# Cognitive tasks during walking affect cerebral blood flow signal features in middle cerebral arteries and their correlation to gait characteristics

- Arthur Gatouillat
^{1}, - Héloïse Bleton
^{1}, - Jessie VanSwearingen
^{2}, - Subashan Perera
^{3}, - Scott Thompson
^{1}, - Traci Smith
^{1}and - Ervin Sejdić
^{1}Email author

**11**:29

https://doi.org/10.1186/s12993-015-0073-9

© Gatouillat et al. 2015

**Received: **27 March 2015

**Accepted: **9 September 2015

**Published: **26 September 2015

## Abstract

Gait is a complex process involving both cognitive and sensory ability and is strongly impacted by the environment. In this paper, we propose to study of the impact of a cognitive task during gait on the cerebral blood flow velocity, the blood flow signal features and the correlation of gait and blood flow features through a dual task methodology. Both cerebral blood flow velocity and gait characteristics of eleven participants with no history of brain or gait conditions were recorded using transcranial Doppler on mid-cerebral artery while on a treadmill. The cognitive task was induced by a backward counting starting from 10,000 with decrement of 7. Central blood flow velocity raw and envelope features were extracted in both time, frequency and time-scale domain; information-theoretic metrics were also extracted and statistical significances were inspected. A similar feature extraction was performed on the stride interval signal. Statistical differences between the cognitive and baseline trials, between the left and right mid-cerebral arteries signals and the impact of the antropometric variables where studied using linear mixed models. No statistical differences were found between the left and right mid-cerebral arteries flows or the baseline and cognitive state gait features, while statistical differences for specific features were measured between cognitive and baseline states. These statistical differences found between the baseline and cognitive states show that cognitive process has an impact on the cerebral activity during walking. The state was found to have an impact on the correlation between the gait and blood flow features.

### Keywords

Transcranial Doppler Gait accelerometry Cerebral blood flow velocity Walking Signal features## Background

Walking is a complex sensory-cognitive interaction which has various demands depending on the environment [1–3]. Initially, cognition and motor control of gait have been believed to be two completely autonomous processes, with walking regarded as an automatic motor function, independent of any cognitive tasks [4, 5]. Walking was thought to be automatic as it is generated by spinal cord oscillating circuits, or at best, locomotor centers in the brain stem but without cortical input under usual conditions. If that were true, there should be little if any interference of cognitive functioning with walking—but recent research shows that a cognitive load has an effect on gait [6–8]. In fact among people with pathological conditions, the dual-task methodology was mainly used to observe the effect of concurrent stimuli while checking the gait state [9]. This technique may underline a cognitive-motor interference that indicates a conflict between concurrent tasks (i.e. a motor and a cognitive challenges), as there may be a deterioration of one or both of the tasks [9, 10].

In general, a dual task (i.e. a cognitive stimulus/walking) causes concurrent demands for attention/cognitive resources. Hence, it generates a cognitive-motor interference that implies tripping, falling, physical instability and/or a decline in performance [2, 4, 11]. These falls occur mainly in elderly subjects and have a strong impact on the health of elderly subjects [6]. These events also have an impact on the health costs [12] and the risk of falling is associated with gait disruptions [13]. Prior studies have illustrated that individuals with neurodegenerative disorders, those recovering from stroke or elderly adults, are more prone to the effects of cognitive load on gait [7, 9, 14]. On the other hand, just a few investigations have investigated the cerebral repercussions of a dual-task in the case of able-bodied young participants [15]. Moreover, there has been limited research on the effects of cognitive load on the cerebrovascular system during gait.

Thus, there is a growing interest in clarifying the correlation between motor control and cognition. Brain imaging methods have revealed activation of various cerebral regions associated with higher cognitive functions during walking (i.e. the dorsolateral prefrontal cortex and anterior cingulate cortex [16–19]).

However, because of the lack of portability of these devices and the fact that they require the subject to lie down during acquisition, the gait is usually modeled as a series of feet tapping in the fMRI case [20, 21] and it is studied by the injection of a radio-tracer, followed by the subject’s walk, and a scan for the PET/SPECT case [22, 23]. These devices, because of their lack of portability and the strong constraints associated with their use, are not optimal for performing a real time study of the brain during walking. These drawbacks led us to chose CBFV recordings using transcranial Doppler to assess brain function during walking.

