Impact of Visual Disturbances on the Trend Changes of COP Displacement Courses Using Stock Exchange Indices

: This work aims to de ﬁ ne a strategy for maintaining a vertical posture of the human body under conditions of con ﬂ icting sensory stimuli using a method of trend change analysis. The investigations involved 28 healthy individuals (13 females, 15 males, average age = 21, SD = 1.3 years). Measurements were conducted with eyes opened and closed and in the virtual environment with two sceneries oscillating at two frequencies. Values in the time domain were calculated—the mean center of pressure (COP) velocity and movement range in the AP direction—as well as values based on the moving average convergence divergence (MACD) computational algorithm—the trend change index (TCI), MACD_dT, MACD_dS, and MACD_dV. After dividing the analysis into distinct time periods, an increase in TCI values was identi ﬁ ed in the oscillating scenery at 0.7 and 1.4 Hz during the 0.5–1 and 0.2–0.5 s time periods, respectively. Statistically signi ﬁ cant di ﬀ erences were observed between measurements with an oscillation frequency of 0.7 Hz and those with an oscillation frequency of 1.4 Hz during the 0.2–0.5 s and 0.5–1 s periods. The use of stock exchange indices in the assessment of the ability to keep a stable body posture supplements and extends standard analyses in the time and frequency domains .


Introduction
Maintaining a stable body posture results from the constant control and corrections performed by many cooperating systems, including the vestibular system and deep sensibility [1].The nervous system constantly stimulates muscles that compensate for momentary disturbances and maintains the center of mass within the boundaries of stability [2,3].Posture stability tests are devised to determine values based on the coordinates of the subsequent center of foot pressure (COP) locations.Commonly analyzed values that describe the ability to maintain balance include COP velocity, COP ellipse surface area, and COP movement ranges in the antero-posterior (AP) and medio-lateral (ML) directions.Analyzing the above-mentioned values, it is assumed that the higher these values, the less likely that one can maintain a stable body posture [4].The above-mentioned analyses in the time domain are supplemented with analyses in the frequency domain.Frequency analyses based on calculations of the fast Fourier transform (FFT) make it possible to determine the cyclic components of the analyzed signal and ascertain whether a cyclic stimulus upsetting balance translates into the cyclicity of COP or center of mass (COM) movements [5,6].Such analysis also finds application in the case of tests performed under conditions of conflicting sensory stimuli.In such situations, individual senses receive contradictory information and a given person (test participant) is affected by stimuli-both in the real-life environment and virtual reality-which, directly by physical push or indirectly by visual stimuli, unbalance the person [1,2,7,8].Research in the virtual environment can be mentioned as an example of measurements under sensory conflict conditions where oscillating virtual scenery is used with the still, real floor [1].Relevant literature also describes other methods to determine the ability of the human body to maintain balance.Popular methods include probabilistic analyses based on entropy [9] and frequency analyses using the wavelet distribution [10,11].The latter is specifically applied to the analyses of low frequencies of COP movements.
The choice of analysis tools depends on the conditions of the conducted tests and the information researchers require from the conducted tests.Analyses in the time and frequency domains enable a complex and full evaluation of the ability to keep balance [12,13].Frequency domain analyses are a natural extension of time domain analyses.The frequency analyses described in scientific publications usually determine the impact of cyclic external disturbances on the ability to maintain balance by checking if cyclic components are part of the movement and whether the following scenery is a dominant one [1,5].To deepen the analyses related to the determination of the cyclicity of COP movements, it is necessary to use a method that would detect momentary, non-cyclic changes occurring during the whole analysis [14,15].Such a possibility is provided by trend change analysis making use of stock exchange indices [16,17].The method of stock exchange indices may be used both under static and dynamic conditions and, as in the analysis of COP movements, during which the patient wears a virtual reality (VR) projection headset.The proposed methodology for the analysis of trend changes based on determining the changing points of the COP displacement signal trend allows us to supplement traditional analysis methods with additional information related to determining the strategy of maintaining balance by a human.The algorithm for determining trend change points is based on time domain analysis, so the results are not as noisy as in the case of FFT analyses and spectral leakage.This procedure enables us, for a certain frequency range, to detect both cyclical components and non-cyclical changes [16].
The objective of this work is to develop a method of analysis for maintaining the vertical position of the human body under the conditions of conflicting sensory stimuli using an innovative method of trend change analysis.This work is a continuation of previous research [16] regarding the assessment of human balance under conditions of conflicting sensory stimuli-oscillating virtual scenery and stable floor.
This paper investigates the application of stock exchange indices connected with the evaluation of stock rate courses to study the ability of the human body to maintain balance in an oscillating virtual reality.The performed analyses may confirm and extend the usability of stock exchange indices as a tool to supplement standard analyses for balance assessments [18].
To maintain a stable body posture, it is necessary to constantly correct COP and center of mass (COM) positions.Analysis using stock exchange indices will allow us to determine the number of posture corrections, the time and distance between these corrections, and the speed of movement of the COP between these corrections [19].We hypothesize that a decrease in the frequency of posture corrections, coupled with an increase in the distance between subsequent points of the trend change, may indicate an increased risk of falling.The proposed method, based on the analysis of posture corrections, will allow for the detection of the impact of changes in the frequency of visual disturbances or different sceneries on postural changes.If validated, this method could effectively assess temporary postural changes.We also assume that changes in the total number of trend changes and in particular time periods may indicate dysfunctions that have an impact on the balance-keeping ability.

