Diapositive 1

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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 Lisboa June 15th, 2005  
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Outline

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

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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
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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
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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 propranolol
  ANS blockage
• Physical conditions
• day ECG Resting
• night ECG Intensive Activity

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Signal Analysis
Control
Power spectrum density
Beat-to-beat interval (RR)
frequency
time
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Signal Analysis
Atropine (effort)
Power spectrum density
Beat-to-beat interval (RR)
Sympathetic branch
Parasympathetic branch
frequency
time
VLF
LF
HF
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Signal Analysis
Propranolol (rest)
Power spectrum density
Beat-to-beat interval (RR)
Sympathetic branch
Parasympathetic branch
frequency
time
VLF
LF
HF
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Signal Analysis
Control
Atropine
Propranolol
Atropine propranolol
Linear Mixed Model proves no significant effect
of atropine on HRV baseline
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Signal Analysis
Day RR time series (resting)
Night RR time series (active)
RR (ms)
Time (s)
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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)
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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) S ak(t) ?k(t) k1 with ak(.)
amplitude modulating functions and ?k(.)
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.
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Signal Analysis Empirical Mode Decomposition
A LF sawtooth

A linear FM

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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
S I F T I N G P R O C E S S
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Signal Analysis Empirical Mode Decomposition
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Signal Analysis Empirical Mode Decomposition
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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

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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

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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

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Statistical modeling
We use Gamma probability distributions to fit RR
data PY(yb,c) cb/G(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 (?)

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Morphological modeling
Ai
?i
ti
Impulse model h(t) Ai exp(-(t-ti)/?i)
U(t-ti) ti random point process to model RR
deceleration arrival times
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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 ?)

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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 ?