INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Bipedal upright stance is inherently unstable. A small sway deviation from a perfect upright position results in a torque due to gravity that accelerates the body further away from the upright position. To maintain upright stance, the destabilizing torque due to gravity must be countered by a corrective torque exerted by the feet against the support surface. A widely held view is that the corrective torque is generated through the action of a feedback control system (see reviews by Horak and Macpherson 1996; Johansson and Magnusson 1991). We will refer to this corrective torque, which necessarily involves a time delay due to sensory transduction, transmission, processing, and muscle activation, as "active" torque. However, controversy remains (Morasso and Schieppati 1999) because another view holds that the corrective torque is generated by muscle "tone" that acts without time delay (Winter et al. 1998, 2001). In this paper, we will refer to corrective torque that acts without time delay as "passive" torque. Finally, a third view recognizes that feedback mechanisms contribute to postural stabilization but states that feedback alone is insufficient and that feedforward predictive mechanisms are required to explain postural control behavior (Fitzpatrick et al. 1996). Our results support the view that active torque generated by feedback control mechanisms is the dominant contributor to quiet stance control.

Visual, proprioceptive, and vestibular systems clearly contribute to postural control because numerous studies have shown that stimulation of visual (Berthoz et al. 1979; Bronstein 1986; Dijkstra et al. 1994a; Lee and Lishman 1975; Lestienne et al. 1977; van Asten et al. 1988a), proprioceptive (Allum 1983; Jeka et al. 1997; Johansson et al. 1988; Kavounoudias et al. 1999), or vestibular systems (Day et al. 1997; Hlavacka and Nijiokiktjien 1985; Johansson et al. 1995; Nashner and Wolfson 1974) evoke body sway. However, little is known about how information from these senses is processed and combined to generate appropriate corrective torque when there is conflicting or inaccurate orientation information from different sensory systems. One possibility is that sensory cues are combined in an essentially linear manner. That is, each sensory system detects an "error" indicating deviation of body orientation from some reference position. Vestibular sensory cues detect deviations of head orientation from earth-vertical (gravity), visual sensors detect head orientation relative to the visual world, and proprioceptors detect leg orientation relative to the support surface. The individual error signals are summed, and appropriate corrective torque is generated as a function of this summed signal. Note that in this paper, for modeling purposes, we use a restricted definition of proprioceptive cues as only those sensory cues signaling body motion relative to the support surface. Additionally, we assume that appropriate neural transformations are performed on the various sensory cues so that the nervous system has information on body center-of-mass (COM) motion relative to each sensory reference (i.e., the direction of gravity for vestibular cues, visual world orientation for visual cues, and support surface orientation for proprioceptive cues). Psychophysical studies support the fact that such transformations can occur (Mergner et al. 1991, 1997).

Previous experimental results, where body sway was evoked by manipulation of individual and combined sensory cues, appear to be consistent with an essentially linear model (Fitzpatrick et al. 1996; Hajos and Kirchner 1984; Jeka et al. 1998, 2000; Johansson et al. 1988; Maki et al. 1987; Schöner 1991; van Asten et al. 1988b). Many of these earlier studies developed linear models that assumed that the postural control system was inherently stable, with experimental stimuli merely perturbing this inherently stable system. A more complete understanding of postural control must explain how this apparent inherent stability is actually achieved.