Since it has been proven that CBFV modifications and neural activity can be correlated [24–28], we use transcranial Doppler recordings to monitor the hemodynamic activities of the main cerebral arteries [29] in order to study a motor-cognition interaction. This non-invasive ultrasound diagnostic tool first introduced by Aaslid et al. measures the cerebral blood flow velocities (CBFV) [30]. Readings are taken with ultrasonic transducers, placed bilaterally in the transtemporal window of the skull of one participant, which allows the monitoring of the left and right side of the circle of Willis’ cerebral arteries [31–34]. Most studies focused on activities of the middle cerebral artery (MCA) given that the MCA carries more than 80 % of blood to the brain [35]. Moreover, previous papers highlighted brain perfusion changes during neural cognitive challenges [36–38]. In concern to physical performance, global cerebral blood flow (CBF) appears to be increased, unchanged or decreased during stimuli [39–41]. Nevertheless, a regional increase of CBF was noticed during physical exercise [42].

The current study was focused on studying the associations between the cerebrovascular system and gait and understanding the repercussions of cognitive load during walking on the system. Specially, we examined CBFV signals in MCA. Our major contributions are the statistical differences found in the central blood flow velocity signals between the baseline and cognitive states during walking. We examined both raw signals and the envelope signals, which are maximum peak velocity outcomes. In addition, baseline is actually walking—and on a treadmill which is a dedicated stepping pattern facilitator, walking could be even more automatic than usual—yet the blood flow changed with added cognitive processing; and the changes in CBF consistency mirrored in part the changes in gait consistency—at least for the performance of some—illustrating the potential interference of cognitive functioning and walking.

## Methods

### Data acquisition

For this preliminary data collection, eleven participants were recruited (4 females and 7 males, ages ranging from 19 to 23 years). None of these subjects had history of concussion, heart murmurs, migraines, strokes or other brain and gait conditions. Participants were asked to signed the University of Pittsburgh Institutional Review Board approved consent form and the procedure was explained prior to the beginning of the experiment and data collection.

The participants were briefed to walk at a pace of 2 mph on the Noraxon MR3 treadmill and to remain thought-free during this 6 min baseline testing period. Upon the completion of this trial, the participants were asked to count backwards from 10,000 in decrements of 7 while walking for 6 min for another trial referred as cognitive. Approximately 1 week later, each participant repeated the experiment.

To observe stride time, Noraxon SciFit treadmill using capacitive sensor technology to analyze individual foot pressure (ranging from 1 to \(120~\,N /cm ^2\)) was used at a sampling frequency of 100 Hz. The treadmill data was recorded and extracted using the manufacturer’s software.

A SONARA TCD System (Carefusion, San Diego, CA, USA) was used to measure blood-flow velocity in the mid-cerebral artery. Two 2 MHz transducers were used to gather simultaneous bilateral CBFV acquisitions from the left-MCA and right-MCA. The transducer were planted on transtemporal windows [43] to reach the MCA blood-flows. The position, angle and insonation depth of transducers were adjusted in order to get the correct MCA signal [34, 44]. Once these adjustments were performed, the transducers were fixed with a headset on both sides of the subject’s head. The data was extracted as audio files sampled at \(44.1\,~kHz\), representing the cerebral blood flow from the R-MCA and L-MCA. These signals were resampled at 8820 Hz (factor 5) to increase the feature extraction’s speed. The downsampled signals, referred as raw signals, are composed of multiple sinusoidal components due to the parabolic speed CBFV distribution [37]. In this study, these raw CBFV along with the envelope of the CBFV were collected. The raw signals are composed of the various velocities of blood particles in cerebral arteries and envelope signals constitute the maximal Doppler shift [37, 45].

Furthermore, the end-tidal carbon dioxide \(ETCO _2\) (BCI Capnocheck Sleep Capnograph, Smiths Medical, Waukesha, Wisconsin, USA) was monitored along with respiration rate, electrocardiogram, head movement and skin conductance via a multisystem physiological data monitoring system (Nexus-X, Mindmedia, The Netherlands).

