1. Statistical analysis of hemodynamics and processes maintaining human stability using force plate Jan Kříž Quantum Circle Seminar16 December 2003

2. 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

3. 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

4. What is the force plate? Only 5 independent signals F x, F y...shear forces F z... vertical force x = - M y / F z... coordinates of COP y = M x / F z

5. 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

6. 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)

7. 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

8. 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

9. 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.

10. Hemodynamics - cardiac activity and blood flow - possible internal mechanical disturbance to balance

11. Known results Measurements quiet standing (different conditions, COP displacements, F z – 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

12. 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

13. 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 (f=0 for upright) f...delayed restoring force x...stochastic force R...distance of COM

14. Pinned polymer model Chow, Collins, Phys. Rev. E 52 (1994), 907 –912. posture control – stochactically driven mechanics driven by phenomenological Langevin equation r  t 2 y + m  t y = T  z 2 y – K y + F(z,t) z...height variable y=y(t,z)...1D transverse coordinate r...mass density m...friction coefficient T...tension K...elastic restoring constant F...stochastic driving force

15. 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) P kk (f) = (1/f s )  R kk (t) e -2pi f t/f s, R kk (t) =  x k (t+t) x k (t) ... autocorrelation -Correlation, Covariance R kl (t) =  x k (t+t) x l (t) , C kl (t) =  (x k (t+t)- m k )(x l (t)-m l )  -Coherence K kl (f) = | P kl (f) | / (P kk (f) P ll (f)) 1/2, P kl (f) = (1/f s )  R kl (t) e -2pi f t/f s.

16. Measured signals

17. Power spectrum

18. COP positions

19. Lowpass filtering

20. Lowpass filtering: Power spectrum

21. Lowpass filtering: COP positions

22. Highpass filtering

23. Highpass filtering: Power spectrum

24. Highpass filtering: COP positions

26. Coherences 1

27. Coherences 2

28. Coherences 3

29. Coherences 4

30. Coherences 5

31. 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