Measurement Stand
The measurement stand consisted of a stabilographic platform (WinFDM-S, Zebris, Isny im Allgau, Germany, 100 Hz sample frequency, 2560 tensiometer sensors, 34 cm × 54 cm sensing area) and a head-mounted display (HMD) Oculus Rift set used for the projection of three-dimensional images.The three-dimensional sceneries were developed in the Unity 3D environment (Figure 1A,B).
The measurement stand consisted of a stabilographic platform (WinFDM-S, Zebris, Isny im Allgau, Germany, 100 Hz sample frequency, 2560 tensiometer sensors, 34 cm × 54 cm sensing area) and a head-mounted display (HMD) Oculus Rift set used for the projection of three-dimensional images.The three-dimensional sceneries were developed in the Unity 3D environment (Figure 1A,B).The 'closed space' scenery (Figure 1A) consisted of a furnished room, in which objects were seen by the tested individual at ~3 m, whereas the 'open space' scenery (Figure 1B) showed a desert, where objects were located at ~100 m.During the tests, the scenery oscillated in the AP direction at a constant frequency.Oscillations were presented by moving the scenery in the AP direction, taking into consideration a slight rotation of the scene by 0.5 degrees [1].The scenery oscillations were perceived by the subject as the movement of the entire environment.The oscillation amplitude was set at 30 cm, whereas the oscillation frequency was set following the procedure described below.

Study Group
The investigations involved 28 individuals (13 females and 15 males) with an average age of 22 years (1.3 standard deviation (SD)), mean body mass of 67.5 kg (12 SD), and an average height of 173.6 cm (8.8 SD).All participants took part in the measurements conducted in a real-life environment.A group of 12 individuals (7 females and 5 males, average age 22.5 years (0.5 SD), mean body mass 65.1 kg (13.1 SD), average height 171.9 cm (8.8 SD)) was subjected to measurements in the VR 'closed space' scenery, while 16 participants (6 females and 10 males, average age 21.7 years (1.6 SD), mean body mass 69.3 kg (10.8 SD), average height 174.9 cm (7.3 SD)) were tested in the VR 'open space' scenery.Health problems related to maintaining balance, for example, neurodegenerative diseases or labyrinth problems, and obesity (body mass index; BMI > 30) were considered as exclusion criteria.This study was first approved by the Ethics in Research Committee of the Academy of Physical Education in Katowice (protocol number 5/2020).Each participant gave verbal consent to the measurements.The 'closed space' scenery (Figure 1A) consisted of a furnished room, in which objects were seen by the tested individual at ~3 m, whereas the 'open space' scenery (Figure 1B) showed a desert, where objects were located at ~100 m.During the tests, the scenery oscillated in the AP direction at a constant frequency.Oscillations were presented by moving the scenery in the AP direction, taking into consideration a slight rotation of the scene by 0.5 degrees [1].The scenery oscillations were perceived by the subject as the movement of the entire environment.The oscillation amplitude was set at 30 cm, whereas the oscillation frequency was set following the procedure described below.

