It is generally accepted that human bipedal upright stance is achieved by feedback mechanisms that generate an appropriate corrective torque based on body-sway motion detected primarily by visual, vestibular, and proprioceptive sensory systems. Because orientation information from the various senses is not always available (eyes closed) or accurate (compliant support surface), the postural control system must somehow adjust to maintain stance in a wide variety of environmental conditions. This is the sensorimotor integration problem that we investigated by evoking anterior-posterior (AP) body sway using pseudorandom rotation of the visual surround and/or support surface (amplitudes 0.5–8°) in both normal subjects and subjects with severe bilateral vestibular loss (VL). AP rotation of body center-of-mass (COM) was measured in response to six conditions offering different combinations of available sensory information. Stimulus-response data were analyzed using spectral analysis to compute transfer functions and coherence functions over a frequency range from 0.017 to 2.23 Hz. Stimulus-response data were quite linear for any given condition and amplitude. However, overall behavior in normal subjects was nonlinear because gain decreased and phase functions sometimes changed with increasing stimulus amplitude. “Sensory channel reweighting” could account for this nonlinear behavior with subjects showing increasing reliance on vestibular cues as stimulus amplitudes increased. VL subjects could not perform this reweighting, and their stimulus-response behavior remained quite linear. Transfer function curve fits based on a simple feedback control model provided estimates of postural stiffness, damping, and feedback time delay. There were only small changes in these parameters with increasing visual stimulus amplitude. However, stiffness increased as much as 60% with increasing support surface amplitude. To maintain postural stability and avoid resonant behavior, an increase in stiffness should be accompanied by a corresponding increase in damping. Increased damping was achieved primarily by decreasing the apparent time delay of feedback control rather than by changing the damping coefficient (i.e., corrective torque related to body-sway velocity). In normal subjects, stiffness and damping were highly correlated with body mass and moment of inertia, with stiffness always about 1/3 larger than necessary to resist the destabilizing torque due to gravity. The stiffness parameter in some VL subjects was larger compared with normal subjects, suggesting that they may use increased stiffness to help compensate for their loss. Overall results show that the simple act of standing quietly depends on a remarkably complex sensorimotor control system.
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.
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 Table1. 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).
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.
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 coefficientsa h, a s, andb Equation 1where 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 ofx h(t) andx 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.
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 Δt = 0.25 s (Fig. 2 B, top). The duration of each stimulus cycle was 60.5 s. The mathematical integration of this PRTS velocity waveform gave a position waveform (Fig. 2 B,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. 2 C) 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).
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) Equation 2 Equation 3 Equation 4where Xi (jω) and Yi (jω) are the DFTs of the ith stimulus and response cycles, respectively, ω = 2πf, 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, Gxs (ω),Gys (ω), andGxys (jω) 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 Equation 5and the gain function (ratio of response amplitude to stimulus amplitude) and phase function (in degrees) were computed by Equation 6 Equation 7where Im(H(jω)) and Re(H(jω)) 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 Equation 8Values 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).
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 valueE given by Equation 9where M(jωi ) and H(jωi ) 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 Pfrequencies 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.
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. 3 B, 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. 3 A), 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. 3 C).
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).
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. 5 A), but on other tests, the phase lag at the highest frequency was much less (about −200°, Fig. 5 B). Coherence functions typically had values in the 0.6–0.8 range at the lower stimulus frequencies, and the values declined with increasing frequency.
The general form of the example transfer functions shown in Fig. 5,A and D, are representative of the majority of experimentally obtained transfer functions. The two transfer functions in Fig. 5, B and C, represent the most extreme deviations from the more common transfer function form. Specifically, these two transfer functions show resonant peaks in their gain functions. In one case, a prominent resonant peak was located at about 0.2 Hz. In the other, a smaller resonant peak was located near 0.9 Hz. Of the 240 tests performed by the eight normal subjects, only about 20 tests showed resonant behavior qualitatively similar to the examples shown in Fig. 5, B and C. Four of the normal subjects did not show resonant behavior on any test. Resonant behavior was most common on test conditions with visual stimulation on a sway-referenced support surface, or with support surface stimulation with eyes closed.
MEAN TRANSFER FUNCTION.
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.
Of all test conditions and amplitudes, the largest mean gain value occurred on the 0.5° visual stimulus condition with a sway-referenced support surface. This gain value was 4.1 at a frequency of 0.36 Hz. Among the other tests performed using the 0.5° stimulus amplitude, maximum gains of about 3.7 were obtained on three conditions (support surface stimulation with eyes closed and with sway-referenced vision, and combined support surface and visual stimulation). A lower maximum gain of about 2.2 was obtained with the 0.5° support surface stimulation with fixed vision, and the lowest maximum gain of about 1.8 was obtained with visual stimulation on the fixed support surface.
Phase functions also showed characteristic differences between the two conditions with only visual stimulation and the four conditions with support surface or combined support surface and visual stimulation. For the two conditions with only visual stimulation, the phase functions for all five stimulus amplitudes were indistinguishable from one another for frequencies greater than about 0.1 Hz. Large phase lags ranging from −342 to −382° were measured in these two conditions at 2.23 Hz. For frequencies less than 0.1 Hz, there was some divergence of these phase functions. At the lowest frequency (0.017 Hz) on the fixed support surface with visual stimulus condition, there was a systematic relationship between the phase and stimulus amplitude with the largest phase advance associated with the lowest stimulus amplitude, and the least phase advance occurring with the largest stimulus amplitude.
The phase functions for all conditions with support surface stimulation showed a different pattern. For three of the four support surface stimulus conditions, the phase functions from different stimulus amplitudes were indistinguishable from one another for frequencies less than about 0.1 Hz. (The exception was the fixed vision condition were there was some divergence of phases at lower frequencies, although no systematic relationship between phase and stimulus amplitude was present.) At frequencies greater than about 0.2 Hz, the phase functions associated with different stimulus amplitudes diverged from one another, and this divergence increased with increasing frequency. At a given frequency greater than 0.2 Hz, there was less phase lag associated with larger stimulus amplitudes. The largest difference between mean phases was seen on the combined support surface and visual stimulus condition where the mean phase from the 8° stimulus was −212°, and the mean phase from the 0.5° stimulus was −386° at 2.23 Hz.
Conditions that evoked body sway, using support surface rotation with either eyes closed or sway-referenced visual surround conditions, resulted in very similar responses in normal subjects (Figs. 4 and 6). This suggests that eye closure and visual surround sway-referencing were both equally effective in eliminating the contribution of visual sensory cues to postural control.
Coherence functions were generally largest at the lowest test frequencies and gradually declined with increasing frequency. Within each of the six test conditions, the coherence function from the 0.5° stimulus typically had lower values than the coherence functions associated with the larger stimulus amplitudes. This is consistent with a lower signal-to-noise ratio for responses evoked by this very low-amplitude stimulus. For 1–8° stimuli, there was no systematic change in coherence with stimulus amplitude for stimulus frequencies less than about 1 Hz. This indicates that each of the responses to the different amplitude stimuli showed a similar degree of linearity even though the overall system responses were clearly nonlinear since gains declined with increasing stimulus amplitude. This suggests that the overall gain decline may be caused by a resetting of system parameters for different amplitudes rather than by a specific nonlinear processing of sensory or motor signals (see discussion).
One might question the validity of averaging transfer functions across subjects, based on the concern that important individual variations might be obscured or biases introduced. However, examination of each individual's results showed that they were consistent with the population mean. In addition, quantitative estimates of the stiffness and damping properties of each subject's control behavior (seeModel interpretation section) showed that each subject effectively normalized his or her postural transfer function dynamics by systematically setting stiffness and damping properties in proportion to individual body mass and height parameters. Similar self-normalizing behavior has been reported previously in a study of head stabilization (Keshner et al. 1999).
The major features of transfer and coherence functions obtained with subjects restrained to sway as a single-link inverted pendulum by the backboard support were also observed in freestanding subjects. As an example, the mean transfer and coherence functions from the four subjects who completed a full set of freestanding tests are shown in Fig. 7 for the combined support surface and visual stimulation condition. Both backboard and freestanding gain functions show a decline with increasing stimulus amplitude, and both show the characteristic convergence of the gain functions from different stimulus amplitudes at higher stimulus frequencies.
