An Optimal Estimator Model of Multi-Sensory Processing in Human Postural Control Sukyung park" and Arthur D. KUO*

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1 Key Engineering Materials Vols (2005) pp online at Trans Tech Publications, Switzerland An Optimal Estimator Model of Multi-Sensory Processing in Human Postural Control Sukyung park" and Arthur D. KUO* 1 Dept. of Mechanical Engineering, Univ. of Michigan, Ann Arbor, MI, USA, sukyungp@umich.edu Systems division, Korea Institute of Machinery & Materials, Taejon, Korea, sukyungp@kimm.re.kr *~ept. of Mechanical Engineering, Univ. of Michigan, Ann Arbor, MI, USA, artkuo@umich.edu Kevwords: sensory processing, optimal estimator, internal model, visually induced motion. Abstract. We hypothesized that multi-sensory processing at the central nervous system (CNS) in human postural control can be described using an optimal estimator model. The estimates on body dynamics from multi-sensory signals contain sensory noise, transmission delays, and process disturbances. The state estimates approximate actual body movement. Erroneous estimates degrade the performance of feedback control and could cause a loss of balance if distorted severely. To test the hypothesis, we examined the frequency response of a visually-induced postural sway with stimulus frequency ranging fiom to I Hz and established an optimal estimator model. Two healthy young (33yrs + 1) subjects stood on a force platform located 1.25m behind a projection screen with their arms crossed over their chests. They were asked to maintain an upright posture against the sinusoidal visual field stimuli. Each sinusoidal visual stimulus was generated by a projector for 200secs in pitch direction with a maximum pitch angle of 20'. Kinematics data was recorded to calculate the frequency response function of the center of mass (COM). There were three components in the modeling procedure: a biomechanical model of body and sensor dynamics, a linear feedback control model to stabilize the biomechanical model, and a state estimator to estimate body dynamic states based on multi-sensory outputs. We modeled the sensor dynamics of the semicircular canal, otolth, vision, and muscle spindles at the ankle and hip joint. We used the Kalman filter and linear quadratic regulator to determine feedback gains. Results showed that the frequency response function of a visually-induced postural sway decreased as stimulus fiequency increased, and this low-pass filtering characteristic with an approximate cutoff frequency of 0.2Hz was also simulated by the postural feedback control model with optimal estimator. Low-pass filtering characteristics of the frequency response are mainly due to body and sensor dynamics, which show reduced responses for high frequency stimulus. The Kalman filter represents that the CNS utilizes redundant sensory information in a way that minimizes discrepancies between actual body dynamics and estimated body dynamics based on sensory output and an internal model. The results suggest that the CNS may make use of an internal representation of body dynamics, and can integrate sensory information in an optimal way to best estimate human postural responses. Introduction To maintain balance under various perturbations, the postural control system monitors body configuration and produces compensatory motor command according to the monitored information. Body movement is detected by sensory systems such as vision, vestibular apparatus, joint proprioreceptors, Golgi tendon organs, muscle spindles, and cutaneous receptors [I]. These multiple sensory signals are then transmitted to the CNS, where the sensory integration is performed. However, sensory signals contain sensory noise, transmission delays, and process disturbances. Therefore the state estimates approximate actual body movement while erroneous estimates degrade the performance of feedback control. This could cause a loss of balance if distorted severely. Many studies have revealed an increased postural sway or inefficient postural responses among elderly patients or those with sensory deficits. Horak, et al. showed that vestibular deficits limit the use of hip strategy while somatosensory deficits increase it [2]. Vestibular impaired subjects appeared to have

