A statistical modeling of A statistical modeling of mouse heart beat rate variabilitymouse heart beat rate variability

   

Paulo GonçalvesINRIA, France

On leave at IST-ISR Lisbon, Portugal

Joint work with Hôpital Lariboisière Paris, France Pr. Bernard Swynghedauw

Dr. Pascale MansierChristophe Lenoir

Laboratório de Biomatemática, Faculdade de Medicina, Universidade de Lisboa June 15th, 2005

 

Outline

Physiological and pharmacological motivations

Experimental set up

Signal analysis

Statistical analysis

Forthcoming work ?

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

Physiological and pharmacological motivations

Autonomic Nervous System

Sympatheticbranch

accelerates heart beat rate

Parasympathetic (vagal) branch

decelerates heart beat rate

Controls cardiac rythm

Better understanding of the role of sympathovagal balance on

mice heart rate variability

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

1. 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 propranolol ANS blockage

2. Physical conditions• day ECG Resting• night ECG Intensive Activity

Signal Analysis

frequency

Power spectrum densityBeat-to-beat interval (RR)

time VLF LF HF

Sympathetic

branch

Parasympathetic branch

Control

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Signal Analysis

frequency

Power spectrum density

VLF LF HF

Beat-to-beat interval (RR)

time

Sympathetic

branch

Parasympathetic branch

Atropine (effort)

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Signal Analysis

frequency

Power spectrum density

VLF LF HF

Beat-to-beat interval (RR)

time

Sympathetic

branch

Parasympathetic branch

Propranolol (rest)

is an index of the sympathovagal balance Energy (LF)

Energy (HF)

(Akselrod et al. 1981)

Signal Analysis

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Control Atropine

Propranolol Atropine & propranololTime (s)

RR (ms)

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

Signal Analysis

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Day RR time series (resting) Night RR time series (active)

Time (s)

RR (ms)

Signal Analysis

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VLF LF HF Frequency (Hz)

Power spectrum density

Time (s)

RR (ms)

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Need to separate (non-stationary) low frequency trends from high frequency spike train (shot noise)

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Signal Analysis: Empirical Mode 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.

Entirely adaptive signal decomposition

Signal Analysis: Empirical Mode Decomposition

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A LF sawtooth

A linear FM

+

=

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

First Intrinsic Mode Function

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

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Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

Second Intrinsic Mode Function

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

Third Intrinsic Mode Function

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

Residu

SIFTING

PROCESS

Signal Analysis: Empirical Mode Decomposition

Signal

1st Intrinsic Mode Function

2nd Intrinsic Mode Function

3rd Intrinsic Mode Function

Residu

Signal Analysis: Empirical Mode Decomposition

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30HF

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150LF + VLF

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Signal Analysis: Empirical Mode Decomposition

Day heart rate variability

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Night heart rate variability

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

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Signal Analysis: Empirical Mode Decomposition

Day heart rate variability

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Night heart rate variability

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

spectrally

Statistical modeling

Empirical distributions of RR-intervals

Non Gaussian distributions

Normal plots

Similar tachycardia for day and night HRV Symmetric distribution for night RR Heavy tail distribution for day RR

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 (?)

Morphological modeling

Impulse model:

h(t) = Ai exp(-(t-ti)/θi) U(t-ti)

ti : random point process to model RR deceleration arrival times

θi

ti

Ai

ti

time

ti+1

Morphological modeling

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 ?)

Impulse parameters estimates

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 ?

Control Atropine

frequency frequency

Power spectrum density Power spectrum density