Both the backboard and freestanding phase functions show a phase lead at frequencies less than 0.1 Hz. The phase functions from different amplitude stimuli were not distinguishable from one another at these lower frequencies. However, as frequency increased greater than about 0.2 Hz, both the backboard and freestanding phase functions diverged from one another, with phase functions showing less phase lag with increasing stimulus amplitude. Coherence functions were also similar for the backboard and freestanding tests.
There was a similar correspondence between backboard-restrained and freestanding results in the other five test conditions. All of the major features of transfer functions for the six test conditions obtained from backboard-restrained subjects (shown in Fig. 6) were also present in the freestanding results.
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. Figure8 A 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. 8 A 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).
Results similar to those in Fig. 8 A (showing little or no gain reduction or phase changes with increasing stimulus amplitude) were obtained in all four VL subjects with support surface stimulation with eyes closed or sway-referenced vision, with combined support surface and visual stimulation, and with visual stimulation on a sway-referenced support surface. In contrast to this pattern of results, different VL subjects showed varying amounts of reduction in gain and changes in phase with increasing stimulus amplitude during support surface stimulation with a fixed visual surround. The data from the subject showing the most change are shown in Fig. 8 B. For comparison, the data from the VL subjects who showed the least change in this same test condition are shown in Fig. 8 C.
The VL subject's transfer function data shown in Fig. 8 Calso illustrate a property of this subject's responses that distinguished her from the other three VL subjects. Note that all three of the transfer functions from this subject in Fig. 8 C are very similar to the transfer function of the other VL subject (Fig.8 B) obtained in response to the 4° PRTS stimulus. That is, the gain functions in Fig. 8 C are relatively flat in the low- and mid-frequencies before beginning to decrease at higher frequencies. Additionally, the maximum phase lag in Fig. 8 Cat the highest frequency is about −280°, which is approximately equal to the phase lag in Fig. 8 B at the highest frequency for the 4° stimulus. The pattern of results for the VL subject shown in Fig. 8 C (subject VL1) will later be shown to be consistent with this subject maintaining a higher level of postural stiffness than other VL subjects and other normal subjects. This subject's high stiffness strategy was evident in all test conditions.
In the test condition with visual stimulation on a fixed support surface, one of the VL subjects (VL2) showed some reduction in gain with increasing stimulus amplitude, whereas the other three VL subjects did not.
VL subjects generally had more difficulty maintaining balance in the test condition where the visual surround was sway-referenced than in the eyes closed condition. Only one of the four subjects was able to complete the 4° support surface stimulus with a sway-referenced visual surround while three of the four were able to complete the 4° stimulus with eyes closed. Some of the highest gains were obtained on tests with support surface stimulation with sway-referenced vision. An example is shown in Fig. 8 D (subject VL2).Subject VL4 was unable to complete any of the tests with the visual surround sway-referenced, including the control test with a fixed support surface, although her performance on all five other test conditions was not distinguishable from the other VL subjects. This poor performance on tests with sway-referenced vision is in contrast to the results from normal subjects where performance on tests with eyes closed was indistinguishable from tests with sway-referenced vision (Fig. 6).
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 andT 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.
The body rotation produced by T c is described by the differential equation of a single-link inverted pendulum Equation 10where J is the body's moment of inertia about the ankle joint axis, m is body mass (not including the feet),g is acceleration due to gravity, h is the height of the COM above the ankle joint, and BS is the angular position of the body with respect to earth vertical. Both BS andT c are time varying. Expressing this equation as a Laplace transform gives Equation 11where s is the Laplace variable and the small angle approximation BS ≈ sin(BS) was used to simplify the equation.
An inverted pendulum is inherently unstable because a small deviation of body position from a perfect upright position produces a torque due to gravity, mgh sin(BS), that accelerates the body further from upright. To counteract this gravitational torque,T c must be generated with a sign opposite to the gravitational torque. The stability and dynamic behavior of the inverted pendulum control depends on the time course ofT c. If we assume initially that the passive torque contribution to T c is negligible, then all of the stabilizing torque must be derived from the sensory error signal, e, given by Equation 12It is known from control system theory that stabilization of an inverted pendulum requires that T aminimally contain two components: one proportional to e (a “stiffness” factor) and a second proportional to the time derivative of e (a “damping” factor). An optional third component contributes a torque proportional to the mathematical time integral of e. This integral component adds low frequency error correcting properties to the overall control system but is not necessary for stability. The equation for a controller that contains all three of these components is Equation 13where t is time, andK P, K D, and K I are gain constants that determine the magnitude of the position, velocity, and integral components, respectively. This type of controller, commonly used in man-made control systems, is referred to as a PID controller (proportional, integral, derivative control).
If all of the sensory systems are assumed to have no dynamic behavior over the bandwidth of movement associated with body sway, then the overall transfer function relating body sway evoked by either visual surround and/or support surface motion is given by Equation 14where VS is the rotational position of the visual surround in space, FS is the foot-in-space rotational position (equal to the support surface rotational angle), and τd is a time delay that includes sensory transduction, neural processing, transmission, and muscle activation delays.
Passive torque may not be negligible.T p could contribute toT c in test conditions where there is body movement relative to the feet (i.e., where BF, defined in Fig. 9, varies over time). This passive torque is assumed to contain both a stiffness component, K, and a damping component,B, and it acts without a time delay. The overall transfer function for conditions with support surface stimulation or combined visual and support surface stimulation is given by Equation 15and for the condition with visual stimulation on a fixed support surface Equation 16In Eqs. 14-16, the parameter W is a factor that influences the overall gain of the transfer function but does not influence the phase. We refer to W as the “sensory weighting factor” because W is a function of the sensory channel weights in the different test conditions. Specifically, in the condition with support surface stimulation with eyes closed or sway-referenced vision, W =w p = 1 −w g , wherew p andw g are the proprioceptive and graviceptive channel weights, respectively. (We assume that the sum of all sensory channels that are contributing to balance control is unity in steady state conditions, in this casew p +w g = 1.) For the test condition with visual stimulation on a sway-referenced support surface,W = w v = 1 −w g. For visual stimulation on a fixed support surface, W =w v = 1 –w p –w g. For support surface stimulation with fixed visual surround, W =w p = 1 –w v –w g. Finally, for combined support surface and visual stimulation, W =w v +w p = 1 –w g. Therefore, estimates ofW obtained from transfer function data can be used to derive estimates of the relative contributions made by different sensory systems to balance control in different test conditions with different stimulus amplitudes.
Although the Fig. 9 model represents the output of the sensory systems as position signals, this is not meant to imply that the postural control system makes use of only position information. This model could be equivalently drawn to include both position and velocity signals (as well as other functions of body motion) derived from the sensory systems, and the active corrective torque would then be generated by appropriately scaling and summing the individual motion signals.
Despite the various simplifying assumptions, the independent channel model can explain experimental transfer function results over a wide range of test frequencies, as illustrated by the curve fits ofEq. 14 to transfer function data shown in Figs. 5 and8 D. These curve fits show that the experimental gain and phase data over a frequency range of about 0.05–1.2 Hz are consistent with Eq. 14 , including results from some tests that showed prominent resonant properties. Limitations of this model were evident in that gain and phase results below and above this frequency range were not always well fit by Eq. 14 . These limitations were not overcome by inclusion of passive properties (Eqs. 15 or 16 ).
Curve fits were made to all individual transfer function curves of normal and VL subjects and to the average transfer function data from normal subjects using Eq. 14 (no passive torque) andEqs. 15 or 16 (including passive torque). To limit the number of unconstrained fit parameters, we used anthropometric estimates of J and h(Winter 1990) and direct measurement of m(less 2.6% of total m to account for mass of the feet). For curve fits to transfer function data obtained using the backboard restraint, the values of J, h, and mincluded the backboard contribution.
Curve fits using Eq. 14 reliably converged to single solutions. Results from these curve fits are discussed in the following text. Later we describe estimates of passive stiffness, K, and damping parameters, B, derived from curve fits ofEqs. 15 and 16 .
PARAMETER VARIATION WITH STIMULUS AMPLITUDE.
