| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1Department of Physical Therapy and Biomechanics and Movement Science Program, University of Delaware, Newark, Delaware; 2Institute für Neuroinformatik, Ruhr University, Bochum, Germany; and 3Department of Kinesiology, University of Maryland, College Park, Maryland
Submitted 26 October 2006; accepted in final form 17 February 2007
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
)]. How these many degrees of freedom (DOFs) are organized around the task of postural control is an important question both scientifically and practically, given the high incidence of falls in the elderly population. In addition, it is unclear which variables are used by the CNS to generate the plan for achieving a stable upright posture.
Stabilization of the spatial position of the center of mass (CM) is often assumed to be the goal of postural responses, either implicitly or explicitly (Corriveau et al. 2004; Gage et al. 2004; Pedrocchi et al. 2002; Peterka 2002), implying that a particular value or range of values of the CM are planned for. Physically, the consequence of the line of gravity falling outside of the base of support provides credence for this assumption. On the other hand, the whole body CM is a concept, i.e., there is no way to directly sense its location in space. Stabilization of the CM may be the indirect result of the control of other variables, for example, the position of the joints relative to their baseline position. Only a few studies have employed experimental methods that test this assumption directly (Krishnamoorthy et al. 2005; Scholz et al. 2007). That the CM may be a controlled variable is consistent, however, with recent evidence that neurophysiological mechanisms exist that encode higher level task variables (Bosco et al. 2003; Poppele et al. 2002).
Knowledge of how the joints and muscles of the body are coordinated for postural stability is important for understanding how the body's position in space is estimated by the nervous system. In general, this is a complex problem; one may ask whether this involves estimation of the position of the head in space, of the CM in space, or of all body segments in space? Different sensors provide information in relation to different parts of the body. Obviously, if there is complex movement of most joints during postural sway, then it is difficult to integrate this information and to characterize the position of the body in space in a simple and unified way. Eliminating visual information, particularly when somatosensory information is also reduced, makes this problem even more challenging (De Nunzio et al. 2005; Krishnamoorthy et al. 2005; Ravaioli et al. 2005).
One hypothesis that, if true, would simplify both the control and estimation problem is that the body acts like an inverted pendulum during quiet standing, stabilized primarily by active control of the ankle joint in combination with passive musculoskeletal properties to maintain alignment of other joints (Winter et al. 1998). If most postural sway takes place around the ankle joint, then the position of the head in space, of the CM in space, or of any other point of the body in space are related to each other trivially. This would simplify the integration of sensory information from multiple sources. This hypothesized "ankle strategy" has served as the basis of many recent postural control models (Horak et al. 1990; Jeka et al. 1998; Kuo 1995; Loram and Lakie 2002; Masani et al. 2006; Maurer et al. 2006; McCollum and Leen 1989; Nashner and McCollum 1985; Nashner et al. 1989; Peterka 2002).
Recent work indicates, however, that inverted pendulum models of quiet stance control represent an oversimplification (Alexandrov et al. 2005; Creath et al. 2005; Horak and MacPherson 1996; Krishnamoorthy et al. 2005; Kuo 1995; Park et al. 2004; Zatsiorsky and Duarte 1999, 2000). For example, Alexandrov et al. (2005) provided data suggesting that the ankle, knee, and hip joints are coordinated as different "eigenmodes," independent combinations of all three joints defined by principal component analysis. Whereas the ankle eigenmode involves predominately ankle motion, motion of the knee and hip make important contributions to the control of upright stance as well. Their approach is consistent with the importance of distinguising between mechanical and functional DOFs (Li 2006).
Creath et al. (2005) used spectral coherence and co-phase analysis to reveal two modes of coupling between variations of leg and trunk segment angles during quiet stance; in-phase coupling was found <1 Hz, whereas a discontinuous shift to anti-phase coupling occurred above that value. This result suggested the simultaneous co-existence of two "excitable" modes of coupling between legs and trunk even during quiet stance.
Finally, two recent studies support the hypothesis that many joints along the kinematic chain are coordinated to achieve postural stability (Krishnamoorthy et al. 2005; Scholz et al. 2007). Krishnamoorthy et al. (2005) studied joint coordination in subjects who stood as quietly as possible on a narrow beam both with and without vision. Significant motions at most joints besides the ankle and hip were found to be coordinated to minimize disturbance of the CM position. This effect was enhanced when vision was eliminated, most of the increased joint variance being consistent with a control strategy that uses redundant joint combinations to control the CM position (Krishnamoorthy et al. 2005). Results of a recent reanalysis of support surface perturbations (Park et al. 2004) also is consistent with this finding. Differences in the configuration of the joints between pre- and postperturbation phases were largely consistent with a motor equivalent response; i.e., different joint combinations between the phases achieved an equivalent CM position (Scholz et al. 2007).
In light of these results, several hypotheses were addressed in the current study. First, we hypothesized that joints other than the ankle and hip would exhibit significant variability during quiet standing on a normal surface. More importantly we hypothesized that the nervous system would coordinate the joint variations such that most variation has little effect on either the CM or head positions, reflecting instead the use of redundant motor patterns to control these performance variables. Such a finding would mean that the CM could still be a stable reference variable for estimating the body's position in space. It would also indicate that the postural control problem is a truly multidimensional one involving most major joints along the body's longitudinal axis.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
Seven females and three males between the ages 20 and 45 volunteered to participate in this study. The subjects had no musculoskeletal injuries or neurological disorders that affected their ability to maintain stable upright posture. All subjects gave informed consent according to the procedures approved by the Human Subjects Review Committee of the University of Delaware in compliance with ethical standards laid down by the 1964 Declaration of Helsinki.
