Board motion analysis and parameters determination.

The motion of the balance board was analyzed by computing the vector orthogonal to the board plane (board normal vector; in Fig 1B). To evaluate the level of stability of the board, the angle α between the normal vector of the board plane and the normal vector of the horizontal plane (that is parallel to the vertical axis; in Fig 1B) was determined. The angle α can be considered the parameter more directly associated with the balance stability: as the postural performance improves the board plane approximates the horizontal plane, and the angle α reduced. The angle α was determined as an absolute value resulting from any combination of pitch and roll board rotations or as separate pitch and roll rotations that are assessments of AP and ML board sways, respectively.

In addition to the angular amplitude measures, the spatial displacement of the board across the horizontal plane and along AP and ML directions was determined. To obtain these measures, the coordinates of the horizontal directional components of the normal vector were computed and the trajectory of the board normal vector over the horizontal plane was traced.

The angle of the board about the vertical axis (yaw board rotation) was obtained by measuring the angle of oscillations of one marker around its initial position before the trial started.

The normal vector computation was performed by using the Cartesian equation of a plane: (1) where x, y, z are the 3D coordinates of an arbitrary point on the plane measured with respect to the reference system configured for the motion capture apparatus (Fig 1B); A, B, C are the coefficients representing the 3D directions of a normal vector () for the plane: ; D = −Ax₀ − By₀ − Cz₀, where x₀, y_0, z₀ are the 3D coordinates of the normal vector position.

The angle of the board with respect to the horizontal plane was determined by computing the directional coordinates A, B, C, of the normal vector given three points lying on the plane. To select the three points among the 8 markers applied on the board, the trajectories of each marker was tracked, and the 3 best signals (with less missing values) were chosen.

The directional coordinates for an equation of the plane passing through the points (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃) are given by the following determinants: (2)

The direction of the normal vector for the horizontal plane () was determined by capturing the coordinates of the three points when the board was on the floor without load, and after the checking of the horizontal alignment by means of a bubble level. Instead, the normal vectors for the board planes that follow one another over the 20-sec trial (), were computed by the coordinates captured bin-by-bin. To simplify the computation of the board angle, the normal vectors and were normalized for their lengths obtaining the unit normal vectors and . Thus, for each data sampling, the current angle (α) of the board with respect to the horizontal plane was computed as follows: (3)

Angle amplitude measures were converted from radiant to degree.

The analysis of the spatial displacement of the board normal vector over the horizontal plane by using the two directional components A and B, was the basis to determine the following parameters: total area covered by the board normal vector computed as the 95% confidence ellipse (see [36]); shape of the ellipse obtained by computing the minor to major axis ratio; total length travelled by the board normal vector (sway path) across the horizontal plane and along AP and ML directions; root mean square (RMS) calculated for each time series associated with AP and ML directions.

In addition to linear measurements of postural stability, we computed the Approximate Entropy (ApEn) and the Fractal Dimension (FD) as non-linear measures to explore the temporal dynamics of the signals along AP and ML directions, and the structure of the planar trajectory tracked by the board normal vector.

Approximate Entropy is a probability statistic that calculates the likelihood that a template pattern repeats over time. It is frequently being used to estimate the variation of regularity in time series associated with physiological signals [37, 38], including postural data [7, 32–35, 39, 40]. According to preliminary tests and the protocols established in former studies, input parameters for the ApEn calculation were the length of the time series (4000 points), a pattern length of 2 data points, a tolerance window normalized to 0.2 times the standard deviation of individual time series, and a lag value of 10. For a detailed explanation of the mathematical procedures to calculate the ApEn see Pincus [37].The outcome of the ApEn calculation ranges between 0 and 2, with a decreasing of regularity in the signal as the value moves toward the highest edge. We obtained a single ApEn value for each time series associated with AP and ML directions.

The Fractal Dimension (FD) was computed using the algorithm described by Prieto et al., [36], who quantified the level of geometrical complexity of a planar trajectory as follows: (4) where N is the number of data points (N = 4000); d = (2a ⋅ 2b)^1/2 where a and b are the major and the minor axes of the 95% confidence ellipse, respectively; Sway path is the total length travelled by the board normal vector. Two-dimensional FD ranges from 0 to 2, with the value increasing when the trajectory is more complex.