Study Group
The investigations involved 28 individuals (13 females and 15 males) with an average age of 22 years (1.3 standard deviation (SD)), mean body mass of 67.5 kg (12 SD), and an average height of 173.6 cm (8.8 SD).All participants took part in the measurements conducted in a real-life environment.A group of 12 individuals (7 females and 5 males, average age 22.5 years (0.5 SD), mean body mass 65.1 kg (13.1 SD), average height 171.9 cm (8.8 SD)) was subjected to measurements in the VR 'closed space' scenery, while 16 participants (6 females and 10 males, average age 21.7 years (1.6 SD), mean body mass 69.3 kg (10.8 SD), average height 174.9 cm (7.3 SD)) were tested in the VR 'open space' scenery.Health problems related to maintaining balance, for example, neurodegenerative diseases or labyrinth problems, and obesity (body mass index; BMI > 30) were considered as exclusion criteria.This study was first approved by the Ethics in Research Committee of the Academy of Physical Education in Katowice (protocol number 5/2020).Each participant gave verbal consent to the measurements.

Experimental Procedure
The experimental procedure encompassed tests in the real-life environment, involving standing with opened eyes (OE) and standing with closed eyes (CE), as well as tests in the virtual environment (Figure 2).The measurements in VR were conducted by presenting the open space scenery and closed space scenery oscillating at frequencies of 0.7 Hz and 1.4 Hz.The selection of frequency values was based on previously conducted research, which proved that during the application of such values and the HMD headset, the oscillating scenery had a strong impact on the tested individuals, such as the movement of following the scenery and increasing the values of basic stabilographic quantities [1,16].The subjects were asked to take off their shoes and stand on the measurement platform in an upright position with their arms crossed on their chest and their vision focused on a point in the form of a dot on the wall located in front of them.The subjects' task was to simply stand still during all measurements.First, measurements in the real-life environment were performed.Then, measurements were taken in the virtual environment while wearing 3D goggles.Measurements in the virtual environment took place directly one after another, without breaks.A measurement in the oscillating scenery at a frequency of 0.7 Hz (0.7), a measurement in the oscillating scenery at a frequency of 1.4 Hz (1.4), a measurement in the oscillating scenery with the change in oscillation frequency from 0.7 Hz to 1.4 Hz (0.7/1.4), and a measurement in the oscillating scenery with the change in oscillation frequency from 1.4 Hz to 0.7 Hz (1.4/0.7) were all taken (Figure 2).The measurement series was performed once for each participant.The change in the oscillation frequency occurred at the half-time of the measurement.Each measurement lasted 60 s.In the measurements with the oscillating scenery, the movement of the scenery began in the 15th s of the measurement and The measurements in VR were conducted by presenting the open space scenery and closed space scenery oscillating at frequencies of 0.7 Hz and 1.4 Hz.The selection of frequency values was based on previously conducted research, which proved that during the application of such values and the HMD headset, the oscillating scenery had a strong impact on the tested individuals, such as the movement of following the scenery and increasing the values of basic stabilographic quantities [1,16].The subjects were asked to take off their shoes and stand on the measurement platform in an upright position with their arms crossed on their chest and their vision focused on a point in the form of a dot on the wall located in front of them.The subjects' task was to simply stand still during all measurements.First, measurements in the real-life environment were performed.Then, measurements were taken in the virtual environment while wearing 3D goggles.Measurements in the virtual environment took place directly one after another, without breaks.A measurement in the oscillating scenery at a frequency of 0.7 Hz (0.7), a measurement in the oscillating scenery at a frequency of 1.4 Hz (1.4), a measurement in the oscillating scenery with the change in oscillation frequency from 0.7 Hz to 1.4 Hz (0.7/1.4), and a measurement in the oscillating scenery with the change in oscillation frequency from 1.4 Hz to 0.7 Hz (1.4/0.7) were all taken (Figure 2).The measurement series was performed once for each participant.The change in the oscillation frequency occurred at the half-time of the measurement.Each measurement lasted 60 s.In the measurements with the oscillating scenery, the movement of the scenery began in the 15th s of the measurement and lasted 30 s.All analyses took into consideration a period from the 15th to the 45th s, in compliance with the description contained in the chapter 'Analyzed Quantities'.