Experimental setup
Joint position data were collected at a sampling rate of 120 Hz using a VICON (Oxford Metrics) motion-measurement system composed of six infrared cameras placed in a semicircle at the right side of the subject. The system was tested for reliability and resolution given the small variations of joint angles during quiet stance. For the test, spherical reflective markers were mounted on the 30-cm-long arms and at the axis of a clinical goniometer. The angle between the goniometer arms were changed in 1° increments; this was the maximum resolution of the device. Angle increments were performed in two ranges, 85–95° (arms close together) and 175–185° (arms close to or co-linear). The goniometer was also positioned at different spatial locations corresponding to the position of various joints along the vertical axis of a standing person's body. Angles were computed as described in Data reduction. Intra-class correlation coefficients (ICC) were computed in SPSS to test for reliability across measurements. ICC values were all >0.999, whether computed separately for each joint angle range or across both ranges taken together.
Both a one-way repeated-measure ANOVA and corrected t-test for comparing adjacent pairs of angles were used to compare separately differences between angles in each of the two ranges separately. Table 1 presents the angles set on the goniometer, corresponding mean angles computed from the reconstructed marker coordinates in Matlab, and the lower and upper bounds of the 95% confidence intervals (CI). As can be seen, the goniometer and measured values were very similar and adjacent angles were well differentiated (average difference between lower and upper bound of 95% CI for a given goniometer position was 0.00063 ± 0.00026°). The differences in angles were highly significant in the ANOVA (P < 0.000000001) as well as the t-test [all t(23) > 704.0, P < 0.000000001]. The average joint excursions measured across subjects in the present study are listed in Table 2. These results show that the system resolution and reliability was sufficient to resolve the joint angle variations measured in this experiment.
|
|
20% of the distance from the greater trochanter to the shoulder and one-third of the distance from the posterior to anterior iliac spines to approximate the L5/S1 junction (de Looze et al. 1992). Experimental procedure
Subjects stood barefoot on a force platform with their feet shoulder-width apart and arms comfortably folded across the chest for each trial. The subject's foot position on both sides was marked to maintain the same foot position for each trial. We attempted to achieve consistent postural alignment at the beginning of each trial by aligning the beam of two fixed laser pointers with small red dots that were placed on the skin overlying the acromion process of the shoulder and over the great trochanter. Subjects were instructed to maintain normal quiet stance throughout each trial, allowing their body to sway naturally; they were not to try to keep their body rigidly aligned or to intentionally oscillate their body during the experiment. They were also told to keep their arms folded and motionless during the trials.
Three 5-min trials each were recorded in each of two conditions for each subject. One set of trials was performed under conditions of normal vision (eyes open, EO). During these trials, subjects were instructed to look straight ahead and focus their attention on a scenic picture that was hung 3-m in front of them. In the second condition, subjects had their eyes closed (EC) during the duration of the trial. After randomly selecting the condition for the first trial for each subject, the condition was presented in alternating order on subsequent trials. Subjects were provided as much rest as they desired between trials to avoid fatigue.
Data reduction
RECONSTRUCTION OF MARKER POSITION. The reflective markers were identified and their three-dimensional (3D) positions from the six camera views were reconstructed off-line using VICON processing software. The coordinates of each reflective marker were then low-pass filtered in Matlab with a 5-Hz cut-off frequency. All signals were filtered with a bi-directional, second-order Butterworth digital filter to eliminate artificial phase shifts in the data induced by filtering. Segment lengths of the body were derived from average marker positions over the first 3 s of the first experimental trial.
JOINT ANGLE CALCULATIONS.
The reflective marker coordinates at each data sample were used to calculate joint angles at the ankle, knee, hip, lumbo-sacral junction, cervical spine (C7–T1 junction), and atlanto-occipital joint in the sagittal plane. The atlanto-occipital joint was included based on previous work that revealed substantial motion of this joint independent of that of the C7–T1 articulation (Park et al. 2004; Scholz et al. 2007). The angle between adjacent limb segments was calculated using a link-segment model. Each joint angle is defined as in Fig. 1. The positive angles were defined clockwise; the negative angles were defined counterclockwise. The general formula used for joint angle computation was
 | (1) |
|
 | (2) |
In current study, we divided the whole body into foot plus shank, thigh, pelvis, and the trunk plus upper limbs, neck, and head segments for whole body CM calculation.
POWER SPECTRUM DENSITY ANALYSIS: CONTRIBUTIONS TO POSTURAL SWAY.
Each subject's mean power spectral density (PSD) for each of six joint angles were calculated and averaged over the three 5-min trials of quiet stance in each condition using the Matlab PSD functions that implement Welch's averaging method (Bendat 1980). Calculations used a 20-s Hanning window with a one-half window overlap after subtracting the mean joint angles from the raw data. All PSD functions were analyzed across frequencies from 0.05 to 2.5 Hz in 0.05-Hz increments to avoid the influence of measurement noise at higher frequencies. Spectral density was plotted on a log-log scale to observe the distribution of power in the sway trajectory, which is typically concentrated at low frequencies.
If the body acts primarily as an inverted pendulum during quiet stance, then variance of the ankle should be substantially higher than that of other joints at the dominant frequencies of sway. If a double pendulum model better characterizes the control of quiet stance, then hip and ankle motion should dominate motion of other joints. If instead substantial variation of all joint angles exists, this would be reflected in the spectra and indicate a more complex control structure involving the coordination of movement among most major joints.
JOINT VARIANCE ANALYSIS AND ITS RELATION TO STABILITY OF THE CM POSITION.
