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A statistical modeling of mouse heart beat rate variability Paulo Gonçalves INRIA, France

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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

Laboratório de Biomatemática, Faculdade de Medicina,

Universidade de LisboaJune 15th, 2005

Outline

- Physiological and pharmacological motivations
- Experimental set up
- Signal analysis
- Statistical analysis
- Forthcoming work ?

- Statistical analysis

- Signal analysis

- Experimental set up

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

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

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

Sympathetic

branch

Parasympathetic branch

VLF

LF

HF

Signal Analysis

Control

Beat-to-beat interval (RR)

Power spectrum density

time

frequency

Signal Analysis

Atropine

(effort)

Beat-to-beat interval (RR)

Power spectrum density

Sympathetic

branch

Parasympathetic branch

time

frequency

VLF

LF

HF

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

RR (ms)

Time (s)

Signal Analysis

Control

Atropine

Propranolol

Atropine & propranolol

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

Signal Analysis

Day RR time series (resting)

Night RR time series (active)

RR (ms)

Time (s)

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)

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.

Signal Analysis: Empirical Mode Decomposition

A LF sawtooth

+

A linear FM

=

Signal Analysis: Empirical Mode Decomposition

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Signal Analysis: Empirical Mode Decomposition

HF

LF + VLF

Signal Analysis: Empirical Mode Decomposition

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

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

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

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 (?)

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

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 ?)

- — not a periodic process

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 ?

- — A consistent cardiovascular regulation system