2 Key Engineering Materials Vols difficulties adapting postural responses with visual sensory perturbation [3], and failed to produce compensative joint torque for the rotational perturbation [4]. The elderly showed postural imbalance under sensory information conflict conditions [5] while older adults with diseases in sensory systems are at high risks for imbalance [6]. To understand the sensory integration mechanism, investigators examined the sensory induced postural responses. Visual stimuli have been used to examine postural adjustment and coordination changes as well as gain saturations [7, 8,9, 101. Galvanic stimulus and vibration stimulus on muscles are also used to investigate sensory integration in posture [I 1,12,13]. As a theoretical framework for the multi-sensory integrations, a sensory fusion mechanism was used to demonstrate multi-sensory posture control of upright stance [14], as well as to estimate an object's shape [15]. A linear additive model was used to explain the nonlinear sensory fusion process of touch and vision [I 61. One of the popular approaches is to assume that the redundant sensory information is integrated in an optimal way. The contribution of sensory information in standing posture El71 as well as arm movement estimation in the dark [I 81 was examined based on the optimal estimation theory. An adaptive model which dynamically weighs sensory error signals was also presented to demonstrate human stance control [19]. Statistical distributions and uncertainties were also considered in recent investigations on sensory integration [20,2 11. In this study, we hypothesized that multi-sensory processing at the CNS in postural control can be described using an optimal estimator model. To test the hypothesis, we examined the fkequency response of postural responses induced by the sinusoidal visual field with stimulus fkequency ranging from to 1Hz and established an optimal estimator model. Our findings suggest that multi-sensory signals may be combined in an optimal way to best estimate human postural responses. Methods Subjects and procedures. We applied the sinusoidal visual field of various fiequencies (from 0.75Hz to 1Hz) to 2 healthy young (33yrs -+ 1) male subjects. Subjects gave informed consent prior to the test. The subjects stood on the force platform, 1.25m behind the projection screen with their arms crossed over their chests. They were asked to maintain an upright posture under the sinusoidal visual field movement. The subjects wore liquid crystal stereo shutter glasses, which separated vertical stereo images and limited the subject's field-of-view to 100' horizontally and 55" vertically. The SGI Onyx II with Infinite Reality Engines creates the image, and the Electrohome Marquis 8500 projects the stereo image fields (1024~768stereo) onto screen. The correct perspective and stereo projections for the screen are computed using values on the current orientation of the head supplied by the position sensor attached to the stereo shutter glasses (head). The projector generated a visual field sinusoidally oscillating in the pitch direction with a frequency of 0.75,0.1,0.15,0.2,0.3,0.4,0.5,0.6, 0.8, and 1Hz for 200sec. Between trials, the subjects had a I -minute break. The maximum amplitude of pitch movement of the image was 20". The subject maintained his balance with the still scene during the first trial. He was asked to close his eyes between trials and was exposed to the oscillating visual field with randomly ordered stimulus frequencies. Data collection and analysis. For each trial, kinematic and ground reaction force data were recorded for a total of 200 secs. Kinematic data were recorded with an Optotrak at a sampling rate of loohz using 3 cameras. Ten infrared sensors were located at the upper and lower part of the glasses, ear, neck, right shoulder, hip, knee, ankle, toe, and the platform surface. The marker positions were used to calculate the segment angles for the head, neck, trunk, thigh, shank, and foot. All segment angles were referenced to zero, defined as the subject's preferred vertical upright position, with a positive sign for extension. Ground reaction forces and moments were recorded at a sampling rate of 1500 Hz fiom force transducers located in the support surface. We then calculated the frequency response of each segment angle for various visual field sinusoid frequencies. To confine the data to a steady state, we discarded the first 20 secs of recordings. We used band-pass filters with cutoff frequencies at 0.05 and 3.5Hz, to reduce the high frequency noise as well as the low frequency drift.

