The simplest Heart Rate Variability continual model

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The simplest Heart Rate Variability continual
model

• Alexander Martynenko
• Kharkov National University, Ukraine

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Aim of the study

• Verify idea we observe representation of
  Autonomic Nervous System (ANS) in Heart Rate
  Variability (HRV) only as discrete function but
  regulation is continuous
• Try to find simple mathematical representation of
  continual ANS regulation of HRV

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First sin model (begin of construction)
Continual RR function
Mean RR
Current RR length
Model RR set
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First sin model (next step)
RR model estimation
Next RR
First step
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First sin model (mathematical description)

• Modelj mean(RR)(max(RR)-mean(RR))sin(2p/mean(R
  R) sum(RRj)f), j observed RR with number j

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Result (compare registered RR vs. modeled)
Correlation0.022
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Result (compare registered spectrum vs. modeled
spectrum)
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Recharging sin model (construction)
Continual RR function
Break point recharge to 0
Mean RR
First step
Next RR
RR model estimation
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Recharging sin model (mathematical description)

• Modelj mean(RR)(max(RR)-
  -mean(RR))sin(2p/mean(RR) RRjf), j observed
  RR with number j
• Model optimization in least-squares
• Modelj mean(RR)OptAmplitude
• sin(2p/mean(RR)RRjOptAngle),
• j observed RR with number j

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Result (compare registered RR vs. modeled)
Correlation0.999
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Result (compare registered spectrum vs. modeled
spectrum)
Correlation1
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Conclusion

• Excellent representation of RR phenomenon by
  recharging sin model (correlation 1)
• Very simple approximative function reflect
  continual and harmonic RR regulation by ANS
• This is starting-point for continual modeling of
  RR and ANS
• Special thanks to Professor Myckola Yabluchansky
  for the discussions around the simplest HRV model