The question of whether the control system utilizes the available redundancy of the six joint motions to control the CM position during quiet stance on a fixed surface was addressed by using the UCM approach to partition the variability of the joint configuration into two components (Scholz and Schöner 1999). The UCM hypothesis is that the control system selects in the space of the motor elements, here the space of joint postures, a subspace or manifold that corresponds to a value of a task-related variable it is trying to stabilize, e.g., the CM position. In the present context, this UCM subspace is composed of all combinations of joint postures that are equivalent with respect to a given CM position. Therefore variations in joint posture that remain within this subspace have no affect on the CM position or leave it stable. In principle, variations within this subspace can be left uncontrolled, hence, the term "uncontrolled" manifold. We recognize, however, the possibility that other constraints act to limit what portion of the UCM actually is used under different circumstances. In contrast, joint variations lying in a subspace that is orthogonal to the UCM will lead to changes in the CM position away from the mean value with which the UCM is associated. The mean value of the joint configuration is used to estimate the "desired" CM position. Questions about the degree of stabilization of the CM position, then, can be addressed by comparing variances in the two subspaces, i.e., within the UCM (VUCM) and in the orthogonal subspace (VORT). Given that the analysis is performed with respect to a UCM based on the mean joint configuration, this makes the analysis somewhat conservative. That is, as long as the CM remains well within the limits of the base of support, a range of CM positions are acceptable and consistent with stable upright posture. Thus some amount of VORT or joint variance leading to different CM positions is expected. A finding that VUCM is substantially larger than VORT, therefore provides strong evidence in favor of the CM control hypothesis.
During voluntary movements the Jacobian relating changes in the task level variable with changes in the motor elements (i.e., the Jacobian matrix; see following text) varies with the limbs configuration. In that case, the UCM variance analysis is performed at the same point in the trajectory across multiple trial repetitions. In the current experiment on quiet stance, where variations in the joint postures are not induced by voluntary movement and postural variations are presumed to be due to involuntary or random fluctuations, we assume a relatively steady-state posture and perform the analysis across time within each trial (see following text).
Because the amplitude of sway in the anterior-posterior (AP) direction is higher than in the medial-lateral or vertical directions during quiet stance (Winter et al. 1998), we report results of variations within and orthogonal to the UCM in relation to the control of the anterior-posterior center of mass (CMAP) positions only. This method, then, addressed the extent to which variations in the joint configuration across time led to variations in the CMAP position or tended to preserve the mean CMAP position. Given this partitioning, we can make predictions based on several hypothesized postural control strategies. A value of VUCM found to be significantly higher than VORT would indicate that variations in the joint configuration tended to lead to a CMAP position consistent with its mean position across time (Fig. 2, B and C). Note that if the postural control system acts primarily as an inverted pendulum (Fig. 2A), most variance is predicted to be VORT, with little or no VUCM, because movement limited largely to the ankle joint is expected to lead to variations in the CMAP position from moment to moment, consistent with VORT. Another alternative would occur if the nervous system used a stiffening strategy to stabilize the CM position. Here, one might expect relatively smaller joint variations at all joints considered, i.e., low VUCM and VORT and VORT 
VUCM (Fig. 2D). As discussed in the preceding text, because variations of the CM position normally occur during postural sway (Duarte and Zatsiorsky 1999; Winter et al. 1998), we expect some degree of VORT to occur that reflects changes in the CMAP position over time. The question is whether there is a substantial and even greater component of variance within the UCM, reflecting more complex coordination of the involved joints to stabilize the average CMAP position.
|
; Scholz and Schöner 1999). The initial step in a formal analysis is to obtain the geometric model relating the task variable (here the CMAP position) to the elemental variables (here the joint angle configuration). In the present experiment, the joint configuration is composed of six angles (angle of the ankle, knee, hip, L5/S1 or lumbar spine (LS), C7/T1 or cervical spine (CS), and atlanto-occipital (AO) joint angles). The geometric model relating the CMAP position to the joint configuration, with origin at the ankle is
 | (3) |
ankle..., AO are the externally defined joint angles; lshank, ..., lhead are the lengths of the respective segments calculated from the static calibration trial; dshank, ..., dhead are the percentages of the segment lengths from the distal end where the mass of that segment lies; and Mfoot, Mshank, ..., Mhead are the proportion of total body mass for each of these segments, both estimated from Winter (1990).
Small changes in CMAP are related to changes in joint angles () through the Jacobian, which is the matrix of partial derivatives of the task variable, CMAP with respect to the joint angles ().
The second step in the method is to estimate the linear approximation to the UCM from the geometric model. We computed the mean joint configuration across all samples within a trial as corresponding to the hypothetically controlled CMAP position. The mean joint configuration was used to construct the UCM. A linear approximation to the UCM was obtained from the geometric model, linearized around the mean joint configuration
 | (4) |
Here, J is the Jacobian matrix, composed of 
CMAP/i, where i = [ankle, knee, hip, LS, CS, AO joints]. The linear approximation of the UCM is then the null-space of the Jacobian based on the mean joint configuration (the linear subspace of all deviations from the mean joint configuration that are mapped onto 0 changes in CMAP position by the Jacobian). Matlab was used for the numerical computation of the null space. At each sample value, the deviation of each segment's joint configuration vector from the mean joint configuration vector was obtained. This is essentially a geometric method: the joint deviation vector at each point in time is projected onto the null space, yielding a scalar value that estimates the degree to which that angle configuration is consistent with the mean joint configuration corresponding to a mean CMAP position. The complement of this projection is also obtained providing a scalar estimate of the extent to which this joint configuration leads to a different CMAP position. The computation of VUCM and VORT was performed on data from 0.5 to 4.5 min, leaving out the first and last 30 s of each 5-min trial. Because the dimensions of the UCM and orthogonal spaces differ, the variances of each subspace were normalized to the number of dimensions of that subspace. Thus the measures of VUCM and VORT are the variances per DOF. For example, with respect to the hypothesis that the horizontal(AP) CMAP position is stabilized by using flexible combinations of the six joint motions, the task space is one dimensional and the UCM is five dimensional (control of horizontal CMAP hypothesis). Therefore variance of projections within the UCM is divided by 5, whereas variance orthogonal to the UCM is divided by 1.