Most studies of human postural control have employed transient stimuli (e.g., sudden support surface motions) to evoke characteristic postural responses (Allum 1983; Diener et al. 1984b; Horak and Nashner 1986; Nashner 1977) or methods that artificially stimulate individual sensory receptors [i.e., muscle or tendon vibration (Kavounoudias et al. 1999) and galvanic vestibular stimulation (Nashner and Wolfson 1974; Watson and Colebatch 1997)]. We chose to investigate postural control using motion stimuli (tilts of the support surface and/or visual surround) that continuously perturb the system. Continuously varying stimuli (often sinusoidal stimuli over a range of frequencies, or more complex random or pseudorandom time series) evoke responses that eventually achieve a steady state. Steady-state stimulus-response data can be used to obtain transfer functions that characterize the dynamic properties of the system (Bendat and Piersol 2000). These techniques have been used previously to investigate postural control in humans and animals (Dijkstra et al. 1994b; Fitzpatrick et al. 1996; Hajos and Kirchner 1984; Ishida and Imai 1983; Jeka et al. 1998, 2000; Johansson et al. 1988; Maki et al. 1987; Peterka and Benolken 1995; Talbott 1980) but have not been systematically applied to investigate dynamic behavior over a wide range of conditions. The use of continuously applied perturbations seems appropriate to study quiet stance behavior, which itself is a continuously active process. This is in contrast to transient stimuli that may trigger specific and equally transient motor programs, which may not be directly related to the continuous regulation of balance.

Our results show that sensory integration and postural regulation do appear to be essentially linear processes for a specific sensory condition and a given stimulus amplitude. However, as stimulus conditions change, nonlinearities become apparent. The major nonlinearity occurs with changing stimulus amplitudes where there is an apparent graded shift in the source of sensory information contributing to postural control, with increasing utilization of vestibular cues as visual and proprioceptive perturbations increase. In subjects with absent vestibular function, this shift cannot occur, and their overall behavior remains quite linear independent of stimulus amplitude.

Such context-dependent changes in sensory utilization are in general agreement with previous views of postural behavior (Forssberg and Nashner 1982; Horak and Macpherson 1996; Nashner et al. 1982), experimental findings using galvanic vestibular stimulation (Britton et al. 1993; Fitzpatrick et al. 1994), and motor control in general (Hultborn 2001; Prochazka 1989). Our results provide quantitative measures of the stimulus-dependent changes in sensory contributions to postural control. In addition, our results provide estimates of important postural control parameters (stiffness, damping, time delay) and demonstrate how these parameters change in different sensory environments and stimulus conditions.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Subjects

The experimental protocols were approved by the Institutional Review Board at Oregon Health & Science University and were performed in accordance with the 1964 Helsinki Declaration. Prior to testing, all subjects gave their informed consent. Twelve subjects participated in this study. Eight were adults who had normal results on clinical sensory organization tests of postural control (Peterka and Black 1990) and had no known history of balance impairment or dizziness. The other four subjects had profound bilateral vestibular loss (VL subjects) as confirmed by clinical rotation testing and results from sensory organization tests of postural control (Nashner 1993a). The causes and durations of vestibular loss in these subjects are given in Table 1. Table 1 also shows the gain of horizontal vestibuloocular reflex (HVOR) for 0.05- and 0.2-Hz yaw rotations for the VL subjects. The HVOR gain for all VL subjects was well below the 95th percentile for the normal population (Peterka et al. 1990). The age range of normal subjects was 24-46 yr, while the VL subjects ranged in age from 45 to 58 yr. Although there was an age difference between these two groups, previous research has identified only minor changes in postural control in subjects in these age ranges (Peterka and Black 1990).

Experimental setup

All experiments were performed on a custom balance-testing device that included a motor-driven support surface and visual surround (Fig. 1). Position servo-controlled motors produced anterior/posterior (AP) tilts of the support surface and visual surround with the rotation axes collinear with the subject's ankle joints. Vertical force sensors in the support surface were used to measure center-of-pressure (COP) data. The visual surround had a half-cylinder shape (70-cm radius) and was lined with a complex checkerboard pattern consisting of white, black, and three gray levels (see Fig. 1). During testing, the room lights were off, and the visual surround was illuminated by fluorescent lights attached to the right and left edges of the surround.

View larger version (121K): [in this window] [in a new window]   Fig. 1. Balance test device. The subject stands on a support surface and views a high contrast visual surround. Both the support surface and visual surround can rotate in the anterior/posterior (AP) direction about the ankle joint axis. Single-link inverted pendulum dynamics are ensured by use of a backboard assembly. During freestanding trials, lightweight rods attached to potentiometers, located to the right and behind the subject, are used to measure AP body sway at hip and shoulder levels.