The mean transfer function data shown in Fig. 6, from the eight normal subjects, were fit with Eq. 14 using the means of the parameters J, m, and h for these subjects (J = 81.1 kg m2,m = 83.3 kg, h = 0.896 m; all of these parameters included the backboard contribution). Figure10 (left) shows the variation in W, K P,K D, and τd as a function of the PRTS stimulus amplitude for the six test conditions. These results, for mean normal transfer function data, are consistent with the results of fits to the transfer function data from each of the individual normal subjects (not shown). The meanK I was 2.2 ± 1.2 (SD) Nm s−1deg−1 for all fits to the mean transfer functions for all conditions and stimulus amplitudes. There was considerable variation in K Iamong the different subjects (see also Fig. 12). TheK I results are not plotted since the trends in K I values from the fits to the mean normal transfer function were not necessarily representative of results from individual subjects.
Also shown in Fig. 10 are results from the four VL subjects. These results were obtained from fits to the transfer function data from individual trials of the six test conditions. The results were not averaged because there was a wider variation of results among the VL subjects compared with normal subjects. Some data points are missing because VL subjects were unable to complete some tests with 4° PRTS stimuli, and subject VL4 was unable to complete any of the trials where the visual surround was sway-referenced.
For normal subjects, the sensory weighting factor, W, declined with increasing stimulus amplitude for all test conditions. The decline in W is indicative of the general decrease in transfer function gain with increasing stimulus amplitude seen in Fig.6. In contrast to normal subjects, VL subjects showed little and, sometimes, no decrease in W with increasing stimulus amplitude in most test conditions. There were some exceptions. In particular, subject VL3 showed a large decline inW with stimulus amplitude for tests with support surface stimulation with a fixed visual surround (transfer function data shown in Fig. 8 B), and smaller declines in other conditions (support surface stimulation with eyes closed and combined support surface and visual surround stimulation). The other three VL subjects also showed small declines in W with stimulus amplitude on various individual test conditions.
For normal subjects, the largest value of W = 0.73 was obtained with the lowest amplitude PRTS stimulus in the condition with both support surface and visual stimulation. Slightly smaller values ofW were obtained in the three other conditions where orientation cues were limited by eye closure or by sway-referencing of the visual surround or support surface. At any given stimulus amplitude, the smallest value of W was always obtained for visual stimulation on a fixed support surface.
For VL subjects, the value of W was close to unity for the four conditions where sensory orientation cues were limited by eye closure or by sway-referencing of the visual surround or support surface, and in the condition with combined support surface and visual surround rotation. In these four test conditions, the mean value ofW over all stimulus amplitudes was 1.00 ± 0.10 (SD). The value of W obtained with visual surround rotation on a fixed support surface varied little with stimulus amplitude and, in most cases, was larger than the largest W value obtained from the mean normal results in the same test condition. In two of the four VL subjects (VL1 and VL4), the values ofW were nearly identical in the conditions with visual stimulation with fixed support surface, and support surface stimulation with fixed vision. This pattern of results differs from normal subjects who always showed lower values of W in the visual stimulus condition with fixed support. The other two VL subjects (VL2and VL3) showed a pattern that more closely resembled the pattern seen in normal subjects.
For normal subjects, the active stiffness parameter,K P, increased with the stimulus amplitude in some conditions but not in others. Specifically,K P did not vary with stimulus amplitude in conditions where the stimulus was provided only by visual surround rotation. (Repeated-measures ANOVA ofK P values from curve fits to transfer functions of all eight normal subjects showed no significant difference among mean K P for 0.5–8° visual surround stimuli, P > 0.2.) In all conditions where the stimulus was provided by support surface rotation, or by combined support surface and visual surround rotation,K P increased with increasing stimulus amplitude (the hypothesis of equal K Pmeans rejected by repeated-measures ANOVA, P < 0.002). This increase was largest for support surface stimulation while viewing a fixed visual surround. In this condition with the 8° PRTS stimulus,K P was 1.65 times the value ofK P in the visual stimulus conditions. Less of an increase with stimulus amplitude occurred with eye closure or sway-referenced vision and still less with combined support surface and visual surround stimulation. The values ofK P obtained at low stimulus amplitudes (0.5 or 1°) were nearly the same for all six test conditions.
The results of K P variations with stimulus amplitude and test condition were more variable among the four VL subjects. In contrast to the results from normal subjects, two of the four VL subjects (VL1 and VL3) showed some increase in K P with stimulus amplitude for conditions where the stimulus was provided only by visual surround rotation. Also in contrast to normal subjects, there was generally no clear difference among test conditions in the variation ofK P with stimulus amplitude, although the largest values of K P usually occurred at the highest stimulus amplitude tested. Subjects VL1 and VL4 did show results similar to normal subjects in that the largest K P values were obtained at the largest stimulus amplitude in the condition with support surface rotation with fixed vision.
Similar to K P, the damping parameter, K D, in normal subjects showed essentially no variation with stimulus amplitude in the two test conditions with visual surround stimulation (fixed and sway-referenced surface). Additionally,K D did not change with amplitude on the combined visual and support surface stimulus condition. (Repeated-measures ANOVA of individualK D values showed no significant difference in means for 0.5–8° visual surround or combined visual and support surface stimuli, P > 0.5.) Although not evident in Fig. 10, K D did increase in normal subjects in the three conditions with only support surface stimulation (repeated-measures ANOVA of individualK D values, P < 0.006), although this increase was proportionally smaller than theK P increase in the same test conditions. The largest K D increase was in the fixed vision condition where the meanK D was 1.33 times larger in the 8° compared with the 0.5° support surface test. The individual transfer functions from all four of the VL subjects showed only small variations in K D with changing stimulus amplitudes and conditions (Fig. 10) even thoughK P often increased with increasing amplitude. The proportionally greater change inK P compared withK D with stimulus amplitude that occurred in many test conditions for both normal and VL subjects was unexpected. In a closed-loop control system, an increase inK P without a corresponding increase inK D would be expected to produce resonant behavior. However, resonant behavior was not typically observed.
A second unexpected finding showed why resonant behavior did not typically occur. The apparent time delay, τd, of the control loop changed as a function of stimulus amplitude and was also dependent on the stimulus condition. This change in τd changed the effective control loop damping and apparently compensated for changes inK P (see discussion). For normal subjects in the two conditions where only visual surround rotation was providing the stimulus, the mean τd was 206 ± 11 (SD) ms across all amplitudes of these two conditions, and there was only a small decrease in τd with increasing amplitude. For the other four test conditions, τd was smaller than for the visual stimulus conditions at all stimulus amplitudes, and there was a large decrease in τd with increasing stimulus amplitude. For these four conditions, the mean τd was 191 ms at the 0.5° stimulus amplitude and decreased to 105 ms at the 8° amplitude. Of these four conditions, τd was smallest for the condition with support surface stimulation and a fixed visual surround. Recall that this is the same condition that showed the largestK P measures. Although the extent of τd change with amplitude varied with the test condition, repeated-measures ANOVA performed on individual τd measures rejected the hypothesis of equal τd means across stimulus amplitudes, even in the two conditions with only visual stimulation (repeated-measures ANOVA, P < 0.005).
Among the four VL subjects, τd changes with stimulus amplitude and test condition were more variable compared with the normal subjects. Two of the VL subjects (VL1 andVL4) showed little change in τd with stimulus amplitude in most test conditions (except for support surface rotation with fixed vision for subject VL4). Subjects VL2 and VL3 showed a trend toward decreasing τd with increasing stimulus amplitude. This trend was present for both visual stimulus conditions and support surface stimulus conditions.
ESTIMATES OF PASSIVE STIFFNESS AND DAMPING.
In most cases, fits to the mean transfer function data using Eqs.15 and 16 produced results with slightly reduced error (E in Eq. 9 ) compared with the Eq. 14 fits. However, some of the Eq. 15 and 16 fits resulted in larger errors or converged to parameters that were quite different from parameters obtained on closely related trials. When these apparently unreliable fits were excluded, there remained a total of 14 fits of Eq. 15 to the 20 trials with support surface stimulation only or combined visual and support surface stimulation and 4 fits of Eq. 16 to the 5 trials with visual stimulation on a fixed support surface.
For the Eq. 15 fits, the mean passive stiffness parameter,K, was 1.6 ± 0.5 Nm deg−1 (range 0.7–2.3). There was some tendency for K to increase with increasing stimulus amplitude. The mean active stiffness parameter,K P (16.9 Nm deg−1), identified from the Eq. 15 fits, was about 10 times larger than K. The corresponding meanK P value from Eq. 14 fits (18.6 Nm deg−1) was very close to the sum of Kand K P from the Eq. 15 model. For theEq. 16 fits, the mean value of passive stiffness parameter,K, was 2.1 ± 0.4 Nm deg−1 (range 1.5–2.6).
