Nonlinear postural control in response to visual translation
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- Ravaioli, E., Oie, K.S., Kiemel, T. et al. Exp Brain Res (2005) 160: 450. doi:10.1007/s00221-004-2030-y
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Recent models of human postural control have focused on the nonlinear properties inherent to fusing sensory information from multiple modalities. In general, these models are underconstrained, requiring additional experimental data to clarify the properties of such nonlinearities. Here we report an experiment suggesting that new or multiple mechanisms may be needed to capture the integration of vision into the postural control scheme. Subjects were presented with visual displays whose motion consisted of two components: a constant-amplitude, 0.2 Hz oscillation, and constant-velocity translation from left to right at velocities between 0 cm/s and 4 cm/s. Postural sway variability increased systematically with translation velocity, but remained below that observed in the eyes-closed condition, indicating that the postural control system is able to use visual information to stabilize sway even at translation velocities as high as 4 cm/s. Gain initially increased as translation velocity increased from 0 cm/s to 1 cm/s and then decreased. The changes in gain and variability provided a clear indication of nonlinearity in the postural response across conditions, which were interpreted in terms of sensory reweighting. The fact that gain did not decrease at low translation velocities suggests that the postural control system is able to decompose relative visual motion into environmental motion and self-motion. The eventual decrease in gain suggests that nonlinearities in sensory noise levels (state-dependent noise) may also contribute to the sensory reweighting involved in postural control. These results provide important constraints and suggest that multiple mechanisms may be required to model the nonlinearities involved in sensory fusion for upright stance control.
KeywordsSensory reweightingMultisensory integrationVisionAdaptationPostural controlHuman
To maintain an upright stance posture, the human nervous system integrates information obtained from several different sensory channels. We are constantly confronted with changing sensory environments, and our ability to adaptively change our behavior to match different sensory conditions is crucial for upright postural stability. With the development of techniques that allowed a sensory input to be selectively diminished through support surface or visual sway-referencing, Nashner and colleagues introduced the concept of sensory reweighting for postural control over 20 years ago (cf. Black and Nashner 1984; Black et al. 1988; Nashner et al. 1982). It is now a generally held view that visual, vestibular, and somatosensory inputs are dynamically reweighted to maintain upright stance as environmental or nervous system conditions change (Horak and Macpherson 1996; Shumway-Cook and Woollacott 2000). Environmental changes such as moving from a light to a dark environment or from a fixed to a moving support surface (e.g., onto a moving walkway at the airport) require an updating of sensory weights to current conditions so that muscular commands are based on the most precise and reliable sensory information available (Teasdale et al. 1991; Wolfson et al. 1985; Woollacott et al. 1986).
To understand the mechanisms underlying sensory reweighting, recent investigations have implemented nonlinear models (Mergner et al. 2003; van der Kooij et al. 2001) to account for the changes in gain that are observed experimentally in response to different amplitudes of stimuli such as visual motion (Oie et al. 2002; Peterka 2002; Peterka and Benolken 1995), support surface rotation (Peterka 2002), and mechanical perturbations at the waist (Mergner et al. 2003). Dependence of gain upon stimulus amplitude at a given stimulus frequency is a nonlinearity that is often attributed to sensory reweighting. For example, Oie et al. (2002) presented subjects with simultaneous visual and somatosensory stimuli, each at different frequencies so that gain could be measured relative to each modality when stimulus amplitude was varied. Using actual sway trajectories to fit parameters of a descriptive, linear, third-order stochastic model, they showed that changes in sway behavior were due to changes in sensory weights in the model, rather than changes in other aspects of the model such as stability parameters (e.g., damping). Evidence for both intramodality (i.e., changes in visual stimulus amplitude leading to changes in visual gain), and intermodality (i.e., changes in somatosensory stimulus amplitude leading to changes in visual gain) reweighting was observed. A linear model is inadequate to account for nonlinearities such as sensory reweighting, requiring modeler-adjusted parameters to account for changing behavior across conditions (cf., Peterka 2002). The need is for a nonlinear model with a scheme that mimics the nervous system’s ability to update sensory weights adaptively.
