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 15 th, 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 Sympathetic branch 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

Signal Analysis frequency Power spectrum density VLF LF HF Beat-to-beat interval (RR) time Sympathetic branch Parasympathetic branch Atropine (effort)

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 ControlAtropine PropranololAtropine & propranolol Time (s) RR (ms) Linear Mixed Model proves no significant effect of atropine on HRV baseline

Signal Analysis Day RR time series (resting)Night RR time series (active) Time (s) RR (ms)

Signal Analysis VLFLFHF Frequency (Hz) Power spectrum density Time (s) RR (ms) Need to separate (non-stationary) low frequency trends from high frequency spike train (shot noise)

Signal Analysis: Empirical Mode Decomposition Objective — From one observation of x(t), get a AM-FM type representation K x(t) = Σ a k (t) Ψ k (t) k=1 with a k (.) amplitude modulating functions and Ψ 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. Entirely adaptive signal decomposition

Signal Analysis: Empirical Mode Decomposition A LF sawtooth A linear FM + =

Signal Analysis: Empirical Mode Decomposition SIFTINGPROCESSSIFTINGPROCESS

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HF LF + VLF

Signal Analysis: Empirical Mode Decomposition Day heart rate variabilityNight heart rate variability Next step: prove significant differences between day and night time series statistically spectrally

Signal Analysis: Empirical Mode Decomposition Day heart rate variabilityNight 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: P Y (y|b,c) = c b /Γ(b) y b-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) = A i exp(-(t-t i )/θ i ) U(t-t i ) t i : random point process to model RR deceleration arrival times θiθi titi AiAi titi time t i+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 ? ControlAtropine frequency Power spectrum density