Statistical analysis of hemodynamics and
processes maintaining human stability using force
plate
Jan Kříž
Quantum Circle Seminar 16 December 2003
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
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
... coordinates of COP
y = Mx / Fz
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
- 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 modelEurich, Milton, Phys. Rev. E 54 (1996),
6681 –6684.
I’’ + ’ – mgR sin f(t-(t)
m ... mass
g ... gravitational constant
I ... moment of inertia
... damping coefficient
... tilt angle (=0 for upright)
f ... delayed restoring force
... stochastic force
R ... distance of COM
Pinned polymer modelChow, Collins, Phys. Rev. E 52 (1994), 907 –912.
posture control – stochactically driven mechanics driven by phenomenological Langevin equation
t2y + ty = T z
2y – K y + F(z,t)
z ... height variable
y=y(t,z) ... 1D transverse coordinate
... mass density
... friction coefficient
T ... tension
K ... elastic restoring constant
F ... 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-2i f t/fs ,
Rkk() = xk(t xk(t) ... autocorrelation- Correlation, Covariance
Rkl() = xk(t) xl(t) , Ckl() = (xk(t)-k)(xl(t)-l) - Coherence
Kkl(f) = | Pkl(f) | / (Pkk(f) Pll(f))1/2,
Pkl(f) = (1/fs) Rkl(t) e-2i 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