During most experiments, the backboard assembly shown in Fig. 1 was used to constrain body motion to that of a single-link inverted pendulum with rotational motion occurring only in the AP direction. The subjects were secured to the backboard with a padded head rest and straps at the level of the subject's knees, hips, and shoulders. The backboard was attached at its base to a pair of bearings aligned with the subject's ankle joint axis. Therefore the subjects were not required to support the full weight of the backboard. However, the influence of backboard mass (12.6 kg) and moment of inertia (11.4 kg m²) was accounted for in the data analysis. The body and backboard together acted as a single-link inverted pendulum. Body/backboard AP COM sway motion was provided by measures of backboard angular position, using a potentiometer, and angular velocity, using a rate sensor (Watson Industries, Eau Claire, WI). We considered these measures to be the output variables of interest.

During some experiments, the backboard assembly was not used and subjects were freestanding. In these experiments, AP body motion was measured by two horizontal rods attached to the subject at hip and shoulder levels (seen in Fig. 1, to the right of the subject). Rotational motion of the sway rods was recorded by potentiometers. Appropriate trigonometric conversions were made later to determine AP body displacement at hip and shoulder levels. A 120-s calibration trial was performed where subjects slowly leaned forward and backward using different combinations of leg and trunk rotations and minimizing knee flexion. A least-squared error curve fit of the following equation was used to obtain estimates of the coefficients a_h, a_s, and b

(1)

where x_cop is AP COP displacement, x_h is AP body displacement at hip level, x_s is AP body displacement at shoulder level, and t is time. Because body movements were very slow, x_cop is essentially equal to AP COM displacement (except for small rapid oscillations about the local COM position indicative of AP body acceleration) (Brenière 1996; Winter et al. 1998). In subsequent trials, Eq. 1 was used to calculate AP COM displacement from measures of x_h(t) and x_s(t). Then an estimate of the subject's COM height (based on anthropometric measures) above the ankle joint was used to calculate the COM rotation angle, which we considered to be the final output variable of interest.

Stimulus delivery and data sampling were computer controlled at a rate of 100/s. Sampled data included: visual surround and support surface angular position, four vertical forces from sensors at the corners of the support surface, rotational position of the hip and shoulder sway rods, and rotational position and velocity of the backboard assembly.

Pseudorandom stimuli

Rotational motion stimuli were based on a pseudorandom ternary sequence (PRTS) of numbers (Davies 1970). The method used to generate the pseudorandom stimulus waveforms is shown in Fig. 2. A stimulus was created from a 242-length PRTS sequence by assigning a rotational velocity waveform a fixed value of +v, 0, or -v°/s according to the PRTS sequence for a duration of t = 0.25 s (Fig. 2B, top). The duration of each stimulus cycle was 60.5 s. The mathematical integration of this PRTS velocity waveform gave a position waveform (Fig. 2B, bottom) that was delivered to the position servo motors to drive visual surround and/or support surface rotation. The PRTS stimulus has a wide spectral bandwidth (Fig. 2C) with the velocity waveform having spectral and statistical properties approximating a white noise stimulus (Davies 1970). As such, this stimulus appeared to be unpredictable to the test subject and thus likely limited any predictive contributions to postural responses that are known to occur (McIlroy and Maki 1994).

View larger version (31K): [in this window] [in a new window]   Fig. 2. Generation of a pseudorandom ternary sequence (PRTS) stimulus. A: a shift register with feedback is used to generate the PRTS. At each time increment, t, the value of each register is shifted to the right. A new value is entered into the left register based on modulo-3 addition of values in registers 3-5, and this new value is taken as the output. With the initial values shown in the 5 shift registers, the first 12 output values of the 242 value periodic sequence are shown below the shift register. This sequence is transformed into a velocity command sequence with values of +v, v, or 0°/s. B: the velocity sequence is transformed into a velocity waveform by holding each velocity command for t = 0.25 s. The position waveform is the time integral of the velocity waveform. With t = 0.25 s, the PRTS waveform has a period of 60.5 s. C: the spectral composition of the complete velocity and position waveforms for a 1° peak-to-peak PRTS stimulus. Only odd-numbered spectral components have nonzero energy.

