1. Statistical analysis of cardiac activity and processes maintaining human stability using force plate Jan Kříž Kochi University of Technology4 February 2003

2. 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

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

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 - generates vertical corrective forces

8. Motor Strategies Hip strategy - larger and more rapid - in anti-phase to movements of the ankle - shear corrective forces Stepping strategy

9. 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

10. 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.

11. Cardiac activity and hemodynamics

12. Hemodynamics = dynamics of blood circulation - forces generated by heart and resulting blood motion

13. Cardiac activity and hemodynamics Total blood circulation: veins  r.atrium  r.ventricle  pulmonary a.  lungs  pulmonary v.  l.atrium  l.ventricle  aorta  branching to capillares  veins

14. Cardiac activity and hemodynamics

15. 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

16. 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

17. Inverted pendulum model Eurich, Milton, Phys. Rev. E 54 (1996), 6681 –6684. If’’ + g f’ – mgR sin f = f(f(t-t)) m...mass g...gravitational constant I...moment of inertia g...damping coefficient f...tilt angle (f=0 for upright) f...delayed restoring force R...distance of COM

18. 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

19. 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)

20. Our approach – balance control -Correlation, Covariance -Coherence

21. Measured signals

22. Power spectrum

23. COP positions

24. Lowpass filtering

25. Lowpass filtering: Power spectrum

26. Lowpass filtering: COP positions

27. Highpass filtering

28. Highpass filtering: Power spectrum

29. Highpass filtering: COP positions

30. Heart rate

31. Averaging

32. Rescaling: Power Spectrum

33. Averaged COP positions

35. Comparison of COP positions and total load force projection

36. Averaged load force

40. Averaging without rescaling

41. Averaging without rescaling Blood flow in coeliac organs  400 ms after systole Šrámek, Valenta, Klimeš: Biomechanics of the cardiovascular system.

42. Averaged load force

45. Averaged load force 400-900 ms

46. Projections of av. load force 400-900 ms

47. 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