Multisensory control of human upright stance

Abstract

The interaction of different orientation senses contributing to posture control is not well understood. We therefore performed experiments in which we measured the postural responses of normal subjects and vestibular loss patients during perturbation of their stance. Subjects stood on a motion platform with their eyes closed and auditory cues masked. The perturbing stimuli consisted of either platform tilts or external torque produced by force-controlled pull of the subjects’ body on a stationary platform. Furthermore, we presented trials in which these two stimuli were applied when the platform was body-sway referenced (i.e., coupled 1:1 to body position, by which ankle joint proprioceptive feedback is essentially removed). We analyzed subjects’ postural responses, i.e., the excursions of their center of mass (COM) and center of pressure (COP), using a systems analysis approach. We found gain and phase of the responses to vary as a function of stimulus frequency and in relation to the absence versus presence of vestibular and proprioceptive cues. In addition, gain depended on stimulus amplitude, reflecting a non-linearity in the control. The experimental results were compared to simulation results obtained from an ‘inverted pendulum’ model of posture control. In the model, sensor fusion mechanisms yield internal estimates of the external stimuli, i.e., of the external torque (pull), the platform tilt and gravity. These estimates are derived from three sensor systems: ankle proprioceptors, vestibular sensors and plantar pressure sensors (somatosensory graviceptors). They are fed as global set point signals into a local control loop of the ankle joints, which is based on proprioceptive negative feedback. This local loop stabilizes the body-on-foot support, while the set point signals upgrade the loop into a body-in-space control. Amplitude non-linearity was implemented in the model in the form of central threshold mechanisms. In model simulations that combined sensor fusion and thresholds, an automatic context-specific sensory re-weighting across stimulus conditions occurred. Model parameters were identified using an optimization procedure. Results suggested that in the sway-referenced condition normal subjects altered their postural strategy by strongly weighting feedback from plantar somatosensory force sensors. Taking this strategy change into account, the model’s simulation results well paralleled all experimental results across all conditions tested.

Appendix

This provides additional specifications of our intersensory interaction model (Fig. 5) and then gives a description of the optimization procedure used for parameter identification.

The PHYSICS portion of the model in Fig. 5 performs a transformation from joint torque into body-in-space rotation, BS. Prior to this, the body-to-foot (support) rotation, BF, is transformed by the box BIOM (for biomechanics) into PASSIVE TORQUE. This passive torque is assumed to arise from the stiffness and damping properties of the muscles and tendons and is proportional to BF and BF velocity (PASSIVE TORQUE=K _pas × BF + B _pas × dBF/dt, where K _pas is a stiffness factor and B _pas a damping factor; direction of passive torque becomes opposite to the direction of the BF signal, see Fig. 5). There is no time delay associated with this passive torque component. The values given in Table 1 for the stiffness and damping correspond roughly to those of Peterka (2002) who estimated them to be in the range of 10% of the P and D parts of the neural controller, respectively (see below). This range is similar to that estimated by van der Kooij et al. (2005).

The PASSIVE TORQUE is combined with the active MUSCLE TORQUE to yield the ANKLE TORQUE. The box labeled ‘-1’ on the latter signal represents the negative effect of the sensory feedback loop via the MUSCLE TORQUE and of the PASSIVE TORQUE. The ANKLE TORQUE acts together with the EXTERNAL TORQUE and the GRAVITY TORQUE on the BODY INERTIA box where this summed torque is transformed into the angular displacement BS by inertia effects described by the equation: T/J=d²BS/dt (T, torque; J, body moment of inertia about the ankle joint, calculated from our subjects mean values for body mass and COM height above the joint, mh ²=72.0 kg m²). The GRAVITY TORQUE is calculated from BS by the equation: mgh sin(BS) (m, COM mass, 74.9 kg; h, COM height, 0.98 m above ankle axis; g, acceleration due to gravity, 9.81 m/s²).

Two perturbing stimuli were applied to the system: (a) a contact force (pull) that produced the EXTERNAL TORQUE stimulus and (b) an angular displacement of the foot support in space (input FS). The effect of FS on BF is given by BF = BS − FS. With the platform level and held stationary in space (foot-in-space angle, FS=0° and the BSRP switch in the closed position), the body-to-foot angle (BF) is coupled 1:1 to the body-in-space angle (BS). However, if FS is made to exactly match BS, this 1:1 coupling is eliminated and the body-to-foot angle becomes either “frozen” (BF=0°; this is represented in the figure by making FS=0° and opening the switch BSRP) or exclusively determined by the tilt stimulus (BF=−FS; this is represented in the figure by applying the FS stimulus and opening the switch BSRP). The latter two model configurations correspond to the PULL + BSRP and to the TILT + BSRP conditions, respectively.

