Discriminating Between Parkinson's Disease and Control Sin-gle Task and Dual Task Groups Using Fractal Dimension Analysis of Center of Pressure (CoP)

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Discriminating Between Parkinson's Disease and Control Sin-gle Task and Dual Task Groups Using Fractal Dimension Analysis of Center of Pressure (CoP)

https://doi.org/10.21203/rs.3.rs-3313053/v1

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Parkinson disease (PD) is one of the well-known neurodegenerative disease that deteriorates human regular planning procedure, motor control, and movements especially walking. PD patients may pay more attention to their gait in order to compensate and achieve a more normal walking. So, this may cause more difficulties for them to do a dual-task (DT) while walking. The center of pressure (CoP) in walking is introduced as a theoretical point where represents distributed pressure between the floor and various parts of the foot. The CoP traces, represents the movement of a person to maintain a stable position in both the sagittal and frontal planes. The aim of this study is to report the results of discrimination between Parkinson and Control subject’s CoP data using nonlinear analysis such az Higuchi Fractal Dimension (HFD). The effect of single-task and dual-task on the non-linear characterestics of CoP in both Parkinson and Control groups are also investigated. A fractal pattern helps us to describe irregular and chaotic shapes such as CoP traces and its complexity. Given the fact that FD can be used to characterize the signal complexity, we explored the ability of HFD to discriminate between CoP signals of 21 PD patients and 15 control subjects.

Health sciences/Medical research

Health sciences/Neurology

Health sciences/Diseases

Health sciences/Diseases/Neurological disorders/Parkinsons disease

Physical sciences/Mathematics and computing/Statistics

Parkinson's disease

signal processing

control single task and dual task

center of pressure

fractal dimension analysis

Parkinson disease (PD) is one of the well-known neurodegenerative disease that deteriorates human regular planning procedure, motor control, and movements especially walking. Patients with PD, generally walk with increased unsteadiness and sharp stride-to-stride variations which appears in the early stages of this deficit [1–8]. The reduction of neurotransmitter Dopamine has known as the cause of emersion of this disorder [9]. PD patients may pay more attention to their gait in order to compensate and achieve a more normal walking [6, 8, 10]. So, this may cause more difficulties for them to do a dual-task (DT) while walking. DT typically creates competition for attention between the two tasks if both gait and a secondary task are attention demanding and performed simultaneously. Thus, one task might overcome the other in priority and deteriorate the performance of the dual-task, depending on demands [11, 12]. Du-al-Task paradigm is one of the standard ways of examining how much deterioration is happened in patient's basic natural movements [8]. Even, DT can help to detect PD patients with no visible disorders in their movements because they may have made their movements more efficient by paying too much attention. However, number of studies have investigated the effect of dual tasking on gait in patients with PD are not sufficient [6, 13–16] and, more generally, it is not clear that how the gait paradigm changes[8].

The center of pressure (CoP) in walking is introduced as a theoretical point where rep-resents distributed pressure between the floor and various parts of the foot [17]. The CoP traces, represents the movement of a person to maintain a stable position in both the sagittal and frontal planes. CoP traces, which are derived from force readings, are easily accumulated, non-invasive, and immediate. They have the ability to inform us about the control strategies used for postural stability[18].

Fortunately, advance progressions in non-linear techniques of mathematics and chaos, revealed the fractal patterns of biological signals [18]. In opposition to the traditional thinking that these patterns are derived from some random mechanism, a fractal pat-tern helps us to describe irregular and chaotic shapes such as CoP traces and its complexity [19, 20]. Yamada [21] used the Lyapunov exponent analysis and determined CoP trajectories to be chaotic. Therefore, the fractal patterns exist as some intrinsic responses in natural systems such as CoP. Presented paper follows the presumption that a trivial deviation away from the fractal pattern may be a sign of a shift towards an unhealthy or less desirable gait control strategies [22, 23].

Higuchi [24] has presented a technique to extract the fractal dimension from time-series data called Higuchi Fractal Dimension (HFD). This method reports a fractal dimension value D={x ϵ R┤| 1 ≤ x ≤ 2} for an applied data such as CoP displacement. For data with too high noise component or randomly generated signals, the D will be near 2, indicating that the signal is indiscriminately uncertain about its under-lying signal. On the Other hand, the signal with no variability e.g. when a person is standing stationary, the fractal dimension will be D = 1 .