To explore the frequency domain of the postural sway, the Power Spectral Density (PSD) was performed on the unfiltered AP and ML time series using the multitaper estimation method, as suggested by Prieto et al., [36]. This analysis was carried out sampling the frequency spectrum in bins of 0.025 Hz. The first bin was removed and, since no discernable spectral peaks were visible above 1.5 Hz, we collected signals within a range of frequencies between 0.025 and 1.5 Hz. The total area of the PSD and the Mean Power Frequency (MPF) were calculated for the power output in AP and ML directions. MPF represents the mean frequency contained within a power spectrum and was determined as follow: (5) where f represents frequencies in the signal and P is the amplitude of the PSD at each frequency.

All the computations were performed using a customized MatLab R2012a code (Mathworks, Natick, MA, USA).

Parameters determination for the static stance.

The center of pressure (COP) of static stance was computed from forces and torques measured by the force platform and elaborated by the software Sway (BTS Garbagnate Milanese MI, IT). To identify similar postural patterns between quiet stance and stance on the oscillating board, we carried out measurements of sway path, RMS, ApEn, and MPF for the COP along AP and ML directions. The determination of these parameters was performed following the processes described in the previous section, replacing the unit normal vector trajectory with the COP trajectory.

Statistical analysis.

For each trial the mean and the variability, expressed as Standard Deviation (SD), of each parameter were determined participant by participant, and grand averages over the 10 participants were computed.

Statistically significant changes across sessions and trials were estimated using a two way Analysis of Variance (ANOVA) with repeated measures, considering sessions and trials as within subject factors. Statistical differences between the AP and ML directions were evaluated by a three way ANOVA with repeated measures, with sessions, trials and directions as within subject factors. The critical value of F was adjusted applying Greenhouse-Geisser correction, which produces a p-value more conservative. This procedure corrects the repeated-measures ANOVA with respect to a possible violation of the sphericity assumption, that is, the variance of the differences among all combinations of independent variables must be equal. Post hoc tests with Bonferroni correction for multiple comparisons were conducted to identify local significant differences between sessions or trials. The level of statistical significance was set to P < 0.05.

The sample size, to detect differences in stability and structural parameters over the sessions, was determined a priori based on preliminary data acquired from 5 participants. Power calculations for within-subjects designs were performed using G-power (version 3.1.9.2; [41]) by taking specification as in Cohen [42] and giving partial eta squared (η²_p) as input. Power analysis revealed that a sample size of 7 was required to achieve a power of 0.95 for 10 out of 12 parameters, while only for the sway path (2D path and along AP and ML directions) a sample size of 10 was required to achieve a power of 0.85. On this basis, we deemed that 10 participants was a sufficient quantity for the results to be meaningful.

The magnitude of significant differences (effect size) for the multivariate within-subjects ANOVA statistics was estimated by using η²_p, which describes the percentage of variance of the dependent variable attributed to the independent variables of interest. For the post-hoc paired tests, the effect size was determined by using Hedges’ g_av, which represents a correction for bias of Cohen's d_av (the standardized mean differences based on the average standard deviation of both repeated measures). The effect size computations was based on the recommendation reported by Lakens [43].

Statistical analysis was performed using SYSTAT, version 11 (Systat Inc., Evanston, IL, USA) and Matlab version R2012a (Mathworks Inc, Natick, MA, USA).

Anisotropic stability between AP and ML directions.

The postural performance showed a parallel improving in AP and ML directions, but several spatial and temporal features of the board fluctuations followed an asymmetric distribution between the two directions: angular rotation amplitude, motion variability and total PSD were higher in AP than in ML direction.

Generally, the discrepancy of stability between AP and ML directions depends on the combination of joints involved in the balance task. Based upon the model proposed for the first time by Nashner and McCollum [47] and supported by several other authors [4, 24], humans use two discrete joint strategies: the ankle strategy where the body behaves as a single segment-inverted pendulum by producing muscular torques around the ankle, and the hip strategy, with the body moves as a double-segment inverted pendulum by rotations of hip and ankle in opposite directions. Given the ankle anatomy, the ankle strategy constrains the body sway mainly along the sagittal plane increasing the instability in the AP direction, while, as the hip strategy is used, the multiaxial rotation at hip joint may perturb the body along both the directions. However, as the posture passes from quiet, side-by-side standing, to more perturbed conditions, the ankle and hip strategies may be concurrently activated, producing a less discrete postural behavior [2, 5, 6, 25, 48, 49]. Some authors deemed that ankle and hip strategies are inadequate in representing a general model of upright standing, suggesting that the control variable for the posture adaptations is the level of coordination dynamics between joints and not the motion of a single joint [50, 51]. Moreover, other joints, such as the knee, may show a significant contribution for both quiet and perturbed stance [51–53].

