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A statistical modeling of mouse heart beat rate variability Paulo Gonçalves INRIA, France On leave at IST-ISR Lisbon, Portugal Joint work with Hôpital Lariboisière Paris, France Pr. Bernard Swynghedauw Dr. Pascale Mansier Christophe Lenoir

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

A statistical modeling of

mouse heart beat rate variability

Paulo Gonçalves

INRIA, France

On leave at IST-ISR Lisbon, Portugal

Joint work with Hôpital Lariboisière Paris, France

Pr. Bernard Swynghedauw

Dr. Pascale Mansier

Christophe Lenoir

Laboratório de Biomatemática, Faculdade de Medicina,

Universidade de LisboaJune 15th, 2005


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Outline

  • Physiological and pharmacological motivations

    • Experimental set up

      • Signal analysis

        • Statistical analysis

          • Forthcoming work ?


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Physiological and pharmacological motivations

Cardiovascular research and drugs testing protocoles are conducted on various mammalians: rats, dogs, monkeys…

Share the same vagal (parasympathetic) tonus as humans

Cardiovascular system of mice has not been very investigated

Difficulty of telemetric measurements on

non anaesthetized freely moving animals

Economic stakes prompts the use of mice for pharmacological developments

Recent integrated technology allows in vivo studies


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Controls cardiac rythm

Physiological and pharmacological motivations

Autonomic Nervous System

Sympathetic

branch

accelerates

heart beat rate

Parasympathetic

(vagal) branch

decelerates

heart beat rate

Better understanding of the role of sympathovagal balance on

mice heart rate variability


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Experimental setup

  • Sample set: eighteen male C57bl/6 mice (10 to 14 weeks old)

  • A biocompatible transmitter (TA10ETA-F20, DataSciences International)

  • implanted (under isofluran mixture with carbogene anaesthesia 1.5 vol %)

  • Electro-cardiograms recorded via telemetric instrumentation

  • (Physiotel Receiver RLA1020, DataSciences International) at a 2KHz sampling frequency

  • on non anaesthetized freely moving animals

  • Pharmacological conditions:

    • saline solution (placebo) Control

    • saturating dose of atropine (1 mg/kg)Parasympathetic blockage

    • saturating dose of propranolol (1 mg/kg) Sympathetic blockage

    • combination of atropine and propranololANS blockage

  • Physical conditions

    • day ECG Resting

    • night ECG Intensive Activity


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Sympathetic

branch

Parasympathetic branch

VLF

LF

HF

Signal Analysis

Control

Beat-to-beat interval (RR)

Power spectrum density

time

frequency


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis

Atropine

(effort)

Beat-to-beat interval (RR)

Power spectrum density

Sympathetic

branch

Parasympathetic branch

time

frequency

VLF

LF

HF


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

is an index of the sympathovagal balance

Energy (LF)

Energy (HF)

(Akselrod et al. 1981)

Signal Analysis

Propranolol

(rest)

Beat-to-beat interval (RR)

Power spectrum density

Sympathetic

branch

Parasympathetic branch

time

frequency

VLF

LF

HF


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

RR (ms)

Time (s)

Signal Analysis

Control

Atropine

Propranolol

Atropine & propranolol

Linear Mixed Model proves no significant effect of atropine on HRV baseline


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis

Day RR time series (resting)

Night RR time series (active)

RR (ms)

Time (s)


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

VLF

LF

HF

Signal Analysis

Power spectrum density

RR (ms)

Time (s)

Frequency (Hz)

Need to separate (non-stationary) low frequency trends

from high frequency spike train (shot noise)


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

Entirely adaptive signal decomposition

Objective— From one observation of x(t), get a AM-FM type representation

K

x(t) = Σ ak(t) Ψk(t)k=1

with ak(.) amplitude modulating functions and Ψk(.) oscillating functions.

Idea— “signal = fast oscillations superimposed to slow oscillations”.

Operating mode—(“EMD”, Huang et al., ’98)

(1) identify locally in time, the fastest oscillation ;

(2) subtract it from the original signal ;

(3) iterate upon the residual.


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

A LF sawtooth

+

A linear FM

=


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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P

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O

C

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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F

T

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G

P

R

O

C

E

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

I

F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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P

R

O

C

E

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S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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N

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P

R

O

C

E

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S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

I

F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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G

P

R

O

C

E

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S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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P

R

O

C

E

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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F

T

I

N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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F

T

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P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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P

R

O

C

E

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S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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T

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P

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O

C

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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P

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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P

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O

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

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T

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P

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O

C

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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P

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O

C

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A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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G

P

R

O

C

E

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S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

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N

G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

N

G

P

R

O

C

E

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S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

S

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F

T

I

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G

P

R

O

C

E

S

S


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

HF

LF + VLF

Signal Analysis: Empirical Mode Decomposition


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

Day heart rate variability

Night heart rate variability

  • Next step: prove significant differences between day and night time series

  • statistically

  • spectrally


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Signal Analysis: Empirical Mode Decomposition

Day heart rate variability

Night heart rate variability

  • Next step: prove significant differences between day and night time series

  • statistically

  • spectrally


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Normal plots

Statistical modeling

Empirical distributions of RR-intervals

  • Non Gaussian distributions

  • Similar tachycardia for day and night HRV

  • Symmetric distribution for night RR

  • Heavy tail distribution for day RR


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Statistical modeling

We use Gamma probability distributions to fit RR data:

PY(y|b,c) = cb/Γ(b) yb-1 e-cy U(y)

Hypothesis testing : variance analysis

  • Deceleration spike trains are :

    • Not individual mouse effects

    • An impulsive command to control mice sympathovagal balance (?)


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

time

ti+1

ti

Morphological modeling

Ai

θi

ti

Impulse model:

h(t) = Ai exp(-(t-ti)/θi) U(t-ti)

ti : random point process to model RR deceleration arrival times


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Morphological modeling

Impulse parameters estimates

  • Time constant (impulse duration) is reasonably constant

  • (~ 10 inter-beat intervals)

  • Spike amplitude is not highly variable

    (RR intervals increase by ~ 25% during HR decelerations)

  • Intervals between deceleration spikes is extremely variable

    • — not a periodic process

      — not a Poisson process

      — long range dependence (long memory process ?)


A statistical modeling of mouse heart beat rate variability paulo gon alves inria france

Power spectrum density

Power spectrum density

Control

Atropine

frequency

frequency

Forthcoming work…

There is still a lot to do…

  • Methodology :

    • Characterize the underlying point process

    • Understand the spectral signature of this impulse control

      (does sympathovagal balance still hold ?)

    • Compound control system with standard continuous regulation ?

  • Physiology :

    • Identify the respective roles of sympathetic and

    • parasympathetic branches of ANS

    • Support this conjecture with physiological evidences :

      • — A consistent cardiovascular regulation system

        • (nerve spike trains)

      • — Why should mice be different from other mammalians ?

      • — Is this a kind specificity or a strain specificity ?


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