For testing the non-linear structure of time series data sets such as CoP, it is commonly believed that using Surrogate data testing is an outperformance technique [25, 26]. Surrogate data analysis is one of these technique to test the non-linearity of the system and has been widely used to assess the variability of gait data or biological signals in the elderly [27]. The result of surrogate data analysis is a new data set derived from the original data. The new data set and the original data are then analyzed and compared to each other using a nonlinear analysis method such as FD. If the results are significantly different (statistically) from each other, then the non-linear analysis can be considered appropriate [25].

The aim of this study is to report the results of discrimination between Parkinson and Control subject’s CoP data using nonlinear analysis such az HFD. The effect of single-task and dual-task on the non-linear characteristics of CoP in both Parkinson and Control groups are also investigated. Additionally, this paper presents author’s interpretation about the effect of DT on the PD and Control patients based on the findings and observations. There maybe some other explanation related to complexity to de-scribe behavior of PD patients in DT procedure.

This section represents the tools, dataset and methods which are utilized and developed step by step to set the strategy of the study. Collected CoP signals, Surrogate data analysis and HFD analysis are introduced.

For simplifying we use symbols for the under study subjects as CT-ST for Control subjects doing a Single-Task, CT-DT for Control subjects doing Dual-Task, PT-ST Parkinson patients doing a Single-Task, and PT-DT for Parkinson patients doing Du-al-Task.

Surrogate Data Analysis

CoP Data of 22 parkinsonian patients and 15 control group is accessible in physionet. Patients of 2–3 on the Hoehn and Yahr scale disease stage were invited [28]. All the experiments were implemented at clinic of the Movement Disorders Unit at the Tel Aviv Sourasky Medical Center. Patients were using antiparkinsonian medications and did not suffer from dementia (specified by DSM IV criteria and scores on the Mini-Mental State Exam (MMSE)) and major depression or neurological disease. They were chosen from 60–90 years old patients [29].

DT paradigm for these groups has been defined as motor-cognitive dual task. First Task was 2 minutes walking with free velocity. No priority has been specified. Secondary task consists of subtract-7 starting from 500. First and second tasks were performing simultaneously and the pressure under the feet has been recorded by 8 sensors implemented under the shoes as schematically plotted in Fig. 1 [29, 30]. CoP extracted from recorded data has been analyzed with nonlinear methods such as surrogate data analysis and then HFD analysis follows as bellow.

Although it is frequently confirmed that nonlinearity traces exist at the brain or lower motor control areas, we cannot endorse the nonlinearity of CoP data. Before any analysis of the biological signals, like Fractal Dimension, being assured of the presence of nonlinearity in original data is important. Surrogate data analysis declares a method for testing nonlinearity of the data if nonlinear techniques may be suitably applied [25, 26].This process transforms the original time-series data, in the present case, using a method known as the Amplitude Adjusted Fourier Transform (AAFT) algorithm [26]. This approach preserves both the linear structure and the amplitude distribution. Moreover, it consists of three steps:

Gaussianization or fitting the data to a Gaussian distribution.
Entering a random phase transformation of the new data.
De-Gaussianization or performing a conversion inverse of the first one.

Results from the generated surrogate data were compared to the results of original data using a paired t-test to assess the possibility of applying nonlinear feature extractions like fractal dimensions. Significant differences between the HFD values obtained from the two data sets indicate that the signals are non-linear.

Fractal Dimension Analysis

Fractal dimension (FD) is a nonlinear measure of signal complexity in the time domain. Higuchi, in 1988, proposed an efficient algorithm for measuring the FD of discrete time sequences [24]. FD can be used to reckon the complexity and self-similarity of a signal. Higuchi’s algorithm calculates the FD directly from time series. This method for computing the fractal dimension is designed specifically for use with time series data such as CoP data. HFD has already been used to analyze the complexity of brain recordings and even CoP data and other biological signals.

