Nonlinear dynamic system analyzing for heart rate variability mathematical model

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Nonlinear dynamic system analyzing for heart rate
variability mathematical model

• A.Martynenko M. Yabluchansky
• Kharkov National University (Ukraine)

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• HRV naturally observing phenomenon of nonlinear
  dynamic behavior of the cardiovascular system
• Non Linear Mathematical Model (NL MM) of HRV
• Why do we need this model?
• What is the advantage of NL MM for investigation
  of ANS?

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Mathematical model differential equations

• Regulatory (ANS) group Nonlinear dynamic
  quasi-periodical processes in humoral (1),
  sympathetic (2), parasympathetic (3) branches of
  nervous system
• d2(ANSi)/dt2 Fi(Ri ?d(ANSi)/dt, Ai ?ANSi, Sj
  ?ANSj, BioMechanics), i,j 1,2,3,
• BioMechanics group equations that describe
  function of biomechanical parameters forming ANS
  activity
• d2(BMi)/dt2 Bi(Ri ?d(BMi)/dt, Ai ?BMi, HRñ,
  ANS), i 4,5,6,
• HR equation - describe HR changes from cycle to
  cycle
• d2(HRñ)/dt2 fi(R ?d(HRñ)/dt, A ?HRñ,Sj ?ANSj),
  j 1,2,3.

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Scheme of cardiovascular regulation(cross-linkage
in mathematical model)
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HRV (corr0.993) and spectrum (corr0.999)
(registration vs. model)
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First result of NL MM new technique of spectral
domain separation
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Nlyzer by TU Darmstadt
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Standard nonlinear analyzes

• Fractal Dimension (D2)
• HRV 4.74 5.3
• ECG 2.65 3.5
• N points for embedding
• N1020.4D210000
• Autocorrelation for time delay
• Entropy and mutual information

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Lorentz attractor (D22.06)
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Attractor reconstruction (20 min)
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Attractor reconstruction (2500 heartbeat)
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Attractor reconstruction (5000 heartbeat)
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Attractor reconstruction (10000 heartbeat)
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Attractor reconstruction (15000 heartbeat)
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Attractor reconstruction (20000 heartbeat or
about 5 hours)
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Attractor reconstruction (3minMM)
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Attractor reconstruction (15000 heartbeat)
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Poincare map (3 min MM)
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Attractor reconstruction (3 min MM)
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Attractor reconstruction (3 min MM)
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HRV attractor and its P-map
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Conclusion

• Cardiovascular regulation is nonlinear dynamic
  system, and then we need nonlinear mathematical
  modeling for their investigation.
• Advantages of NL MM
• New technique of spectra domain separation
• Great time compression We dont need 4-5 hours
  of registration for attractor reconstruction
  only 3 min of registration and NL MM
• Attractor visualization in Humoral - Sympathetic
  - Parasympathetic phase space is very good