A Novel Segmentation, Mutual Information Network Framework for EEG Analysis of Motor Tasks
 Z Jane Wang^{1}Email author,
 Pamela WenHsin Lee^{1} and
 Martin J McKeown^{2}
https://doi.org/10.1186/1475925X89
© Wang et al; licensee BioMed Central Ltd. 2009
Received: 29 October 2008
Accepted: 04 May 2009
Published: 04 May 2009
Abstract
Background
Monitoring the functional connectivity between brain regions is becoming increasingly important in elucidating brain functionality in normal and disease states. Current methods of detecting networks in the recorded electroencephalogram (EEG) such as correlation and coherence are limited by the fact that they assume stationarity of the relationship between channels, and rely on linear dependencies. In contrast to diseases of the brain cortex (e.g. Alzheimer's disease), with motor disorders such as Parkinson's disease (PD) the EEG abnormalities are most apparent during performance of dynamic motor tasks, but this makes the stationarity assumption untenable.
Methods
We therefore propose a novel EEG segmentation method based on the temporal dynamics of the crossspectrogram of the computed Independent Components (ICs). We then utilize mutual information (MI) as the metric for determining also nonlinear statistical dependencies between EEG channels. Graphical theoretical analysis is then applied to the derived MI networks. The method was applied to EEG data recorded from six normal subjects and seven PD subjects off medication. Oneway analysis of variance (ANOVA) tests demonstrated statistically significant difference in the connectivity patterns between groups.
Results
The results suggested that PD subjects are unable to independently recruit different areas of the brain while performing simultaneous tasks compared to individual tasks, but instead they attempt to recruit disparate clusters of synchronous activity to maintain behavioral performance.
Conclusion
The proposed segmentation/MI network method appears to be a promising approach for analyzing the EEG recorded during dynamic behaviors.
Keywords
Background
Connectivity between brain regions is important for normal brain functioning, and may be impaired in many neurological diseases [1]. The electroencephalogram (EEG), with its excellent temporal resolution (~1 msec), is the most widely available technology used for inferring transient synchronization between brain regions. Both linear and nonlinear measures have been applied to assess the interdependencies between EEG channels [2]. For example, coherence and correlation methods [3, 4], which measure the dependencies between a pair of EEG signals in the frequency and time domains respectively, have been applied to the EEG to study the cortical synchrony that can be modulated as a function of task, and may systematically differ between normal and disease groups [5, 6]. Nevertheless, these measures consider only linear dependencies and may be particularly sensitive to outliers. Other methods may also be used to investigate both linear and nonlinear relationships between multivariate time series in the EEG, such as the Synchronization Likelihood (SL), but this and related methods assume a fixed phase relationship between time series [7]. However, in some diseases such as PD, transient phaselocked behavior between different parts of the motor system may be interrupted by "phase slips" [8] making the assumption of prolonged periods of phase synchrony potentially unsuitable.
An alternative to the linear methods of coherence and correlation and phase synchronization is to consider the mutual information (MI) between channels within a specified window. This enables estimation of both the linear and nonlinear statistical dependencies between time series and can be used to detect functional coupling. MI is a statistical technique that quantifies the information transmitted from one time series to another, with maximum value when two time series are the same and a value of zero if two time series are statistically independent. Previously, researchers have utilized MI as a suitable metric to investigate EEG coupling in various pathological conditions [9–11]. For example, by estimating the MI between the time series of multiple pairs of EEG channels, Jeong et al. demonstrated abnormalities in the information transmission between different cortical areas in Alzheimer's patients [9]. Similar studies have used MI as a marker for corticocortical connections in schizophrenic patients [10] and odor stimulation [11].
Another disease where altered connectivity may be important is Parkinson's disease (PD), a movement disorder that is characterized by muscle rigidity, tremor, and bradykinesia (slowing of physical movement). These symptoms do not reflect a primary failure of the cortex (making resting EEG less likely to be abnormal), but rather the effects of failure of the basal ganglia to prime the cortex for preparation and execution of movement. As a result, PD patients have a difficult time performing simultaneous movements compared to normal subjects [12, 13]. In order to assess the indirect effects of basal ganglia dysfunction on the cortex in PD, it is necessary to have subjects perform a motor task. Furthermore, stressing the motor system by having PD subjects performing simultaneous movements is more likely to induce abnormalities in the recorded EEG.