The clear need to develop nonlinear models requires that the corresponding nonlinear properties of postural sway be identified (Jeka et al. 2003). Nonlinear postural responses to stimulus properties such as amplitude of oscillation (Oie et al. 2002; Peterka 2002; Peterka and Benolken 1995) and perturbation force (Mergner et al. 2003) are known. The present experiment was designed to investigate postural sway in response to a commonly encountered property of the visual environment, namely, translation. Translatory visual motions are known to influence the control of locomotion (Bardy et al. 1999) and can produce illusions of self-motion during quiet stance such as the perception of movement aboard a stationary train, while an adjacent train moves slowly.
Investigating translatory visual motion was also motivated by the postural control model of van der Kooij et al. (2001) that adaptively reweights sensory information based upon continuous, internal-model estimates of the sensory environment. The inclusion of internal-model environmental dynamics allows the neural controller to decompose relative motion into components of self-motion and environmental motion. Such a decomposition scheme makes specific predictions of the effects of translation. At one extreme, a neural controller that estimates the position of the visual environment, as van der Kooij et al. (2001) assumed, would be continually biased by a constant-velocity visual translation. With an increase in the velocity of translatory visual motion, we hypothesize a resultant downweighting of vision and a decrease in sway relative to the visual stimulus (i.e., gain). At the other extreme, if instead the controller continually estimates the velocity of the visual environment, the neural controller would be able to decompose relative motion correctly into self-motion and translatory visual motion components. The postural control system would then be able to obtain estimates of self-motion that would not be biased by constant-velocity translation of the visual environment. In this case, we would predict constant gain relative to the oscillatory motion.
Here, we had subjects stand quietly in front of a visual display whose motion consisted of two distinct components: a constant-frequency, low-amplitude medial-lateral oscillation and a constant-velocity translation from left to right. The oscillation was used as a probe, allowing us to compute sway gain and to measure the effect of different velocities of translation on the postural response to oscillatory visual motion that has been well-studied (Dijkstra et al. 1994a, 1994b; Jeka et al. 2000; Oie et al. 2002).
Ten young adults aged 20–27 years were drawn from volunteers recruited from the staff and student population at the University of Maryland and the surrounding greater Washington, DC–Baltimore area. Criteria for selecting subjects included good health status as determined by medical history to eliminate subjects with health problems and those taking medications that could affect posture and movement control. Subjects must have met the following inclusion criteria: (1) no history or evidence of orthopedic, muscular, psychological, or neurological disability, including normal strength and joint range of motion, (2) no current medication that might affect balance, and (3) vision corrected to 20/20. All potential subjects were interviewed and informed of the experimental procedures approved by the Institutional Review Board with its risks and benefits and their rights as experimental subjects before signing a consent form. Efforts were made to include ethnic minorities as potential subjects by advertising for subjects in community newspapers (two Asian subjects, one African-American, and seven Caucasian). An equal number of males and females were recruited although we did not anticipate gender-related differences in our data.
Custom software was written in Visual C++, which has an absolute resolution of 1 ms, in order to generate the visual displays, utilizing the standard OpenGL libraries. We utilized a visual frame rate of 25 Hz that was far below the maximal possible frame rates the computer could generate (>66 Hz), to maintain a consistent frame rate throughout a trial. The subjects wore a pair of goggles (not shown in Fig. 1) that limited the field of view to approximately ±60° wide and ±50° high. This ensured that the edges of the screen were not visible to the subject.
Body kinematics were measured using an OptoTrak (Northern Digital, Inc., Waterloo, Ontario, Canada) system. The bank of three infrared cameras was placed about 1.5 m behind and 2.5 m to the right of the subject to measure the movements of the markers used to estimate the body center of mass (COM) in the frontal plane. All signals were collected at 100 Hz and stored on a personal computer (Gateway E4200) for offline data analysis.