Protocol

The PRTS stimulus position waveform was scaled to provide five different stimulus amplitudes (0.5, 1, 2, 4, and 8° peak-to-peak). On most trials, six complete stimulus cycles were presented. On all 0.5° trials, and some 1° trials, eight cycles of the stimulus were presented. Table 2 provides a summary of all six test conditions. Appropriate control trials with duration equivalent to a six-cycle stimulus were also given. The starting value of the PRTS stimulus was selected so that about 80% of the rotational tilt occurred in the positive direction (i.e., toe down support surface tilt and visual surround tilt directed forward and away from the subject) because subjects are able to tolerate larger angle forward body tilts.

Two of the test conditions used "sway-referencing" of the support surface or visual surround to manipulate the orientation cues available for postural control (Nashner and Berthoz 1978). Sway-referencing was performed by commanding the support surface or visual surround servo systems to continuously track the subject's AP body-sway angle. When the backboard assembly was used, sway-referenced rotations of the visual surround or support surface tracked the rotational movement of the backboard. For freestanding trials, sway-referenced motions of the support surface or the visual surround were in direct proportion to body-sway angles determined from sway-rod measures at the level of the hip or the shoulder, respectively. Sway-referencing alters the normal relationship between body sway and proprioceptive cues (during support surface sway-referencing) or visual cues (during visual surround sway-referencing) and presumably greatly reduces the contribution of these sensory orientation cues.

For normal subjects, all five stimulus amplitudes were presented for each of the six test conditions, and the stimulus and control trials were presented in a randomized order. Trials with sway-referencing included a 10-s delay prior to stimulus onset during which sway-referencing was active. All eight normal subjects completed a full set of trials with the backboard assembly. Four of these subjects also completed the full set of trials without the backboard assembly (free-standing). Data collection for backboard and freestanding conditions was completed in five testing sessions. Each session lasted about 2 h with one session performed per day. A 5-min break was given between trials.

For VL subjects, testing time was limited. Only backboard trials were performed, and the duration of control trials was reduced (to 130 s) compared with those used for normal subjects. Results from the first VL subject showed that 8° amplitude trials were extremely difficult to complete without falling. Therefore all other VL subjects were presented with 1, 2, and 4° PRTS stimuli. Some VL subjects were unable to complete a 4° trial for a given test condition (Table 2). If this occurred, a 0.5° stimulus was substituted so that results were obtained for each test condition at a minimum of three different stimulus amplitudes. There were three testing sessions for each VL subject lasting about 2.5 h each. Two sessions were performed on the same day (morning and afternoon), and a third session was completed on another day. A 5-min break was given between trials.

All subjects were instructed to maintain a relaxed upright stance position. If a subject fell during a trial, the trial was immediately repeated once or twice. Subjects wore headphones and listened to audio tapes of novels and short stories to mask equipment sounds, maintain alertness, and distract them from concentrating on their balance control.

Transfer function analysis

Results were analyzed primarily by calculating transfer function and coherence function estimates from stimulus-response data from each test trial. A transfer function characterizes the dynamic behavior of a system by showing how response sensitivity (gain) and timing (phase) change as a function of stimulus frequency. At each frequency, the transfer function gain gives the ratio of the amplitude of the response (COM body-sway angle) to the stimulus amplitude (support surface and/or visual surround tilt angle) at that frequency. The transfer function phase (in degrees) expresses the relative timing of the response compared with the stimulus at each frequency.