The afferent interface between the PHYSICS part and the SUBJECT part of the model is represented by three sensors. We assume that BF is sensed by ankle proprioception (PROP), BS by the vestibular system (VEST) and COP shifts by plantar somatosensory receptors (SOMAT).

PROP is taken to stem mainly from spindle receptors in the ankle joint muscles and to inform the brain about the angle BF (yielding its internal representation, bf) with broadband frequency characteristics (the 1 in box PROP represents ideal transfer characteristics). Evidence for a role of PROP in posture control comes from the observation that direct stimulation of muscle spindles by muscle vibration during stance produces body sway, which linearly combines with vestibular evoked sway (e.g., Hlavacka et al. 1996).

The VEST sensor is considered to contain two parts, one representing the canal system, the other the otolith system. We assumed that, by way of a canal–otolith interaction (not shown; see Merfeld 1995; Mergner and Glasauer 1999; Zupan et al. 2002), the semicircular canal transfer characteristics are improved in the vertical rotational planes such that an essentially veridical internal representation of body-in-space angular position results (output signal bs of box VEST which is given ideal transfer characteristics, 1).

SOMAT is taken to register reaction forces. It is represented by plantar somatosensory pressure receptors deep in the foot arch, which provide a low-pass-filtered estimate of COP shift at the foot soles (note the low-pass filter symbol in box SOMAT; further details below and in experimental studies of Maurer et al. 2000, 2001). The assumption of a low-pass filter is derived from the experimental work and requires further evaluation (for the simulation we used a first-order filter with a cutoff frequency of 0.8 Hz).

The SUBJECT part of the model is thought to contain two functional subdivisions. The first would be the proprioceptive bf signal which we consider to form, together with a transformation by a neural controller and the system’s efference, a ‘local feedback loop’ that stabilizes the ankle joint and takes into account body inertia (e.g., during voluntary movements; see Mergner 2004). The second subdivision represents the three internal estimates of the external stimuli.

An estimate of the support surface tilt (FS)

The estimate of FS is in the form of fs=bs − bf. The bs and bf signals used for this fusion are thought to stem originally from vestibular and proprioceptive velocity signals, respectively, which we omitted here for simplification. Thus, also fs would actually carry velocity information and the presumed threshold of it therefore represents a velocity threshold (in the simplified version of Fig. 5, we run the fs signal before the velocity threshold through a differentiation and after it through an integration; box T1, applied after an additionally scaling by a gain factor, G1). In the parameter identification procedure (see below) we originally applied thresholds for both a fs velocity and position part of the parameter space. The procedure demonstrated that the velocity threshold alone could account for the experimental data.

An estimate of the external torque stimulus (τ _ext)

The estimate of τ _ext is based on the physics of inverted pendulum motion. Specifically, the dynamics of inverted pendulum motion are given by:

$$ \begin{aligned} J\frac{{{\text{d}}^{2} {\text{BS}}}} {{{\text{d}}t^{2} }} & = mgh\,\sin ({\text{BS}}) + T_{{{\text{ank}}}} + T_{{{\text{ext}}}} \\ & = T_{{{\text{grav}}}} + T_{{{\text{ank}}}} + T_{{{\text{ext}}}} , \\ \end{aligned} $$

where T _grav is the gravitational torque caused by body lean, T _ank the ankle torque, T _ext the externally applied torque, J (=72.0 kg m²) the moment of inertia of the body (not including the feet) about the ankle joint axis. The internal estimate of external torque, τ _ext, is derived using internal estimates of the physical variables BS and T _ank:

$$ \begin{aligned} \tau _{{{\text{ext}}}} & = {\left( {J\frac{{{\text{d}}^{2} {\text{bs}}}} {{{\text{d}}t^{2} }} - mgh\,\sin {\left( {{\text{bs}}} \right)}} \right)} - \tau _{{{\text{ank}}}} \\ & \approx {\left( {J\frac{{{\text{d}}^{2} {\text{bs}}}} {{{\text{d}}t^{2} }} - mgh \times {\text{bs}}\,} \right)} - \tau _{{{\text{ank}}}} , \\ \end{aligned} $$

where τ _ank is the internal estimate of T _ank provided by the SOMAT output and bs the internal estimate of BS provided by the VEST output.

The input to the SOMAT box is COP displacement (in meters) calculated in the COP box by multiplying ANKLE TORQUE by −1/mg (=−0.00136, with the minus sign representing the fact that a negative ankle torque, using the sign convention shown in the inset of Fig. 5, produces a positive COP value; see Winter et al. 1998, for the equations relating torque to COP).

