Pronounced overestimation of support surface tilt during stance

Abstract

A veridical internal notion of the kinematic state of the foot support is essential for postural control. The means by which this is obtained is still a matter of debate. We therefore measured the conscious perception of support tilt during transient anterior–posterior rotations of a motion platform in six healthy subjects, using a psychophysical matching procedure. Furthermore, we evaluated subjects’ postural responses (in terms of displacement of subjects’ center of mass, COM, and their ankle torque, as represented by the center of foot pressure, COP). The platform tilts were applied in absence of visual and auditory orientation cues. The platform rotations consisted of smoothed position ramps with different dominant frequencies (0.025, 0.05, 0.1, 0.2, 0.4, and 0.8 Hz) and different amplitudes (0.125°, 0.25°, 0.5°, 1°, 2°, 4°, and 8°) for the forward and backward directions, which yielded a 6×14 stimulus matrix. The stimuli were repeated five times in a random order. For the matching procedure, subjects tried to maintain an upright body orientation, while trying to orient a light-weight rod, which was attached to a belt around their waists, parallel to the perceived platform surface. We measured the stimulus-evoked angular excursions of the rod and of the subjects’ COM as well as the COP shift. We found that the subjects’ rod indications overestimated the platform tilts, particularly with small stimulus amplitudes. To characterize the overestimation, we compared the rod indications obtained while subjects stood on the tilting platform, to rod indications in a situation in which they stood next to the platform and tried to match the rod angle to the now visually perceived platform angle. From this comparison, we inferred that the subjects’ kinesthetically derived notion of platform tilt overestimates the actual tilt by a factor of ≈4. The estimates were linearly related to the angle between body (COM) and platform, i.e., to approximately the angle of the ankle joint, a finding which suggests a proprioceptive source of the overestimation. Further analyses supported this view; they showed that the onset latencies of the rod indications could be approximated by a theoretical indication mechanism with a reaction time of about 0.31 s, a velocity threshold of 0.099°/s, and a displacement threshold of 0.12°. These threshold values are well in line with previous work on the leg proprioceptive detection threshold of conscious perception of body sway. We therefore assume that the phenomenon of support tilt overestimation reflects a still unknown mechanism of leg proprioception in postural control.

Appendix

When analyzing the time delay values, which occurred between the stimulus onset and the beginning of the rod indication, we found that neither the detection time of a velocity threshold alone nor a combination of it with a position threshold could explain the experimental findings. Furthermore, there appeared to be a minimal time delay with the highest frequency of the platform tilts tested, indicating that a rather fixed reaction time is contained, in addition to the total time delay between stimulus onset and response. These considerations led us to determine in an parameter identification procedure, estimates of position and velocity threshold values as well as reaction time values that could optimally account for the time-delay pattern. The parameter identification procedure varied the values for the thresholds and the reaction time. We used the Matlab Optimization toolbox function “fminsearch” to find the minimum of a scalar error function of the time delay pattern, starting at an initial estimate. The algorithm ‘fminsearch’ uses the simplex search method of Nelder–Mead (Lagarias et al. 1998). We started with zero threshold values and zero reaction time as initial estimates. With each iteration of the parameter identification procedure, the current threshold and reaction time values were applied to all 84 platform trajectories to determine a new pattern of time delays, and a scalar error function was evaluated. Then, the parameter identification procedure made changes to the threshold and reaction time values, a new pattern of time delays was calculated, and the error function re-evaluated. This sequence was repeated until the error function was minimized. In order to normalize the error contribution from each data point of the time-delay pattern and to achieve a symmetrical error distribution around the reference values, we used the error function:

$$E = \sum\limits_{i = 1}^N {\left({\left| {\frac{{T_i - \hat T_i}}{{T_i + \hat T_i}}} \right|} \right)} $$

where N is the number of data points of the pattern of time delays (N = 84), T _i is the experimentally measured reference pattern of time delays, and $\hat T_i$ is the estimated pattern of time delays, obtained with each iteration of the parameter identification procedure. This procedure is based on the assumption that the velocity and position thresholds were parallel and independent. When assuming a serial assembly of a velocity first and then a position threshold, the identified velocity threshold and reaction time were similar, but the position threshold was 3% lower compared to the parallel assembly. A serial assembly of first position threshold and then velocity threshold led to a reduction of the velocity threshold by 4%.