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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
0 10 20 30 40 50 60 70 80 90 1007.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
0 10 20 30 40 50 60 70 80 90 1007
8
9
10
11
12
13
Signal Analysis
frequency
Power spectrum density
VLF LF HF
Beat-to-beat interval (RR)
time
Sympathetic
branch
Parasympathetic branch
Atropine (effort)
0 10 20 30 40 50 60 70 80 90 1007
8
9
10
11
12
13
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
0 50 100 150 200 250 300100
110
120
130
140
150
160
170
0 50 100 150 200 250 300100
110
120
130
140
150
160
170
0 50 100 150 200 250 300100
110
120
130
140
150
160
170
0 50 100 150 200 250 300100
110
120
130
140
150
160
170
Control Atropine
Propranolol Atropine & propranololTime (s)
RR (ms)
Linear Mixed Model proves no significant effect of atropine on HRV baseline
Signal Analysis
0 50 100 150 200 250 300
100
120
140
0 50 100 150 200 250 300
100
120
140
160
180
0 50 100 150 200 250 300100
120
140
0 50 100 150 200 250 30080
100
120
140
160
0 50 100 150 200 250 300100
120
140
160
0 50 100 150 200 250 300
100
120
140
0 50 100 150 200 250 300
100
150
200
0 50 100 150 200 250 30070
80
90
Day RR time series (resting) Night RR time series (active)
Time (s)
RR (ms)
Signal Analysis
0 50 100 150 200 250 30080
100
120
140
160
0 2 4 6 8 1010
-4
10-2
100
102
104
VLF LF HF Frequency (Hz)
Power spectrum density
Time (s)
RR (ms)
0 50 100 150 200 250 30080
100
120
140
160
Need to separate (non-stationary) low frequency trends from high frequency spike train (shot noise)
0 50 100 150 200 250 30080
100
120
140
160
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
0 1
-1
0
1
0 1
-1
0
1
0 1
0
A LF sawtooth
A linear FM
+
=
Signal Analysis: Empirical Mode Decomposition
Signal
1st Intrinsic Mode Function
2nd Intrinsic Mode Function
3rd Intrinsic Mode Function
Residu
Signal Analysis: Empirical Mode Decomposition
0 50 100 150 200 250 30090
100
110
120
130
140
150
0 50 100 150 200 250 300
-15
0
15
30HF
0 50 100 150 200 250 30090
100
110
120
130
140
150LF + VLF
0 50 100 150 200 250 300-50
0
50
0 50 100 150 200 250 300-20
0
20
40
0 50 100 150 200 250 300-20
0
20
0 50 100 150 200 250 300-50
0
50
Signal Analysis: Empirical Mode Decomposition
Day heart rate variability
0 50 100 150 200 250 300
-20
0
20
0 50 100 150 200 250 300-20
0
20
0 50 100 150 200 250 300
0
50
100
0 50 100 150 200 250 300-5
0
5
10
15
Night heart rate variability
Next step: prove significant differences between day and night time series statistically spectrally
0 50 100 150 200 250 300-50
0
50
0 50 100 150 200 250 300-20
0
20
40
0 50 100 150 200 250 300-20
0
20
0 50 100 150 200 250 300-50
0
50
Signal Analysis: Empirical Mode Decomposition
Day heart rate variability
0 50 100 150 200 250 300
-20
0
20
0 50 100 150 200 250 300-20
0
20
0 50 100 150 200 250 300
0
50
100
0 50 100 150 200 250 300-5
0
5
10
15
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