Transcript Statistical analysis of hemodynamcs and processes

Statistical analysis of
hemodynamics and processes
maintaining human stability using
force plate
Jan Kříž
Quantum Circle Seminar
16 December 2003
Program of the seminar
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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
What is the force plate?
4 load transducers
piezoelectric (Kistler)
strain gauge (Bertec)
Data are mixed by
Wheatstone bridges
6 signals
linear cross talks =>
calibration matrix
What is the force plate?
Only 5 independent signals
Fx , Fy ...
shear forces
Fz
...
vertical force
x = - My / Fz
...
y = M x / Fz
coordinates of COP
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
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)
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
Postural Control
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- 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
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.
Hemodynamics
- cardiac activity and blood flow
- possible internal mechanical disturbance to balance
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
Known results
• suppressing of some receptors -> 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
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
g
I
g
f
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upright)
f
...
x
mass
gravitational constant
moment of inertia
...
damping coefficient
...
tilt angle (f=0 for
delayed restoring force
...
stochastic force
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
y=y(t,z)
r
m
T
K
F
...
...
...
...
...
...
...
height variable
1D transverse coordinate
mass density
friction coefficient
tension
elastic restoring constant
stochastic driving force
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(t+t) xk(t) 
...
autocorrelation
- Correlation, Covariance
Rkl(t) = xk(t+t) xl(t) , Ckl(t) = (xk(t+t)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 .
Measured signals
Power spectrum
COP positions
Lowpass filtering
Lowpass filtering: Power spectrum
Lowpass filtering: COP positions
Highpass filtering
Highpass filtering: Power spectrum
Highpass filtering: COP positions
Coherences 1
Coherences 2
Coherences 3
Coherences 4
Coherences 5
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