Suppose a given one-dimensional time series such as:

$$A=a\left[1\right] .a\left[2\right]. a\left[3\right].\dots . a\left[N\right]$$

The algorithm to calculate the HFD can be described as follows:

construction in a new self-similar time series ${A}_{k}^{m}$:

$${A}_{k}^{m}=\{a\left[m\right]. a\left[m+k\right]. a\left[m+2k\right]. \dots . a\left[m+int\left(\frac{N-m}{k}\right).k\right]\}$$

Parameter m is an initial time where m = 1.2.….k; parameter k is time interval where$k=2. \dots .{ k}_{max}$;

K_max is a free parameter, and int () is integer part of the real number in the parenthesis.

The length ${L}_{m}\left(k\right)$ was calculated for each of the k time series or curves ${A}_{k}^{m}$.

$${L}_{m}\left(k\right)=\frac{\left\{\right(\sum _{i=1}^{int\left(\frac{N-m}{k}\right)}|a\left[m+ik\right]-a[m+\left(i-1\right).k\left]\right|\left)\frac{N-1}{int\left(\frac{N-m}{k}\right).k}\right\}}{k}$$

Where N is length of the original time series $A$ and $\frac{N-1}{int\left(\frac{N-m}{k}\right).k}$ is a normalization factor.

Then, the length of the curve $L\left(k\right)$ for the time interval k is defined as the average of ${ L}_{m}\left(k\right)$ for all $m=1. 2. \dots . k$ forming the mean value of the curve length $L\left(k\right)$ for each $k=2. \dots .{ k}_{max}$ as:

$$L\left(k\right)=\frac{\sum _{m=1}^{k}{L}_{m}\left(k\right)}{k}$$

Finally, when $\text{ln}\left[L\left(k\right)\right]$ is plotted against $\text{ln}\left[\frac{1}{k}\right]$ on a double logarithmic scale, with $k=2. \dots .{ k}_{max}$, the data should fall on a straight line, with a slope equal to the FD of X. Consequently, HFD is defined as the slope of the line that fits the pairs $\{\text{l}\text{n}[L\left(k\right)]$ ,$\text{l}\text{n}\left[\frac{1}{k}\right]\}$ in a least-squares sense:

$$HFD=\frac{\text{l}\text{n}\left[L\left(k\right)\right]}{\text{l}\text{n}\left[\frac{1}{k}\right]}$$

After elementary tests, the independence of HFD from the length of the window has been confirmed based on our results, at least for N > 100, but much more dependent on the parameter${ k}_{max}$. Determining${ k}_{max}$was by a process of examining the data and plotting the fractal dimension over a range of ${ k}_{max}$; the point at which the fractal dimension plateaus was considered a saturation point beyond which no benefit could be gained from further calculations. A value of ${ k}_{max}=80$ was chosen for our study.

Surrogate Data Analysis

Surrogate data analysis produces higher fractal dimension in comparison to the original data within all four studying categories consist of CT-ST, CT-DT, PT-ST, PT-DT all for the right foot and there was a significant difference between the surrogated data and original data (P < 0.05). The measured fractal dimensions with the same${ k}_{max}=80$for the mentioned four groups were [mean (SD)] CT-ST = 1.5505 (0.0410), CT-DT = 1.5520 (0.0262), PT-ST = 1.5305 (0.0674), PT-DT = 1.4925 (0.0786) (Also stated in Table.1). Since the results will be discussed in all four groups, surrogate data were calculated for all categories. Figure 2.A to Fig. 2.D illustrates the surrogate data and its original data for each four categories, respectively. In order to achieve a clarity of illustrating, a range of 10 seconds of these signals has been showed. Therefore, significant differences between the AHFD values obtained from the data sets reveals that the signals are nonlinear.

Table 1

The HFD values of surrogate data analysis in control single-task/dual-task and patient single-task/dual task CoP data(Note that the values are in mean ± SD).
Feature	Control		Patient
Feature	Single Task	Dual Task	Single Task	Dual Task
AHFD	1.5505 ± 0.0410	1.5520 ± 0.0262	1.5305 ± 0.0674	1.4925 ± 0.0786

Fractal and Statistical Analysis

Paired-sample t-tests were used to determine the significance of within-group differences between conditions, for example, the significance of single task and dual task HFDs within the control group. Independent-samples t-tests indicated the significance of between group's differences for the same condition, for example, the significance of single task's HFD between control and patient groups. An alpha level of 0.05 was used as the boundary for the significance of the effect. Levene’s test for uniformity was performed on all data sets.