In line with this view, the multiaxial perturbation and the number of body segments used to perform our task would suggest that a discrete selection of ankle or hip strategy is inadequate to explain the anisotropic behavior between AP and ML directions. Rather, a more plausible explanation may be achieved by considering patterns of interjoint coordination and muscle synergies able to constrain most of the body oscillations along the AP axis.

During the board fluctuations along AP direction, the body weight is distributed between the heel and the toe, and the board motion is controlled by the activity modulation of flexor and extensor muscles of the ankle, knee, and hip joints. Instead, when the board oscillates along ML direction the body alternatively loads one foot while unload the other. In this case, ankle and knee rotations around anterior-posterior axis are limited by their anatomical constrains, and the load/unload behavior mainly depends on the muscle modulation of the hip abductor/adductor activity. Such a synergy for the control of hip motion was proposed by Winter et al., [24] to explain differences between AP and ML balance during quiet standing with different feet configurations. Flexor/extensor and abduction/adduction modulations of ankle, knee and hip muscles were found also during postural adjustments in response to surface translation along different perturbation directions [6, 49]. We acknowledge that our data are inadequate to support interpretation based on muscle dynamics since no electromiographic recording was performed. However, the intrinsic stability of ankle and knee joints in ML direction and the control of abduction/adduction synergy to limit ML oscillations at hip joint may be a parsimonious functional schema to explain the predominant fluctuations along AP direction observed in this study.

Although this interpretation suggests an intrinsic contribution of joint mechanical constrains to the anisotropic stability observed between the two orthogonal directions, this behavior may also arise from memorized strategies produced during previous postural experiences and adapted to the novel task performed in the current study. In fact, large body oscillations in the AP direction are common in daily living activities, such as taking a step or standing up from the chair. The results reported for the static posture performed by our participants confirm the data from other studies [24, 36, 54] and support the presence of a comparable structure between quiet standing and the stance on the balance board. Moreover, the AP-ML discrepancy was also replicated during postural perturbations associated with stability of the support surface [2, 4, 5, 25, 26], changes in sensory information [3, 48], and changes in demands of precision aiming [27, 55].

A possible transfer of postural strategy can also be supposed considering that the value of parameters as the ellipse shape or the rotation angle around the vertical axis, remained unchanged over the training time even though the amplitude of board oscillations around the horizontal plane decreased.

Further support to the idea that a common schema may be shared across diverse postural contexts is provided by the evidences that few muscle synergies may account for different perturbation directions and different levels of instability [49, 56], and that upright standing control may depend on the formation of internal models [54, 57–60]. An internal model is a set of neuronal encoded rules aimed to predict the body motion in relation to the physical environment dynamics. For example, the upright standing on a stable surface is controlled by using an internal representation of the effects of the gravitational torque on the body segments. When this type of relationship is learned in a particular context, it can be easily transferred in a novel condition by integrating the model with the variables related to the new physical environment [61]. In the case of our task, the learning process might have been accomplished by encoding the dynamics of the board movements and, by using this information, an updating of a memorized internal model was elaborated. It is possible that the rapid early improvement of the performance could partially depend on the use of these memorized structures.

Changes in spatio-temporal structure and frequency domain.

Although the early fast phase of learning could be compatible with the functional frame discussed in the previous section, different explanations need for the changes observed for nonlinear (ApEn and FD) and frequency domain (MPF) parameters during the retention session. In fact, while stability measures maintained similar values, passing from the second to the retention session for both the directions, the structure of the temporal sway variability and the frequency content of the signal changed in the AP direction during the retention test.