### Analysis of stride interval time series

The mean, standard deviation, coefficient of variation (which is the ratio of the standard deviation to the mean) and the spectral exponent were estimated for stride interval time series extracted from both feet.

- 1.
The wavelet transform of the centred version of the signal, \(WV _x(\tau ,s)\), is computed using the Daubechies 12 wavelet.

- 2.The mean average with respect to translation coefficient \(\tau\) of the magnitude of the wavelet transform is evaluated for each scale. This quantity is called:$$\begin{aligned} WV _x(s) = \left\langle |WV _x(\tau ,s)| \right\rangle _\tau \end{aligned}$$(1)
- 3.
The log-log plot of \(WV _x(s)\) as a function of the scale

*s*is plotted. The linear regression of the resulting graph is computed. The slope of this line is \(H_{fBm} + 1/2\) [46]. - 4.The spectral exponent \(\beta\) is evaluated using the expression:$$\begin{aligned} \beta = 2 H_{fBm} + 1 \end{aligned}$$(2)

### Analysis of MCA signals

#### Statistical features

In this study, four distinct statistical features where evaluated. The standard deviation, the skewness, the kurtosis along with the cross-correlation coefficient of right and left MCA signals were extracted and compared. The first three parameters characterize the shape of the signal’s distribution [48], while the last one characterizes the similarity between two signals.

*n*is its length.

*X*and

*Y*represent signals from the right and the left side of the MCA.

#### Information-theoretic features

With regard to the information-theoretic feature space, the Lempel–Ziv complexity (LZC), which represents the amount of new pattern formation in finite time sequences built upon the original signal (which can be interpreted as the randomness, the predictability and the regularity of a given discrete-time signal) [50] and the entropy rate, which represents the statistic degree of recurrence of patterns in a stochastic process [51].

In order to obtain a finite time sequence to compute the LZC, the signal is divided into \(\alpha\) finite equal spaces using \(\alpha -1\) threshold values given as \(T_h | h \in \{1, \ldots , \alpha - 1\}\) [52].

*n*. The blocks are a time series of successive data.

Then, for each length *L*, an analyse of each block is performed the following way: a counter *c*(*j*) is defined to illustrate the amount of new pattern formation. If the sequence represented in a block has not appeared in a previous analysis, this counter is incremented by one.

*c*(

*n*) is the value that the counter takes when the entire analysis is performed and \(\alpha\) represents the total number of quantized levels in the signal, chosen such as \(\alpha = 100\) in that study.

*L*such that \(10 \le L \le 30, \; L \in \mathbb {Z}^+\). Subsequently, the distribution made up of the different blocks was encoded into \(\Omega _L=\{ \omega _1, \omega _2,\ldots ,\omega _{n-L+1}\}\) such as [54]:

*j*in \(\Omega _L\), which is approximated by its sample frequency in this study.

*L*arising only once in \(\Omega _L\), \({\rm pe} _\%(L)\), with \({\rm S} (1)\) the conditional entropy estimation of the process with unit length

*L*, which is the Shannon entropy of white Gaussian noise process. This term corrects the underestimation of \({\rm S} (L)-{\rm S} (L-1)\) for large lengths

*L*[56]. Considering the opposite nature of the variation of the terms in the denominator (the first term decreases with

*L*while the second term increases), the function \({\rm N} (L)\) exhibits a minimum \(\min _{L}\left[ N(L)\right]\). This minimum is the best estimation of the normalized conditional entropy, and it can be seen as an indicator of complexity of the process. Conversely, the complement to this indicator, given as \(\rho = 1 - \min _{L}\left[ N(L)\right]\), is an index of the regularity of the stochastic process, ranging between 0 and 1 [55].

For comparison between two probability density functions purposes, one can use the cross-entropy rate. This index quantifies the amount of mutual information between two given distributions, and aims to predict the data of a considered signal using the previous and current information found in another signal. The two distributions *X* and *Y* were normalized and quantized in a similar fashion than the one used to compute the entropy rate, giving as a result the two quantized distribution \(\tilde{X} = \{\tilde{x}_1, \tilde{x}_2,\ldots ,\tilde{x}_n\}\) and \(\tilde{Y} = \{\tilde{y}_1, \tilde{y}_2,\ldots ,\tilde{y}_n\}\).