Subjects were tested in five conditions, one with eyes closed and four with eyes open. During the eyes-open trials, the visual field of white triangles simultaneously oscillated and translated. All triangles oscillated at 0.2 Hz with an amplitude of 4 mm while translating from left to right at 0, 1, 2, or 4 cm/s. The frequency of the stimulus oscillation was chosen at 0.2 Hz, which is in the range of the natural frequency of the human postural control system, to ensure a strong gain to visual input by examining the system in a regime where the signal-to-noise ratio would be high. The amplitude was chosen at 4 mm, a relatively small amplitude, because experimentally we have seen stronger gain at low amplitude versus high amplitude, with gain found to decrease as stimulus amplitude is increased (Oie et al. 2002).
Each condition was run three times for a total of 15 trials and the order of trials across conditions was randomized for each subject. All trials were 270 s in duration: the onset and offset of the 240 s oscillatory component of the stimulus motion was preceded by 20 s and followed by 10 s of only translatory visual motion, respectively. The initial period of only translatory stimulus motion was used to minimize any transient effects due to the initiation of the translation. Data collection was initiated at least 10 s prior to the onset of the oscillatory component of stimulus motion, though only the 240 s during which the oscillatory component was present is considered in our analysis. At least 120 s of seated rest was taken between trials.
The subject stood at a distance of 40 cm from the visual display screen in a modified tandem stance (see Fig. 1), with one foot in front of the other and the inside edges of the feet aligned. A small piece of tape on the platform marked the position of the toes of the front (right) foot so that the same foot position was maintained on each trial. The modified tandem stance was used to increase instability in the medial-lateral plane, while minimizing the discomfort of the subjects due to the length of the trials. COM motion was analyzed only in the medial-lateral direction.
The subject was instructed to maintain his/her gaze directly in front of him/herself, which corresponded to the horizontal black strip that the experimenter positioned at the height of the subject’s eyes at the start of the experimental session. The subjects were asked not to fully extend their knees and to keep their weight distributed equally between their feet. Again, the subjects wore goggles in order to limit their peripheral field of view, and they kept the goggles on throughout the experiment. After a trial was completed, the subject was asked to sit and rest. Two experimenters stayed in the room with the subject at all times.
To calculate the trajectories of COM we used Winter’s method (Winter 1991), which is based on segmental kinematics. A two-dimensional model was used to represent the kinematics of the body in the frontal plane. The anatomical structure was assumed as a set of three rigid segments representing head-arms-trunk (HAT), thighs, and legs, based upon markers placed at the ankle (lateral malleolus), knee (lateral femoral condyle), hip (greater trochanter) and shoulder (acromium) on the right side of the subjects’ bodies. The COM location of each segment was assumed to lie on the line connecting two adjacent joints based upon anthropometric measures presented in Winter (1991), and the total body COM was computed as a weighted summation of the segmental COM estimates.
Gain and phase
Linear, spectral analysis was performed for each trial by computing the individual Fourier spectra of the time series of COM postural displacements and of the oscillatory component of stimulus motion using Welch’s method (Marple 1987) with a 40-s Hanning window and 50% overlap. For each modality, the transfer function (frequency response function) at the stimulus frequency was computed by dividing the Fourier spectra of the estimated COM by the Fourier spectra of the stimulus resulting in a complex-valued transfer function. Because stimuli were presented at the same frequency in every condition, we evaluated the transfer function only at the stimulus driving frequency. Gain was thus recovered as the absolute value of the transfer function at the stimulus frequency. Unity gain indicates that the component’s amplitude at the stimulus frequency exactly matches the amplitude of the sensory stimulus.
Phase indicates the temporal relationship between the sensory stimulus and body sway and was defined as the angle of the transfer function at the stimulus frequency. A phase lead means that body sway is temporally ahead of the sensory stimulus (and vice versa for a phase lag). In-phase motion with unity gain effectively minimizes the relative motion between the postural component and the sensory environment. Phase values other than zero mean that the sensory environment moves relative to the body.
Power spectral densities
Power spectral densities (PSD) were also computed to examine the distribution of power in the observed COM sway trajectories. PSD for the medial-lateral COM postural sway trajectories of each trial were also computed using the Welch method with a 40-s Hanning window and 50% overlap.
