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