However, as soon as a subject performs a dynamic motor task, the nonstationarity nature of the EEG must be considered [14]. The nonstationarity likely reflects the switching of inherently metastable states of neural assemblies during task performance causing abrupt transitions. The nonstationary property of EEG suggests that techniques assuming stationarity may result in misleading interpretations. To address this concern, a conventional approach is to incorporate a sliding time window into the original signal models, and assume that the stationarity assumption is valid for the segment of data in the window. However, the selection of an appropriate (possibly timevarying) window length is nontrivial and could have a significant effect on the analysis results.
In order to obtain quasistationary segments in EEG signals and select taskrelated segments, we first propose a novel segmentation method of the EEG based on the temporal dynamics of the crossspectrogram of the Independent Components (ICs), and then compute the MI between channels within the temporallysegmented regions. We then apply graph theoretical analysis to the network of each group defined by edges whose MI values exceed a suitable threshold, and compute the clustering coefficient (C) and shortest path length (L) [15, 16]. In order to accommodate the magnitude of MI values above a given threshold, the intragroup (ie. task) and intergroup (ie. subject groups) network differences are further analyzed by oneway analysis of variance (ANOVA).
For motor tasks, changes in the EEG are most likely related to eventrelated synchronization/desynchronization (ERS/ERD), particularly in the beta band [17]. In selfpaced movements, ERD corresponds to changes in coherence between brain regions [18]. Thus we suggest the use of transient synchronization of between ICs as suitable markers for segmentation [19, 20]. We emphasize that the concept of "taskrelated sections" is flexible and may be dependent upon the underlying behavioral paradigm subjects are asked to perform. For example, if a subject was asked to push a button every 10 seconds, then transient synchronization of ICs occurring approximately every 10 seconds may be a suitable marker for segmentation. Here we demonstrate the proposed segmentation method in a less obvious situation: ongoing modulation of continual manual force production.
To our knowledge, this is the first application of using transient synchronization of ICs for temporal segmentation of time series. Also, it is the first application of joint MI and network analysis to assess information transmission abnormalities between different cortical areas in PD. The main contributions of this paper are as follows:

Propose a novel EEG segmentation approach to address the nonstationary nature of EEG data especially during performance of motor tasks, and to select taskrelated segments.

Present a coherent MIbased network analysis framework for modeling EEG to determine dependencies between EEG channels and infer statistically significant difference between groups.

Demonstrate how the proposed framework can be used for assessing the EEG during dynamic motor behaviors in pathological conditions, such as PD.
The paper is organized as follows: the detailed discussion of the proposed framework is presented in the Methods section. The Results and Discussion section describes the EEG experimental design and summarizes the results in a real case study of PD. Finally, we summarize and conclude the paper in Conclusions.
Methods
We recorded five minutes of EEG data while subjects performed simple hand movements in order to gain insight into the difficulty that PD subjects face when performing simultaneous movements.
Preprocessing
Bandpass Filtering
EEG data contain a wide range of frequency components, many of which are not of clinical or physiological interest. The data are therefore initially bandpassfiltered by a 4th order Butterworth filter between 0.5–55 Hz [21].
ICA Noise Removal
Here the infomaxICA algorithm [23] is applied to decompose the EEG signals. ICA finds a coordinate frame in which the data projections have minimal temporal overlap by minimizing the mutual information among the data projections or maximizing the joint entropy of a nonlinear function of s. It is most appropriate to perform ICA decomposition on sources that are linearly mixed in the recorded signals without time delays. After the artifactual sources are identified, the corresponding columns of the mixture matrix (i.e. calculated as the pseudoinverse of W) that multiply the artifactual sources are set to zero to eliminate the artifacts and thus obtain the "corrected" EEG signal. In our study, we only remove wellknown, obvious artifacts by identifying 1 to 2 components (e.g. representing eyemovements and/or electrocardiac signals) by visual inspection. Failure to remove these artifacts may result in correspondence between EEG channels being falsely attributed to synchronized brain activity.