The variability of the position and velocity of the COM was computed as the standard deviation of body sway after the deterministic response to the sensory stimulus was subtracted (cf. Jeka et al. 2000). To determine COM variability, the Fourier transform of COM position was calculated at the stimulus frequency (0.2 Hz) and then inverse transformed to compute the sway response at only the stimulus frequency. The corresponding residual COM position trajectory was recovered by subtracting this component from the original COM position trajectory. The residual COM velocity trajectory was computed by finite differences using every 10th point of the residual position trajectory, which corresponds to a time step of 0.1 s. This time step was chosen to reduce the effect the experimental measurement noise on the velocity computation. Position or velocity variability was then computed as the standard deviation of the residual position or velocity trajectory, respectively.
Sway lean angle and velocity skewness
The mean sway lean angle in the medial-lateral direction was also computed to examine whether the visual translation imparted a bias on the mean position of the subjects’ bodies. The sway lean angle was estimated from the difference between the computed COM trajectory in the medial-lateral direction and the position of the marker on the ankle. In addition, skewness of COM velocity was computed to assess any potential left-right asymmetries in the postural responses across conditions. The skewness of a distribution is defined as its third central moment divided by the cube of its standard deviation. Velocity was computed by finite differences using every 10th point of the original COM position trajectory.
Separate statistical analyses were performed on gain, phase, position variability, velocity variability, lean angle, and velocity skewness. We used Hotelling’s T2 statistic to test whether the mean across subjects depended on condition. In the case of velocity skewness, our overall null hypothesis was that the means in all conditions was 0. For the other measures, our overall null hypothesis was that the means in all conditions were equal. We also tested for condition effects in each subject using a one-way analysis of variance (ANOVA). In each case we tested for an overall effect and all possible pairwise differences, using a closed testing procedure (Hochberg and Tamhane 1987) to control the family-wise type I error rate at significance level alpha=0.05.
COM: time series and power spectral density
COM gain and phase
The mean phase values were found to be consistent across subjects (see Fig. 5b and d). Mean phase showed a slight increase with increasing translation velocity, and a significant effect for condition (P=0.00122) was observed as a function of the velocity of translation. Pairwise comparisons revealed significant differences between the 0 cm/s <4 cm/s (P=0.01306), 1 cm/s <2 cm/s (P=0.00122), and 1 cm/s <4 cm/s (P=0.00244) conditions. It was expected that mean phase values for stimuli at the same frequency and amplitude should not have changed across frequency. However, while significant differences were observed, the range of the mean phase values (~0–50°) in all conditions is consistent with values seen previously for stimuli at 0.2 Hz (e.g., see Jeka et al. 2000; Oie et al. 2002). At the individual subject level, six of the ten subjects showed significant overall condition effects (P<0.05), with pairwise comparisons showing differences mainly between the 0 cm/s and 4 cm/s (five subjects, P<0.05) and 1 cm/s and 4 cm/s conditions (six subjects, P<0.05).
COM position and velocity variability
In contrast, mean velocity variability, which is presented in Fig. 6b and d, showed a strongly significant effect for condition (P=0.00203). All pairwise comparisons, except between 1 cm/s and 2 cm/s, showed a significant increase when translation speed increased or when the eyes were closed (P<0.02). Eight of ten subjects showed significant condition effects with seven of those subjects showing P<0.01. The pairwise comparisons showed that these effects were mainly driven by differences between the 0 cm/s and 4 cm/s, 1 cm/s and 4 cm/s, and the 2 cm/s and 4 cm/s conditions, which showed significant differences (P<0.05) for all eight subjects with the exception of subject 7 in the 2 cm/s and 4 cm/s comparison. Six subjects showed significant differences between the 0 cm/s and 4 cm/s conditions, and four subjects showed differences between the 1 cm/s and 4 cm/s, and the 2 cm/s and 4 cm/s conditions (P<0.05).