3 150 Bio-, Information-, Environmental-, Energy-, Space- and Nano-Technologies We compared our results with previously published data, which examined attenuated sensory processing for limited stimulus hquencies [lo]. Theoretical Model. We hypothesized that the CNS used the states of body dynamics estimated fiom the internal representation of body dynamics for postural feedback control (Figure 1). There are three components in the modeling procedure: a biomechanical model of body and sensor dynamics, a linear feedback control model to stabilize the biomechanical model, and a state estimator to estimate body dynamics states based on multi-sensory outputs. Fig. 1. A state estimator model of sensory processing in postural balance. Estimates of actual body dynamics, containing process noise and sensor noise, are obtained though the state estimator (shaded in gray), which internally includes biomechanical model The biomechanical model is based on the equations of motion of a three-segment (feet, lower extremity, torso) linkage confined to the sagittal plane, with the feet flat on the support surface. Details on equations of motion on the biomechanical model are presented in previously published papers [22,23]. We modeled the sensor dynamics of the semicircular canal, otolth, vision, and muscle spindles at the ankle and hip joint. The otolith organs measure head translational acceleration. Vision and the semicircular canals measure head velocity while the muscle spindles sense joint angle. We used the transfer function of each sensory organ to formulate the state equation form, and augmented it with body dynamics [24]. A feedback control system and state estimator were devised to model stabilized postural responses. We used linear state feedback control [23,25,26,27], producing joint torques as a function of the joint angles and velocities to stabilize the body. In ideal situations, the CNS integrates visual, vestibular, and somatosensory information to produce the equivalent of the state information. However, actual body dynamics and its measurement through each sensory organ may contain process noise and sensory noise. Therefore, body states should be estimated from the state estimator, which internally includes the biomechanical model and produces estimated body dynamic states based on the feedback of errors between the actual and estimated sensory output. We modeled process noise w, and sensor noise v for an augmented state variable x, which represents sensor and body dynamics. The state estimate i, and sensory output state y, and its estimate 9 were also defined. The state equations of both body dynamics and state estimators are of the following forms [24]: x=ax+bu+w where u =-Kjr y=cx+du+v where A, B, C, D are the augmented system matrices for body and sensory dynamics, u is the control input, (here joint torques) and L is the feedback gain of the state estimator determined by the Kalman filter. We used the optimal estimator and controller to determine the feedback gains. A Kalman filter determines the sensory afferent signal error feedback gain, L, based on the relative magnitude of sensory noise to process noise in a way that the overall uncertainty in the state estimate is minimized. Once the best estimate of the body dynamics state, 2, is obtained, it is used to feedback control. To

4 Key Engineering Materials Vols produce feedback gain K, we used a linear quadratic regulator (LQR), which minimizes the objective penalizing excessive state deviation and control effort. min J = IxT~x+uT~u dt K We used simple optimization parameters for the simulation. For example, we used Q = Imp R = I, implying that the CNS penalizes the deviation of the joint angle and angular velocity and control effort with an equivalent importance. For the Kalman filter, we used L = I, which implies that the CNS weighs 6-multisensory information equally to estimate body dynamics. A difference in the choice of Q, R, and L gives a different closed loop response, and in turn, a different cutoff frequency. However we would rather emphasize on matching qualitative behavior of the model than obtaining specific quantitative values. Sensory conflict plays a role in the external perturbation of visually-induced po~al sway. If the visual field moves, the vision senses the movement while the other sensors such as semicircular canals, otolith, and somatosensors do not sense any movement of the body. The CNS estimates body dynamics and uses the estimate to produce compensatory postural responses. If the CNS relies more on visual sensory information than other sensory signals, body dynamics are estimated as if the subject moves in an opposite direction to the visual field. The CNS then exerts the compensatory motor correction on each joint, and this produces a visually-induced postural sway. By applying various frequencies of sinusoidal visual field to the model, we were able to obtain frequency responses of the postural sway. Results The magnitude of frequency response of visually-induced postural sway decreases as stimulus fiequency inmases, and this low-pass filtering characteristic is also simulated by the Kalman filter implanted postural feedback control model. The Kalman filter represents that the CNS utilizes redundant sensory information in a way that minimizes