*X*,

*Y*and \(\Omega _L^{X|Y}\).

*L*that were present only once in \(\Omega _L^{X|Y}\) and \({\rm S} _X(1) \cdot {\rm pe} _{X|Y}(L)\) is a corrective term added for the same reasons as the one stated herein above. Similarly to the previously given algorithm, \({\rm S} _X(1)\) is the conditional entropy estimation of the stochastic process

*X*for a unit length. The function \({\rm NC} _{X|Y}(L)\) features a minimum \(\min _L\left[ {\rm NC} _{X|Y}(L), {\rm NC} _{Y|X}(L) \right]\). The synchronization index is then defined by \(\Lambda _{X|Y}=1 -\min _L\left[ {\rm NC} _{X|Y}(L), {\rm NC} _{Y|X}(L) \right]\), and it ranges from 0 (when

*X*and

*Y*are independent) to 1 (when

*X*and

*Y*are synchronized stochastic processes).

#### Frequency features

Features were also extracted with regard to the frequency domain: the peak frequency, spectral centroid and bandwidth were computed as characterization indexes for the extracted from the TCD signals [45].

*X*and \(f_{\max }\) the spectrum’s maximum frequency, equal to the sampling frequency divided by two.

*BW*, representing the dispersion of the spectrum, was computed as [45]:

#### Time-frequency features

*k*th level [58]) using a discrete wavelet transform approach and the Meyer wavelet as a mother wavelet. The relative wavelet energy from both the approximation coefficient and detail coefficients are then computed as [59]:

These metrics describe the relative energies repartition within distinct frequency bands based upon the ratio of the *k*-th level of decomposition to the total energy of the signal.

### Statistical test

SAS version 9.3 (SAS Institute, Inc., Cary, North Carolina) was used for all statistical analyses. Our overall strategy was to keep the two trials separate and fit a sufficiently complex model in order to account for between-trial correlation to maximize the use of information and statistical power. For simpler methods such as correlation analyses, we averaged participant measures across the two trials. To examine significance of systematic differences in measures between the two trials we fitted a series of linear mixed models using the SAS MIXED procedure with each gait/blood flow measure as the dependent variable; trial as the factor of interest; and a subject random effect to account for multiple correlated measurements from the same participant. We computed baseline condition vs cognitive task difference for each measure, and fitted a similar mixed model with the said differences as dependent variables but in an intercept-only model to obtain statistical significance for the between-condition difference under two correlated trials. To examine whether participant characteristics (age, gender, height, weight, BMI), we fit another series of models with each gait/blood flow measure under each task condition as the dependent variable; each participant characteristic as the fixed effect of interest; and a participant random effect to account for multiple trials. To examine correlation coefficients across measures, we first averaged all measures across the two trials. Next, we used Pearson correlation coefficients between gait measures and blood flow measures; as well as between left and right sides for the blood flow measures. Additionally, we obtained partial correlations adjusted for participant characteristics. We are aware of the large number of measures and statistical tests performed in our analysis, and thus use false discovery rate (FDR) methodology for adjusting p-values for multiplicity [60].

## Results

The end-tidal carbon dioxide level does not influence the mean diameter of the middle cerebral arteries [61]. Consequently, it is not taken into consideration. The results are presented in tables in the form of \(({\rm mean} ~\pm ~ {\rm standard deviation} )\) where the baseline period is pointed out by a “B” and the cognitive task is indicated by a “C”. R-MCA indicates the right MCA, while L-MCA indicates the left MCA. The test-retest were not found to introduce statistical differences if the FDR adjusted p-values are considered.

### Stride interval features

Stride interval features

Right foot | Left foot | |
---|---|---|

Mean (s) | ||

B | 1.24 ± 0.07 | 1.24 ± .07 |

C | 1.26 ± 0.07 | 1.26 ± 0.07 |

Coefficient of variation | ||

B | (3.09 ± 0.97) | (2.89 ± 0.76) |

C | (2.76 ± 1.17) | (2.44 ± 0.82) |

Spectral exponent \(\beta\) | ||

B | 0.64 ± 0.49 | 0.66 ± 0.42 |

C | 0.41 ± 0.27 | 0.47 ± 0.22 |

### MCA signal features

#### Time features

Table 2 summarizes time-domain feature values for the raw and the envelope signals. For every metrics considered in that table, no statistical differences between the left side and the right side were observed. However, statistical differences between cognitive state and baseline state were observed for the standard deviation of the envelope signal (\(p \approx 0.018\)) for both R-MCA and L-MCA, and for both the envelope and raw signals’ R-MCA and L-MCA cross-correlation (\(p \approx 0.018\)).