Approximate entropy estimates the level of regularity of the signal in a time series, with high values indicating a more irregular motion and, therefore, a more complex response organization [37, 38]. The temporal modifications detected by this technique may depend on a more strict integration between sensory and motor elements that control upright posture. For example, proprioceptive, visual and vestibular inputs could be less associated during practice sessions, producing simple relationships between the sensory input and the motor outcome. As the linkages among the sensory channels increase, the resulting signal becomes less predictable and more complex. Similarly, the formation of new internal representation of the motor commands may be a source of complexity, since more elements are increasingly included to improve the adaptation of the motor response to the environmental requirements. Increasing of both the sensory integration and motor adaptation matches with what a postural task, such as balancing on a multiaxial board, needs to be learned. This functional schema is in line with many studies focusing on ApEn as a tool to capture the dynamics of the postural adaptations. Increase of ApEn in COP time series was observed during postconcussion recovery of postural stability [32], after training on a dynamic platform in patients with bilateral labyrinthine deficit [39], and as a consequence of the effects of secondary cognitive task on postural control [33]. In addition, ApEn values of COP were found higher in health participants compared with patients with Ehlers-Danlos syndrome [34] or Multiple Sclerosis [40]. In all of these cases, the increase of ApEn was parallel with the need to increase the complexity of the postural adaptation. Likewise, the increase of FD, also observed after the week pause, may be linked to a more complex spatial structure of the board motion.

Many authors found that the increase of ApEn or homologues parameters was focused on the AP axis [7, 32, 33, 35, 55, 62] and that this direction-dependent augmentation of complexity may depend on the level of task difficulty as suggested by Balasubramaniam et al. [55]. In fact, as the difficulty of the task increases, more joints need to be coordinated in the AP than in the ML direction, and more alternative strategies can be explored to cope with AP instability.

This line of considerations is also supported by the higher values of FD detected in the retention session with respect to the training sessions. As the FD value increases, the board trajectory gains a more complex geometrical structure. Interestingly, Duarte and Zatsiorsky, [63] reported that the level of FD observed during unconstrained upright bipedal posture, was greatly stable for long time, indicating a specific schema in the structure of static stance. The strong variation of FD observed in the current study contrasts with this stability, reinforcing the idea that novel postural structures took place during the first week of the consolidation process.

Further insights on the structure of the postural adaptations associated with the control of the multiaxial balance board may be provided by the modifications observed for the MPF. Some authors reported that changes in frequency band may be indicative of the type of sensory channel involved in the balance task: low frequencies (0–0.3 Hz) are linked to visual control, the medium-low frequency band (0.3–1 Hz) is associated with vestibular regulation, and the medium-high frequency band (>1 Hz) mostly account for proprioceptive and muscular activities [28, 29, 64]. Other studies focused on the possibility that the frequency content may be modulated by changes in the dynamic strategy of postural control [3, 30, 31].

A possible rearrangement of the coordination dynamics of the ankle, knee and hip motion to deal with AP instability may enhance the contribution of proprioceptive information [64, 65], which in turn would increase the MPF. However, the frequency increasing observed in this work (from 0.15 to 0.19 Hz) disagrees with the data reported in some studies indicating that the contribution of proprioception to balance control is associated with frequencies above 1 Hz [28, 29, 64]. On the contrary, the possibility that a new movement strategy could influence the frequency of sway oscillations reported in the current work is more in accord with the results of Fransson et al., [3], who found that fast movements are linked to frequencies above 0.1 Hz, while smooth changes in the body sway are associated with lower frequencies. Interestingly, a reduction of the body sway along AP direction was found parallel to an increase of frequency during balance improvement determined by visual biofeedback [31] or by an increase of the support instability [30]. Similarly, in this work the board sways over the AP direction moved from an initial phase, with large amplitude and low frequencies, to a final consolidation phase, with smaller oscillations and higher frequencies. Thus, we deemed that most of the contribution to the MPF increasing observed in AP direction may depend on the formation of new kinematic patterns rather than changes in sensory information.

Changes in spatio-temporal structure and frequency band showed during the retention session suggest that something more than the only amount of exercise influenced the long-term postural adaptation; that is, processes occurred during the offline periods refined and further improved the postural response. Many studies analyzing this issue found that memory consolidation occurs within a critical time frame following the practice [15], with an additional consolidation effect of the sleep [16]. Depend on the context this timing window may span from seconds [17] to several hours [15, 18], and one sleep night may be enough to influence the post-training improvements [16]. Although, these factors might have influenced the consolidation process during the week pause after the end of training, the limitation of our experimental design prevents appropriate interpretation about the role played by these factors in determining the behaviors observed in the current study.

Overall, while the comparison of amplitude and variability changes in AP and ML directions over the course of the learning process suggests that postural control evolves on the basis of previous experienced strategies, later, after the week pause, the changes in ApEn, FD and MPF may represent signals indicating the formation of new stance strategies aimed to further stabilize the learned postural performance.