Analyzed Quantities
The analysis involved displacements of the COP in the AP direction at the time of the middle 30 s of the test with the frequency change (15 s before and 15 s after the change), obtaining the courses of 0.7_before and 1.4_after from the 0.7/1.4measurement as well as courses 1.4_before and 0.7_after from the 1.4/0.7 measurement.In the case of the OE and CE measurements, the time of the middle 15 s was analyzed.Conversely, the 0.7 and 1.4 measurements used the first 15 s (0.7_1, 1.4_1) and the second 15 s (0.7_2, 1.4_2) of the test for analysis.The analyses were performed using the MATLAB R2021b software program.The signal from the platform was filtered with a Butterworth low-pass filter.The pass frequency of the filter was set to 7 Hz.Basic stabilographic values were determined, namely the COP velocity and the COP movement range in the AP direction.For each course, the trend change index (TCI) was calculated [18,20,21].The TCI defines the number of trend changes, which is the number of intersections of the signal resulting from the computations of the algorithm: moving average convergence divergence (MACD) (Equations ( 1)-( 3)).
To calculate TCI values, the MACD line for the COP signal was determined by computing the difference between two exponential moving averages (EMAs) with lengths of 12 and 26 samples, as per Equations ( 1) and ( 2): where EMA COP,12 -faster exponential moving average for COP signal, and EMA COP,26 -slower exponential moving average for COP signal.
where p 0 -ultimate value, p 1 -penultimate value, p N -value preceding N periods, N = number of periods, and α = a smoothing coefficient equal to 2/(N + 1).Moving on to the subsequent phase, the signal line was calculated as an EMA with a length of nine samples from the MACD line signal, in accordance with Equation (3): The TCI was presented as the total number of all trend changes for the analyzed measurement and the total number of trend changes segmented into the following time periods: These time periods denote the times after which the subsequent trend change occurred after the previous one.Based on the MACD algorithm, the following values were also computed: the mean distance between subsequent points of the trend change (MACD_dS), the mean time between subsequent points of the trend change (MACD_dT) (Figure 3), and the mean velocity of changes of displacements between subsequent points signifying trend changes (MACD_dV).

Statistical Analysis
Statistical analysis was performed using the MATLAB R2021b software program.The compared values were evaluated using the Shapiro-Wilk test to check for the occurrence of normality in the distribution.The results did not confirm the occurrence of normal dis-

Statistical Analysis
Statistical analysis was performed using the MATLAB R2021b software program.The compared values were evaluated using the Shapiro-Wilk test to check for the occurrence of normality in the distribution.The results did not confirm the occurrence of normal distributions in all sub-groups.Therefore, medians are presented in the diagrams and non-parametric tests were used.
In the first stage of comparative analysis, comparisons were made between the results calculated for the group of people assessed in the closed scenery and the group of people tested in the open scenery.The Mann-Whitney U test was used for the analysis, considering different group sizes.Comparisons were made for all calculated values separately and no statistically significant differences were found (p < 0.05, effect size d > 0.7).
Due to the lack of significant differences, it was decided to combine the groups into one.For all persons, the following values were determined: COP velocity, COP movement, range of COP motion in the AP direction, TCI, MACD_dT, MACD_dS, and MACD_dV, and then for all parameters, the differences between subsequent tests were examined (OE, CE, 0.7_1, 0.7_2, 1.4_1, 1.4_2, 0.7_before, 0.7_after, 1.4_before, and 1.4_after).To verify whether there were statistically significant differences in the case of the analyzed groups, the ANOVA Friedman test was conducted followed by the pairwise Wilcoxon post hoc test with Holm correction.All performed tests obtained high test power.