For the Eq. 15 fits, the mean passive damping parameter,B, was 0.43 ± 0.19 Nm s deg−1 (range 0.16–0.75). There was no clear change in B with increasing stimulus amplitude. The mean active damping parameter,K D (5.8 Nm s deg−1), identified from the Eq. 15 fits, was about 13 times larger than B. The corresponding meanK D value (6.1 Nm s deg−1) from Eq. 14 fits was close to the sum of B andK D from the Eq. 15 model. For the Eq. 16 fits, the mean value of passive damping parameter, B, was 3.3 ± 0.7 Nm s deg−1(range 2.5–4.3). The mean active damping parameter,K D (5.0 Nm s deg−1), identified from the Eq. 16 fits, was only 1.5 times larger than B on these trials, suggesting that passive damping may contribute more to overall damping when the surface is fixed than when it is moving.
TIME DELAY VARIATION WITH STIFFNESS.
The results from normal subjects in Fig. 10 suggest that τd may be related toK P because tests producing smaller values of τd typically gave larger values ofK P. This correlation is evident in plots of τd versusK P shown in Fig.11. Figure 11 A showsK P and τdparameters obtained from curve fits to transfer functions of 30 different tests (6 conditions times 5 stimulus amplitudes) for three representative normal subjects. The data from all eight normal subjects suggest that a linear relation exists between τd and K P.
Linear regressions were performed on the τdversus K P data from curve fits to the mean normal transfer functions and from curve fits to the individual transfer functions. The regression slope of the τd versus K Pdata from fits to the mean normal transfer functions was −14.4 ms/Nm deg−1. For the individual normal subjects, the regression slopes ranged from −10.1 to −18.4 ms/Nm deg−1 and had a mean of −13.8 ± 3.6 ms/Nm deg−1. The τd versusK P correlation coefficient, r, for data derived from the mean transfer functions was r = −0.92. For the individual τd versusK P data, r ranged from −0.76 to −0.92 and had a mean of −0.84.
VL subjects also showed some correlation between τd and K P. Data from three of the VL subjects are shown in Fig. 11 B(the fourth subject's data partially overlapped with subject VL1's data, and was not included for clarity). In general, the correlation coefficients for the VL results were lower than results from normal subjects (mean r = −0.73, range −0.54 to −0.92). These generally lower correlations appear to be due to the fact that two of the four VL subjects (VL2 andVL3) showed relatively little variation inK P across the various test conditions. The correlation values for the other two VL subjects, whoseK P measures did vary more across test conditions, were compatible with the results from normal subjects.
The linear regression slopes of the τd versusK P data for three of the four VL subjects were smaller in magnitude than any of the regression slopes for normal subjects. The regression slopes for these three subjects ranges from −5.2 to −8.9 ms/Nm deg−1. The fourth VL subject (VL2) had a regression slope close to the mean of normal subjects.
PARAMETER VARIATION WITH SUBJECT MASS.
Stiffness, K P, and damping,K D, were strongly correlated with subject mass, moment of inertia, and other related body mass measures. In contrast, the integral control factor,K I, showed only a weak correlation, and time delay, τd, was essentially uncorrelated with measures of mass and moment of inertia. Figure12 plots these various parameters versus the product of subject mass and COM height. The mass times COM height product is related to the amount of destabilizing torque due to gravity associated with deviation of body orientation from a perfect upright position.
The data in Fig. 12 include results from the eight normal subjects who performed tests with the backboard restraint, the four VL subjects with backboard restraint, and the subset of the four normal subjects who also performed tests in a freestanding condition. For the tests performed with the backboard, the measures included the added mass of the backboard, and the COM height measure included the effect of the backboard on overall COM height, which slightly lowered the COM height compared with the freestanding subject. Each data point in Fig. 12represents the mean value of the control parameters obtained from curve fits to transfer function data of the six different test conditions using 1° PRTS stimuli. Results from the 1° PRTS stimuli were used because, at this low stimulus amplitude, there tended to be a convergence of K P and τd measures to a common value independent of the test condition (see Fig. 10), and a full set of results from VL subjects was available at this stimulus amplitude. Figure 12 plots (—) the results of linear regression analysis performed on the mean data values from the eight backboard-restrained normal subjects. The correlation coefficients shown apply to these same data.
The K P measures show a high correlation with mass times COM height (r = 0.97 for data from backboard-restrained normal subjects). The minimal torque required to overcome the destabilizing torque due to gravity is represented as - - -. The difference between each subject'sK P value and the dashed line represents the amount of corrective torque that is in excess of the minimal amount required to maintain stance. In some sense, this represents a “safety factor” of actively generated corrective torque. The regression line K Pintercept was close to zero, and its slope [0.226 (Nm deg−1)/(kg m)] was slightly greater than the minimal torque line [0.171 (Nm deg−1)/(kg m)]. This indicates that larger mass subjects maintained a proportionally larger safety factor than lower mass subjects [i.e.,K P/(minimumK P) ≈ 1.3 independent of subject mass].
The K P data from the four freestanding normal subjects remained very close to the regression line for theK P data from the eight backboard-restrained subjects. This indicates that these four subjects altered their K P to account for the change in mass/moment of inertia associated with use of the backboard.
The K P data from the VL subjects were also reasonably close to the regression line for theK P data from normal subjects. However, one of the four VL subjects (VL1) had a meanK P value that was noticeably larger than normal subjects with similar body mass. A second VL subject (VL4) also had a somewhat larger meanK P. These differences compared with normal subjects will be more evident when normalized values ofK P are considered later.
The K D data from normal subjects (freestanding and with backboard) and VL subjects also were highly correlated with body mass times COM height. The linear regression line and correlation coefficient (K D = 0.0871 mh − 0.463, r = 0.95) shown for the K D data in Fig. 12 (top right) are for the mean K D data from backboard-restrained normal subjects on 1° PRTS tests. The meanK D results from the four freestanding normal subjects were close to the linear regression line, again indicating that subjects adjusted theirK D to account for altered body dynamics due to backboard use. The meanK D values from VL subjects were also close to the regression line for normal subjects.
The time delay measure, τd, showed essentially no variation with body mass measures (Fig. 12, bottom right). There was no change in τd noted in the normal subjects who performed tests both with and without the backboard. However, the mean τd measures from the VL subjects deviated from the normal subject τd results. The two subjects with the largest mean τd measures were both VL subjects (VL2 and VL3). The two subjects with the smallest mean τd measures were also both VL subjects (VL1 and VL4). Note that the two subjects with the smallest τds also had relatively largeK P measures. This combination of results suggests that these subjects were maintaining an overall increased level of stiffness, possibly as a strategy for compensating for their vestibular deficit. However, increased stiffness requires increased damping to avoid resonant behavior. This increased damping was provided not only by slightly increased values ofK D for these subjects but also by a decrease in apparent time delay.
Finally, K I measures showed large variability, and only a weak correlation with body mass measures (Fig.12, bottom left). This parameter accounts for the low-frequency phase advance and gain decline seen in the experimental transfer functions. The transfer function given by Eq. 14 often did not fit the low-frequency data well. The large variability inK I may reflect the fact that this parameter does not provide a complete explanation for the observed low-frequency behavior.
NORMALIZED STIFFNESS AND DAMPING COEFFICIENTS.
If Eq. 14 is simplified by ignoring the effects ofK I and time delay (setK I and τd to 0) and dividing the numerator and denominator by the subject's moment of inertia, J, then the denominator is given bys 2 + (K D/J)s + (K P − mgh)/J. Setting the denominator equal to zero gives the characteristic differential equation relating the body-sway response, BS, to the stimulus, either VS or FS. The characteristic equation is an important determiner of the dynamic properties of the system. Therefore if the normalized stiffness and damping factors of this equation, (K P − mgh)/Jand K D/J, respectively, are similar across subjects, then this implies that the transfer function dynamic properties are also similar across subjects.