Moreover, the inspection of the mean peak blood flow velocity revealed an increase during the cognitive task (\(57.8~\pm ~9.0 {\rm cm} ~s ^{-1}\) in the baseline trial vs \(59.5 ~\pm ~ 10.3 {\rm cm} ~s ^{-1}\) in the cognitive trial for the R-MCA and \(59.1~\pm ~8.4 {\rm cm} ~s ^{-1}\) in the baseline trial vs \(59.3~\pm ~10.1 {\rm cm} ~s ^{-1}\) in the cognitive trial for the L-MCA).

Time features from raw and envelope CBFV signals

Raw | Evvelope | |||
---|---|---|---|---|

R-MCA | L-MCA | R-MCA | L-MCA | |

Standard deviation | ||||

B | 0.13 ± 0.10 | 0.13 ± 0.08 | 3.77 ± 1.01 | 4.03 ± 1.13 |

C | 0.15 ± 0.10 | 0.14 ± 0.08 | 5.02 ± 1.62 | 5.44 ± 1.36 |

Skewness | ||||

B | (−4.99) | (−1.52) | −1.03 ± 0.74 | −0.80 ± 0.76 |

C | (7.15) | (−0.11) | −1.22 ± 0.82 | −1.07 ± 0.75 |

Kurtosis | ||||

B | 4.38 ± 2.74 | 5.08 ± 3.31 | 5.50 ± 3.95 | 4.73 ± 3.13 |

C | 4.51 ± 1.67 | 5.11 ± 3.22 | 5.41 ± 2.98 | 4.47 ± 1.91 |

Cross-Correlation | ||||

B | (7.27 ± 2.04) | 0.98 ± 0.01 | ||

C | 0.02 ± 0.02 | 0.97 ± 0.02 |

#### Information-theoretic features

Information-theoretic features from raw and envelope CBFV signals

Raw | Envelope | |||
---|---|---|---|---|

R-MCA | L-MCA | R-MCA | L-MCA | |

LZC | ||||

B | 0.71 ± 0.04 | 0.71 ± 0.04 | 0.70 ± 0.02 | 0.70 ± 0.02 |

C | 0.70 ± 0.04 | 0.70 ± 0.03 | 0.68 ± 0.02 | 0.68 ± 0.03 |

Entropy rate | ||||

B | 0.09 ± 0.10 | 0.10 ± 0.15 | (7.61 ± 1.75) | (7.56 ± 2.43) |

C | 0.11 ± 0.13 | 0.11 ± 0.11 | 0.01 ± 0.01 | 0.01 ± 0.01 |

Synchronization index | ||||

B | 0.17 ± 0.13 | 0.07 ± 0.03 | ||

C | 0.16 ± 0.12 | 0.12 ± 0.06 |

#### Frequency features

Frequency features from raw and envelope CBFV signals (values are in Hertz)

