Assessment of Postural Sway Area in Single-Leg Balance: A Comparative Analysis of Center-of-Pressure Area Metrics with the Convex Hull approach

Article information

Exerc Sci. 2025;34(2):199-206

Publication date (electronic) : 2025 May 30

doi : https://doi.org/10.15857/ksep.2025.00248

Seung-Hee Nam, MS

, Kyung-Min Kim, PhD ^,

Department of Sport Science, Sungkyunkwan University, Suwon, Korea

Corresponding author: Kyung-Min Kim Tel +82-31-299-6917 Fax +82-31-299-6929 E-mail km.kim@g.skku.edu

*This research was supported by the SungKyunKwan University and the BK21 FOUR (Graduate School Innovation) funded by the Ministry of Education (MOE, Korea) and National Research Foundation of Korea (NRF).

Received 2025 April 21; Revised 2025 May 9; Accepted 2025 May 23.

Abstract

PURPOSE

Quantifying postural control using Center-of-Pressure (COP) data obtained from a force plate is commonly used in balance assessments, yet the sensitivity of various sway area metrics remains unclear. This study introduced the convex hull area as a novel metric and aimed to examine how four COP-based sway area measures—rectangular, 66% effective, 95% ellipse, and the convex hull area—respond to progressively restricted visual conditions during single-leg balance. We also aimed to identify how the convex hull area performed relative to traditional sway area metrics.

METHODS

Forty healthy adults (20 males and 20 females) performed three 10-second single-leg balance trials on a force plate under progressively restricted visual conditions using stroboscopic goggles. Three traditional COP-based sway area parameters and the introduced convex hull area were used to quantify single-leg postural control. All participants completed the balance tests under six visual conditions.

RESULTS

A two-way repeated measures ANOVA revealed a significant interaction between sway area parameters and visual conditions (F=5.90, p<.001). The 95% ellipse area showed the highest sensitivity, followed by the convex hull, rectangular, and 66% effective area parameters across different visual conditions. The 95% ellipse and convex hull area produced similar results and were significantly different from the rectangular and 66% effective area (p<.001).

CONCLUSIONS

These findings suggest that the convex hull area is capable of detecting changes in postural control alongside the 95% ellipse area, performing comparably to traditional sway area metrics. Our results may contribute to the standardization of COP-based sway area metrics.

Keywords: Posturography; Postural control; COP area calculation; Boundary area

INTRODUCTION

Postural control plays a fundamental role in maintaining balance and enabling functional movement [1]. It relies on the integration of multiple sensory inputs, including somatosensory, vestibular, and visual systems, within an efficient postural control system that generates appropriate motor responses [2-4]. Assessment of postural control provides critical insights into an individual's ability to maintain balance under various environmental or task-specific demands [4-6]. This measurement is particularly valuable for identifying balance deficits in clinical population with neuromuscular disorders [7-10], predicting risk of fall or reinjury [11,12], and monitoring rehabilitation strategy in patients with musculoskeletal disorders [13]. Thus, accurate and standardized quantification of postural control is crucial for both clinical setting and scientific evidence research [11,14].

Among the various methods for assessing postural control, the force plate is widely regarded as the most reliable tool for single-leg balance tasks [15-17]. It indirectly captures changes in postural control by recording ground reaction forces (GRFs) generated from the body movement [17,18]. From these data, the center of pressure (COP) was calculated, representing both the center of mass and the torque applied to the support surface to regulate the acceleration of the body mass [19]. From these trajectories, a range of COP-derived metrics can be computed, including path length, velocity, and sway area [17,18]. Among these, sway area parameters are particularly useful for capturing the spatial charac-teristics of postural sway and have been commonly employed in both research and clinical settings [7,11,17], largely because their spatial representation is more intuitive to interpret than other COP metrics such as velocity or path length.