Sway lean angle and skewness
Mean sway lean angle did not show a significant dependence on condition (P=0.3186); that is, lean angle did not depend on translation velocity or whether the eyes were open. The mean sway lean angle across all five experimental conditions was 8.23°±0.16°, with a bias imparted by the configuration of the semi-tandem stance and the position of the body markers employed in this protocol. There were no significant condition effects for sway lean angle for any of the ten subjects. Finally, for the skewness of the COM velocity distributions, the data were consistent with the null hypothesis that mean skewness was 0 in all conditions (P=0.15274).
The experimental results showed that gain computed with respect to the oscillatory component of the stimulus (which was constant across condition) changed with increasing visual translation velocity. Gain was found to either increase or to be approximately constant at low translation velocities (0–1 cm/s) and to decrease as translation velocity increased (see Figs. 5 and 6). These results can be interpreted in a similar manner as previous studies which manipulated stimulus amplitude (Mergner et al. 2003; Oie et al. 2002; Peterka and Benolken 1995; Peterka 2002). As the velocity of visual motion translation became large, gain relative to the constant-amplitude oscillatory motion decreased systematically, suggesting that the dependence upon visual information (i.e., the weighting of visual input) decreased as the velocity of visual translation increased. However, these results are not consistent with either of the predictions based upon estimating the position or velocity of the visual environment as a means to update sensory weights. The mechanism underlying such reweighting remains unclear, as we discuss below.
The idea that visual, vestibular, and somatosensory inputs can be dynamically reweighted to maintain upright stance when sensory conditions change is not a new one (e.g., Black et al. 1988; Bronstein 1986; Horak and Macpherson 1996; Nashner et al. 1982; Woollacott et al. 1986), reflected in current modeling efforts (Oie et al. 2002; Kiemel et al. 2002; van de Kooij et al. 2002; Peterka and Loughlin 2004). When one sensory channel is downweighted (e.g., vision), it is often thought that other channels (e.g., proprioception, vestibular) may be weighted more heavily (i.e., intermodality reweighting). For example, weights for visual, proprioceptive, and graviceptive inputs in Peterka’s (2002) model are dependent upon sensory conditions, but the sum of all the sensory channel weights is assumed to be unity. This assumption implies that when a sensory weight decreases, one or more alternative sensory weights must increase accordingly (i.e., intermodality reweighting).
In the present experiment, if weights for sensory channels other than vision are being increased in response to vision being downweighted, the variability results indicate that reweighting does not fully compensate for such downweighting. With full compensation by other sensory inputs (e.g., proprioceptive, vestibular), one would expect sway variability levels to remain constant across translation condition. However, significant changes were seen in both velocity and position variability as visual translation velocity was increased, with the largest variability observed when translation velocity was highest (see Fig. 6), arguing against full compensation due to upweighting by other sensory inputs. The benefit of upweighting seems only to partially compensate for the deficit of downweighting. Typically, one would expect an increase in sway variability with the loss of sensory information in control theory or optimal control theory models (e.g., van der Kooij et al. 2001). Sensory reweighting can thus be seen as providing an optimal solution under given sensory conditions, but it cannot compensate for a loss of information such as experienced under conditions of environmental motion.
Notably, a significant difference was found in the pairwise comparison of velocity variability between the 4 cm/s and eyes-closed conditions. This result indicates that even with whole-field, visual environment translation of 4 cm/s, the postural control system is able to extract information from visual input to effectively stabilize postural sway and reduce postural sway variability to a level less than that achieved when visual information is completely absent. Further support for this point is found in the fact that peaks in the power spectrum at 0.2 Hz were clearly observed in all conditions, with the obvious exception of the eyes-closed condition. As visual translation velocity increased, peak power at 0.2 Hz systematically decreased, but a visible peak remained at all translation velocities (see Figs. 3 and 4). We would predict that further increases in translation velocity would eventually lead to the disappearance of this peak in the power spectrum and to position or velocity variability that is not significantly different than the eyes-closed condition. In such conditions, one might suggest that the postural control system has reweighted visual information to the same value as in the eyes-closed condition (effectively=0).