Although it has been argued that the CMAP is an important control variable for maintaining stable upright posture, the stability of other variables likely also are important for postural control. Because of the importance of vision and vestibular information (for more dynamic tasks) to postural control, stabilization of the head's position or orientation might also be important. Moreover, because the head is relatively massive, control of CMAP is likely linked to control of the head. Other control hypotheses are also possible. Indeed, it is possible that variance is structured with respect to a variety of variables. Therefore to better assess the extent of CMAP control, we also performed the UCM analysis relative to control of both the head's position and spatial orientation (i.e., with the vertical). In addition, if the body was controlled as a double-inverted pendulum, using combined ankle and hip strategies (Bardy et al. 1999; Creath et al. 2005; Horak and MacPherson 1996; Kuo 1995; Park et al. 2004), then negative covariation of the ankle and hip joints could also lead to CMAP position stabilization. A strategy that limits motion to the hip and ankle (2 DOF) would provide a minimally redundant system for stabilizing the CMAP position (1 DOF). Thus we performed the UCM analysis on a reduced model of CMAP control involving only the ankle and hip joints. The test of this model assumes, therefore, that most motion is restricted to these 2 DOF and that control of upright posture can be assumed to be related to control of these two angles. In this model, the combined mass of the head, arms, and trunk and their resultant location were used to represent the "trunk" segment, whereas the combined mass of the shanks and thighs and their resultant location were used to represent the "leg" segment (Winter 1990). Note that the masses of both legs and both arms were used in all models estimating CM position to get the accurate position along the anterior-posterior and vertical dimensions although this report is limited to the former dimension.
To compare the UCM effect for the different control hypotheses, (i.e., CMAP position based on the 6-DOF model, head position, head orientation and CMAP position based on the 2-DOF model), the ratio of VUCM to VORT for each control hypothesis was computed for each trial of a given individual's data
 | (5) |
This ratio then was transformed to natural log value to correct for a nonnormal distribution. Using the ratio is particularly important for comparing the 6- and 2-DOF model of CMAP control because of the different number of total joints contributing to the variance of each hypothesis, whereas the hypotheses about controlling the head position and spatial orientation are also based on 6 DOF.
Statistics
Paired t-test were performed to compare the total joint configuration variance as well as the actual variance of the CMAP across the two vision conditions. A two-way repeated-measures ANOVA (variance component by vision condition) was performed to determine how the variance of joint motion was organized and its dependence on the vision condition for each control hypotheses. When there was a significant interaction related to our hypotheses, planned contrasts were performed using the m-matrix structure in SPSS.
A two-way repeated-measures ANOVA was performed to compare the different control hypotheses (CMAP and head positions and head orientation, based on 6-DOF model, and CMAP position based on 2-DOF model) and their relationship to vision condition, using the log transform of the ratios of VUCM to VORT. A significant interaction related to our hypotheses was examined using the m-matrix structure in SPSS.
The log(PSD) value for joint angles was analyzed using a three-way repeated-measures ANOVA with vision (2), joint (6) angles and frequencies (50) as factors. When there was a significant interaction effect of joint angles x frequencies, paired t-test at each of the 50 frequencies were performed to determine the frequency range of the differences. To control the false discovery rate from the multiple testing, the method of Benjamini and Hochberg (1995) was applied to the resulting P values. All statistical analyses were performed using the SPSS 13.0 package and the 
-level was set at 0.05. Cross-spectral analysis of all possible joint pairs was also performed and the peak of the coherence function examined to determine if covariation of individual pairs of joints could explain any observed UCM effects.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
The actual range of motion at each joint in the static posture was quite small. The top six panels of Fig. 3 show the fluctuations of each measured joint angle across all three trials for a given exemplar subject (subject 3), for both EO condition (A) and EC condition (B). The bottom panel of the figure shows the variations of the CMAP position for the same trials. Figure 4 shows comparable data for one atypical subject (subject 10) who showed a more noticeable slow drift of the joint angles across the 5-min trials superimposed with the faster fluctuations. Note that in both subjects, the CMAP position appears to be relatively stable across time compared with the joint angles, suggesting that many different combinations of joints were used in an attempt to attain a stable CMAP position. Another way of looking at this is that joints compensated for each others fluctuations to achieve a more stable CMAP position, which would require interjoint coordination.
|
|
Table 3 presents the variance across all samples within a given trial of joint excursion and averaged across three trials for a given subject. As might be expected, the mean variance for each joint as well as the total joint configuration variance was higher in the EC condition than in the EO condition. The total joint configuration variance (i.e., geometric mean of individual joint variances) was 0.0019 ± 0.002 radian2/DOF in EO condition and 0.0029 ± 0.003 radian2/DOF in EC condition. The paired t-test showed a significant difference in total joint variance between EO and EC condition (t = –3.01 P < 0.05). Note that the proximal joint angles exhibited larger variance than did the distal joint angles.