Fractal dimension analysis was applied for the evaluation of the center of pressure (CoP) in control and patient groups participating in a single task and dual task procedures. After testing the reliability of Higuchi algorithm, it was applied to CoP signals in each subject. The AHFD values for each group were measured by the HFD of subjects’ CoP signals and then average on the whole group was calculated. The remarks originated from the Fig. 3 are as follows.

As shown in Fig. 3 the fractal dimensions were 1.4368 ± 0.04 (mean ± SD) and 1.4295 ± 0.03 for the single task and dual task, respectively, for the control group (Also stated in Table.2). Those were 1.4174 ± 0.06 and 1.3776 ± 0.08 for patient group. The fractal dimension for patient group was significantly higher with the single task than that with the dual task (p < 0.05). The fractal dimensions for CT-DT group were significantly higher than that for PD-ST group (p < 0.05).

In contrast, no significant correlation was found between CT-ST and CT-DT groups and also CT-ST and PD-ST groups, but the value of HFD in CT-ST was higher than that in CT-DT and PD-ST.

Table 2

The HFD values of real control single-task/dual-task and patient single-task/dual task CoP data(Note that the values are in mean ± SD).
Feature	Control		Patient
Feature	Single Task	Dual Task	Single Task	Dual Task
AHFD	1.4368 ± 0.04	1.4295 ± 0.03	1.4174 ± 0.06	1.3776 ± 0.08

Postural control is the result of proper integration of the visual, vestibular, and somatosensory systems [31, 32]. Normal balance is make changes when this relation is throw into confusion, and The other signals that are left can serve as adequate substitutes to ensure proper balance is maintained. Generally, patients with Parkinson's disease (PD) experience decreased gait velocity, shorter stride, gait unsteadiness, decreased swing times, and increased risk of falls [1, 2, 4–6, 33, 34]. to attain a more organic walking rhythm, individuals with PD might depend on heightened focus to make up for the reduced automaticity caused by their condition. [6, 10]. Moreover, some patients experience cognitive deficit, e.g., impairments in executive function (EF), even in the early disease stages[35, 36]. As expected, PD patients show difficulties in dual tasking (DT) while executing a secondary task. Attention and allocation of cognitive resources are two key parameters that DT causes competition for them and might cause a priority of one task on the other task depending on the characteristics and environmental demands of a task.

In this study, the subjects separated into two categories of control and PD patient group participated in single and dual task procedures that indeed arranges them into four groups. This was to address the issue of whether or not a fractal dimension analysis of CoP data could provide information to categorize and study these groups. Results from this research indicate that the use of Higuchi’s method for fractal dimension analysis can be used for differentiate between conditions of being healthy and patient and also discriminating between a single-task and dual-task related CoP data. Beside the complexity analysis with HFD, the stationarity and the non-linear structure of the recordings were tested.

The appropriateness of applying nonlinear techniques (for example HFD) to the data could be tested by the use of surrogate data analysis. The interest of this study was the use of a non-linear analysis technique applied to CoP data. Results from the Surrogate data analysis confirm the presence of nonlinear properties in the CoP data. This method has been used earlier and is the accepted mean for identifying nonlinearity in a signal[18].

Our Research revealed that chaos in biological systems might be quantified by calculating fractal dimension, Df, of the time series representing a biological signal[37]. This method, in contrast to an attractor’s fractal dimension, does not require preliminary reconstruction of the system’s phase space but can be directly applied to experimental data. So it is more intuitive to implement and a less time-consuming method. Df denotes the fractal dimension of the signal’s time series itself and should not be confused with attractor’s fractal dimension measured in the system’s phase space. In [38] it has been previously explored that brains affected by Alzheimer’s disease(AD) show a less complex behavior. Moreover, a finding of the current project suggests that CoP data of Parkinson disease would have a less complex behavior which supports the fact that an illness ruins cells normal acts and results in a synchronized process causing a simpler behavior.