Figure 13 plots these normalized stiffness and damping factors for the eight normal subjects (with backboard, ○), the four VL subjects (with backboard, ▴), and the subset of four normal subjects who performed the tests freestanding (●). All data are from tests with 1° PRTS amplitudes, and each point is the mean of results from the six different test conditions. The regression lines and correlation coefficients are determined from the mean data from the eight normal subjects who performed tests with the backboard. The results show that there is little variation among normal subjects in the normalized stiffness and damping factors. The normalized stiffness and damping factors determined in the freestanding condition were not distinguishable from those determined with the backboard. The limited variation in these normalized parameters indicates that the general dynamic behavior varied little among the normal subjects despite the wide range of body mass, height, and moment of inertia. Therefore little or no distortion resulted from the averaging of transfer function data across subjects (Figs. 6 and 7), and the transfer function parameters derived from curve fits to the mean transfer functions accurately reflect the mean behavior of the population.
The normalized stiffness and damping factors for VL subjects did show some differences compared with normal subjects. The largest two normalized stiffness factors were both from VL subjects (VL1and VL4). The mean normalized damping factors for these two subjects were also greater than for any normal subject or the other two VL subjects, although these values were only slightly greater than the largest values from normal subjects.
VARYING CONTRIBUTIONS OF SENSORY CHANNELS.
In the previous description of the independent channel model, it was stated that the sensory channel weighting factor, W, could be used to derive estimates of the relative contributions (w v,w p, andw g) made by different sensory systems to balance control in different test conditions and with different stimulus amplitudes. The derivation of these estimates assumes that, in steady-state conditions, the sum of the weights from all sensory channels that are contributing to postural control is unity. The derivation also assumes that sway-referencing of the visual surround or support surface effectively eliminates the contribution of visual or proprioceptive sensory cues, respectively (i.e., VB = 0 or BF = 0 in the Fig. 9 model).
The graphs in Fig. 14 show the change in sensory channel weights as a function of PRTS stimulus amplitude as derived from different test conditions using the backboard support. The mean results from normal subjects are represented by ○ and ●. Results from individual example VL subjects are also shown (× forVL3 and ▵ and ▴ for VL2). The left column shows w v, the middle column w p, and the right column w g.
The results in the top row were derived from W values for tests where the stimulus was provided by visual surround motion while the subject stood on a sway-referenced support surface. In this case,w v = W,w g = 1 −w v. In this condition, the visual contribution to postural control for normal subjects was largest (w v = 0.77) at the lowest stimulus amplitude. The contribution of the visual channel steadily decreased with increasing stimulus amplitude such that at the highest stimulus amplitude, postural control was dominated by the contribution from graviceptors (w g = 0.87,w v = 0.13).
For the example data from the VL subject (VL2) shown in Fig.14, top, we also assumed thatw v = W andw g = 1 −w v. If the graviceptor contribution was entirely provided by vestibular-derived sensory cues, then we would expect to find that w v = 1 andw g = 0, independent of stimulus amplitude. This was approximately the case for this subject except thatw v was actually slightly greater than 1 (mean w v = 1.17). This gave a seemingly nonsensical mean w g of −0.17. It is uncertain if there is any physiological significance to these unexpected values, but similar results were obtained for three of the four VL subjects in this test condition (as can be surmised fromW values shown in Fig. 10 for the individual VL subjects). One could speculate that the assumption ofw v +w g = 1 is not valid, and this subject was able to derive some orientation information from support surface cues (possibly due to imperfections in sway-referencing of the support surface or due to nonvestibular graviceptors).
Figure 14, middle row, shows the results for normal subjects from tests with a support surface stimulus and either eyes closed (● and —) or sway-referenced vision (○ and - - -). The results for these two test conditions for normal subjects were nearly identical. In this condition, w p = W,w g = 1 −w p. At the lowest stimulus amplitude, proprioceptive cues provided the major contribution to postural control (w p = 0.70,w g = 0.30) while at the highest stimulus amplitude, the contribution of graviceptive cues dominated (w p = 0.24,w g = 0.76). These results were similar to the visual stimulation results described previously. However, with support surface stimulation, there was a smaller shift from proprioceptive to graviceptive contributions than occurred with visual stimulation.
The results for the example VL subject were somewhat different for tests with eye closure compared with sway-referenced vision (Fig. 14,middle row, ▴ and — for eyes closed, ▵ and - - - for sway-referenced vision). For the eyes closed condition,w p was very close to 1 for all stimulus amplitudes tested (mean w p = 0.995). Therefore w g = 1 −w p was nearly zero. This result suggests that the source of sensory information used for postural control was derived entirely from proprioceptive receptors in this condition and that graviceptor information did not contribute to postural control. Because this was a VL subject, the absence of a graviceptor contribution also implies that vestibular sensors were the entire source of this subject's graviceptor information used for postural control in this condition. However, unlike normal subjects, the results from the sway-referenced condition were not quite the same as from the eyes closed condition. In this case,w p was slightly less than 1 at all stimulus amplitudes (mean w p = 0.88), and w g was therefore equal to 0.12, suggesting that this subject had some access to graviceptive information in this condition. Alternatively, one could speculate that this subject was able to derive some useful information from visual cues (possibly due to imperfections in sway-referencing of the visual surround). A similar discrepancy between eyes closed and sway-referenced vision results also occurred with subjects VL1 and VL3, with w pvalues determined from the sway-referenced condition being lower than from the eyes closed condition. Subject VL4 was unable to complete any trial with a sway-referenced visual surround even though she was able to perform tests with eyes closed.
Figure 14, bottom, shows the results derived from three different test conditions. In each of these test conditions, we anticipated that visual, proprioceptive, and graviceptive information would all be contributing to postural control. Thew v results were derived from tests with visual stimulation on a fixed support surface. In this condition,w v = W = 1 –w p –w g. Thew p results were derived from tests with support surface stimulation and a fixed visual surround. In this condition, w p = W = 1 – w v –w g. Oncew v andw p were known,w g was calculatedw g = 1 –w v –w p. The results for normal subjects are shown in the three lower row plots in Fig. 14 (● and —). The calculation of w g in this case depended on the possibly invalid assumption thatw v andw p values obtained at a given stimulus amplitude in two different test conditions were comparable. An approximate check on this assumption was provided by results from the test condition with combined support surface and visual surround stimulation. In this condition, W =w v +w p, and thereforew g = 1 – W. Results for normal subjects of this w gcalculation, plotted in the lower right graph of Fig. 14 (○ with - - -), show a close, but not exact, correspondence to thew g values derived from the two separate test conditions.
The results for normal subjects shown in Fig. 14, bottom,demonstrate that in conditions where two of the three sensory channels were providing veridical orientation cues, the visual channel contribution to postural control was always smaller than the proprioceptive channel contribution. The average difference betweenw p andw v across all stimulus amplitudes was 0.17. With increasing stimulus amplitudes, the contribution of both visual and proprioceptive channels decreased and the graviceptive channel showed a corresponding increase. At the highest stimulus amplitude tested, the graviceptive channel contribution dominated, and there was essentially no contribution from the visual channel (w g = 0.82,w p = 0.15,w v = 0.03).
Results for two example VL subjects derived from test conditions with the visual surround fixed, support surface fixed, or combined visual and support surface stimulation, are also plotted in Fig. 14(bottom, ▵, ▴ and ×). These results were derived in the same manner as the results from the normal subjects. In one of the VL subjects (VL2, ▴ and — for results derived from fixed visual surround or fixed support surface conditions),w p was always larger thanw v, and there was only a small decline in these sensory channel weights with increasing stimulus amplitude. The graviceptive channel contribution was close to zero except at the highest stimulus amplitude tested (4°). Thew g values derived from the combined stimulus conditions (▵, · · ·) were similar tow g values derived from test conditions with either the visual surround or the support surface fixed and showed that there was essentially no graviceptive contribution to postural control in this subject with absent vestibular function. The results from two of the other VL subjects (VL1 and VL4) were similar to this subject with the exception thatw v andw p were approximately equal in these two subjects. Subject VL3, who had the most preserved vestibular function (Table 1), showed a different behavior. His results are also plotted in Fig. 14 (bottom, × with — for results derived from conditions with fixed surround or support surface and · · · for results derived from combined stimulation). This subject showed a visual channel contribution ofw v = 0.4 that was independent of the stimulus amplitude. However, w pdeclined with increasing stimulus amplitude. The overall result was that w g was zero for the 1° stimulus condition but increased to a value of about 0.2 at the 4° stimulus condition. The w g values from the combined stimulus condition were in close agreement with those derived from the separate test conditions.