However, the methods used to calculate sway area vary widely across studies, resulting in inconsistencies in interpretation and limited compa-rability of findings [7]. Some studies use a rectangular boundary based on maximum excursions [20,21], while others rely on statistical con-structs such as 95% confidence ellipses [13,20,22], or effective areas that exclude outliers [23]. These approaches may either overestimate or underestimate true postural sway, depending on how well the area boundary captures the actual COP trajectory [23]. The rectangular method, for example, includes areas never occupied by the COP, while the 66% effective area omits significant outer sway. Even the 95% ellipse area, although more statistically robust, may fail to reflect the actual sway path, as it estimates dispersion around a mean COP position rather than the true boundary of movement [22].

To address these limitations, we propose the convex hull area as a novel sway area metric [24]. This approach involves computing the smallest convex polygon that encloses all COP data points, effectively capturing the full spatial extent of postural sway without relying on dis-tributional assumptions or arbitrary cutoffs [24,25]. Unlike conventional sway area parameters— which may either over- or underestimate sway due to rigid geometrical boundaries or probabilistic modeling [22]— the convex hull offers a geometric solution that directly reflects the actual boundary of the COP path [26]. Moreover, it may be particularly useful when examining subtle postural adjustments, as it accommodates non-linear or asymmetrical trajectories commonly observed under sensory perturbations [27].

Given these theoretical advantages, it is important to evaluate how the convex hull area performs relative to established sway area metrics under standardized conditions. Thus, the purpose of this study was to assess how four COP-based sway area parameters— rectangular area, 66% effective area, 95% ellipse area, and the convex hull area— respond to progressively restricted visual input during single-leg stance. By applying six levels of visual occlusion using stroboscopic goggles, we aimed to de-termine which area metrics were most responsive to sensory perturbations.

METHODS

1. Participants

Forty healthy adults (20 males and 20 females) were recruited from the university community through advertisements. The inclusion criteria were: (1) participants aged between 19 and 35 years and (2) no history of lower limb musculoskeletal injuries within the past six months. Exclusion criteria included: (1) any history of lower limb surgery or fracture, (2) any neurological disorders that could adversely affect their balance, and (3) inability to maintain a single-leg stance for at least 10 seconds. This study was approved by the Sungkyunkwan University's Institutional Re-view Board, and all participants provided written informed consent pri-or to participating in this study (IRB approval no: SKKU 2023-07-016).

2. Testing procedures and instruments

The single-leg balance test procedures used in this study followed the established methods reported in previous studies [28,29]. All participants performed three 10-second single-leg stance trials on a force plate under six different visual conditions, using stroboscopic goggles (Senaptec Strobes, Senaptec LLC, Beaverton, OR, USA) [30]. The participants stood barefoot with their arms free for balance and focused on a target 3 me-ters ahead. Visual input was manipulated using the stroboscopic goggles, which offer eight levels of visual occlusion [31]. For this study, we applied six different visual conditions as following order: (1) eyes open (EO), (2) stroboscopic vision level 2 (5 Hz frequency; transparent lens duration=0.1s; opaque lens duration=0.1s, 50% visual occlusion, SV2), (3) stroboscopic level 4 (3 Hz frequency; transparent lens duration=0.1s; opaque lens duration=0.23s, 69.7% visual occlusion, SV4), (4) stroboscopic level 6 (1.75 Hz frequency; transparent lens duration=0.1s; opaque lens duration=0.47s, 82.5% visual occlusion, SV6), (5) stroboscopic level 8 (1 Hz frequency; transparent lens duration=0.1s; opaque lens duration=0.90s, 90% visual occlusion SV8), and (6) eyes closed (EC). This sequence of testing was selected to minimize abrupt transitions between sensory perturbation and ensure participant safely, align with previously established test protocols [28]. Each participant completed a total of eighteen test trials (three per visual condition). Prior to data collection, the participants were allowed three to five practice trials for each condition. If a participant failed to maintain balance for the 10 seconds, the trial was discarded, and the trial was repeated until three successful trials were achieved for each condition.