Results
The values were obtained based on the algorithm calculating the MACD index.No statistically significant differences were found in any groups for all of the analyzed values between the measurements of open and closed space sceneries.Therefore, the obtained values were merged into one group.The results were divided into three groups: standard values in the time domain and values computed based on the MACD algorithm, including MACD_dT, MACD_dS, MACD_dV, and TCI, with division into time periods.

Data Analysis in Time Domain
The diagrams below (Figure 4A,B) present the medians of the stabilographic values in the time domain-the mean COP velocity in the AP direction and the range of COP movement in the AP direction.
The values of the COP velocity in the AP direction (Figure 4A) increased statistically significantly after a participant closed their eyes and after the introduction of disturbances in VR.Statistically significant differences were present while comparing the OE measurements with measurements using VR and while comparing the CE measurements with tests in the virtual environment, except for 1.4_2, 0.7_before, and 1.4_before.No statistically significant differences occurred in the comparison of values obtained during the measurements conducted in VR.The diagram (Figure 4B) shows an increase in the values of the COP movement range in the AP direction with the application of disturbances in VR in comparison with the values obtained in the real-life environment.An increase occurred in the case of the median values, interquartile distribution, and data distribution.In the case of the median value, statistically significant differences were observed between the OE measurements and the measurements performed in VR, except for 1.4_2, 0.7_before, and 1.4_before.An analogous situation occurred between the CE measurements and measurements with the oscillating scenery 0.7_1.4 and 1.4_1.

Trend Change Index
The diagrams below (Figure 5A-D) present the medians of the TCI value.Table 1 presents the p-values obtained for the comparison of the TCI values.
In the diagram presenting the TCI values for individual measurements (Figure 5A), one can observe that the TCI value obtained for the measurements using the oscillating scenery at a frequency of 1.4 Hz was at a similar level to the OE and CE measurements.The TCI values in the case of disturbances at a frequency of 0.7 Hz were lower than the values obtained in other measurements.The data distribution was also noticeably higher.The comparison of the OE and CE measurements did not reveal any statistically significant differences.Statistically significant differences were observed when comparing the OE test in a real-life environment to measurements in the virtual environment for the case of the oscillating scenery at a frequency of 0.7 Hz-both before (0.7_before) and after (0.7_after) the change in frequency.However, in the case of the CE test, statistically significant differences did not occur except for the oscillating scenery experiment at a frequency of 0.7 Hz after the change in frequency (0.7_after).When comparing the tests conducted in VR, statistically significant differences were found only in experiments where the frequency of the oscillating scenery changed from 1.4 Hz to 0.7 Hz.  Figure 5B shows the TCI values obtained for the period of 0-0.2 s.The introduction of disturbances into VR decreased the values of the median TCI in this period.A decrease in the median values was noticeable in the case of higher frequency oscillations in comparison to those with a lower frequency.Based on the diagram presenting the TCI values for the period of 0.2-0.5 s (Figure 5C), one can observe that higher values of the median occurred in the measurements using the scenery oscillating at a frequency of 1.4 Hz.The median values in the case of disturbances at a frequency of 0.7 Hz were similar to the OE and CE values.For the period of 0.5-1 s, the highest values were observed in the VR tests with disturbances at a frequency of 0.7 Hz (Figure 5D), whereas the lowest values were observed at a 1.4 Hz frequency.
When comparing OE and CE measurements, no statistically significant differences were observed.By contrast, statistically significant differences were observed between the results obtained in the real-life environment and those in the virtual environment for all time periods in most cases.From 0-0.2 s, statistically significant differences were observed between measurements 0.7_1 and 0.7_2, 1.4_1 and 1.4_before, and 0.7_before and 1.4_after.From 0.2-0.5 s, statistically significant differences were found between each measurement in which the oscillation frequency of 0.7 Hz was used and the measurements with the oscillation frequency of 1.4 Hz.A similar trend was observed for the 0.5-1 s period.