Human postural control behavior over a bandwidth of 0.017–2.23 Hz was characterized by applying pseudorandom support surface and/or visual perturbations of varying amplitudes and interpreting responses based on a simple negative feedback model (Fig. 9). Subjects tended to align their body to the perturbing stimulus such that the general waveform of the body-sway angle response was similar to the stimulus waveform (Fig. 3). As the stimulus amplitude was increased, the body-sway response initially increased but then saturated for peak-to-peak stimulus amplitudes greater than about 2° for subjects with normal vestibular function (Fig. 4, ● and —). For subjects with bilaterally absent vestibular function, responses continued to increase with increasing stimulus amplitude (Fig. 4, · · · ).
The stimulus-response waveforms were analyzed using Fourier methods to calculate gain, phase, and coherence measures as a function of stimulus frequency (Figs. 5-8). A gain of unity and phase of zero indicates that the subject remained perfectly aligned to the stimulus in amplitude (e.g., body-sway angle equals support surface or visual surround tilt angle) and time (i.e., no time delay or advance of body sway relative to the stimulus). Such perfect alignment was never achieved. Phase measures typically showed a phase lead at frequencies less than about 0.1 Hz. Phase functions crossed zero in the 0.1–0.2 Hz range, increased with increasing frequency, and reached lags as high as 350–400° at 2.23 Hz (Fig. 6).
The large and increasing phase lags with increasing frequency are consistent with the existence of a significant time delay between the stimulus and the resulting body-sway response. This time delay was present in responses to both visual and support surface stimuli. The existence of a large time delay seems incompatible with the possibility that stabilizing torque might be obtained primarily via passive mechanisms as suggested previously (Winter et al. 1998,2001) because passive stiffness mechanisms should act without time delay. Also, our estimates of passive stiffness and damping parameters obtained from curve fits of Eq. 15 to experimental transfer function data showed these passive factors to be about 1/10th the value of active stiffness and damping parameters.
Explanation of response dynamics
Gain functions were maximal between about 0.1–0.5 Hz for both normal (Fig. 6) and VL subjects (Fig. 8). For frequencies greater than 0.5 Hz, gains monotonically declined with increasing frequency. The peak gain values were often greater than unity, particularly for low-amplitude stimuli where mean gains as large as 4.1 were obtained (mean normal gain for 0.5° visual stimulus on sway-referenced surface). Gain values greater than unity indicate that the amplitude of stimulus-evoked body sway was greater than the stimulus amplitude.
Gain values greater than unity may seem to be an unlikely result. However, large gains have been demonstrated previously (Gurfinkel et al. 1995; Lee and Lishman 1975; Peterka and Benolken 1995) in response to low-amplitude stimuli. Large gains are also consistent with postural regulation via a negative feedback control mechanism where, in steady state, corrective torque is generated in proportion to a position error signal. This is easiest to see if one considers a postural control system consisting of only one sensory system. Consider, for example, a system with only proprioceptors, which signal body orientation relative to the support surface (Fig. 9 with w v= w g = 0,w p = 1). In this system, an error signal, indicating body sway relative to the support surface, is used to generate a corrective torque that changes the body-sway angle in space and reduces the error signal. If this control system could maintain zero error, then the body would remain oriented to the support surface, and the transfer function gain would be unity across all stimulus frequencies. However, a control system typically will not be able to achieve a zero error condition. The error depends on the system's overall properties that include body and neural controller dynamics. To see that gains can be greater than unity, consider a simplified neural controller that does not include the integral control factor, K I (integral control mainly affects very low-frequency dynamics). In this system, the steady-state gain is predicted to beK P/(K P− mgh). This result is obtained from Eq. 14 by setting W = 1, K I = 0 and setting the Laplace variable s = 0 [seePeterka and Benolken (1995) and also a similar derivation in Gurfinkel et al. (1995)]. Because the gravity-related factor mgh is a positive value, the predicted gain is greater than unity, and the gain value tells us about the size of K P relative tomgh. Qualitatively, this result means that when the support surface tilts, a steady-state body-sway angle is reached that represents the equilibrium point where the torque due to gravity,mgh sin(BS), is balanced by the compensatory torque generated by the neural controller,K P(FS − BS). At this equilibrium point, the body-sway angle from vertical will always be greater than the tilt angle of the support surface, and therefore the gain is greater than unity.
Experimental results show that the highest gains typically occur in the 0.1–0.2 Hz frequency range where the response phases are also closest to zero. It is reasonable to assume that responses in this mid-frequency region are dominated by the stiffness component of the neural controller and its interaction with the spring-like torque due to gravity. Body motions at these frequencies are slow enough that there is time for the body to reach an equilibrium position that reflects the torque balance between neural controller and gravity torques.
At higher frequencies, the body-sway response becomes increasingly dominated by inertial torques, which tend to keep the body fixed in space (gains approach 0) and therefore resist orientation toward the stimulus. The interplay between inertial torque and active torque due to stiffness and damping components of the neural controller would result in response phases approaching −90° at higher frequencies, if there was no time delay in the system. With the addition of time delay, phase lags continue to increase with increasing frequency, consistent with the experimental data. The inclusion of a time delay in the model was able to account for much of the phase lag at higher frequencies (e.g., Fig. 5, C and D). However, even with the inclusion of a time delay, the transfer function fit (Eq.14 ) was not always able to account for all of the phase lag in the experimental data (e.g., Figs. 5, A and B, and8 D). This poor fit to the higher-frequency data was more common for data obtained in response to 0.5 or 1° stimuli (Fig. 5,A and B) than for data from higher-amplitude stimuli (Fig. 5, C and D). Failure of the independent channel model to fully explain the higher-frequency data indicates that this model is not accounting for all of the factors that contribute to dynamic behavior greater than about 1.2 Hz. These factors might include low-pass dynamics in the sensory channels and muscle mechanics that have low-pass characteristics (Zajac 1989).
At frequencies lower than about 0.1 Hz, experimental results show gain declines and phase advances. This dynamic behavior cannot be explained if corrective torque is only generated in proportion to body position and velocity relative to the support surface (FS − BS). In a system with only one sensor signaling orientation with respect to the support surface, this low-frequency dynamic behavior necessarily requires that corrective torque be generated as some function of body orientation that emphasizes low frequencies. One possibility is that a component of corrective torque is generated in proportion to the time integral of the error signal FS − BS as represented by theK I factor in the neural controller in Fig. 9. The inclusion of an integral control component has been previously suggested to explain the dynamic properties of vibration-evoked body sway (Johansson et al. 1988). In this previous study, the normalized integral control parameter was referred to as a “swiftness” factor. Alternatively, low-frequency gain declines could be produced by a contribution from an additional sensory cue that only influenced low-frequency behavior and was opposed to the sensory cue that encoded body sway relative to the stimulus. For example, if the corrective torque included a contribution from a sensory system conveying low-frequency graviceptive information, then low-frequency behavior might be dominated by the graviceptive cue producing orientation toward earth-vertical, while mid-frequency behavior is dominated by proprioceptive and/or visual cues that produce orientation to the support surface and/or visual surround.
For a one sensor system, the use of integral control would only be able to reduce the low-frequency gain to unity. This prediction seems compatible with the gain data from some VL subjects tested in conditions that limited either visual or support surface cues (e.g., Fig. 8, A and D). However, the observed low-frequency phase data from both normal subjects and VL subjects were not always fully explained by the addition of an integral control factor. Specifically, the phase data often showed significant phase leads at frequencies less than about 0.1 Hz (Figs. 5, 6, and 8). Inclusion of a K I factor in the neural controller was only able to account for some of this phase lead. In a model transfer function that includes aK I factor (Eq. 14 ), the maximum phase advance will always be less than 90°, and the phase will approach zero at very low frequencies. However, the average normal phase data in Fig. 5 showed that there was little or no tendency for the phase lead to decline toward zero with decreasing frequency, and the experimentally measured phase often showed a larger phase lead than could be explained by the model. The model's phase behavior and the disparity between the low-frequency model and experimental phase data can be clearly seen in Figs. 5, B and C, and8 D. Therefore, inclusion of aK I factor in the model neural controller did not provide a full explanation of the low-frequency behavior of the postural control system.