EEG Segmentation based on the CrossSpectrogram
We note that if the derived ICs were truly independent, then the crossspectrum would not be significant. However, in real data many of the assumptions of ICA are violated. The data are not stationary, and the time courses are not temporally white. By using infomaxICA, which does not incorporate time delays, the derived components will be maximally independent at zero lag. As such, it will deal with the problem of volume conduction – where a deep electrical source may impart common electrical activity to two or more channels. Even though ICs are maximally independent over the whole time range, they may exhibit partial synchronization within specific time/frequency window [24], through which the transient coupling of neural networks might be revealed. By examining the ICs within a short moving window, the nonstationary nature of the EEG will be explored, and significant dependencies between ICs become apparent. Recent studies such as [19, 20] have also explored the transient synchrony between ICs and suggested transient correlation between ICs.
with f being the frequency normalized by the sampling frequency. By using a shortterm time shifting window, we are able to obtain localized frequency contents of the two signals and their relationship with respect to time and frequency. The crossspectrum is computed based on a short (3 s) time window shifted by 0.5 s to obtain the localized time information. Power in the higher frequency ranges, such as the gamma band (> 20 Hz) are more likely to distributed over a broad frequency range. To avoid any potential confounds from the AC current at 60 Hz, we look for sharp increases in activity in the range 45 Hz–55 Hz as a good marker for transient broadband artifacts that were not eliminated by the ICA Noise Removal step. In contrast, by examining the crossspectrogram of pairs of ICs within the lower frequency bands of physiologic interest, we can identify taskrelated segments.
Mutual Information based Network
where P_{ X }(x) is the probability that x is drawn from X and P_{ XY }(x, y) is the joint probability density function for the measurements of X and Y that produce the values x and y.
where I_{ r }(X, Y) is in the range [0, 1], and H(X) and H(Y) are the entropies. Entropy H(X), defined asΣ_{ x }P_{ X }(x)log_{2}P_{ X }(x), is regarded as a measure of uncertainty about a random variable X.
Network Analysis
In order to graphically represent a large set of data, we have derived both a relevance network [29] and an MI network. A relevance network, originally devised for graphically depicting the relationship between genes [29], can be generalized to take large data sets of experimental data and graphically depict the result of pairwise MI. It is obtained by applying a threshold and only the connections that are above the threshold are displayed in the network. The relevance network can then be used in graphical theoretical analysis (discussed in Methods – Network Analysis).
In addition, we have also taken into account the magnitude of MI values and obtained an MI network from the oneway ANOVA test (with details given in Methods – Network Analysis (Statistical Analysis)). The connections are established in the MI network if their MI values exceed a specified threshold and the ANOVA tests indicate significantly different values between groups.
Graphical Theoretical Analysis on Relevance Network
with n being the total number of vertices in the graph. Such C measures the local connectivity and ranges from 0 to 1. The higher the C, the greater the intensity of connections within a cluster.
The L of a graph is the mean of all shortest paths (shortest distance) connecting all pairs of vertices. It has a value greater than 1 and measures the global connectivity of the graph. A detail graphical explanation of a graph and graph theoretical measures can be found in [16].
Statistical Analysis
In addition to the graphical theoretic analysis on the thresholded matrices, we created an "MI network" which also incorporated the magnitude of the MI values. As before, MI values were first thresholded by zeroing values less than the 95th percentile on a null distribution. A null distribution was obtained by repeatedly (n = 100) randomly permuting the order of the second signal and computing the pairwise MI based on them [30]. The MI differences between segments are analyzed by oneway ANOVA with subject number, groups, and tasks as factors [31]. The connections between any two channels are established for the MI network if they are significantly different according to the ANOVA test and have magnitudes that are greater than the permutation threshold. The normality of the distribution of the MI values is verified by the KolmogorovSmirnov (KS) test [31].
In the oneway ANOVA test for each pairwise MI I(X, Y), the effect of a factor (e.g. Group) is tested, by comparing with the Ftest the variance of I(X, Y) explained by the factor against the variance of the residuals. Consequently, a pvalue was calculated for each possible connection in the MI network. To account for the effect of testing multiple connections simultaneously, the pvalues are corrected for multiple hypothesis testing using Storey's positivefalsediscoveryrate (pFDR) procedure [32] which computes a qvalue, the expected ratio of falsely rejected hypotheses among all those being rejected. Connections whose qvalues were smaller than 5% are considered statistically significant.
Because we are more interested in the connection with greater MI values, the permutation test is used in conjunction with the ANOVA test to select the relevant features for the MI based network. We have chosen the largest observed value of the permutation test as our threshold. A connection is thus established in the MI network if the MI values are significantly different based on the qvalue and are above the maximum observation from the permutation test.