MACD_dS, MACD_dT, and MACD_dV
The next stage of the analysis involved the computation of the following values: MACD_dS, MACD_dT, and MACD_dV.The medians of these three values are presented in the diagrams below (Figure 6A-C).Analyzing the MACD_dS values (Figure 6B), one can notice a significantly increase in the obtained values in the VR tests in comparison with the measurements taken in the real-life environment-both in the median values and the interquartile distribution of the data.No statistically significant differences were found when comparing the OE and CE tests.For the real-life environment and VR results, statistically significant differences were observed between the OE tests and all measurements in the virtual environment as well as between the CE tests and the 0.7_1, 0.7_2, 1.4_1, 0.7_before, 0.7_after, and 1.4_after measurements.When comparing the measurements obtained using VR between individual tests, no statistically significant differences were found.
In the case of the analysis of the MACD_dT values (Figure 6C), significantly higher values were obtained for the measurements conducted at a frequency of 0.7 Hz.Statistically significant differences were noted while comparing the measurements in the real-life environment (OE and CE) and the 0.7_after, 1.4_before, and 1.4_after measurements.
Figure 6A presents the diagram of the median MACD_dV values for individual measurements.Importantly, the closure of eyes increased the MACD_dV values.A similar trend took place in the case of the introduction of VR; the MACD_dV values were higher in the measurements with the oscillating scenery.Also, an increase in the data distribution was observed in the 0.7_after and 1.4_after tests in relation to measurements 0.7_before and 1.4_before.The analysis of the MACD_dV values did not reveal any statistically significant differences in the OE and CE tests.When comparing the values obtained in the real-life environment and the virtual environment, statistically significant differences were observed between OE and all measurements using the virtual scenery, as well as between CE and the 1.4_1, 0.7_1, 0.7_2, and 1.4_after measurements.No statistically significant differences were found when comparing the measurements in VR.

Data Analysis in the Time Domain
The analysis of stabilographic values, such as the COP velocity and the COP movement range, constitutes the basis for evaluating a human being's ability to keep balance [1,5,16].The introduction of oscillation into the virtual scenery in the AP direction led to a statistically significant increase in values in both the cases of the COP velocity and the COP movement range in the AP direction in relation to the measurements with OE (Figure 4A,B).Similar conclusions were drawn in previous research conducted by the authors [1].The increase in these values results from the balance of the body following the oscillating scenery, which was confirmed by the authors' preceding investigations, where FFT analysis proved the presence of an additional harmonic at a frequency equal to the frequency of the scenery movement.The investigations also demonstrated the presence of additional harmonic at other frequencies, which may indicate a change in the balance-keeping strategy or destabilization of the tested person [20,21].
In the measurements with the change in frequency (0.7/1.4 and 1.4/07), one could observe a greater interquartile distribution for the data obtained after the frequency change (0.7_after and 1.4_after) in the case of the COP velocity values in the AP direction in comparison with the data obtained before the frequency change (0.7_before and 1.4_before) (Figure 4A,B).This result may mean that the change from one frequency to another exerts a destabilizing impact and somehow forces the tested participant to search for a new strategy to maintain balance.
Analyses in the time domain and additional analyses in the frequency domain make it possible to determine if and how virtual disturbances influence changes in the balancekeeping strategy [21] and body-balancing strategy during movement [22].However, the frequency analysis is limited to the discovery of movement components of a cyclic character.In addition, such an analysis is burdened with noise related to spectral leakage and incomplete signal periods in the measurement window.The application of computational methods drawn from stock exchange analyses makes it possible to supplement the performed analyses with signal components that do not have a cyclic character [13,14].