There remains one result for which we presently have no definitive explanation; the fact that gain did not decrease between the 0 cm/s and 1 cm/s conditions. Previously, we have argued that gain to vision decreases when relative visual motion between the subject and the environment becomes a less reliable indicator of self-motion (Oie et al. 2002). By this reasoning, gain should decrease as translation speed increases. However, the expected decrease in gain only occurred at higher translation speeds, for which we offer a two-part explanation.
First, we hypothesized above that the neural controller contains an internal dynamic model of the visual environment (cf. van der Kooij et al. 1999, 2001) that allows it to decompose relative motion into self-motion and environmental motion. In the models of van der Kooij et al. (1999, 2001), the neural controller contains a Kalman filter that continually estimates the position of the visual environment. We have argued that such a position-based internal model under the presence of a constant-velocity visual translation would produce an immediate decrease in gain. The finding that gain did not change significantly between the 0 cm/s to the 1 cm/s refutes such a prediction.
Instead the internal model could estimate the velocity of the visual environment. In its simplest form, a model with such a decomposition mechanism would predict that gain in our experiment should not depend on translation speed. This also was not observed in the current investigation; gain decreased as translation velocity increased to higher than 1 cm/s. To explain the eventual decrease in gain as translation speed increases, we propose the additional hypothesis that the accuracy of visual information decreases as the relative velocity between environmental motion and self-motion increases. For example, if visual information consists of relative velocity plus noise, we hypothesize that the amount of noise increases as relative velocity increases. Given such state-dependent noise (cf. Harris and Wolpert 1998), it is advantageous for the postural control system to decrease the weight given to visual information as relative visual motion increases, leading to a decrease in gain.
Together, the decomposition mechanism plus reweighting in response to state-dependent noise provides a possible explanation for the delayed decrease in gain as translation speed increases. If visual noise is roughly constant for low relative velocities, then there is no need to downweight vision as translation speed initially increases. The decomposition mechanism allows the postural control system to make full use of visual information. It only becomes advantageous to downweight vision at those relative speeds that produce a substantial increase in visual noise.
While we have interpreted our results relative to the concept of sensory reweighting, it should be noted that other explanations of these results have been considered. With a constantly translating left-to-right visual stimulus, one can imagine that subjects may respond by following the stimulus until a biomechanical limit is reached, followed by a corrective return to vertical before retracking the visual translation (similar to nystagmus observed with eye movements). If this sway “nystagmus” remained constant as translation velocity increased, a decrease in gain and a larger phase lag would be observed. However, we observed no such asymmetry in the body kinematics. No differences were found in average body lean and skewness of COM velocity between the eyes-closed condition and any of the visual translation conditions. Phase results suggest an increased lead rather than a lag with increasing translation velocity. Furthermore, a biomechanical explanation would not explain the lack of gain decrease between the 0–1 cm/s translation velocity conditions. In short, there is no evidence indicating that biomechanical factors were contributing to the observed sway behavior.
Another approach to dealing with the nonlinearities found in human postural responses has been proposed by Mergner et al. (2003). Their model produces qualitative agreement with gain and phase functions under the influence of external, mechanical perturbations without the use of an explicit sensory reweighting mechanism. Instead, multisensor fusion of proprioceptive, vestibular, and somatosensory inputs is achieved through idealized sensor dynamics and central threshold functions to provide internal representations of the environment and the body’s relationship to the environment that are used as set point signals in a negative feedback loop. It remains to be seen whether this approach can account for nonlinearities such as presented here.
Empirical results that elucidate the properties of postural responses under different sensory conditions, including specific nonlinear responses such as the dependence of gain on translation velocity identified here, provide important constraints for more sophisticated models of postural control that address its inherent nonlinear properties. Future modeling efforts will be focused on mechanisms which may account for multiple nonlinear phenomena to determine the most plausible mechanisms necessary to characterize the multisensory fusion required for human upright stance control.
Support for this research provided by: NIH grants 2RO1NS35070 and 1RO1NS046065 (John Jeka, PI).