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Statistical analysis of hemodynamics and processes maintaining human stability using force plate. Jan K říž Quantum Circle Seminar 16 December 2003. Program of the seminar. What is the force plate? (elementary classical mechanics) Postural control (biomechanics, physiology)
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Statistical analysis of hemodynamics and processes maintaining humanstability using force plate Jan Kříž Quantum Circle Seminar 16December 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 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
Pinned polymer model Chow, Collins, Phys. Rev. E 52 (1994), 907 –912. posture control – stochactically driven mechanics driven by phenomenological Langevin equation rt2y + mty = T z2y – 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
Our approach - signals = information of some dynamical system, we do notneed 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-2pi f t/fs , Rkk(t) = xk(t+t)xk(t) ... autocorrelation -Correlation, Covariance Rkl(t) = xk(t+t)xl(t) , Ckl(t) = (xk(t+t)-mk)(xl(t)-ml) • Coherence Kkl(f) = | Pkl(f) | / (Pkk(f) Pll(f))1/2, Pkl(f) = (1/fs) Rkl(t) e-2pi f t/fs .
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