 558 780 0 258 558 7800 258 558 780 0 258 558 780 0 258 558 780

RSP RRI

RSP RRI

RSP PTT

RSP PTT

RSP SAP

RSP SAP

Pow

|H|

||


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



21/23

RRI RSP PTT RSP SAP RSP


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


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, Spain2. 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 Orini1 Gaetano Valenza2 Luca Citi3

Riccardo Barbieri3


Background

Physiological aspectsHeart rate variability (HRV)

Important information about the autonomic control of the circulation

LF HF

Clinical relevance:• miocardial infarction • risk of sudden cardiac death.

Unclear aspects:• Physiological interpretation • Origin of LF and HF components

• HF [0.15-0.4 Hz] (T=1/Fresp ) Parasympathetic• LF [0.04-0.15 Hz] (T=10 s) Sympathetic & Parasympathetic

Spectral analysis


Results

0.7

1

1.3

120 240 360 480 600 720

0.05

0.1

0 0.5 10

0.5

1

0 5 10 15 20

-0.2

-0.1

0

0.1

0.2

𝜇𝑅𝑅𝐼

❑(𝑡

)𝜎

𝑅𝑅𝐼

❑(𝑡

)

Results : goodness-of-fitExample (1 subject)

good fit

Model’s Quintiles

Empi

rical

Qui

ntile

s

Time lag

Auto

-cor

r

Statistical results (all subject)satisfactory

goodness-of-fit19/23



x1 x2

x3

w1(t) w2(t)

w3(t)

𝑥3 (𝑛 )=∑𝑘=1

𝑃

𝑎31(𝑘)𝑥1 (𝑛−𝑘 )+¿∑𝑘=1

𝑃

𝑎32(𝑘)𝑥2 (𝑛−𝑘 )+¿∑𝑘=1

𝑃

𝑎33(𝑘)𝑥3 (𝑛−𝑘)+𝑤3(𝑛)¿¿

𝑥1 (𝑛)=∑𝑘=1

𝑃

𝑎11(𝑘)𝑥1 (𝑛−𝑘 )+¿∑𝑘=1

𝑃

𝑎12(𝑘)𝑥2 (𝑛−𝑘 )+¿∑𝑘=1

𝑃

𝑎13(𝑘)𝑥3 (𝑛−𝑘)+𝑤1(𝑛)¿ ¿

𝑥2 (𝑛)=∑𝑘=1

𝑃

𝑎21(𝑘)𝑥1 (𝑛−𝑘 )+¿∑𝑘=1

𝑃

𝑎22(𝑘)𝑥2 (𝑛−𝑘 )+¿∑𝑘=1

𝑃

𝑎2(𝑘)𝑥3 (𝑛−𝑘 )+𝑤2(𝑛)¿¿

influence that xj(n-k) exerts over xi(n)

Multivariate autoregressive models (MVAR)



𝑿 (𝑛)=∑𝑘=1

𝑃

𝑨 (𝑘 ) 𝑿 (𝑛−𝑘 )+𝑾 (𝑛)

[𝑥1(𝑛)𝑥2(𝑛)𝑥3(𝑛) ]=∑

𝑘=1

𝑃 [𝑎11(𝑘) 𝑎1 2(𝑘) 𝑎1 3(𝑘)𝑎2 1(𝑘) 𝑎22(𝑘) 𝑎23(𝑘)𝑎31(𝑘) 𝑎32(𝑘) 𝑎33(𝑘)] [𝑥1(𝑛−𝑘)

𝑥2(𝑛−𝑘)𝑥3(𝑛−𝑘)]+[𝑤1(𝑛)

𝑤(𝑛)𝑤3 (𝑛)]

𝑿 ( 𝑓 )=𝑨 ( 𝑓 ) 𝑿 ( 𝑓 )+𝑾 ( 𝑓 )

𝑿 ( 𝑓 )=𝑯 ( 𝑓 )𝑾 ( 𝑓 )

𝑨 ( 𝑓 )=∑𝑘=1

𝑃

𝑨 (𝑘)𝑒−𝑖2 𝜋 𝑓𝑘𝑇

𝐇 ( 𝑓 )= 1𝑰 −𝑨 ( 𝑓 )

x1 x2

x3

w1(t) w2(t)

w3(t)

Multivariate autoregressive models (MVAR)



Spectral analysis

𝑺 ( 𝑓 )=𝑯 ( 𝑓 )𝜮 𝑯𝐻 ( 𝑓 )

𝑆23 ( 𝑓 )=[𝐻21 ( 𝑓 )𝐻 2 2 ( 𝑓 ) 𝐻2 3( 𝑓 )][𝜎1 12 0 0

0 𝜎 222 0

0 0 𝜎332 ] [𝐻31

∗ ( 𝑓 )𝐻32

∗ ( 𝑓 )𝐻33

∗ ( 𝑓 )]𝑆23 ( 𝑓 )=𝑆3 2

∗ ( 𝑓 )

Spectra do not provide directional information

x1 x2

x3

w1(t) w2(t)

w3(t)



x1 x2

x3

w1(t) w2(t)

Coherence

Γ 𝑖𝑗 ( 𝑓 )=𝑆𝑖𝑗( 𝑓 )

√𝑆𝑖 𝑖( 𝑓 )𝑆 𝑗𝑗 ( 𝑓 )

Γ 23 ( 𝑓 )=𝑆23( 𝑓 )

√𝑆22( 𝑓 )𝑆33( 𝑓 )

=1 → at

=0 → at

Γ 23 ( 𝑓 )=Γ32∗ ( 𝑓 )

Coherence does not provide directional information

0<Γ𝑖𝑗 ( 𝑓 0 )<1

w3(t)



x1 x2

x3

w2(t)

Directed Coherence𝑑 Γ 𝑖𝑗 ( 𝑓 )=

𝜎 𝑗𝐻 𝑖𝑗( 𝑓 )

√∑𝑚=1

𝑀

𝜎𝑚2 ∨𝐻 𝑖 𝑚 ( 𝑓 )∨2

𝑑 Γ23 ( 𝑓 )=𝜎 3𝐻 23( 𝑓 )

√𝜎12𝐻 21 ( 𝑓 )+𝜎 2

2𝐻 22 ( 𝑓 )+𝜎 32 𝐻23 ( 𝑓 )

0<𝑑 Γ𝑖𝑗 ( 𝑓 0 )<1

w1(t)

Causal index:when xi xj, i.e. when there at least one pathway (direct or indirect) from xj to xi

𝑆 𝑖𝑖( 𝑓 )=∑𝑚=1

𝑀

¿𝑑 Γ 𝑖𝑚 ( 𝑓 )∨2𝑆𝑖𝑖 ( 𝑓 )

Part of due to xm(t)

w3(t)



RRI

RSP SAP

Tetra-variate modelCharacterization 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




RRI PTT

RSP SAP

Tetra-variate modelCharacterization 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



Background

Heart rate variability (HRV) Important information about the autonomic control of the circulation

LF HF

Clinical relevance:• miocardial infarction • risk of sudden cardiac death.

Unclear aspects:• Physiological interpretation • Origin of LF and HF components

• HF [0.15-0.4 Hz] (T=1/Fresp ) Parasympathetic• LF [0.04-0.15 Hz] (T=10 s) Sympathetic & Parasympathetic

Spectral analysis

Cardiovascular system: variables

2/23

1. University of Zaragoza, CIBER-BBN, Spain 2. University of Pisa, Italy 3. Harvard Medical School,...

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Transcript of 1. University of Zaragoza, CIBER-BBN, Spain 2. University of Pisa, Italy 3. Harvard Medical School,...