Putting your Heart into Physics

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Putting your Heartinto Physics

• Jonas Sperber (Medical Student)
• Axel Urhausen (Medical Doctor, Professor,
  Physician for
• Olympic Rowing Team)
• Peter Siegel (Physicist)
• Wilfred Kindermann (Medical Doctor, Head of
  Institute,
• Professor, Former European
  Champion, Physician
• for German National Soccer
  Team, Olympic Team,
• etc. )
• Institut fuer Sport- und Praeventivmedizin
• Universitaet des Saarlandes

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Outline

• 1. Measurement of RR intervals
• 2. Some Physiology (three time scales)
• Short Time Scale (3-4 seconds)
• Response function of the heart (short time
  scale)
• a) to sinusoidal input
• b) Square wave input
• Middle Time Scale (10-30 seconds)
• a) Fourier Analysis
• Long Time Scale
• a) Methods from non-linear dynamics
  (long time scale)
• 6. Dynamics of heart rate and its variability
  (a new analysis method)

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RR Interval The time between successive R
peaks in an EKGData a series of
times (in milliseconds) t1, t2, t3,
.Analysis Mathematics of Time Series Analysis
(TSA)
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Measurement Equipment

• Cardia (TF4)- Monitor belt telemetry to PC
  15,000
• Polar Heart Rate Monitor S810 Monitor belt
  telemetry to watch for download 600
• Pickup loop with HC11 microprocessor, download to
  PC 120
• Pickup loop with comparator chip to PC 20

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Example of RR Interval Variation
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Resting Heart Rate

• Heart Rate at rest is regulated by the Autonomous
  Nervous System
• Average Resting rate (B) determined from 3
  parameters
• B0 Basic Rate
• n Para-Sympathetic activity factor
  (1 P)
• m Sympathetic activity factor (1
  S)

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Dynamics of RR Interval Variations

• Short
  time scale Medium time scale

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Example of Lying vs. Standing HRVBreathing
oscillations vs. Meyer WavesShort time scale
vs. Long time scale
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Respiratory Sinus ArrythmiaLying positionShort
time scale
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Blood Pressure-Heart Rate Control
InteractionStanding PositionLong time scale
(Meyer Waves)
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Response Function of the Human HeartShort Time
Scale

• Signal in
  Signal out
• ? ?
• Signal in Breathing Function
• Signal out RR Interval time series
• Periodic Inputs result in Periodic Outputs of the
  same period.
• Examples Sinusoidal, Square Wave

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Sinusoidal Breathing Input
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Respiratory Sinus Arrythmia as a function of
breathing frequencyResponse Spectrum
Solid line lying Dashed line -
standing
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Response Spectrum
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Amplitude of response is proportional tothe
Amplitude of the input
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Response to Step Function BreathingInhale
(breath hold for 10 heartbeats)Exhale (breath
hold for 10 heartbeats)
Non-linear response response to step up not
equal to minus the response to step down.
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• Are there any stochastic aspects in beat to beat
  heart rate variations?

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Summary of Short time-scale dynamics

• Most important influence is breathing
  Respiratory Sinus Arrhythmia
• The response spectrum (sinusoidal breathing) has
  the characteristics of a resonance. The
  resonance frequency is between 0.05 and 0.1 Hz
  (10-20 heartbeats).
• The response spectrum depends on posture (lying
  vs standing)
• Changes affected by para-sympathetic nerve
  activity

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Analysis of Medium Time scale changes(10 30
heartbeats)

• Fourier Spectrum

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Scaling Analysis of Long Time scale dynamics
1. Choose a quantity F that is a measure
of heart rate variability or fluctuation on a
time scale of n heartbeats. Examine the
scaling properties of this quantity
a) F Fourier Amplitude b) F
Detrended Fluctuations c) F
Wavelet Coefficients d) etc
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Plot of Fourier Amplitude vs. Period
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Fixed Counting time Measurements

• Find average number of heartbeats and its
  standard deviation for a fixed counting time
• Note this is similar to the statistics of
  nuclear counting experiment where

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Dynamics of Heart Rate and its Variability

• Measure Pulse (B) and a variability parameter (V)
  as the system undergoes quasi-static change
• Since both variables depend on the
  Para-sympathetic activity, P, plot B vs. V . One
  can learn about the para-sympathetic activity.
• Assumptions
• a)
• b)

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Since Plt0.5, the series converges rapidly. Also,
V goes to zero as P goes to zero, so

• We choose V Respiratory Sinus Arrythmia at a
  breathing rate of 12 breaths/min.

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Equation of State

• By plotting the pulse B vs. the variability V,
  one obtains information about the type of process
  that is causing the change in heart rate!
• If m is constant during the process, one can
  determine mB0 and P from the graph!!!

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