Interpretation of response saturation
In subjects with normal sensory function, responses to increasing amplitudes of visual or support surface stimuli showed saturation behavior (Fig. 4). One might speculate that this is the result of some nonlinear processing of sensorimotor signals that limit the responses to larger amplitude stimuli. If this were the case, then one would expect that coherence functions should show some evidence for increasingly nonlinear stimulus-response behavior with increasing stimulus amplitude. That is, with perfectly linear stimulus-response behavior in the absence of noise, the coherence function will be unity across all test frequencies. The presence of noise and/or nonlinear behavior results in a decrease in coherence function values. If increasing stimulus amplitudes drove the system further into some type of saturating nonlinearity, one would expect to see decreases in coherence function values with increasing stimulus amplitude. This was not observed. At stimulus amplitudes of 1° and above, there was no obvious decrease in coherence function values with increasing stimulus amplitude that might indicate the influence of a saturating nonlinearity. Note that decreases in coherence function values do not necessarily occur when a nonlinearity is present (Maki 1986). However, simulation results using our specific PRTS stimulus applied to a system with a saturating nonlinearity did show decreased coherence function values with increasing stimulus amplitude.
The similar coherence function values suggest that stimulus-response behavior was as linear in the 1° stimulus condition as in the 8° condition even though gain functions differed greatly between these two stimulus conditions, indicating overall nonlinear behavior of the system. This apparent contradiction can be explained if one assumes that sensory weighting factors changed as a function of stimulus amplitude, thereby providing quasi-linear behavior at each stimulus amplitude. The large decrease in gain can occur if the predominant sensory contribution shifts from the proprioceptive and/or visual system to a graviceptive system with increasing stimulus amplitude.
The absence of some fundamental saturating nonlinearity in the postural control system is further supported by the results from VL subjects. These subjects did not show saturating behavior (Fig. 4, · · ·), and transfer function results showed very limited changes in gain with stimulus amplitude. However, their coherence function results were nearly the same as those in normal subjects (e.g., Fig. 8 A). From this observation in VL subjects, we can postulate that both the interaction of proprioceptive and visual orientation cues, and the overall behavior of the motor output system are essentially linear. If this essentially linear proprioceptive/visual interaction is also true for subjects with normal sensory function, then the overall nonlinear behavior to changing stimulus amplitude must involve a nonlinear interaction of vestibular cues with proprioceptive/visual cues. One likely possibility is that this nonlinear interaction is representative of a sensory selection mechanism that alters the relative contribution of different sensory orientation cues in different conditions. This effect can be functionally characterized as a stimulus-dependent reweighting of sensory channels. Our results showed that the variation in channel weights among normal subjects for any given stimulus amplitude and condition was very small (see SD error bars in Fig. 14), indicating that all of our normal subjects used nearly identical selection strategies for a given condition and amplitude.
A recent adaptive model of sensory integration for human postural control has been proposed based on optimal estimation theory (van der Kooij et al. 2001). This model was able to predict the amplitude-dependence of body sway evoked by sinusoidal visual surround rotations for both normal and VL subjects (Peterka and Benolken 1995). These previous data are qualitatively similar to the PRTS responses reported here, showing response saturation in normal but not in VL subjects. Therefore it appears that this new adaptive model provides a basis for interpreting sensory reweighting in terms of the goals and limitations of the sensorimotor integration process as it applies to postural control.
Optimal estimation models also provide a basis for understanding how the nervous system might transform raw sensory signals into internal estimates of body motion and spatial orientation (Merfeld 1995; van der Kooij et al. 1999; Zupan et al. 2002). Although our simple model (Fig. 9) does not include mechanisms for optimal estimation of body motion, it does assume that wide bandwidth motion information is available to the postural control system. Complex sensory integration processes represented by optimal estimation models likely are necessary to provide the wide bandwidth motion information used in postural control.
Sensory channel reweighting and “torque normalization”
Consider a test condition where only two modalities are available for balance control in normal subjects. Specifically, consider support surface stimulation with eyes closed, where proprioceptive and graviceptive cues contribute to balance control. The observed decrease in transfer function gain with increasing support surface amplitude implies that a relative reduction in responsiveness to proprioceptive cues occurs with increasing stimulus amplitude. This relative reduction in responsiveness can be expressed as a decrease in the proprioceptive channel weight, w p, with increasing stimulus amplitude. In a closed-loop control system, a reduction of a gain factor inside a feedback loop can severely affect dynamic behavior. In the Fig. 9 model, a reduction inw p alone causes the overall transfer function to develop resonant properties as the level of net corrective torque decreases. If w p is so low that the corrective torque is insufficient to resist the torque due to gravity, the system becomes unstable. The fact that the transfer function dynamics do not change greatly with changing stimulus amplitude (Fig. 6) implies that the net corrective torque does not change greatly with decreasing w p. This indirectly implies that another signal contributing to torque generation increases as w p decreases. A reasonable assumption consistent with the experimental data and embodied in the Fig. 9 model is that the graviceptive contribution (represented by w g) to net torque generation increases as the proprioceptive contribution decreases. The same argument applies for the condition where only visual and graviceptive cues contribute to balance control (visual stimulation on sway-referenced support surface). In this case,w g increases asw v decreases.
Therefore the modeling assumption that the sum of sensory channel weights is unity is essentially a “torque normalization” hypothesis. This hypothesis implies that some mechanism exists that ensures that an appropriate level of corrective torque is generated to not only maintain stance but to maintain good (i.e., nonresonant) dynamic behavior independent of the particular source of sensory cues that are contributing to torque generation in a particular environmental condition. Complete adherence to a torque normalization principle would imply that the shapes of the transfer functions never change even though the overall contribution of individual sensory channels changes with varying stimulus conditions. It is likely that torque normalization is not always perfectly maintained, and this could account for the relatively rare occurrences where resonant transfer function dynamics were observed. For example, the Fig. 5 Btransfer function with a resonant peak at about 0.2 Hz is consistent with there being too little corrective torque generated in proportion to body sway, and the Fig. 5 C transfer function showing a 0.9 Hz resonance peak is consistent with there being too much corrective torque.
Sensory channel weighting in VL subjects
For VL subjects tested in the three conditions that limited sensory orientation cues from one modality (either vision or proprioception) or in the one condition that provided an identical stimulus to both the visual and proprioceptive systems, the prediction of the independent channel model (Fig. 9) is that the identified sensory weighting factor, W, should be unity if all of the graviceptive information used for postural control were derived from the vestibular system. To a good approximation, this was true for all four VL subjects (Fig. 10, VL results in top row). The small deviations from this prediction might be accounted for by various experimental imperfections including misestimates of body moment of inertia and COM height used in the curve fit procedures, imperfections in sway-referencing, the fact that vestibular function may not be entirely absent in these subjects, and the possibility that VL subjects may compensate for their loss by making some small use of nonvestibular graviceptive information (Mittelstaedt 1998).
Another clear difference between normal and VL subjects was evident in test conditions where either the visual surround or the support surface was fixed. In normal subjects, the value of W decreased with increasing stimulus amplitude (Fig. 10, bottom 2 curves intop left plot), indicating that there was a decrease in responsiveness to the stimulus with increasing amplitude and indirectly implying a decrease in w p orw v channel weights. In contrast, VL subjects showed a more limited ability, and in some cases, no ability (e.g., VL2 in Fig. 14, bottom) to modifyw p andw v with increasing stimulus amplitude. If only two sensory modalities contribute to postural control and neither of these modalities provide absolute earth-referenced information, then a reasonable strategy may simply be to generate corrective torque as a fixed combination of signals from these two modalities independent of the stimulus amplitude and without attempting to make a decision about which of the two sensory systems might possibly be providing veridical orientation information.
In conditions where both visual and proprioceptive cues were available, three of the four VL subjects showed little ability to alter the visual and proprioceptive channel weights with varying stimulus amplitude as indicated by the limited changes in W (Fig. 10, VL results in top row, bottom 2 traces in each plot). One subject,VL3, could markedly decrease his proprioceptive channel weight with increasing support surface rotation (fixed visual surround condition). Given that other test conditions showed that this subject was unable to utilize graviceptive cues for postural control, this decreased proprioceptive weight was likely associated with an increased visual channel weight. That is, over the course of our relatively long duration tests, this subject may have been able to determine that visual cues were providing veridical orientation information and therefore relied more heavily on them. One could imagine trial and error changes in sensory channel weights occurring with the effectiveness of the weight change judged by monitoring the muscular effort necessary to maintain balance. One could also imagine that in a richer sensory environment than that afforded by our test apparatus, cognitive factors based on prior knowledge of the stability of the visual world or surface condition could influence sensory channel weight selection.