3. Data processing

The COP data were recorded for each trial utilizing an Accusway force platform (AMTI Corp., Watertown, MA, USA) at a sampling rate of 100 Hz. The data were processed using a fourth-order, zero-lag But-terworth filter with a 5 Hz cut-off frequency, consistent with previous studies [32]. Traditional COP metrics were computed using custommade MATLAB software (MATLAB; The MathWorks Inc., Natick, MA, USA). Specifically, three traditional area parameters such as rectangular area, 66% effective area, and 95% confidence ellipse area were calculated based on formulas provided in the AMTI force platform manual and implemented using MATLAB. We also computed a novel convex hull area. Larger sway area values indicate poorer postural stability [23]. Detailed descriptions and formulae for these area metrics are presented in Table 1 [33]. Fig. 1 presents the sway area metrics calculated from a sample COP data recorded for 10 seconds during single-leg balance trial. To facilitate understanding, four distinct sway area parameters— rectangular area, 66% effective area, 95% ellipse area, and convex hull area— overlaid on the COP trajectory.

Table 1.

Detailed descriptions and formulas of Center-of-Pressure (COP) based sway area parameters

Fig. 1.

Center of Pressure trajectory with different postural sway area metrics.

4. Statistical analysis

We conducted a two-way repeated measures ANOVA (4 sway area metrics×6 visual conditions) to examine the interaction between sway area parameters and visual conditions during single-leg balance. When a significant interaction was observed, Bonferroni-adjusted post hoc tests were performed to (1) identify differences among visual conditions within each sway area parameter, and (2) compare sway area parameters within each visual condition. The significance level was set at p <.05 for all statistical tests. All statistical analyses were executed using SPSS (version 29.0; IBM Corp, Armonk, NY, USA).

RESULTS

A total of 40 participants were included in this study, comprising 20 males and 20 females (mean age: 22.7±2.4 years; height: 169.2±7.3 cm; body mass: 68.2±14 kg). All participants successfully completed all single-leg balance tests under six visual conditions. A two-way repeated measures ANOVA (4 sway area metrics×6 visual conditions) revealed a significant interaction between sway area and visual condition (F=5.90, p <.001), indicating that the influence of visual input on postural sway varied depending on the sway area parameters used (Fig. 2).

Fig. 2.

Descriptive summary of postural sway area across six different visual conditions. Alphabets (a-d) denote significant differences between sway area parameters under the same visual condition (vertical comparison: a=Rectangular area, b=66% Effective area, c=95% Ellipse area, d=Convex Hull area). Numerals (1-6) indicate significant differences between visual conditions within each sway area parameter (horizontal comparison: 1=eyes open, 2=SV2, 3=SV4, 4=SV6, 5=SV8, 6=eyes closed), based on post hoc Bonferroni tests (p<.05). *Indicates that the convex hull area shows the same pattern of significant differences as the 95% ellipse area under the same visual condition.^† Indicates that the convex hull area and the 95% ellipse area exhibit equivalent significant differences across visual conditions.

Post hoc comparisons indicated that the rectangular area and 66% effective area consistently significantly differed from the other three area parameters across all visual conditions (p <.001). In contrast, the 95% ellipse area and convex hull area did not differ significantly from each other, but both were significantly different from the rectangular and 66% effective areas. Within each sway area parameter, all four metrics showed significant differences, particularly under the eyes open condition. However, under partial visual occlusion (SV2-SV8) and the eyes closed condition, the ability to distinguish between visual conditions diminished, es-pecially in the 66% effective area. Among all sway area metrics, the 95% ellipse area revealed the largest number of significant differences across visual conditions, followed by the convex hull area, rectangular area, and 66% effective area. As shown in Fig. 2, the 95% ellipse area and convex hull area exhibited nearly identical significance patterns. In terms of sway area magnitude, the 95% ellipse and convex hull areas ranged from 11.2 to 11.7 cm/s², while the rectangular averaged approximately 1.5 times larger (16.7 cm/s², 145%), and the 66% effective area averaged less than half (5.4 cm/s², 47.3%).

