**3. Results**

The assumption of normality was confirmed, indicating a normal distribution. As no significant between-sex differences for COP displacement trajectory were found, the data were analyzed for the entire sample (*n* = 102). Furthermore, *t*-tests revealed no significant differences between the first and second trial, hence analysis involved only data from the first trial.

The correlations between right and left foot COP trajectory in the mediolateral and anteroposterior directions are presented as a histogram (Figure 3). Strong and very strong positive correlations (0.6 to 1.0) for right and left foot COP displacement trajectory in the mediolateral direction were observed in 91 participants while 11 individuals presented weak or negative correlations. In the anteroposterior direction, moderate and strong negative correlations (−0.5 to −1.0) were observed in 69 participants while 30 were found with weak negative or positive correlations. Strong positive correlations (0.6 to 1.0) in the mediolateral direction were observed in only three individuals.

**Figure 3.** Histogram of correlation coefficients between right and left foot COP trajectory in the mediolateral and anteroposterior directions.

In order to better illustrate the correlations of COP trajectory between the mediolateral and anteroposterior directions, a scatter plot was generated in which the correlations were plotted for each participant (Figure 4). The *x*-axis was used to delineate the right foot correlations between COP trajectory directions whereas the *y*-axis represented the left foot. Based on this structure, four quadrants were defined.

**Figure 4.** Scatter plot illustrating the correlations between right (*x*-axis) and left foot (*y*-axis) mediolateral and anteroposterior COP trajectories for each participant.

The first quadrant (Quadrant I) contains the participants (42 females and 41 males) presenting positive left foot and negative right foot correlations. The second quadrant (Quadrant II) represents those participants (five females and three males) with a positive correlation between the mediolateral and anteroposterior directions in both the right and left foot The third quadrant (Quadrant III), in turn, contains those participants (seven females and one male) with negative right and left foot correlations in both directions whereas the fourth quadrant (Quadrant IV) entails the small group of participants (three males) with positive right foot and negative left foot correlations.

The majority of the sample (*n* = 83) was grouped in the second quadrant (Quadrant II). A statokinesigram representative of this group was extracted from Participant 1 (Figure 5), who was found with a correlation coefficient of 0.94 for the left and −0.94 for the right foot. Furthermore, 57 participants (more than half the sample) in this quadrant presented strong correlations in both the left (*r* = 0.6 to 1.0) and right (*r* = −1.0 to −0.6) feet. A box was drawn in Figure 4 to highlight this congregation.

**Figure 5.** Stabilogram of right and left foot COP trajectories in the mediolateral (Ax) and anteroposterior (Ay) directions for Participant 1 (Quadrant II).

On the opposite spectrum, the three individuals composing the fourth quadrant (Quadrant IV) can be characterized by the statokinesigram of Participant 13 (Figure 6), who was found to present a correlation coefficient of −0.72 for the left and 0.74 for the right foot. The third quadrant (Quadrant III) can be represented by the statokinesigram of Participant 72 (Figure 7), with correlation coefficients of −0.65 for the left and 0.62 for the right foot. An exemplary statokinesigram of the participants located in the first quadrant (Quadrant I) is provided by Participant 93 (Figure 8), with correlation coefficients of 0.67 for the left and 0.59 for the right foot.

**Figure 6.** Stabilogram of right and left foot COP trajectories in the mediolateral (Ax) and anteroposterior (Ay) directions for Participant 13 (Quadrant IV).

**Figure 7.** Stabilogram of right and left foot COP trajectories in the mediolateral (Ax) and anteroposterior (Ay) directions for Participant 72 (Quadrant III).

**Figure 8.** Stabilogram of right and left foot COP trajectories in the mediolateral (Ax) and anteroposterior (Ay) directions for Participant 93 (Quadrant I).

## **4. Discussion**

This investigation considered how balance is maintained during an upright stance when COP is assessed over two points of application (both feet) with respect to the supporting surface. At first glance, it seems logical that the COP of each foot should be equal and, therefore, exhibit symmetry when balance is being maintained in a static position. The present study operated under the premise that a positive correlation between right and left foot COP trajectories (in the mediolateral and anteroposterior directions) indicates symmetry whereas a negative correlation indicates asymmetry. We hypothesized that the incidence of fluctuations or asymmetry between right and left foot COP can indicate foot pathology resulting from improper footwear or decreased neuromuscular control.