|
As noted in the preceding text, the bottom panel of Figs. 3 and 4 illustrates the fluctuations of the CMAP position for all three trials for a typical subject (subject 3) and the atypical subject who exhibited a slow drift of the mean joint posture of his joints across the trial (subject 10). Table 4 presents the variance of the CMAP position across all samples within a trial, and then averaged across three trials for a given subject. Note that the SE was very small for both vision conditions. The variance of the CMAP position was generally larger in the EC condition than in the EO condition. However, this difference did not reach statistical significance (t = –1.06, P = 0.317), indicating that the differences in joint variance between vision conditions did not translate directly into variance of the CMAP position.
|
Another way to address differences in variance among different joints and the effect of vision is to compute the PSD function of each joint angle. This allowed us to determine if the differences in overall joint variance depended on the sway frequency. The results for the mean PSD of each joint angle across all subjects in both EO and EC conditions are presented in Fig. 5, A and B, respectively. Main effects for vision, joints, and frequency were found in the repeated-measures ANOVA [vision: F(1,9) = 5.4, P < 0.05; joint: F(5,45) = 51.4, P < 0.001; frequency: F(49, 441) = 666.23, P < 0.001]. Spectral power was larger in the EC than in the EO condition, consistent with the direct analysis of joint variance. The AO joint showed higher power than any other joint at all spectral frequencies. Of particular interest is that the ankle and hip joint powers tended to be lower than those of several other joints, particularly at the lower frequencies where most of the power lies (Fig. 5, A and B).
|
|
Given that there is relatively equal variability of all measured joints during quiet upright stance, a complex form of coordination among the joints likely accounts for the relatively stable CMAP position depicted in Figs. 3 and 4. The UCM analysis allowed us to link joint angle variance to variations of the CMAP position via a geometric model. Figure 6A presents the mean (+1 SE of estimation) of VUCM and VORT related to control of the CM position based on the 6-DOF model.
|
Structure of joint configuration variance related to the stability of other hypothesized control variables
The structure of joint variance, when considered in relation to control of head position (Fig. 6C) and head orientation (Fig. 6D), was similar to that when considering CMAP control involving the 6-DOF model. VUCM was significantly higher than VORT with respect to stabilizing both the head's position [F(1,9) = 11.4, P < 0.01; Fig. 6C] and its spatial orientation [F(1,9) = 8.1, P < 0.05; Fig. 6D]. There was also a significant effect of vision, with joint configuration variance being higher for the EC condition [head position: F(1,9) = 7.7, P < 0.05; head orientation: F(1,9) = 10.9, P < 0.01]. An interaction between vision condition and variance component was present, however, only in relation to control of the head's spatial position [F(1,9) = 7.7, P < 0.05]. As with CMAP control, VUCM was significantly higher for the EC condition [F(1,9) = 7.7, P < 0.05; Fig. 6A], whereas VORT did not differ between the vision conditions (P = 0.345). Regarding head orientation, removal of vision resulted in a relatively proportional increase in both VUCM and VORT.
If the body was to behave as a double-inverted pendulum, with most joint fluctuations occurring about the hip and ankle joints, coordination of the two joints could achieve a similar stabilization of the CM across time by negative covariation of the two joints. This effect might be limited, however, because this model of postural control is minimally redundant. Indeed when the UCM analysis was performed with respect to the two-joint model, a different result occurred (Fig. 6B). There were no significant differences between VUCM and VORT (P = 0.818), no effect of the vision condition (P = 0.385), and no interaction between these factors (P = 0.386). Thus an analysis based on assuming that the body acts as a double-inverted pendulum, anticipated by the joint spectral analysis results, would lead to the conclusion that the CMAP position is not a well-stabilized variable of the control system. Based on the joint variance and spectral analysis results and the UCM analysis based on the full six-joint model, we concluded that this assumption is not correct.
Comparison of various control hypotheses
Because of the different number of DOF included in the 6-DOF model of CMAP control compared with the 2-DOF model, we decided to directly compare the different control hypotheses by comparing the ratio of VUCM/VORT, reflecting the relative amount of variance per DOF in each subspace, rather than individual variance components. The ratio was computed separately from the results of the UCM analysis performed on each trial. Then each subject's median value across trials was log transformed to account for the nonnormal distribution of this variable and subjected to a repeated-measure ANOVA to compare the different control hypotheses. The results are presented in Fig. 7.
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
; Kuo 1995; Loram and Lakie 2002; Masani et al. 2006; Maurer et al. 2006; McCollum and Leen 1989; Nashner and McCollum 1985; Nashner et al. 1989; Peterka 2002; Winter et al. 1998). This strategy would establish a direct correspondence between motion at the ankle joint and the body's position in space. As a result, both postural control and estimation of the position of the body in space would be vastly simplified. Although attractive, this strong version of the inverted pendulum hypothesis has been challenged based on several lines of evidence. For example, Alexandrov et al. (2005) showed that the ankle, knee, and hip joints are coordinated into different modes of action for various tasks, including postural control, whereas Creath et al. (2005) revealed signatures of both in- and anti-phase coupling of the legs and trunk during quiet stance. Most major joints along the body's longitudinal axis are coordinated to stabilize upright posture.
Spectral analysis performed on all six measured joint angles in the current study revealed considerable variance at the relevant frequencies of postural sway in all cases. The ankle and hip joints were not found to be special among the joint DOFs examined. In terms of overall variability, these joints ranked fourth and fifth with more variance present at the atlanto-occipital and LS joints. In addition, the computed coherence between pairs of joint angles was found to be quite low, in most cases well <0.5. This underscores that correlations between pairs of joint angles is too weak for motion of one joint to represent motion at the other. Taken together, these observations run counter to a strict ankle or even ankle-hip control strategy for postural control.
