Statistical analysis of hemodynamics and processes maintaining human stability using force plate

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Statistical analysis of hemodynamics and
processes maintaining human stability using force
plate
Jan Krí Quantum Circle Seminar 16 December
2003
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Program of the seminar

• What is the force plate? (elementary classical
  mechanics)
• Postural control (biomechanics, physiology)
• Hemodynamics
• Known results (mathematical models of postural
  control)
• Our approach
• Illustration of data analysis
• Conclusions

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What is the force plate?
4 load transducers piezoelectric
(Kistler) strain gauge (Bertec) Data are mixed
by Wheatstone bridges 6 signals linear cross
talks gt calibration matrix
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What is the force plate?

• Only 5 independent signals
• Fx , Fy ... shear forces
• Fz ... vertical force

x - My / Fz ... coordinates
of COP y Mx / Fz
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Postural Requirements

• Quiet standing
• - support head and body against gravity
• - maintain COM within the base of support
• Voluntary movement
• - stabilize body during movement
• - anticipate goal-directed responses

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Postural Control Inputs

• Somatosensory systems
• - cutaneous receptors in soles of the feet
• - muscle spindle Golgi tendon organ
  information
• - ankle joint receptors
• - proprioreceptors located at other body
  segments
• Vestibular system
• - located in the inner ear
• - static information about orientation
• - linear accelerations, rotations in the space
• Visual system
• - the slowest system for corrections (200 ms)

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Motor Strategies

• - to correct human sway
• - skeletal and muscle system
• Ankle strategy
• - body inverted pendulum
• - latency 90 100 ms
• - generate vertical corrective forces
• Hip strategy
• - larger and more rapid
• - in anti-phase to movements of the ankle
• - shear corrective forces
• Stepping strategy

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Postural Control

• - central nervous system
• Spinal cord
• - reflex ( 50 ms )
• - fastest response
• - local
• Brainstem / subcortical
• - automatic response (100 ms)
• - coordinated response
• Cortical
• - voluntary movement (150 ms)
• Cerebellum

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Why to study the postural control?

• Somatosensory feedback is an important component
  of the balance control system.
• Older adults, patients with diabetic neuropathy
  ... deficit in the preception of cutaneous and
  proprioceptive stimuli
• Falls are the most common cause of morbidity and
  mortality among older people.

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Hemodynamics

• - cardiac activity and blood flow
• - possible internal mechanical disturbance to
  balance

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Known results

• Measurements
• quiet standing (different conditions, COP
  displacements, Fz cardiac activity, relations
  between COP and COM)
• perturbations of upright stance ( relations
  between the perturbation onset and EMG
  activities)
• Results
• two components of postural sway (slow 0.1 0.4
  Hz, fast 8 13 Hz slow estimate of dynamics,
  fast translating the estimates into commands)
• corrections in anterio-posterior direction
  ankle in lateral direction hip

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Known results

• suppressing of some receptors -gt greater sway
• stochastic resonance noise can enhance the
  detection and transmission of weak signals in
  some nonlinear systems ( vibrating insoles,
  galvanic vestibular stimulation)
• Models of postural sway
• Inverted pendulum model
• Pinned polymer model

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Inverted pendulum model

• Eurich, Milton, Phys. Rev. E 54 (1996), 6681
  6684.
• If g f mgR sin f f(f(t-t)) x(t)
• m ... mass
• g ... gravitational constant
• I ... moment of inertia
• g ... damping coefficient
• f ... tilt angle (f0 for upright)
• f ... delayed restoring force
• x ... stochastic force
• R ... distance of COM

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Pinned polymer model

• Chow, Collins, Phys. Rev. E 52 (1994), 907 912.
• posture control stochactically driven mechanics
  driven by phenomenological Langevin equation
• r?t2y m?ty T ?z2y K y F(z,t)
• z ... height variable
• yy(t,z) ... 1D transverse coordinate
• r ... mass density
• m ... friction coefficient
• T ... tension
• K ... elastic restoring constant
• F ... stochastic driving force

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Our approach

• - signals information of some dynamical
  system, we do not need to know their physical
  meaning
• we are searching for processes controlling the
  dynamical system by studying the relations
  between different signals
• Power spectrum (related to Fourier transform)
• Pkk(f) (1/fs) ? Rkk(t) e-2pi f t/fs ,
• Rkk(t) ? xk(tt) xk(t) ? ... autocorrelation
• - Correlation, Covariance
• Rkl(t) ?xk(tt) xl(t)? , Ckl(t)
  ?(xk(tt)-mk)(xl(t)-ml)?
• Coherence
• Kkl(f) Pkl(f) / (Pkk(f) Pll(f))1/2,
• Pkl(f) (1/fs) ? Rkl(t) e-2pi f t/fs .

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Measured signals
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Power spectrum
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COP positions
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Lowpass filtering
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Lowpass filtering Power spectrum
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Lowpass filtering COP positions
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Highpass filtering
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Highpass filtering Power spectrum
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Highpass filtering COP positions
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Coherences 1
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Coherences 2
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Coherences 3
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Coherences 4
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Coherences 5
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Conclusions

• - we have data from an interesting dynamical
  system
• - we are searching for the processes controlling
  the system
• - results (if any) can help in diagnostic
  medicine