DISCUSSION

This study is the first to compare how four COP-based sway area parameters - rectangular, 66% effective, 95% ellipse, and convex hull - re-spond to progressively restricted visual conditions during single-leg balance and introduce the convex hull area as a novel metric. Our results confirmed that each sway area parameter produced distinct outcomes depending on visual occlusion levels (F=5.90, p <.001). Among the parameters, the 95% ellipse area demonstrated the highest sensitivity to changes in postural control across visual conditions, followed by convex hull and rectangular area (p <.001). In contrast, the 66% effective area showed the lowest sensitivity, likely due to its exclusion of approximately one-third of the actual COP trajectory. Notably, the 95% ellipse and convex hull area parameters produced statistically comparable estimates of postural sway across all visual conditions, indicating that both metrics respond similarly to varying levels of visual perturbation.

Specifically, our results identified the rectangular area parameter tended to overestimate postural sway by including spatial regions not actually traversed by the COP trajectory. This metric is calculated based on the maximum anterior-posterior and medial-lateral COP excursions [20,33], is prone to inflation from single extreme postural sway fluctuations. Such overestimation contributes to high inter-individual variability and ultimately diminishes its sensitivity to capture subtle changes in postural control [20,34]. In contrast, the 66% effective area parameter consistently underestimated postural sway region by omitting relevant portions of the COP excursion. Although this metric is designed to encompass the main postural sway region, it naturally excludes approximately 34% of the actual COP trajectory [33]. This exclusion may result in overlooked detection of brief but clinically meaningful episodes of postural instability during balance tasks, particularly in patients with impaired postural control or at risk of reinjury. Overall, while traditional sway area metrics such as the rectangular and 66% effective areas offer some clinical value [7,20], their limitations highlight the need for more inclusive and robust alternatives that better reflect the true nature of postural sway during balance tasks. Therefore, to enhance the clinical utility of single-leg balance tests, it is recommended to choose sway area metrics that minimize both over- and underestimation.

The 95% ellipse area has been widely used in previous studies [7,13,20,35] due to its ability to address the limitations of traditional sway area metrics. In this study, its consistent sensitivity was confirmed by capturing significant differences in postural control across various visual conditions compared to other sway area parameters. This parameter is val-ued for its capacity to reduce the influence of outliers and to provide more sensitively estimates of postural sway area [14,20]. Although its sensitivity in detecting subtle postural control differences under partially restricted visual conditions (e.g., SV4, SV6, SV8) may still be limited, it successfully distinguished between two clearly defined visual conditions (eyes open and eyes closed). This finding supports the clinical applicability of the 95% ellipse area in single-leg balance assessment, particularly under the two visual conditions most used to evaluate balance deficits following clinical population. However, its reliance on confidence inter-val assumptions and exclusion of 5% of the COP data may limit its accuracy in capturing the total COP-based sway path [22,23]. These excluded COP data points may represent brief but clinically meaningful episodes of postural instability, particularly in populations with balance deficits. Additionally, the effectiveness of the 95% ellipse area is contingent upon assumptions of normal data distribution and adequate sample sizes [22], which are not always met in clinical or small-cohort studies.

To address this limitation, the convex hull area could offer a more complete representation of postural sway by encompassing the entire COP trajectory without depending on the confidence interval-based ellipse area calculations [24]. Notably, our results revealed no statistically significant difference between the convex hull area and the 95% ellipse area under each visual condition, indicating that these two parameters produce comparable estimates of postural sway. This finding suggests that the convex hull area, despite being a novel metric, may capture postural sway area similarly to the widely used 95% ellipse area. Given that both measures are designed to encompass the majority of the COP trajectory while minimizing the influence of outliers [24,33], their similari-ty in output reinforces the potential of the convex hull area parameter as an alternative for assessing single-leg balance with 95% ellipse area parameter under varying visual conditions. Our findings may have important clinical implications for the standardization of sway area parameters in postural control assessment. Specifically, the novel convex hull area suggest that is possible to serve as an alternative to the tradition rectangular and 66% effective area parameters for capturing subtle changes in postural control. Therefore, the newly introduced convex hull area, alongside the 95% ellipse area, may have potential as a sway area parameter for the early identification of balance impairments and the evaluation of intervention outcomes in clinical populations. To the best of our knowledge, few studies have directly compared COP-based sway area parameters in isolation. Conducting such comparative analyses may help facilitate the standardization of these area metrics by identifying which parameters tend to overestimate or underestimate postural sway, thereby enhancing the consistency of postural control assessments.