Given the fact that FD can be used to characterized the signal complexity [37], We explored the ability of HFD to discriminate between CoP signals of 21 PD patients and 15 control subjects. DT is an attention-demanding process in which an affected brain caused by PD could diminish the manipulation of performing the main task. Having this fact in mind, the HFD value of a dual-task showed a decrease in value in both control and patient groups in comparison to a single-task, which also the value of HFD in PD-ST was significantly higher than its value in PD-DT (p < 0.05). Moreover, The HFD value of control group was higher than PD patient group which support the fact that reduced complexity is a consequence of a disease. Comparing the HFD values of CT-DT and PD-DT reveals a significant difference between the control’s dual-task and patient’s dual-task which introduces HFD as a reliable mean to distinguish between healthy and PD affected people.

In summary, nonlinear analysis like fractal dimension can be used to identify the complexity of signal such as CoP data which has been endorsed before that they can be more reliable and faster in comparison to traditional measurements [39]. Another fact supported by this study is that diseases such az AD or PD cause brain to demonstrate less complex behavior in comparison to a normal healthy subject.

Acknowledgements (not compulsory)

Not applicable.

Author contributions statement

Ali Niaty: Collected the data, Performed the analysis, Wrote the paper

AliReza Ghorbani: Conceived and designed the analysis, Contributed data or analysis tools, Edit the paper

Marzieh Jalali: Performed the analysis, Wrote the paper

Ali Abdolali*, Conceived and designed the analysis, Edit the paper

Additional information

Used data is available at www.physionet.org.