The strong UCM effect found in relation to control of the spatial positions of the CM and head provide support for a more complex control scheme that involves most joints along the body's longitudinal axis. Only a small portion of the measured temporal variability of the joint configuration affected either the CM or head positions. If most motion was to take place at the ankle joint, as would be the case if the body acted as an inverted pendulum, then ankle joint variability would load exclusively on VORT, leading to variable CM and head positions (Fig. 2A), contrary to our results. Moreover, the UCM effects obtained with a two joint ankle-hip model (Fig. 2B) did not approximate the effects of the more realistic six-joint model (Fig. 6A). In fact, test of the reduced model resulted in no significant difference between the two variance components (Fig. 6B), although there was a tendency for VUCM to be larger than VORT (Fig. 6B). In addition, this result was inconsistent with the measured changes in the variance of CMAP; the 2-DOF result predicts a substantial increase in CM variance in the EO condition due to higher VORT.
Observed UCM structure of variance is consistent with evidence from other recent studies
An earlier study by Krishnamoorthy et al. (2005) analyzed joint variance in participants who stood on a narrow support surface. The results revealed the same structure of variance observed in the present study. All measured kinematic DOFs were engaged, but more variance was generated in directions in joint space that left the CM position invariant. DOFs were thus coordinated to stabilize the CM position. When the sensory conditions were made more difficult by removing vision, there were significant increases in joint variance. These increases had a limited effect on the CM position, however, being primarily directed into the UCM. In other words, combinations of joint motions leading to an equivalent CM position were more extensively activated than combinations that would shift the CM position (Krishnamoorthy et al. 2005; Scholz et al. 2001). The observation of the same UCM structure of variance in the present study confirms that this effect is not a consequence only of the limited postural support on a narrow support surface. Instead, the UCM structure of variance can be readily observed when standing on a normal surface as well.
How does the UCM structure of variance relate to postural adjustments after perturbations? Unlike the typically emphasized ankle and hip strategy, recent work suggests that both response components are present, their relative contributions depending on the nature of the perturbation and the stance conditions (Alexandrov et al. 2005; Park et al. 2004). A re-analysis of the data of Park and colleagues (2004) decomposed postural adjustments induced by perturbations of the support surface into joint configuration changes that leave the CM unchanged (changes within the UCM) and joint configuration changes that shift the CM (changes orthogonal to the UCM) (Scholz et al. 2007). The analysis found that significantly more of the postural adjustment occurred within the UCM than orthogonal to it. Given that postural adjustments at the ankle load primarily on the subspace orthogonal to the UCM (causing CM motion), this means that the postural response was not primarily ankle motion or even a combination of ankle and hip motion (Scholz et al. 2007) but involved substantial motion at all measured joints. This response pattern was particularly prominent for responses to low-amplitude perturbations.
Based on spectral coherence and co-phase analyses, Creath et al. (2005) reported two modes of coupling between the trunk and the leg segment of the body. Coherent in-phase coupling occurred at frequencies <1 Hz. At 1 Hz, they described a discontinuous shift to anti-phase coupling between these two body segment angles, although the anti-phase pattern was associated with far less spectral power than the in-phase pattern. Based on these results, the authors proposed that the control structure underlying quiet stance involves two excitable modes of coupling that are always present but differentially scaled depending on environmental and task conditions or on the nature of perturbations. The present results expand this view and suggest an even more complex control structure involving the variation of most major joints. Thus while there is coherent movement of the body in space, illustrated by coherent in-phase movement between leg and trunk segmental angles, this movement is superimposed on low coherence between pairs of joint angles (Table 5). We should point out that we replicated with the current data set (not reported) the co-phase and coherence analyses of Creath et al. (2005), confirming that our data were obtained under similar conditions.
A recent study by Freitas and colleagues used the UCM approach to study postural responses to voluntary shifts in the COP (Freitas et al. 2006). Subjects achieved these shifts by oscillating either about the ankle, knee, or hip (which included trunk flexion-extension). Both the instantaneous CM position and the trunk's orientation in space (assessed across similar cycles) were found to be stabilized by coordinated changes in joint motions. However, the UCM effects (VUCM > VORT) were relatively weak with respect to CM control compared with stabilization of trunk orientation. We did not examine trunk orientation here (Scholz et al. 2007), but the different results concerning CM control are likely due to several factors. First, their geometric model included only the hip, knee, and ankle joints. As was shown in the current experiments, the 2-DOF model of CM control produced relatively weak UCM effects. Second, the two tasks differed substantially. Although we studied the postural steady state, their results come from attempts to voluntarily change the postural state; this may partially account for the relatively weak effects on CM stabilization.
Effect of vision on joint coordination and implications for proprioception
When vision was eliminated by asking subjects to close their eyes (EC), overall joint configuration variance increased compared with the eyes open (EO) condition. However, this increase was not general as one might expect if the loss of vision were to lead to an overall upregulation of proprioceptive gains, accompanied by some increase in noise levels. Instead, the increased joint configuration variance was found to lie mostly in the UCM versus the region of joint space that would cause increased CM or head position variability (Fig. 6, A and C). This result contrasts with a relatively equal increase in both variance components when considering the control of head orientation (Fig. 6D) or no effect when considering the 2-DOF CMAP control model (Fig. 6B). The fact that head orientation showed such an increase in the component orthogonal to its UCM indicates that the opposite observation regarding control of the CM and head position based on the 6-DOF model is not trivial.