This study had some limitations. First, the participants consisted sole-ly of healthy young adults, which limits the generalizability of our findings to other age groups or clinical populations such as patients with musculoskeletal or neurological balance impairments. Second, the single-leg balance tests were conducted in a fixed sequence from easy (full vision) to difficult (no vision) conditions, rather than in a randomized visual condition order. This sequential approach may have affected the learning effect of balance test [36], potentially influencing the accuracy of the results. Therefore, future assessments should consider using randomized visual conditions to minimize potential bias. Finally, in terms of the computational method, the convex hull area was calculated by connecting the outermost points of the COP trajectory [24], which might have included regions not actually traversed by the COP data points, potentially leading to a slight overestimation of postural sway. Therefore, future studies should include larger sample sizes are warrant-ed to validate whether the introduced convex hull area parameter can accurately detect subtle postural control deficits. In addition, more pre-cise formulas should be developed to compute the area metrics by connecting only the boundaries of the actual COP trajectory, thereby im-proving the accuracy and standardization of these area-based parame-ters.

CONCLUSION

In conclusion, our findings demonstrated that 4 COP-based sway area parameters respond differently to progressively restricted visual conditions during single-leg balance. The newly introduced convex hull area parameter shows the potential for detecting subtle changes in postural control under varying visual conditions and, alongside the 95% ellipse area parameter, may serve as an alternative to traditional sway area metrics such as the rectangular and 66% effective areas for evaluating postural control. Future research should validate its clinical applicability in larger and clinical populations and explore the feasibility of incorporating it into standard COP-based area metrics.

Notes

ACKNOWLEDGMENT

The authors would like to express their sincere gratitude to Kyoung Jae Kim from the EVA & Environmental Physiology Laboratory, NASA Johnson Space Center, KBR, for providing valuable support, particularly in data analysis and the creation of a formula for calculating the convex hull area. His expertise and insight have greatly contributed to this study.

CONFLICT OF INTEREST

The authors declare that they do not have conflict of interest.

AUTHOR CONTRIBUTIONS

Conceptualization: SH Nam, KM Kim; Data curation: SH Nam, KM Kim; Formal analysis: SH Nam, KM Kim; Methodology: SH Nam, KM Kim; Project administration: SH Nam, KM Kim, Visualization: SH Nam; Writing - original draft: SH Nam, KM Kim; Writing-review & ed-iting: SH Nam, KM Kim.

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	Descriptions	Formulae
Rectangular Area (cm²)	The bounding rectangular area, which encompasses 100% of the data	A _rect =(x_max-x_min)×(y__max-y__min)
66% Effective Area (cm²)	The effective area, which encompasses approximately 66% of the data	A _effect =π×[Σ((x_i-x_avg)²+ (y_i-y_avg)²)/n]
95% Ellipse Area (cm²)	These measures are based on a calculation of the 95^th percentile ellipse, which encompasses 95% of the data points if the data is normally distributed	A _ellipse =π×√[F·(x²_sd+y²_sd+D)]×√[F·(x²_sd+y²_sd-D)] where D=√[(x²_sd-y²_sd)²+4×cov²]
Convex Hull Area (cm²)	Convex hull area refers to the total area enclosed by connecting the outermost points of the COP trajectory during a balance test. It quantifies the postural sway by measuring the area within the COP trajectory, indicating overall postural performance. A larger area indicates poor postural stability	A _convex =1/2×\| Σ (x_i y_i+₁-x_i+₁ y_i)+(x_n y_₁-x_₁ y_n) \|