Results and Discussion
Subjects and Experiment Design
All research was approved by the University of British Columbia Ethics Board. After giving informed consent, seven PD and six agematched control subjects volunteered to participate in the study. All patients were diagnosed with mild to moderately severe PD (Hoehn and Yahr stage 1–3) [33]. The control subjects were confirmed to be without active neurological disorders by a qualified neurologist. All patients were taken off LDopa medication after overnight withdrawal of at least 12 hours.
EEG Data Preprocessing
Noisy EEG Segment Removal
TaskRelated EEG Segmentation
The amount that subjects were asked to squeeze was based on two sinusoids with period of 10 and 18 seconds. For the BO condition, the color change occurred every 20 seconds. Therefore, autocorrelations of the crossspectrogram of the ICs over the three physiologicallyrelevant frequency bands [21] 5–8 Hz (Theta), 8–12 Hz (Alpha), 12–30 Hz (Beta) that have a peak at 10 seconds or 18–20 seconds are selected for sections of EEG segmentation. Depending on the features of each dataset, approximately five pairs were chosen for each task. Only segments that are above the mean plus the mean absolute deviation are considered as taskrelated and obtained for further analysis.
Mutual Information based Network Analysis
Graphical Theoretical Analysis Applied to the Relevance Network
The MI matrix for each subject is converted to a graph separately, and the means of the cluster coefficient C and the shortest path length L of the graph within the group (ie. NSQ, PDSQ, NBO, PDBO) were computed as a function of the threshold T.
As T is varied from 0.01 to 0.3, the graphs started to break into subgraphs. In addition, at higher T, some subjects start to have empty graphs meaning the graphs contain no connection at all. Therefore, when we interpret the results, we need to make note of where those points are and they are summarized in Table 1. Again, we see that the points between N and PD do not differ much because their means are very close. The overall mean C of the graph for each group as a function of T was computed and compared. Because the means of the four groups (ie. NSQ, PDSQ, NBO, PDBO) as a function of T follow the same pattern and we are more interested in the differences between groups, the deviation from the overall mean of the four groups as a function of T is illustrated at the top panel of Fig. 11. The overall mean of the four group as a function of T is displayed at the bottom left corner of the top panel. The bottom panel shows the region that is significantly different between groups (at 2: N vs. PD during SQ; at 3: N vs. PD during BO; at 4: SQ vs. BO for N; at 5: SQ vs. BO for PD). The significance of the C between groups is tested with the pairwise ttest (p < 0.05). In general, the intensity of connections within the cluster does not differ significantly between tasks (SQ and BO) within a group. The intensity of connections within the cluster is higher for PD compared to N for SQ task and BO task, especially at higher threshold T (T > 0.15). The consistently lower C seen in N compared to PD across all frequency bands probably reflects the widespread, excessive synchronization seen in PD [34, 35]. Unlike prior studies that have emphasized synchronization in the beta band, we have observed excessive synchronization in all bands, especially the theta band.
Squeeze Task (SQ) and Both Task (BO): Threshold T when graphs start to split into subgraphs or become empty graphs
NSQ  PDSQ  NBO  PDBO  

Subgraphs  Empty Graphs  Subgraphs  Empty Graphs  Subgraphs  Empty Graphs  Subgraphs  Empty Graphs  
5–8 Hz  0.0600  0.2340  0.0660  0.2380  0.0760  0.2600  0.0600  0.2360 
8–12 Hz  0.0520  0.2140  0.0560  0.2120  0.0460  0.1980  0.0580  0.1980 
12–30 Hz  0.0500  0.2060  0.0520  0.1660  0.0440  0.1920  0.0540  0.1640 
Squeeze Task (SQ): Clustering coefficient C per vertex and the pvalue of the pairwise Ttest between Normal and Parkinson's subjects.