In our sample of healthy young adults, strong negative correlations between right and left foot COP in the mediolateral direction were found in approximately 67% of the participants. This indicates that during the quiet standing task the participants exerted pressure on the lateral boundary of the left foot while concurrently exerting pressure on the medial boundary of the right foot and, therefore, exhibit asymmetry. In turn, approximately 29% of the sample presented correlations coefficients between −0.4 and 0.3 between right and left foot mediolateral COP, which was considered to indicate more balanced symmetry albeit without any characteristic trend. More puzzling is the fact that the remaining 3% of the sample was found to show COP displacement simultaneously towards the medial and lateral sides of the right and left foot. From a biomechanical perspective, this type of balance control is difficult to understand. Interpretation of the correlation coefficients between right and left foot anteroposterior COP displacement found that approximately 88% of the sample presented considerable symmetry between both feet and that compared with mediolateral COP, anteroposterior COP trajectory shows a greater level of symmetry between both feet. In e ffect, these results find that the majority of the sample presented asymmetry albeit defined as mediolateral COP trajectory traversing towards both the medial and lateral boundaries of the feet. Symmetry, in turn, was observed in the anteroposterior direction in which COP trajectory was along the toes or heel of the foot. This asymmetry and symmetry were presented by 86 participants (*n* = 102) and, therefore, suggests that this form of postural control defines healthy and active adults.

Research has suggested that the occurrence of asymmetry when maintaining balance to be the result of musculoskeletal dysfunction or lower extremity dominance. These conclusions were drawn by Ageberg [13], Lin [14] or Barone [15] who performed posturography on two force plates or by comparing COP variables between the dominant and non-dominant leg in static bilateral conditions. However, during single-leg testing, Ho ffmann [16] and Greve [17] or Cu ˘g et al. [18] did not observe any di fferences in postural balance between the dominant and non-dominant leg in young adults. The aforementioned studies have mentioned that functional leg dominance may play an important role in bilateral postural stability, where, in most individuals, the left leg is the functionally dominant extremity and the right leg the functionally non-dominant extremity. Interestingly, Micarelli et al. [19] found greater COP displacement in the right rather than left leg during quiet standing in a group of children 4–13 and 4–7 years old. Research on the development of postural control by Assaiante [20] found that the trunk serves as an important reference frame in the emergence of structured postural strategies. It has been suggested that shifting the center of mass over the left increases weight-bearing load of the left leg over time.

Of consideration is the use of a scatter plot as presented herein as it can provide facile comparisons with other cohorts or normative data or illustrate more clearly the relationships of COP trajectories between the right and left foot. For example, when considering left foot COP trajectory in both directions, over half of the sample was found to present a pattern in which COP displacement traversed in the anteroposterior direction with a rightwards slant (medial direction) whereas right foot COP followed an anteroposterior displacement with a leftwards shift (medial direction). This medial shift of right and left foot COP trajectory with an anteroposterior displacement in the majority of the sample is contrasted by the marginal number of participants (three individuals) who presented an inverse pattern. In this small group, anteroposterior COP trajectory was associated with a lateral COP displacement (towards the outside of both feet) in the forward direction whereas in the backward direction COP transversed in the medial direction (towards the outside of the feet). In addition, the visualization of COP data by mapping its trajectory in the spatial domain can show patterns in COP trajectory over the base of the support, i.e., the feet. The trends that we observed in the majority of the sample (Quadrant II, Figure 5) confirm the findings of Oba et al. [21], Rival et al. [22] and Cumberworth et al. [23], who concluded that postural stability (COP displacement) is limited to an area between the heel and toe alongside the lateral edge in adults.

Our sample, as previously mentioned, was composed of young and asymptotic individuals free of lower extremity injury or disability. Although not assessed in the present study, it can be presumed that the incidence of foot or leg pathologies can modify the maximum displacement of COP trajectory and, therefore, stability. The literature contains numerous reports that utilize data on COP area and its relation to the base of support as a measure of postural stability [24–26]. Riach and Starkes [20] sound that children show a larger area of stability than adults and that the limit of stability decreases with age. Young adults aged 18–27 years appropriate on average 73% of the anteroposterior and 75% of the mediolateral base of support during upright standing. By ages 40–70, individuals use only 54% and 59%, respectively [22]. Cli fford and Holder-Powell [23] indicated that the elderly show an even further reduced base of support for postural stability. Bottaroa [24] reported that this observation is associated with the fact that young asymptotic adults use up to 80% while older adults only up to 50% of foot length to maintain balance.

The present findings raise a number of questions concerning the etiology of disturbed COP displacement trajectory between the right and left foot and indicate the need for additional investigation in this area. Further research on COP symmetry in various populations (athletes, physically impaired, sedentary individuals) can provide further insight on the causes of asymmetry (e.g., decreased neuromuscular control) and aid clinicians with the diagnosis of various posture-related pathologies.
