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Statistical analysis of cardiac activity and processes
maintaining human stability using force plate
Jan Kříž
Kochi University of Technology 4 February 2003
Program of the seminar
• What is the force plate? • Postural control • Cardiac activity and 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
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
- generates vertical corrective forces
Motor Strategies
• 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.
Cardiac activity and hemodynamics
Cardiac activity and hemodynamics
Hemodynamics = dynamics of blood circulation
- forces generated by heart and resulting blood motion
Cardiac activity and hemodynamics
Total blood circulation:
veinsr.atriumr.ventriclepulmonary a.lungspulmonary v.l.atriuml.ventricleaortabranching to capillares veins
Cardiac activity and hemodynamics
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-
m ... mass
g ... gravitational constant
I ... moment of inertia
... damping coefficient
... tilt angle (=0 for upright)
f ... delayed restoring 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)
frequency sampling ...
ation,autocorrel ...
s
kkkk
s
N
tkk
skk
f
txtxR
tf
iftR
ffP
)()()(
,2
exp)(1
)(1
Our approach – balance control- Correlation, Covariance
- Coherence
.)()()(
,)()()(
llkkkl
lkkl
txtxC
txtxR
.2
exp)(1
)(
,)()(
)()(
1
tf
iftR
ffP
fPfP
fPfK
N
tkl
skl
llkk
klkl
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
Heart rate
Averaging
Rescaling: Power Spectrum
Averaged COP positions
Averaged COP positions
Comparison of COP positions and total load force projection
Averaged load force
Averaged load force
Averaged load force
Averaged load force
Averaging without rescaling
Averaging without rescalingBlood flow in coeliac organs 400 ms after systole
Šrámek, Valenta, Klimeš: Biomechanics of the cardiovascular system.
Averaged load force
Averaged load force
Averaged load force
Averaged load force 400-900 ms
Projections of av. load force 400-900 ms
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