5–8 Hz  8–12 Hz  12–30 Hz  

Channel #  N mean  PD mean  Pvalue  N mean  PD mean  Pvalue  N mean  PD mean  Pvalue 
2Fp2  0.5786  0.6075  4.42E01  0.6229  0.7133  4.97E03  0.6982  0.7660  6.75E03 
3F7  0.2106  0.2770  9.33E02  0.2705  0.3638  2.58E02  0.3961  0.5643  5.95E05 
4F3  0.5290  0.6062  3.28E02  0.6170  0.6470  3.35E01  0.6781  0.7039  2.37E01 
5FZ  0.4791  0.6041  6.92E06  0.5648  0.6767  6.15E06  0.6439  0.7440  2.82E07 
6F4  0.5204  0.6574  8.34E05  0.5363  0.6728  4.11E06  0.6148  0.7013  1.39E04 
7F8  0.1958  0.2478  1.40E01  0.2806  0.3679  2.95E02  0.4731  0.4819  8.31E01 
8T3  0.0159  0.0630  7.14E03  0.0312  0.1073  1.20E03  0.1767  0.2333  1.10E01 
9C3  0.2138  0.2895  2.82E02  0.3395  0.3392  9.92E01  0.5177  0.4640  7.19E02 
10CZ  0.2229  0.3275  9.49E04  0.3466  0.3913  1.35E01  0.5209  0.5234  9.20E01 
12T4  0.0054  0.0739  2.38E04  0.0453  0.1346  8.02E04  0.1734  0.2746  4.57E03 
13T5  0.1844  0.1034  1.06E02  0.2824  0.1384  7.93E05  0.4799  0.2557  8.59E08 
14P3  0.2241  0.1917  3.05E01  0.3117  0.2322  1.17E02  0.4765  0.3414  7.11E06 
15PZ  0.2409  0.1787  3.92E02  0.3340  0.2310  8.52E04  0.5111  0.3665  8.04E07 
16P4  0.2139  0.1838  3.25E01  0.2691  0.2423  3.85E01  0.4560  0.3563  6.30E04 
17T6  0.1123  0.1057  8.14E01  0.2228  0.1265  3.59E03  0.4521  0.2778  2.94E05 
18O1  0.1310  0.1537  4.61E01  0.2029  0.1955  8.25E01  0.4547  0.3436  4.26E03 
19O2  0.1428  0.1402  9.35E01  0.2083  0.1900  5.93E01  0.4615  0.3422  1.86E03 
Both Task (BO): Clustering coefficient C per vertex and the pvalue of the pairwise Ttest between Normal and Parkinson's subjects. (T = 0.2 for 5–8 Hz; T = 0.18 for 8–12 Hz; T = 0.15 for 12–30 Hz)
5–8 Hz  8–12 Hz  12–30 Hz  

Channel #  N mean  PD mean  Pvalue  N mean  PD mean  Pvalue  N mean  PD mean  Pvalue 
2Fp2  0.5988  0.6179  5.83E01  0.6801  0.7089  3.26E01  0.7158  0.7630  2.37E02 
3F7  0.1758  0.3215  8.66E05  0.2286  0.3980  1.72E05  0.3552  0.5811  1.91E08 
4F3  0.5665  0.6533  8.77E03  0.6233  0.6993  9.53E03  0.6844  0.7434  5.65E03 
5FZ  0.5188  0.6053  1.40E03  0.5661  0.6955  1.14E08  0.6334  0.7611  4.61E12 
6F4  0.4917  0.6331  1.03E05  0.5972  0.6808  1.75E03  0.6668  0.7204  7.50E03 
7F8  0.2554  0.3190  9.12E02  0.3399  0.4300  2.19E02  0.5210  0.6103  1.71E02 
8T3  0.0237  0.1047  2.86E04  0.0520  0.1321  2.12E03  0.1746  0.2498  4.09E02 
9C3  0.2392  0.3473  1.54E03  0.3431  0.4263  1.87E02  0.4820  0.5116  3.13E01 
10CZ  0.2741  0.3395  2.41E02  0.3627  0.4190  4.90E02  0.5087  0.5213  6.16E01 
11C4  0.3185  0.3149  9.15E01  0.4567  0.4056  1.25E01  0.4975  0.5294  2.26E01 
12T4  0.0133  0.0900  4.02E05  0.0580  0.1366  1.70E03  0.1689  0.2995  2.04E04 
13T5  0.2043  0.1184  6.77E03  0.3055  0.1369  2.05E06  0.4810  0.2283  3.19E10 
14P3  0.2537  0.1812  1.67E02  0.3270  0.2357  2.92E03  0.4320  0.3747  5.79E02 
15PZ  0.2377  0.2390  9.63E01  0.3323  0.3010  3.00E01  0.4923  0.4195  8.46E03 
18O1  0.1629  0.1489  6.29E01  0.2441  0.1898  9.16E02  0.4316  0.3235  3.39E03 
19O2  0.1652  0.2749  2.02E03  0.2322  0.3291  8.20E03  0.4322  0.4095  5.38E01 
Statistical Analysis on MI Network
Conclusion
This paper proposed a novel segmentation, mutual information network framework for EEG connectivity analysis for subjects performing a motor task. The greatest EEG changes during motor performance are typically eventrelated synchronization/desynchronization: EEG responses are not phaselocked to motor performance, but rather tend to be associated with augmentation or attenuation of specific frequency bands. This means that standard methods of averaging the EEG timelocked to the motor performance will tend to be inaccurate, necessitating the use of alternate methods. In addition, ERS/ERD is typically investigated in univariate fashion, where each EEG channel is examined independently for altered localized neuronal synchrony resulting in changes in the frequency spectra at that channel. Here we have used the crossspectrum of ICs as a marker for segmentation. This has multiple benefits: first, consistent with ERS/ERD, it examines the data in the frequency domain, second, it allows the examination of multiple channels simultaneously, as each IC will consist of a linear weighting of all channels, and lastly, it will allow unmixing of the raw data so that task related activity can be extracted from ongoing background brain rhythms. After segmentation, we used mutual information to measure both linear and nonlinear dependencies, without assuming strict phase locking of signals. This allowed us to create a relevance network suitable for graphtheoretic analysis methods, and an MI network which further incorporated the magnitude of the MI at each channel pair to allow statistical analysis with ANOVA.