Transfer functions were computed using a discrete Fourier transform (DFT) to decompose the PRTS stimulus and response waveforms into sinusoidal component parts (Bendat and Piersol 2000). The DFT was applied to each 60.5 s cycle of each trial's stimulus and response waveforms. The DFT was calculated at 150 frequencies ranging from f = 1/60.5 = 0.0165 Hz to f = 150/60.5 = 2.48 Hz. A property of the PRTS stimulus is that all even frequency components have zero amplitude (Davies 1970). These even frequency points were discarded leaving 75 frequency samples.

Various power spectra were computed and averaged over the N cycles (N = 6 or 8)

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where X_i(j) and Y_i(j) are the DFTs of the ith stimulus and response cycles, respectively,  = 2f, j is , and * indicates a complex conjugate. Higher-frequency portions of these spectra were further smoothed by averaging adjacent spectral points to produce the final smoothed spectra, G_xs(), G_ys(), and G_xys(j) at 17 frequencies ranging from 0.0165 to 2.23 Hz. (The number of adjacent points averaged increased with increasing frequency such that 15 points contributed to the highest frequency spectral estimate).

The transfer function was then estimated

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and the gain function (ratio of response amplitude to stimulus amplitude) and phase function (in degrees) were computed by

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where Im(H(j)) and Re(H(j)) are the imaginary and real portions, respectively, of the complex numbers representing transfer function estimates. The phase function was computed using the Matlab (The MathWorks, Natick, MA, version 5.3) function "phase" from the Systems Identification Toolbox. This function "unwraps" the phase values, meaning that phase measures more negative than 180° could be obtained in cases where phase lags were increasing with increasing frequency.

COHERENCE FUNCTION ESTIMATES. The smoothed power spectra were used to estimate a "coherence function" given by

(8)

Values of the coherence function can vary from 0 to 1, with 0 indicating that there is no linear correlation between the stimulus and response, and 1 indicating a perfect linear correlation with no noise. Values less than 1 occur in practice either because there is noise in the system or there is a nonlinear relation between stimulus and response (Bendat and Piersol 2000). Coherence function estimates were also used in the calculation of 95% confidence limits on the transfer function gain and phase data (Otnes and Enochson 1972).

CURVE FITTING. Transfer function curve fits were made to the experimentally determined transfer function estimates. These curve fits were based on a theoretical model of the postural control system (Fig. 9, Eqs. 14-17) and were used to derive estimates of model parameters. The curve fits were made using a constrained nonlinear optimization algorithm ("constr" from the Matlab Optimization Toolbox) that adjusted model transfer function parameters to minimize the error value E given by

(9)

where M(j_i) and H(j_i) represent the complex value of the model and experimental transfer function, respectively, at the ith frequency point. The error magnitude at each frequency point was summed over the P frequencies included in the fit. The error was normalized by the magnitude of the model to account for the fact that estimation errors were lower for the higher-frequency lower-gain data due to averaging of spectral data. Although 17 frequency points were calculated for experimental transfer functions, P was typically less than 17 (usually 12). The lowest frequency and highest four frequencies were excluded from the fit procedure because the model transfer function was often unable to account for these data. (Large systematic errors between experimental data and fits occurred if all points were included.) Extensive simulations (using the Fig. 9 model and including variability to represent spontaneous body sway) were performed to validate our data analysis and parameter estimation procedures.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Stimulus-evoked body sway

Examples of COM body sway rotational responses to five different amplitudes of the PRTS stimulus for one representative normal subject and one VL subject are shown in Fig. 3. In the example in Fig. 3B, the subjects were standing with eyes closed, and the PRTS stimulus was applied to the support surface. The COM sway responses clearly followed the general PRTS stimulus waveform (Fig. 3A), indicating that both normal and VL subjects tended to orient to the moving support surface. At the three lowest stimulus amplitudes (0.5, 1, and 2°) for this test condition, the amplitude of body sway was noticeably larger than the stimulus amplitude in both the normal and VL subjects. In the normal subject, the sway amplitude appeared to saturate as the stimulus amplitude increased, such that the body-sway responses to the two highest stimuli (4 and 8°) were clearly smaller than the stimulus. However, in the VL subject, body sway continued to increase with increasing stimulus amplitude, and body-sway amplitude remained noticeably larger than the stimulus at the highest stimulus amplitude tested (4°). A similar pattern of body-sway responses was seen with the PRTS stimulus applied to the visual surround while subjects stood on a sway-referenced support surface (Fig. 3C).