Examining posture on narrow support, Krishnamoorthy et al. (2005) recently provided a hypothesis to explain this result. They reported a similar but even stronger differential effect of removing vision on the two variance components. In view of the substantial amount of variance observed in all measured joints and the UCM structure found in that variance (VUCM >> VORT), Krishnamoorthy et al. hypothesized that the problem that the postural system needed to solve on the narrow base of support was to keep the body scheme updated so as to be able to predict which joint motions are allowed and which are not. That requires estimates of all joint angles and joint velocities. Because proprioception depends on the dynamic contribution of muscle receptors (Clark et al. 1989), increasing joint variability may be a useful strategy to increase the sensory signal from proprioceptive systems that support estimation of the whole body joint configuration. By allowing an increase in joint motion to occur primarily within the UCM, the negative impact of such a strategy on variance of the critical variables CM and head position is limited.
More generally, proprioception and the estimation of the whole body joint configuration play a much more important role in the UCM based conception of postural control than, for example, within the inverted pendulum conception. In the UCM-based conception, the sizeable variance at all measured joints needs to be coordinated such that postural sway of the CM and head position is minimized. This requires an estimate of all joint angles, that is, a representation of the body scheme. A direct test of this consequence of the UCM picture of postural control could be based on the prediction that patients with a complete loss of proprioception should not show the same variance structure as shown here.
Revised conception of postural control
This revised argument for the importance of CM and head position emphasizes the importance of relating sensory information across different reference frames. Because most joints along the body axis are highly variable, these transformations are not trivial and are all the more critical. The observed UCM structure in joint space simplifies some of these transformations but conversely relies on reliable estimates of the body configuration. Maurer and colleagues recently proposed a multi-sensory model of control of upright stance that might help simplify the problem of integrating sensory information (Maurer et al. 2006). The model involves the up- and downstreaming of sensory information (ankle proprioceptors, pressure sensors at the feet, and vestibular receptors). In model simulations that combined sensor fusion and sensory thresholds, an automatic context-specific sensory re-weighting of these different sources occurred across different stimulus conditions. Our results highlight the need for an understanding of the transformations modeled by Maurer et al. Their model was, however, based on a single-inverted pendulum model of the body. Accounting for the coordination among joints that underlies the UCM structure of variance will complicate the picture but should provide important insights into how sensory-motor integration is achieved in the postural system.
In conclusion, the observation of a UCM pattern of joint variance both confirms and disputs common assumptions about the nature of the postural system. The UCM result disconfirms that the CNS simplifies the postural control problem by using primarily a single DOF, the ankle, to achieve stability of the body in space, and is consistent with other recent results (Alexandrov et al. 2005; Creath et al. 2005). The UCM result confirms, however, that the CNS makes special efforts to limit sway of the body by coordinating variance at all joints such that most joint motion is decoupled from motion of the body in space. This finding has important implications for problems of both estimation and control.
|
GRANTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
|
ACKNOWLEDGMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
|
FOOTNOTES |
|---|
Address for reprint requests and other correspondence: J. P. Scholz, Dept. of Physical Therapy, Biomechanics and Movement Science Program, 307 McKinly Laboratory, University of Delaware, Newark, DE 19716 (E-mail: jpscholz{at}udel.edu)
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
Balasubramaniam R, Riley MA, Turvey MT. Specificity of postural sway to the demands of a precision task. Gait Posture 11: 12–24, 2000.[CrossRef][Web of Science][Medline]
Bardy BG, Marin L, Stoffregen TA, Bootsma RJ. Postural coordination modes considered as emergent phenomena. J Exp Psychol Hum Percept Perform 25: 1284–1301, 1999.[CrossRef][Web of Science][Medline]
Bendat JS. Engineering Applications of Correlation and Spectral Analysis. New York: Wiley, 1980.
Benjamini Y, Hochberg Y. Controlling the false discovery rate—a practical and powerful approach to multiple testing. J Roy Stat Soc B Method 57: 289–300, 1995.
Bosco G, Rankin A, Poppele RE. Modulation of dorsal spinocerebellar responses to limb movement. I. Effect of serotonin. J Neurophysiol 90: 3361–3371, 2003.
Clark FJ, Grigg P, Chapin JW. The contribution of articular receptors to proprioception with the fingers in humans. J Neurophysiol 61: 186–193, 1989.
Corriveau H, Hebert R, Raîche M, Dubois MF, Prince F. Postural stability in the elderly: empirical confirmation of a theoretical model. Arch Gerontol Geriatrics 39: 163–177, 2004.[CrossRef][Web of Science][Medline]
Creath R, Kiemel T, Horak FB, Peterka RJ, Jeka JJ. A unified view of quiet and perturbed stance: simultaneous co-existing excitable modes. Neurosci Lett 377: 75–80, 2005.[CrossRef][Web of Science][Medline]
de Looze MP, Kingma I, Bussmann JBJ, Toussaint HM. Validation of a dynamic linked segment model to calculate joint moments in lifting. Clin Biomechan 7: 161–169, 1992.[CrossRef]
De Nunzio AM, Nardone A, Schieppati M. Head stabilization on a continuously oscillating platform: the effect of a proprioceptive disturbance on the balancing strategy. Exp Brain Res 165: 261–272, 2005.[CrossRef][Web of Science][Medline]
Duarte M, Zatsiorsky VM. Patterns of center of presure migration during prolonged unconstrained standing. Mot Control 3: 12–27, 1999.[Web of Science][Medline]
Freitas SMSF, Duarte M, Latash ML. Two kinematic synergies in voluntary whole-body movements during standing. J Neurophysiol 95: 636–645, 2006.
Gage WH, Winter DA, Frank JS, Adkin AL. Kinematic and kinetic validity of the inverted pendulum model in quiet standing. Gait Posture 19: 124–132, 2004.[CrossRef][Web of Science][Medline]
Horak FB, MacPherson JM. Postural orientation and equilibrium. In: Handbook of Physiology. Exercise, Regulation and Integration of Multiple Systems, edited by Rowell L, Shepherd J. New York: Oxford, 1996, sect 12, chap 7, p. 255–292.