The internal estimate τ _ank is subtracted from the output of the SOMAT′ box to obtain τ _ext. The SOMAT′ box performs the operation J×d²bs/dt ²–mgh×bs, with mgh=721 kg m²/s².

The SOMAT′ box represents an internal inverse dynamics model of the body. Model simulations showed that the subtraction of τ _ank from the torque estimate provided by the inverse model in SOMAT′ gave an accurate estimate of EXTERNAL TORQUE. However, relatively small errors in τ _ext, such as those produced by errors in the internal model parameters J, m or h or by errors in sensing τ _ank, resulted in unstable postural control. The sensitivity to errors in the τ _ext estimate was greatly reduced if higher frequencies were eliminated from the calculation of τ _ext by including a low-pass filter in both the SOMAT and the SOMAT′ boxes (first-order filter with 0.8 Hz cutoff frequency). The low-pass filter in the SOMAT box could be interpreted as reflecting earlier experimental findings that the SOMAT sensor output is mainly used with low-frequency stimuli (Maurer et al. 2000, 2001). The matching low-pass filter in the SOMAT′ box would then be interpreted as providing a match of the inverse internal model dynamics to those of the SOMAT sensor.

The τ _ext estimate was additionally scaled by a gain factor (G3). The value of G3 was adjusted by the optimization procedure to explain the experimental results.

An estimate of the gravitational torque (τ_grav)

The τ _grav estimate is obtained from the vestibular derived estimate of body lean, bs, by the scaling factor mgh (with the implicit assumption that sin(bs)≈bs for small angles). This τ _grav estimate was additionally scaled by a gain factor (G2). The value of G2 was also adjusted by the optimization procedure to explain the experimental results.

In the model of the normal subjects, τ _ext and τ _grav are combined and then transformed into an equivalent of the COM angle with respect to the earth vertical such that a body tilt by this equivalent COM angle would produce a torque that matched the combination of τ _ext and τ _grav. This equivalent angle is then passed through the angular position threshold (T2).

In the model of the vestibular loss patients, VEST and the fs signal were set to zero, and G3 and T2 were adjusted to fit the experimental data. Thus, chronic vestibular loss is thought to lead, in addition to the loss of vestibular signals (bs, τ _grav), also to the loss of internal estimates of external torque and foot-in-space that are derived using bs. Noticeably, the minus sign that τ _ext receives in the model reflects the fact that, for example, a negative ankle torque would be interpreted by a vestibular loss patient as a positive body lean, which would produce an even greater negative ankle torque required to reduce the body lean. This represents a positive force feedback loop in the model that can lead to instability. Instability can be avoided if it is assumed that patients have found a way to eliminate the body acceleration component of τ _ank (J×d²bs/dt ²) such that only the COM-related component remains (mgh×bs). In normals subjects the elimination of the acceleration component occurs via the box SOMAT′.

As mentioned in Discussion, the various delay times in the system are represented by a single dead time element (box Δt). This even included the local loop, since the study of Peterka (2002) identified a similarly long time delay in a condition where postural control is likely to be dominated by proprioception, i.e., in vestibular loss subjects standing eyes closed on a tilting surface. Admittedly, future studies are still needed to clarify if a single time delay provides an adequate representation.

In a feedback system, the COP is not independent from the COM. The relationship between COP, representing ANKLE TORQUE (van der Kooij et al. 2005), and the torque-evoked COM displacement, representing body movement, is mainly determined by the biomechanical properties of the body. Applying external forces to the human body further influences the relationship between COP and COM, however, in a predictable way (van der Kooij et al. 2005). Therefore, a separate model fit to experimental COP data would not be justified.

The optimization procedure, by which we estimated model parameters from the experimental data, was initially applied to data from the 37 test trails that were obtained in the TILT and PULL conditions (4 TILT frequencies times 3 amplitudes plus 5 PULL frequencies times 5 amplitudes). The procedure varied the model parameters shown in Table 1, using the Matlab Optimization toolbox function ‘fminsearch’ (which is based on the so-called simplex search method of Nelder–Mead; see Lagarias et al. 1998) in order to minimize the deviation between the simulated responses and the corresponding experimental data (in polar coordinates; as mentioned before, an error of unity would indicate that the value of the distance between experimental and simulated responses equals a gain of unity). With each iteration of the search, simulated responses to the 37 stimulus conditions were obtained from the model using Matlab Simulink, the simulated data were analyzed in the same manner as the experimental data, and a scalar error function was evaluated that compared the difference between simulated and experimental results. Then, the search procedure changed the parameters and the error function was re-evaluated. This sequence was repeated until parameters were identified which minimized the error function. In a second application of the optimization procedure, parameters were identified for the TILT + BSRP and PULL + BSRP conditions.