Blin, O., et al., Dopa-sensitive and dopa-resistant gait parameters in Parkinson's disease. Journal of the neurological sciences, 1991. 103(1): p. 51–54.
Blin, O., A.-M. Ferrandez, and G. Serratrice, Quantitative analysis of gait in Parkinson patients: increased variability of stride length. Journal of the neurological sciences, 1990. 98(1): p. 91–97.
Factor, S.A. and W. Weiner, Parkinson's Disease: Diagnosis & Clinical Management. 2007: Demos Medical Publishing.
Hausdorff, J.M., et al., Gait variability and basal ganglia disorders: Stride-to‐stride variations of gait cycle timing in parkinson's disease and Huntington's disease. Movement disorders, 1998. 13(3): p. 428–437.
Hausdorff, J.M., et al., Dynamic markers of altered gait rhythm in amyotrophic lateral sclerosis. Journal of applied physiology, 2000. 88(6): p. 2045–2053.
Morris, M.E., et al., Stride length regulation in Parkinson's disease. Brain, 1996. 119(2): p. 551–568.
Schaafsma, J., et al., Characterization of freezing of gait subtypes and the response of each to levodopa in Parkinson's disease. European Journal of Neurology, 2003. 10(4): p. 391–398.
Yogev, G., et al., Dual tasking, gait rhythmicity, and Parkinson's disease: which aspects of gait are attention demanding? European journal of neuroscience, 2005. 22(5): p. 1248–1256.
Guthrie, M., C. Myers, and M. Gluck, A neurocomputational model of tonic and phasic dopamine in action selection: a comparison with cognitive deficits in Parkinson's disease. Behavioural brain research, 2009. 200(1): p. 48–59.
Rubinstein, T.C., N. Giladi, and J.M. Hausdorff, The power of cueing to circumvent dopamine deficits: a review of physical therapy treatment of gait disturbances in Parkinson's disease. Movement Disorders, 2002. 17(6): p. 1148–1160.
Yogev-Seligmann, G., et al., Effects of explicit prioritization on dual task walking in patients with Parkinson's disease. Gait & posture, 2012. 35(4): p. 641–646.
Sala, S.D., et al., Dual-task paradigm: a means to examine the central executive. Annals of the New York Academy of Sciences, 1995. 769(1): p. 161–172.
Camicioli, R., et al., Verbal fluency task affects gait in Parkinson's disease with motor freezing. Journal of geriatric psychiatry and neurology, 1998. 11(4): p. 181–185.
Bloem, B.R., et al., “Stops walking when talking” does not predict falls in Parkinson's disease. Annals of Neurology, 2000. 48(2): p. 268–268.
O'Shea, S., M.E. Morris, and R. Iansek, Dual task interference during gait in people with Parkinson disease: effects of motor versus cognitive secondary tasks. Physical therapy, 2002. 82(9): p. 888.
Hausdorff, J.M., J. Balash, and N. Giladi, Effects of cognitive challenge on gait variability in patients with Parkinson’s disease. Journal of Geriatric Psychiatry and Neurology, 2003. 16(1): p. 53–58.
Chapman, A.E. and S. Fraser, Biomechanical analysis of fundamental human movements. 2008: Human Kinetics Champaign, IL.
Doyle, T.L., et al., Discriminating between elderly and young using a fractal dimension analysis of centre of pressure. Int J Med Sci, 2004. 1(1): p. 11–20.
Collins, J.J. and C.d. Luca, The effects of visual input on open-loop and closed-loop postural control mechanisms. Experimental Brain Research, 1995. 103(1): p. 151–163.
Capra, F., The web of life: A new scientific understanding of living systems. 1996: Anchor.
Yamada, N., Chaotic swaying of the upright posture. Human Movement Science, 1995. 14(6): p. 711–726.
Moghadam, S.M., A. Niaty, and F. Towhidkhah. Improving stabilization of passive walking using chaos. in Biomedical Engineering and 2016 1st International Iranian Conference on Biomedical Engineering (ICBME), 2016 23rd Iranian Conference on. 2016. IEEE.
Moghadam, S.M., et al., The simple chaotic model of passive dynamic walking. 2018: p. 1–17.
Higuchi, T., Approach to an irregular time series on the basis of the fractal theory. Physica D: Nonlinear Phenomena, 1988. 31(2): p. 277–283.
Spasic, S., et al., Different anesthesia in rat induces distinct inter-structure brain dynamic detected by Higuchi fractal dimension. 2011. 19(01): p. 113–123.
Schreiber, T. and A.J.P.D.N.P. Schmitz, Surrogate time series. 2000. 142(3–4): p. 346–382.
Buzzi, U.H., et al., Nonlinear dynamics indicates aging affects variability during gait. Clinical biomechanics, 2003. 18(5): p. 435–443.
Hoehn, M.M. and M.D.J.N. Yahr, Parkinsonism: onset, progression, and mortality. 1998. 50(2): p. 318–318.
Yogev, G., et al., Dual tasking, gait rhythmicity, and Parkinson's disease: which aspects of gait are attention demanding? 2005. 22(5): p. 1248–1256.
Yogev-Seligmann, G., et al., Effects of explicit prioritization on dual task walking in patients with Parkinson's disease. 2012. 35(4): p. 641–646.
Horak, F.B., Clinical measurement of postural control in adults. Phys ther, 1987. 67(12): p. 1881–1885.
Manabe, Y., et al., Fractal dimension analysis of static stabilometry in Parkinson’s disease and spinocerebellar ataxia. Neurological research, 2001. 23(4): p. 397–404.
Morris, M.E., et al., Gait disorders and gait rehabilitation in Parkinson's disease. Advances in neurology, 2001. 87: p. 347.
Morris, M.E., et al., The pathogenesis of gait hypokinesia in Parkinson's disease. Brain, 1994. 117(5): p. 1169–1181.
Brown, R.G. and C.D. Marsden, Dual task performance and processing resources in normal subjects and patients with Parkinson's disease. Brain, 1991. 114(1): p. 215–231.
Dubois, B. and B. Pillon, Cognitive deficits in Parkinson’s disease. Journal of neurology, 1996. 244(1): p. 2–8.
Accardo, A., et al., Use of the fractal dimension for the analysis of electroencephalographic time series. Biological cybernetics, 1997. 77(5): p. 339–350.
Gómez, C., et al., Use of the Higuchi's fractal dimension for the analysis of MEG recordings from Alzheimer's disease patients. Medical engineering & physics, 2009. 31(3): p. 306–313.
Doyle, T.L., R.U. Newton, and A.F. Burnett, Reliability of traditional and fractal dimension measures of quiet stance center of pressure in young, healthy people. Archives of physical medicine and rehabilitation, 2005. 86(10): p. 2034–2040.

No competing interests reported.

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Discriminating Between Parkinson's Disease and Control Sin-gle Task and Dual Task Groups Using Fractal Dimension Analysis of Center of Pressure (CoP)

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Abstract

Figures

Introduction

Methods

Surrogate Data Analysis

Fractal Dimension Analysis

Results

Surrogate Data Analysis

Fractal and Statistical Analysis

Discussion and Conclusion

Declarations

References

Additional Declarations

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