Compensation for bilateral VL
All of the VL subjects received their loss several years prior to our testing, and would clinically be considered well compensated. (One possible exception would be subject VL4, who showed visual preference behavior.) An interesting question is whether or not there was evidence for sensory substitution for their vestibular loss. For example, there is evidence that subjects have access to graviceptive cues that are not of vestibular origin (Mittelstaedt 1998). Perhaps these could be substituted for missing vestibular cues. Our results show little evidence that some other nonvestibular graviceptive source was utilized by our VL subjects. When VL subjects were tested under conditions that eliminated or greatly limited visual or proprioceptive orientation cues (by eye closure or sway-referencing of the visual surround or by support surface sway-referencing), the sensory weighting factor, W, identified from our transfer function fits was very close to unity and varied little with changing stimulus amplitudes (Fig. 10,top). By our interpretation, a unity value of Win these conditions indicates that VL subjects were deriving all of their orientation information from one source, either vision or proprioception.
There was evidence some VL subjects used an increase in stiffness to compensate for their vestibular loss. Among all of the normal and VL subjects tested, the two subjects with the greatest relative stiffness (K P normalized for body moment of inertia) on low-amplitude tests were both VL subjects (Fig. 13,left). As discussed previously, maintenance of a relatively high stiffness could provide a compensatory strategy which reduces the sensory error signal (“e ” in Fig. 9), and thereby enhances orientation toward the available sensory reference. As is appropriate to maintain nonresonant dynamics, the increase inK P in these two subjects was accompanied by both a relative increase inK D and decrease in τd to provide for increased damping.
A compensation strategy that uses increased stiffness necessarily requires an increased energy expenditure. Perhaps this is the reason that the other two VL subjects did not adopt a strategy of increased stiffness. In fact, one of the VL subjects had the second lowest relative stiffness among all subjects tested.
Changes in apparent feedback time delay
There was a consistent difference between the family of phase functions obtained from visual stimuli and those obtained from support surface stimuli (Fig. 6). For visual stimuli, the phase functions at frequencies greater than about 0.2 Hz were nearly identical for all stimulus amplitudes. In contrast, for support surface stimuli, the phase functions greater than 0.2 Hz showed less phase lag with increasing stimulus amplitude. A reduced phase lag could be consistent with a smaller time delay (this is the interpretation based on curve fits of Eq. 14 derived from the independent channel model). However, other mechanisms that might explain this phenomenon are considered in the following text.
One might speculate that a shorter time delay could result from an increased contribution of a sensory system that acts with a shorter time delay (i.e., there might be a shorter time delay in the vestibular contribution to corrective torque generation compared with the proprioceptive time delay). Alternatively, if there was an increased contribution of corrective torque due to “passive” muscle/tendon properties (which act with zero time delay) compared with active torque generation, then the time delay might appear to decrease. However, preliminary results from recent experiments using a time domain analysis of responses to high bandwidth PRTS stimuli suggest that the actual time delay does not change with stimulus amplitude (Peterka 2001). These results favor the existence of a mechanism that compensates for time delay without changing the actual time delay or changing the active versus passive contributions to torque generation. Such a mechanism is not included in the independent channel model but has been suggested in other postural control models (Morasso et al. 1999; van der Kooij et al. 1999,2001) and in motor systems in general (Kleinman et al. 1970; Miall et al. 1993). Therefore the time delay parameter, τd, in the independent channel model should be thought of as an “effective time delay” rather than as a parameter representing actual delays in neural processing, transmission, and muscle activation.
If a mechanism for time delay compensation exists, why does it exist? When the independent channel model is simulated, it becomes easy to appreciate that an increase in the active stiffness parameterK P by 60% (as shown in Fig. 10 for increasing support surface stimulus amplitudes with fixed visual surround) causes a 1 Hz resonant peak to develop in the transfer function indicating that the system is close to instability. However, experimental data never showed a 1 Hz resonant peak because this stiffness increase was apparently accompanied by an appropriate increase in overall damping. There are two ways to increase damping, the most obvious of which is to increaseK D, but a decrease in τd has a nearly identical effect. Our results showed that there was a small increase inK D in conditions whereK P increased (Fig. 10,left), but a larger portion of the overall damping increase was accomplished by a decrease in the effective time delay. Additionally, Fig. 11 A shows a strong correlation between τd and K P. We suggest that a relationship exists between τdand K P because changes in the effective time delay are the primary method used by the postural control system to regulate the overall damping to compensate for changes in stiffness in different test conditions.
Is feedback control sufficient?
Our general conclusion is that a feedback control mechanism is sufficient to account for postural control behavior over a wide bandwidth. This was not the conclusion reached previously (Fitzpatrick et al. 1996), where it was postulated that feedforward predictive control mechanisms were required. We suggest that Fitzpatrick's well-reasoned attempt to break open and test individual components of the feedback system was confounded by the postural control system's ability to reweight sensory information in different test conditions. Specifically, this unanticipated reweighting resulted in an underestimation of the overall sensory contribution to feedback control in this previous study.
The results of stabilogram-diffusion analysis of quiet stance COP data have been used to infer the existence of both “open loop” and “closed loop” control of posture (Collins and De Luca 1993). However, recent results have shown that stabilogram-diffusion functions obtained from simulations using a feedback model like the one in Fig. 9 are indistinguishable from experimental stabilogram-diffusion functions (Peterka 2000), thus demonstrating that feedback control mechanisms alone are sufficient to explain the shape of stabilogram-diffusion functions obtained from experimental COP data.
We find further support for a feedback control scheme that relies on actively generated corrective torque and sensory reweighting because it appears compatible with a number of pathological conditions. For example, this model predicts and is consistent with experimental results (Nashner et al. 1982) that stance is impossible for VL subjects deprived of visual cues (eye closure) and veridical proprioceptive cues (support surface sway-referencing). However, stance is possible, and even potentially indistinguishable from normal, if VL subjects have either veridical visual or proprioceptive cues (Black et al. 1983). A number of pathological postural behaviors are also compatible with failure of feedback regulation, resulting in an underproduction of corrective torque. Specifically, patterns of behavior revealed on clinical sensory organization tests referred to as “visual preference”, “somatosensory dependent” (also called “visual and vestibular dysfunction”), or “vision dependent” (Nashner 1993b) could potentially result from a failure of sensory reweighting and/or torque normalization. Similarly, normal subjects initially show diminished responses to surface perturbations when the visual surround is sway-referenced, but responses return to normal with repeated stimulus presentations (Nashner 1982). Because normal subjects typically derive about one-third of their orientation information from vision during eyes-open quiet stance (Fig. 14, bottom left graph), initial exposure to a sway-referenced visual condition, where VB = 0 in the Fig. 9 model, results in a reduced generation of corrective torque. With repeated stimulus presentations, torque normalization occurs such that w p +w v = 1, and responses return to normal levels. Finally, a failure of feedback regulation that results in an overproduction of corrective torque is predicted by the Fig. 9 model to produce 1–3 Hz oscillatory behavior (depending on whetherK P, K D,or both are greater than normal). Such behavior has been seen in subjects with cerebellar deficits (Dichgans et al. 1976; Diener and Dichgans 1992; Diener et al. 1984a), in normal subjects with experimentally applied leg ischemia (Diener et al. 1984c;Mauritz and Dietz 1980), and following environmental transitions that suddenly increase access to accurate sensory orientation cues (Peterka and Loughlin 2002).
The author gratefully acknowledges the technical and editorial assistance of J. Roth and S. Clark-Donovan.
This work was supported by National Aeronautics and Space Administration Grant NAG5-7869 and National Institute on Aging Grant R01 AG-17960.
Address for reprint requests: R. J. Peterka, Neurological Sciences Institute, OHSU West Campus, Bldg. 1, 505 NW 185th Ave., Beaverton, OR 97006 (E-mail:).
- Copyright © 2002 The American Physiological Society