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Heart rate variability: challenge for both experiment and modelling

I. Khovanov,. Heart rate variability: challenge for both experiment and modelling. N. Khovanova, P. McClintock, A. Stefanovska. Physics Department, Lancaster University. Outline ● Motivations ● Experiment ● Modelling ● Summary. Heart rate variability (HRV).

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Heart rate variability: challenge for both experiment and modelling

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  1. I. Khovanov, Heart rate variability: challenge for both experiment and modelling N. Khovanova, P. McClintock, A. Stefanovska Physics Department, Lancaster University

  2. Outline ● Motivations ● Experiment ● Modelling ● Summary Heart rate variability (HRV)

  3. Heart rate variability (HRV) The object of investigation is heart rate SinoAtrial Node ElectroCardioGram Heart Rate Variability

  4. Heart rate variability (HRV) 24h RR-intervals Medical people: Average over one hour rhythm RR-intervals, sec Physicists: Entropies, Dimensions, Long-range correlation, Scaling, Multifractal etc Number of interval

  5. Heart rate variability (HRV) Vagal SAN HRV is the product of the integrative control system Cortex (higher centres) Parasympathetic branch Vagus nerve fibres Fast and - Hypothalamus + - Input Nucleous Symp - Medulla Sympathetic branch Postganglionic fibres Slow and + From receptor afferents: baro-receptors, chemo-receptors, stretch receptors etc

  6. Respiration masks other rhythms respiration Circles corresponds to RR-intervals, Dashed line corresponds to respiration

  7. Use of apnoea (breath holding)? 1) The use of breath holding as longer as possible, BUT physiologists discussed a long breath holding as one of unsolved problems with a specific dynamics (Parkers, Exp. Phys. 2006) 2) We can notice: In spontaneous respiration there are apnoea intervals (not very long) An idea is to prolong by keeping normocapnia Physiology literature said 30 sec is fine(!)

  8. Specific form of respiration Intermittent type (intervals of fixed duration, 30 sec)

  9. Intrinsic dynamics of regulatory system The idea is to consider HRV without dominate external perturbation, but keeping all internal perturbation and without modification of a net of regulatory networks The task is to study intrinsic dynamics on short-time scales ●Special design of experiments: relaxed, supine position,records of 45-60 minutes ●Time-series analysis of sets of short time-series (appr. 40Apn.int X 35RR-int)

  10. Decomposition (nonlinear transformation) of heart rate by specific forms of respiration Circles corresponds to RR-intervals, Dashed line corresponds to respiration respiration Object of analysis: a set of RR-intervals {RRi}j corresponded to apnoea intervals

  11. Non-stationary dynamics of RR-intervals. RR-intervals RRi-RR1 [sec] Increments DRR DRRi=RRi-RRi-1 DRRi-DRR1 [sec] Number of interval, i

  12. Non-stationary dynamics of RR-intervals. RR-intervals during apnoea intervals is non-stationary. The use of random walk framework. DFA (detrended fluctuational analysis): scaling exponent b (Peng’95) Aggregation analysis: scaling exponent b (West’05) Both methods for the considered time-series estimate a diffusion velocity

  13. Scaling exponent bby DFA DFA method (C.-K. Peng, Chaos,1995) (1) Integration of RR-intervals: (2) Calculation of linear trend yn(k) for time window of length n (3) Calculation of scaling function for set of n n (4) Determination of b b=1,5 corresponds to Brown noise (free Brownian motion)

  14. Scaling exponent bby aggregation analysis Aggregation method (B. J. West, Complexity, 2006) Invention by L. R. Taylor, Nature, 1961 (1) Creating a set of aggregated time-series: (2) Calculation of the variance and mean for each m=1,2…: (3) Determination of b b=2 corresponds to Brown noise (free Brownian motion) The aggregation method is close to the stability test for the increments DRR

  15. Scaling exponents b and bon the base of 24h RR-intervals DFA and the aggregation method in the presence respiration (the previous published results) Brown noise, Brownian motion White noise

  16. Scaling exponents b and bRR-intervals during apnoea DFA and the aggregation method without respiration Brown noise, Brownian motion White noise

  17. Dynamics of increments DRR. ACF RR-intervals during apnoea intervals is non-stationary. So let us use stationaryincrements DRRi=RRi-RRi-1 then use the modified definition of ACF r(t) to use non-overlapped windows corresponding apnoea intervals t - time delay kj – number of RR-intervals in each apnoea N –total number of apnoea intervals Finally use fitting by the function

  18. ACF of DRR-intervals Fast decay of ACF with weak oscillations near 0.1 Hz Crosses corresponds to calculations using DRR The solid line corresponds to approximation by Oscillations are on-off nature and observed for parts of apnoea intervals and, not in all measurements.

  19. Distribution of increments of RR-intervals P(DRR) Calculate histogram and fit by a-stable distribution. A random variable X is stable, if for X1 and X2independent copies of X, the following equality holds: Means equality in distribution a is a stability index defines the weight of tails a=2 a=1.5 a=1 a=0.5 a=2 Normal (Gaussian) distribution a=1 Cauchy (Lorentz) distribution

  20. Distribution of increments of RR-intervals Yellow areas and cycles correspond to histograms The solid lines is fit by the normal distribution (a=2) The dashed lines corresponds to the a-stable distributions Apnoea intervals The previous published results for 24h RR-intervals

  21. HRV intrinsic dynamics Summary of experimental results: RR-intervals show stochastic diffusive dynamics. HRV during apnoea can be described as a stochastic process with stationary increments Increments DRR describes by a-stable process with a weak correlation In zero approximation DRR corresponds to uncorrelated normal random process and RR-intervals show classical free Brownian motion. Conclusion: Intrinsic dynamics is a result of integrative action of many weakly interacting components

  22. Modelling Heart beat is initiated in SAN Sinoatrial node

  23. Modelling Isolated heart (e.g. in case of brain dead) No signal from nervous system Nearly periodic oscillations, but heart rate is 200 beats/min whereas in normal state 60-80 beats/min

  24. Modelling Vagal activation ●Decreasing depolarization slope ● Increasing hyperpolarization potential Parasympathetic branch Vagus nerve fibres Fast and - Threshold potential Potential of hyperpolarization Slope of depolarization

  25. Modelling Sympathetic activation ● Increasing depolarization slope ● Decreasing hyperpolarization potential Sympathetic branch Postganglionic fibres Slow and +

  26. Modelling Integrate & Fire model Threshold potential Ut Integration slope 1/t ti ti+1 ti+2 Ur Hyperpolarization potential Random numbers having the stable distribution

  27. Modelling FitzHugh-Nagumo model ● Additive versus multiplicative noise ● Noise properties What kind of noise will produce non-Gaussianity of incrementsDRR

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