Horak FB, Nashner LM, Diener HC. Postural strategies associated with somatosensory and vestibular loss. Exp Brain Res 82: 167–177, 1990.[Web of Science][Medline]
Jeka J, Oie K, Schoner G, Dijkstra T, Henson E. Position and velocity coupling of postural sway to somatosensory drive. J Neurophysiol 79: 1661–1674, 1998.
Krishnamoorthy V, Yang J-F, Scholz JP. Joint coordination during quiet stance: effects of vision. Exp Brain Res 164: 1–17, 2005.[CrossRef][Web of Science][Medline]
Kuo AD. An optimal control model for analyzing human postural balance. IEEE Trans Biomed Eng 42: 87–101, 1995.[CrossRef][Web of Science][Medline]
Li ZM. Functional degrees of freedom. Mot Control 10: 301–310, 2006.[Web of Science][Medline]
Loram ID, Lakie M. Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability. J Physiol 545: 1041–1053, 2002.
Masani K, Vette AH, Popovic MR. Controlling balance during quiet standing: proportional and derivative controller generates preceding motor command to body sway position observed in experiments. Gait Posture 23: 164–172, 2006.[CrossRef][Web of Science][Medline]
Maurer C, Mergner T, Peterka RJ. Multisensory control of human upright stance. Exp Brain Res 171: 231–250, 2006.[CrossRef][Web of Science][Medline]
McCollum G, Leen TK. Form and exploration of mechanical stability limits in erect stance. J Mot Behav 21: 225–244, 1989.[Web of Science][Medline]
Nashner LM, McCollum G. The organization of human postural movements: a formal basis and experimental synthesis. Behav Brain Sci 8: 135–172, 1985.[Web of Science]
Nashner LM, Shupert CL, Horak FB, Black FO. Organization of posture controls: an analysis of sensory and mechanical constraints. Prog Brain Res 80: 411–418, 1989.[Web of Science][Medline]
Park S, Horak FB, Kuo AD. Postural feedback responses scale with biomechanical constraints in human standing. Exp Brain Res 154: 417–427, 2004.[CrossRef][Web of Science][Medline]
Pedrocchi A, Baroni G, Mouchnino L, Ferrigno G, Pedotti A, Massion J. Absence of center of mass control for leg abduction in long-term weightlessness in humans. Neurosci Lett 319: 172–176, 2002.[CrossRef][Web of Science][Medline]
Peterka RJ. Sensorimotor integration in human postural control. J Neurophysiol 88: 1097–1118, 2002.
Poppele RE, Bosco G, Rankin AM. Independent representations of limb axis length and orientation in spinocerebellar response components. J Neurophysiol 87: 409–422, 2002.
Ravaioli E, Oie KS, Kiemel T, Chiari L, Jeka JJ. Nonlinear postural control in response to visual translation. Exp Brain Res 160: 450–459, 2005.[CrossRef][Web of Science][Medline]
Reisman DS, Scholz JP. Aspects of joint coordination are preserved during pointing in persons with post-stroke hemiparesis. Brain 126: 2510–2527, 2003.
Scholz JP, Reisman D, Schöner G. Effects of varying task constraints on solutions to joint coordination in a sit-to-stand task. Exp Brain Res 141: 485–500, 2001.[CrossRef][Web of Science][Medline]
Scholz JP, Schöner G. The uncontrolled manifold concept: identifying control variables for a functional task. Exp Brain Res 126: 289–306, 1999.[CrossRef][Web of Science][Medline]
Scholz JP, Schöner G, Hsu WL, Jeka JJ, Horak FB, Martin V. Motor equivalent control of the center of mass in response to support surface perturbations. In: Exp Brain Res Online First. Berlin: Springer Berlin/Heidelberg, 2007.
Winter DA. Biomechanics and Motor Control of Human Movement. New York: Wiley, 1990.
Winter DA, Patla AE, Prince F, Ishac M, Gielo-Perczak K. Stiffness control of balance in quiet standing. J Neurophysiol 80: 1211–1221, 1998.
Zatsiorsky VM, Duarte M. Instant equilibrium point and its migration in standing tasks: rambling and trembling components of the stabilogram. Mot Control 3: 28–38, 1999.[Web of Science][Medline]
Zatsiorsky VM, Duarte M. Rambling and trembling in quiet standing. Mot Control 4: 185–200, 2000.[Web of Science][Medline]
This article has been cited by other articles:
|
|
 |
|
  I. J. Pinter, R. van Swigchem, A. J. K. van Soest, and L. A. Rozendaal The Dynamics of Postural Sway Cannot Be Captured Using a One-Segment Inverted Pendulum Model: A PCA on Segment Rotations During Unperturbed Stance J Neurophysiol, December 1, 2008; 100(6): 3197 - 3208. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 W. Ilg, M. A. Giese, E. R. Gizewski, B. Schoch, and D. Timmann The influence of focal cerebellar lesions on the control and adaptation of gait Brain, November 1, 2008; 131(11): 2913 - 2927. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
W. Zhang, J. P. Scholz, V. M. Zatsiorsky, and M. L. Latash What Do Synergies Do? Effects of Secondary Constraints on Multidigit Synergies in Accurate Force-Production Tasks J Neurophysiol, February 1, 2008; 99(2): 500 - 513. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
L. B. Oude Nijhuis, B. R. Bloem, M. G. Carpenter, and J. H. J. Allum Incorporating Voluntary Knee Flexion Into Nonanticipatory Balance Corrections J Neurophysiol, November 1, 2007; 98(5): 3047 - 3059. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