The proposed method provided several novel insights into abnormalities in PD subjects. The well known clinical observation of difficulty in performing simultaneous movements [12] appears to be related to an inability to recruit different brain areas independently. When normal subjects were asked to perform tasks with two hands compared to a task with one hand, there was no significant difference in the theta bands, and only mild changes in connectivity in the alpha and beta bands (Fig. 16). In contrast, when PD subjects attempted to perform simultaneous movements, they appeared unable to recruit different brain areas independently, resulting multiple areas of synchronization in the theta range, and also in the beta range. These results appear novel, as previous research has emphasized excessive synchronization in the beta range in PD [36].
Additionally, the widespread synchrony that is normally already seen during regular unimanual or bimanual performance was of a different form in PD (Figs. 11, 12, and 17). PD subjects tended to have higher cluster coefficients, C, and lower shortest path lengths, L suggesting focal clusters of synchronous activity. Taken together, these results suggest that normal subjects can synchronously activate broad areas or cortex independently in response to differing task demands. In contrast, PD subjects appear to have islands of hypersynchronicity that cannot be recruited independently. This is consistent with known biology of PD, where bradykinesia is most likely the result of "noisy" basal ganglia input to the frontal cortex and appears to critically depend upon dopamine depletion [37] as would be seen in the PD subjects off medication in this study. The higher MI values in the frontal region at lower and medium frequency bands and motor cortex at higher frequency in PD (Fig. 17) are also consistent with the cortical regions that receive output from the basal ganglia. Since the EEG is normally assumed to reflect cortical activity, isolation of clear abnormalities from PD subjects who have predominantly basal ganglia dysfunction and preserved cortical function is notable.
Although we suggest that our results demonstrate strong evidence to support the proposed framework as a tool to study EEG signals, there are nevertheless limitations of the proposed method. For example, currently only pairwise MI, one particular case of calculating the MI between M random variables, is investigated. In a more general presentation, the corresponding M–dimensional MI can be defined. Since pairwise independence does not necessarily imply global independence, M–dimensional MI may reveal additional information from that of pairwise MI, and thus may be a fruitful avenue to explore in the future for EEG analysis. Similarly, pairwise MI may suffer from a high false discovery rate, i.e. nodes are erroneously associated while in truth they only indirectly interact through one or more other nodes. Therefore, to prune the reconstructed network of such false positives, we can extend the current work by exploring the concept of conditional mutual information (CMI) instead. Also, in the current approach, we did not consider the temporal information embedded in the timeseries EEG data. As one future work, we intend to introduce temporality into the proposed MI network construction.
Declarations
Acknowledgements
This work was supported by the Canadian Natural Sciences and Engineering Research Council (NSERC) under grant STPGP 36520808, and by the CHRP grant.
Authors’ Affiliations
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