View larger version (33K): [in this window] [in a new window]   Fig. 3. Example PRTS stimulus and body-sway responses for normal and vestibular loss subjects. A: one cycle of the PRTS stimulus waveform with peak-to-peak amplitude ranging from 0.5 to 8°. B: corresponding body-sway responses of a normal and vestibular loss subject to support surface rotations with eyes closed (, mean of 6 cycles, grayed area represents the 95% confidence interval about the mean). C: body-sway responses of a normal and vestibular loss subject to visual surround rotations with the support surface sway-referenced.

To illustrate the general pattern of responses to all six test conditions, Fig. 4 plots the mean root-mean-square (rms) COM body sway for normal subjects and individual results for the VL subjects. The plots include results for all six test conditions as a function of the peak-to-peak PRTS stimulus amplitude. The rms amplitude of the PRTS stimulus is shown for reference. In the two test conditions where two or more sensory systems were providing veridical orientation cues (i.e., fixed support surface with visual stimulation and fixed visual surround with support surface stimulation), normal subjects showed reduced rms body sway compared with the other test conditions, where fewer sensory systems were providing veridical orientation cues. In the fixed-support-surface condition with visual stimulation, there was no significant difference among mean rms sway for 0.5, 1, 2, and 4° amplitudes for normal subjects, although rms sway was greater for the 8° stimulus compared with the 0.5 or 1° stimuli (Tukey-Kramer multiple comparisons test, P = 0.05 significance level). In the fixed-visual-surround condition with support surface stimulation, the mean body-sway response increased in proportion to the stimulus for the 0.5 and 1° amplitudes but then showed no further increase with increasing stimulus amplitude (no significant differences among mean rms sway for 1-8° stimulus amplitudes, Tukey-Kramer multiple comparisons test, P > 0.05).

View larger version (28K): [in this window] [in a new window]   Fig. 4. Stimulus-response relationships for all 6 test conditions. The root-mean-square (rms) center-of-mass (COM) body sway for normal subjects (, , mean ± SD), and rms COM body sway of individual vestibular loss subjects (, · · · ) are shown as a function of the peak-to-peak stimulus amplitude. The rms amplitude of the PRTS stimulus is shown for reference (, ).

In the four conditions where veridical orientation cues were provided by fewer sensory systems, the mean rms sway amplitude was always greater than the rms stimulus amplitude for 0.5 and 1° stimuli. For stimuli greater than 1°, the rms body-sway response did not increase in proportion to the stimulus. For the 2° stimuli, the mean rms sway amplitude was approximately equal to the rms stimulus amplitude. For the 4 and 8° PRTS stimuli, the mean rms sway amplitude was always less than the rms stimulus amplitude. In most conditions, the general pattern of results suggests that the body-sway response saturated, with no further increase in response occurring with PRTS stimuli at or above about 4°. Pairwise multiple comparisons showed no significant difference between 4 and 8° responses in normal subjects (P > 0.05, Tukey-Kramer multiple comparisons test).

In contrast, responses of VL subjects generally showed greater levels of stimulus-evoked body sway for each test condition and at each stimulus amplitude, and some subjects were unable to complete all trials (Table 2). Figure 4 plots the rms response amplitudes of individual VL subjects. With the exception of only two individual trials, the individual rms responses of VL subjects were greater than the mean normal responses on all test conditions and at all stimulus amplitudes. In the four test conditions where the number of sensory systems providing veridical orientation cues was reduced, the rms responses of individual VL subjects were always greater than the rms stimulus amplitude, even at the 4° stimulus amplitude where normal subjects showed rms responses that were always less than the stimulus. Overall, the VL subjects' responses increased with increasing stimulus amplitude and showed little evidence for the response saturation seen in normal subjects.