discrepancies between actual body dynamics and estimated body dynamics based on sensory input and the internal model. The magntiude of sinusoidal response of the COM reduced as stimulus frequency increased (Figure 2). The magnitude reduction ratio is almost 40dB for the visual stimulus frequency ranging fiom O.1Hz-1Hz. The drastic magnitude changes are shown especially at a stimulus frequency greater than 0.2Hz, and this trend was similarly illustrated in the data of a previous study done by Perterka, et al. [lo]. Low pass filtering characteristics of the fi-equency response are mainly due to the body and sensor dynamics. The magnitude of sinusoidal response of lower extremeties was smaller than that of the upper extremeties at low frequency. For example, 8, consistently decreased while Oh, showed an almost constant amplitude at a stimulus frequency of less than 0.2Hz. Fig. 2. Frequency response function - h m (FRF) of center of mass (COM). The gs 0 z simu'"'"dfrfofcom FRF of COM of sinusoidal visual G m zz -20 Data of 2 subjects stimulus ranging fiom 0.075Hz to lhz, 3 O.% 5-40 Data of 5 subjects based on experiments and simulations, 2s obtained Frwn et decreases as stimulus fiequency 2 " I increases. We also included previously Frequency OIz) published data by Perterka et. al. (1995) (2) With a Kalman filter model representing multisensory processing, the feedback control model was able to reproduce the fkquency response of a visually-induced postural response reasonably well. Visual field movement, sensed by translational and rotational vision, is considered as external perturbation, and induces compensative postural responses. This compensative response is also

5 152 Bio-, Information-, Environmental-, Energy-, Space and Nano-Technologies sinusoidal with the same frequency as stimulus fiequency, but the magnitudes tend to be reduced as stimulus frequency increases. Figure 2 shows the frequency response of the COM and segment angles as a function of stimulus. Similar to the empirical data, the magnitude of the FlU; is almost constant for the low frequency region and starts decreasing with an approximate slope of IlOdBIdecade, implyimg a highly damped second order mechanical system. Discussion We observed that the magnitude of a visually-induced postural response decreases when the frequency of sinusoidal visual input increases. The fiequency response function of empirical data, as well as, an optimal controller model with a Kalman filter showed lowpass-filter characteristics with a cutoff frequency of approximately 0.2 Hz. The decreased magitude of postural response indicates that the subjects do not produce large enough compensative postural responses in high frequency stimulus. This is mainly due to the body and sensor dynamics, which are known to have lowpass-filter characteristics. The inner ear sensors such as semicircular canals and somatosensory sensors are more sensitive to higher frequencies, while the vision and otolith are more responsive for low fiequency movement. Therefore, the magnitude reduction of a visually-induced postural response resulted from fkquency dependent characteristics of multi-sensory processing. The cutoff fiequency is dependent on the choice of feedback gains of the controller and estimator. Diffmt cutoff frequencies between the upper and lower extremities indicates the frequency dependent contribution of each body segment in maintaining balance. A smaller 8, than O,, for a stimlus frequency less than 0.2Hz indicates that hip joint movement becomes more dominant for higher frequency visual stimulus. Consistently, previous studies observed that human employs hip joint movement for larger and more challenging perturbations [28, 291, and suggested that biomechanical constraints restrained ankle sway in maintaining balance and forced the CNS to use more hip joint sway with increased efficiency. Upper extremities including the head, at which high fiequency sensitive vestibular organs are located, showed more variation for the larger, more challenging, high frequency perturbations [30]. The Kalman filter model was able to represent the multisensory process well, implying that the CNS may best use redundant sensory information in a way that minimizes overall uncertainty in body dynamic estimates, as previous studies suggested [17, 181. Acknowledgements We wish to thank Emily A. Keshner and, Jessica A. Langston for their help in data collection. References [I] R.A. Schmidt: Motor control and learning : a behavioral emphasis. Human Kinetics, Champaign, ni, (igss), p [2] F.B. Horak, L.M. Nashner, and H.C. Diener: Postural strategies associated with somatosensory and vestibular loss. Exp. Brain. Res. Vol. 82 (1990), p [3] P.J.Loughlin, M.S. Redfern and J.M. Furman: Time-varying characteristics of visually induced postural sway. IEEE Trans. Rehab. Eng. Vol. 4 (1996), p [4] J.H. Allum and F. Honegger: A postural model of balance-correcting movement strategies. J. Vest. Res. Vol. 2 (1992), p [5] M.H. Woollacott, A. Shurnway-Cook and L.M. Nashner: Aging and posture control: changes in sensory organization and muscular coordination. Jnt. J. Aging. Hum. Dev. Vol. 23 (1986), p [6] N.B. Alexander: Postural control in older adults. J. Am. Ger. Soc. Vol. 42 (1994), p

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