Trend Change Index (TCI)
An increase in the mean value of the COP velocity or movement range may indicate problems with maintaining balance.There is evidence, based on the analyses of COP movement in the frequency domain, that the lines appearing in FFT diagrams may be used for the assessment of the balance-keeping strategy.For instance, the movement of the body following the cyclically oscillating virtual scenery, which may be observed in the FFT or short-time Fourier transform (STFT) diagrams in the form of lines, can be used for this purpose [1].Studies performed by Bizid R. et al. [23] and Micarelli A. et al. [24] indicate that there might be a connection between the frequency of COP oscillation and the strategy of maintaining balance.They claim that low frequencies (0-0.5 Hz) mostly account for visual-vestibular regulation, medium frequencies (0.5-2 Hz) for cerebellar regulation, and high frequencies (>2 Hz) for proprioceptive regulation.
However, the above-described frequency analyses enable only the detection of the signals of a cyclic character, whereas the real COP movement may include both cyclic and non-cyclic components [16].The developed TCI, calculated using the detection of trend changes based on stock exchange analysis methods, makes it possible to extend the analyses and supplement them with a non-cyclic component of the signal [19,25].The TCI value shows how often the COP was subjected to trend changes during the movement performed during the whole measurement (Figure 4A,B).
The conducted investigations demonstrated that in most cases, the value of the TCI, which was calculated for the whole interval from 0 to 1 s, did not change significantly, irrespective of the measurement conditions (Table 1).Such constancy, independent of the measurement conditions, may signify that to maintain a stable body posture, even in a situation of visual stimulation, a certain number of trend changes is required, which enables the correct functioning of the proprioceptive and visual-vestibular systems [13,16].An important exception occurs in the case of the measurement of the scenery oscillating at a frequency of 0.7 Hz, which took place after preceding oscillations at a frequency of 1.4 Hz.There was a clear decrease in the TCI values in relation to other measurements, i.e., the number of discovered changes in the trend, which may indicate a calmer movement at a frequency of 0.7 Hz when it occurs after a frequency of 1.4 Hz.Additional interpretation of this fact is supported by the TCI values determined individually for three time periods equal to the time between subsequent trend changes.The diagrams showed a significant decrease in the TCI values in the 0.2-0.5 s period and an increase in the interval of 0.5-1 s (Figure 5A-D), denoting considerable calming of COP movement.There appeared to be fewer 'leaps' of the COP lasting shorter than 0.5 s in favor of a greater number of leaps lasting longer than 0.5 s.This interval included COP movements performed at a frequency of 0.7 Hz.Therefore, from a statistical perspective, the tested individuals were more prone to disturbances at a frequency of 0.7 Hz if they had been previously exposed to disturbances at a higher frequency.Notably, such differences were undetectable based on the analysis of the COP mean velocity or the COP movement range, where a statistically significant difference appeared only between the OE and 0.7_after tests but did not occur in other cases (Figure 4A,B).
The analysis of measurements conducted at a frequency of 1.4 Hz revealed a significant increase in the TCI values in relation to other measurements in the 0.2-0.5 s period and a decrease in the 0.5-1 s period.The increase in the 0.2-0.5 s period was related to the fact that the body follows the moving scenery.This interval includes the 1.4 Hz frequency, which is also visible in the analyses in the frequency domain.This difference was noticeable, particularly in relation to the OE and CE measurements.In the remaining two time periods, 0-0.2 s and 0.5-1 s, at a frequency of 1.4 Hz, there was a decrease in the TCI values in relation to the measurements with OE and CE.
COP movement is connected not only to the constant loss of balance and the return to the balance-keeping position but also with the fact that it constitutes a source of information for the balance-keeping systems on what is happening with the body.The lack of significant changes in the total TCI value in individual measurements (Figure 4A), i.e., the number of trend changes in COP movement, leads to at least two interpretation possibilities.First, the lack of a considerable increase in the number of trend changes in COP movement by a given person, i.e., an increase in the number of trend changes in the interval corresponding to 1.4 Hz, which occurs at such disturbances of the scenery, forces an increase in these changes in other time periods.The second interpretation may be that a healthy person does not need to maintain a constant number of trend changes in each of the indicated three time periods.What is essential in the case of these individuals is the total number of such changes.Both hypotheses may be particularly important in the case of testing participants with balance-keeping deficits.However, in the case of such individuals, further studies and investigations regarding these hypotheses are required to be scientifically useful.