Adaptation and habituation

There was no evidence for adaptation or habituation in normal subjects in their responses to the PRTS stimuli over the six or eight cycles presented in the different test conditions. When cycle by cycle rms sway data from all six test conditions were grouped according to the stimulus amplitude, rather than a decrement in the response due to habituation, the only trends were small increases in the rms response amplitude over the course of the stimulus. Linear regression analyses showed slopes ranging from 0.002°/cycle for the 1° PRTS data to 0.021°/cycle for the 8° PRTS data. The linear regression slope was significantly different from zero only for the 8° PRTS stimulus data (P < 0.046). VL subjects also did not appear to habituate to the various stimuli.

Postural control dynamics

Body-sway responses to PRTS stimuli were analyzed using Fourier methods to compute stimulus-response transfer functions (gain and phase as a function of stimulus frequency) and coherence functions. In these transfer functions, a gain measure of one and phase of zero indicates that the body orientation remained perfectly aligned (in amplitude and timing) with the support surface (for tests with support surface stimulus), or with the visual surround (for tests with visual surround stimulus). A gain greater (less) than one at a particular component stimulus frequency indicates that the body sway amplitude was larger (smaller) than the stimulus amplitude at that frequency. A gain of zero indicates that the body orientation was not influenced by the stimulus and remain perfectly aligned with earth-vertical.

EXAMPLE TRANSFER FUNCTIONS. Figure 5 shows individual transfer functions and their associated coherence functions from four different normal subjects and four different test conditions. All of these transfer functions are from trials where the subjects were restrained to sway as a single-link inverted pendulum by the backboard assembly. The general pattern of gain and phase changes, as a function of stimulus frequency, was similar for all test conditions and stimulus amplitudes. The gain was largest in the 0.1-0.8 Hz frequency range and was often greater than unity in this range. At frequencies less than about 0.1 Hz, the gain gradually decreased with decreasing frequency. At higher frequencies, the gain typically showed a steep decline with increasing frequency. A prominent phase lead was typically present for stimulus frequencies less than about 0.1 Hz. The phase crossed zero in the 0.1-0.2 Hz region and then showed increasing phase lags with increasing frequency. Phase lags of as much as 400° were seen at the highest frequency (2.23 Hz) on some tests (Fig. 5A), but on other tests, the phase lag at the highest frequency was much less (about 200°, Fig. 5B). Coherence functions typically had values in the 0.6-0.8 range at the lower stimulus frequencies, and the values declined with increasing frequency.

View larger version (31K): [in this window] [in a new window]   Fig. 5. Example transfer functions and coherence functions from 4 different stimulus conditions in 4 different normal subjects. Transfer function gain data (log scale) and phase data (linear scale) are plotted against stimulus frequency (log scale). Error bars indicate 95% confidence intervals around the gain and phase estimates ( and ). Unity gain and 0 phase responses ( · · · ) signify the result expected if subjects were able to maintain perfect body alignment to the moving visual surround and/or support surface stimulus. , fits of Eq. 14 to the transfer function data. Only transfer function data points indicated by  were used for the curve fit procedure. Coherence function estimates as a function of stimulus frequency are shown for each test condition. Results are from backboard supported trials.

MEAN TRANSFER FUNCTION. Backboard support. The mean transfer functions from eight normal subjects are shown in Fig. 6 for the six different test conditions at each of the five different stimulus amplitudes. These transfer function families illustrate that mean gains were greater than unity for all test conditions at the 0.5 and 1° stimulus amplitudes in the 0.1-0.8 Hz frequency range. As the stimulus amplitude increased, the gain generally decreased. For the two visual stimulus conditions with a fixed or sway-referenced support surface, the decrease in gain with increasing stimulus amplitude was more uniform across the bandwidth of test frequencies compared with the other four conditions with support surface stimulation or combined visual and support surface stimulation. In these four support surface stimulus conditions, there was little or no decrease in gain at the highest test frequencies. However, for frequencies less than about 1 Hz, the decline in gain with increasing stimulus amplitude was similar to that for the two visual stimulus conditions. As a result, the gain functions corresponding to the five stimulus amplitudes for all four support surface stimulus conditions converged at about 2 Hz.