Raw | Envelope | |||
---|---|---|---|---|

R-MCA | L-MCA | R-MCA | L-MCA | |

Spectral centroid | ||||

B | 546 ± 47.3 | 523 ± 62.1 | 2.92 ± 0.43 | 2.91 ± 0.40 |

C | 504 ± 80.6 | 488 ± 68.2 | 2.80 ± 0.46 | 2.72 ± 0.49 |

Peak frequency | ||||

B | 574 ± 115 | 539 ± 144 | 1.25 ± 0.62 | 1.08 ± 0.71 |

C | 437 ± 202 | 421 ± 196 | 0.84 ± 0.81 | 0.71 ± 0.84 |

Bandwidth | ||||

B | 172 ± 15.8 | 174 ± 12.4 | 2.38 ± 0.33 | 2.40 ± 0.30 |

C | 186 ± 16.1 | 193 ± 17.7 | 2.43 ± 0.24 | 2.37 ± 0.21 |

#### Time-frequency features

Wavelet entropy values for raw and envelope CBFV signals

Raw | Envelope | |||
---|---|---|---|---|

R-MCA | L-MCA | R-MCA | L-MCA | |

\(\Omega\) | ||||

B | 1.02 ± 0.21 | 1.11 ± 0.27 | 0.03 ± 0.02 | 0.04 ± 0.03 |

C | 1.22 ± 0.23 | 1.32 ± 0.23 | 0.05 ± 0.06 | 0.06 ± 0.03 |

#### Correlation between left and right MCA blood flow

Statistical significance for the correlation between the left and right MCA CBFV are only found for the wavelet decomposition of the raw CBFV signals: the levels \(d_5\) to \(d_7\) exhibit a correlation coefficient greater than 0.8 with \(p \le 0.005\). The levels \(d_2\) and \(d_1\) feature a correlation coefficient greater than 0.9 with \(p \ll 0.001\).

### Impact of anthropometric variables on features

The anthropometric variables were not found to have an impact on any of the features.

### Correlation between gait and MCA features

## Discussion

Our major finding is that there are statistical differences in cerebral blood flow velocities in MCA between the baseline and cognitive states during walking. These differences were observed both in the raw signals and in the envelope signals (i.e., the maximal velocities) associated with cerebral blood flow velocities.

The statistical differences revealed in this study between blood flow during walking and blood flow during walking with an added cognitive processing task illustrate the suggested performance pattern seen in older adults with greater difficulty walking under challenging conditions such as walking and talking or walking and thinking. Under the challenge of the added cognitive task, it was more difficult to maintain usual gait performance. The difficulty manifested in gait as largely greater inconsistency in the pattern of strides than in the mean of the stride interval time series. This difficulty was also mirrored in the cerebral blood flow. Thus, under the cognitive processing task condition, the range of gait performance was expanded for some variables, despite no change in the group mean for the gait characteristics. The expanded range of gait performance may underlie the different and greater number of correlations between gait and blood flow in the walking plus cognitive processing condition. A cognitively challenging task during walking may alter the range of gait performance, which is also associated with greater cerebral blood flow or ‘work’ of the brain.

Among the stride measures, the standard deviation of the stride interval exhibited the strongest correlation with blood flow velocity features. This finding may indicate that while the cognitive processing did not disrupt gait described by the mean of the stride interval, the added cognition may have influenced the consistency of gait performance (eg, standard deviation). While all participants accomplished the task of walking and thinking on the treadmill with no change in the mean stride characteristics, the difference in the level of cognitive challenge for participants was apparent in the inconsistency of gait. Greater cognitive challenge for some was associated with greater blood flow. Moreover, the increase in the bandwidth of the raw signals denotes a change in individual behavior of the erythrocytes, as a higher bandwidth value denotes higher spectral spread, which is caused by more erratic flow of red blood cells. The lack of statistical differences between the first and second trials denotes that the extracted features tend to be trial-independent.

## Limitations of the study

A potential limitation of this study comes from the fact that the participants were instructed to walk on a treadmill: indeed, changes in the gait characteristics are very likely concealed by the walking rhythm induced by the treadmill.

## Conclusion

In this paper, the dual task methodology exhibited that the cerebral blood flow velocity signals in the baseline and cognitive states during walking are statistically different. These differences can be found in extracted features for both the raw and envelope of the L-MCA and R-MCA central blood flow velocity signals. While the changes in gait features were subtle, the different and more relations between gait and blood flow with the added cognitive processing during walking suggests cerebral blood flow velocity may represent the work of the brain when thinking and walking.

## Declarations

### Authors’ contributions

AG wrote the main manuscript, participated in the feature extraction and created all the presented figures. HB participated in the feature extraction. JV helped with the interpretation of the results and wrote part of the discussion section. SP helped with the statistical analysis and wrote the related part in the methods section. ST and TS collected the data. ES helped with the writing of the manuscript and the correction of the multiple drafts. All authors read and approved the final manuscript.

### Acknowledgements

The work was supported by the Pittsburgh Older Americans Independence Center (NIA P30 AG024827).

### Compliance with ethical guidelines

**Competing interests** The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

## Authors’ Affiliations

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