MACD_dS, MACD_dT, and MACD_dV
The determined MACD_dS, MACD_dT, and MACD_dV values (Figure 6A-C) make it possible to further extend the analyses performed based on the trend change detection using the methods of stock exchange analysis [21].The obtained values of the MACD_dV strongly correlate with the values of the COP mean velocity, which seems obvious.However, the knowledge of the time between trend changes and the distance covered by the COP at that time enables the collection of additional information on COP movement to be obtained [18].Information on the changes in the MACD_dT and MACD_dS values may indicate if the resulting changes in the velocity values, or their lack thereof, result from the change in the length of individual leaps of the COP, the time in which such a leap takes place, or from both of these values simultaneously.
Statistically significant differences between the OE and CE measurements and all other measurements occurred only in the case of the MACD_dS, where an increase in the median value was observed (only measurements between OE and 1.4_2 lacked significance).At the same time, most cases displayed a lack of statistically significant differences at the MACD_dT time.This showed that, in these cases, the observed increase in the velocity values occurred because of an increase in the mean distance between the subsequent COP locations in which the trend change took place, whereas the mean time between those leaps remained constant.An exception was the measurement performed for 0.7_after, where statistically significant differences were noted in the OE and CE measurements.A simultaneous increase in the MACD_dS and MACD_dT values caused a lack of change in the velocity between 0.7_after and CE, which could be seen both in the case of MACD_dV and the COP mean velocity.
What is worth mentioning is the fact that no case showed a statistically significant decrease in the MACD_dT value.A MACD_dT value that does not significantly decrease is essential from the perspective of the ability to maintain balance by the tested individuals.A simultaneous increase in MACD_dS and a decrease in MACD_dT might indicate much longer leaps of the COP performed at a shorter time.Such a case might potentially lead to destabilization and a subsequent fall of the tested person [25,26].

Conclusions
The use of stock exchange indices to assess human body stability complements standard analyses in both the time and frequency domains.Analyzing TCI, MACD_dV, MACD_dT, and MACD_dS values provides additional insight into factors affecting standard parameters like path length, mean velocity, and movement range.By integrating trend change analysis with stabilographic parameter analysis, we can glean information on posture correction frequency, intervals between corrections, and COP movement speed.Unlike FFT analysis, our time domain-based algorithm ensures the results are unaffected by noise.Decomposing the TCI analysis into intervals reveals shifts in COP movement patterns, indicating changes in balance strategy.TCI, MACD_dT, and MACD_dS analyses could prove valuable in testing patients with balance disorders.Elevated MACD_dS values coupled with shortened MACD_dT may signify increased fall risk.Deviations in total TCI value and intervals compared to healthy individuals may indicate balance-related dysfunctions, necessitating further investigation in specific patient groups.
However, our algorithm's sensitivity is limited to rapid postural corrections due to short time windows and MACD parameter values.Future plans involve consulting neurologists to refine the methodology and application, particularly in diagnosing neurological diseases.

16 Figure 3 .
Figure 3. COP course with trend change moments detected by the algorithm (marked as red dots in the diagram) and graphic interpretation of MACD_dT and MACD_dS for two random trend change moments [21].

Figure 3 .
Figure 3. COP course with trend change moments detected by the algorithm (marked as red dots in the diagram) and graphic interpretation of MACD_dT and MACD_dS for two random trend change moments [21].

Figure 4 .
Figure 4. (A,B).Stabilographic values in the time domain (EO-eyes opened, EC-eyes closed, 0.7_1-first 15 s of measurement in the oscillating scenery at a frequency of 0.7 Hz, 0.7_2-second 15 s of measurement in the oscillating scenery at a frequency of 0.7 Hz, 1.4_1 first 15 s of measurement in the oscillating scenery at a frequency of 1.4 Hz, 1.4_2 second 15 s of measurement in the oscillating scenery at a frequency of 1.4 Hz, 0.7_before-first 15 s of measurement in the oscillating scenery with the change in oscillation frequency from 0.7 Hz to 1.4 H, 1,4_after-second 15 s of measurement in the oscillating scenery with the change in oscillation frequency from 0.7 Hz to 1.4 Hz, 1.4_before-first 15 s of measurement in the oscillating scenery with the change in oscillation frequency from 1.4 Hz to 0.7 Hz, and 0.7_after-second 15 s of measurement in the oscillating scenery with the change in oscillation frequency from 1.4 Hz to 0.7 Hz).(A) Median of mean COP velocity in the AP direction and (B) Range of COP movement in the AP direction.

Table 1 .
The p-values (p = 0.05) obtained for the comparison of TCI values.Statistically significant value differences (p < 0.05) (between conditions in first column and second column) are designated using the green color.