View larger version (37K): [in this window] [in a new window]   Fig. 6. Mean transfer function gain and phase data, and coherence function data plotted vs. stimulus frequency for the 6 different test conditions and 5 different stimulus amplitudes (mean of data from 8 normal subjects on backboard supported trials).

View larger version (35K): [in this window] [in a new window]   Fig. 7. Comparison of transfer functions and coherence functions obtained in backboard supported (left) and freestanding (right) conditions. Results are from the combined visual and support surface stimulus condition at 5 different stimulus amplitudes. Each curve represents the mean data from 4 normal subjects who performed both backboard and freestanding trials.

VL TRANSFER FUNCTIONS. Unlike the normal subject transfer functions, transfer functions derived from VL subjects showed specific characteristic variations between the subjects. These variations precluded any averaging of transfer function results across VL subjects. However, there were some consistent findings across all VL subjects. The most obvious and consistent difference between results from normal and VL subjects was that the transfer function gain functions showed little change with increasing PRTS stimulus amplitude. Figure 8A overlays four transfer functions obtained from one representative VL subject in response to support surface stimulation with eyes closed and PRTS stimulus amplitude varying from 0.5 to 4°. A small decrease in gain can be appreciated by comparing the 0.5° with the 4° data in the lower and mid-frequency range, but this decrease is small compared with the approximate fourfold gain decrease in normal subjects on the same test conditions (see Fig. 6). The phase functions in Fig. 8A also show that there was little change in phase with increasing stimulus amplitude. This is in contrast to the phase data from normal subjects who showed less phase lag with increasing stimulus amplitude in this test condition (Fig. 6).

View larger version (34K): [in this window] [in a new window]   Fig. 8. Example transfer function gain and phase data and coherence function data vs. stimulus frequency from 3 VL subjects. A: results from subject VL3 showing little change in gain and phase functions on tests performed with eyes closed and support surface stimulus amplitudes varying from 0.5 to 4°. B: results from subject VL3 showing a decrease in gain and some change in phase functions when the support surface stimulus amplitude increased from 1 to 4° on tests performed with a fixed visual surround. C: results from subject VL1 performing the same tests as in B but showing little change in gain and phase functions as the stimulus amplitudes varied from 1 to 4°. D: results from subject VL2 showing large mid-frequency gains in response to a 1° support surface stimulus with a sway-referenced visual surround. , from a fit of Eq. 14 to the transfer function data. Error bars indicate 95% confidence intervals. Only transfer function data points indicated () were used for the curve fit procedure. All results are from backboard supported trials.

Model interpretation

INDEPENDENT CHANNEL MODEL. To achieve further insight into the postural control behavior revealed in the experimental results, we used a simple control system model to parameterize our transfer function results. This "independent channel" model (shown in Fig. 9) uses negative feedback control from sensory systems to generate an active torque, T_a, and muscle/tendon stretch caused by body sway relative to the support surface to generate a passive torque, T_p. T_a and T_p sum to produce the total corrective torque, T_c, acting about the ankle joint. This model assumes that three types of sensory information contribute to the generation of T_a. The sensory information is provided by the visual system, detecting body orientation with respect to the visual environment, proprioceptive system, detecting body orientation with respect to the support surface, and graviceptive system, detecting body orientation with respect to earth vertical. All sensory channels act separately, and the "goal" of each channel is to minimize deviation from its individual internal reference.

View larger version (19K): [in this window] [in a new window]   Fig. 9. "Independent channel" model of sensory integration in postural control showing a weighted addition of contributions from visual, proprioceptive, and graviceptive systems to the generation of an active corrective torque, Ta, as well as a passive torque contribution, Tp, related to body movement relative to the feet.

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