EEG functional network topology is associated with disability in patients with amyotrophic lateral sclerosis

Amyotrophic Lateral Sclerosis (ALS) is one of the most severe neurodegenerative diseases, which is known to affect upper and lower motor neurons. In contrast to the classical tenet that ALS represents the outcome of extensive and progressive impairment of a fixed set of motor connections, recent neuroimaging findings suggest that the disease spreads along vast non-motor connections. Here, we hypothesised that functional network topology is perturbed in ALS, and that this reorganization is associated with disability. We tested this hypothesis in 21 patients affected by ALS at several stages of impairment using resting-state electroencephalography (EEG) and compared the results to 16 age-matched healthy controls. We estimated functional connectivity using the Phase Lag Index (PLI), and characterized the network topology using the minimum spanning tree (MST). We found a significant difference between groups in terms of MST dissimilarity and MST leaf fraction in the beta band. Moreover, some MST parameters (leaf, hierarchy and kappa) significantly correlated with disability. These findings suggest that the topology of resting-state functional networks in ALS is affected by the disease in relation to disability. EEG network analysis may be of help in monitoring and evaluating the clinical status of ALS patients.

over time. Schmidt et al. 10 , have recently shown that structural and functional connectivity degeneration in ALS are coupled and that the pathogenic process strongly affects both structural and functional network organization. Other resting-state fMRI studies [11][12][13] have reported alterations in specific resting-state networks. Recently, Iyer and colleagues 14 have investigated the use of resting-state electroencephalographic (EEG) as a potential biomarker for ALS, suggesting that a pathologic disruption of the network can be observed in early stages of the disease. However, it still remains relevant to address methodological issues that may affect both connectivity estimation and network reconstruction 15 .
Although the results described above are promising, it is not yet clearly understood how whole-brain functional networks are perturbed in ALS patients, and how this relates to disability. Resting-state EEG analysis may represent a practical tool to evaluate and monitor the progression of the disease. Despite the wide use of EEG in the assessment of brain disorders 5,16,17 , it has not been used widely to evaluate functional network changes induced by ALS. To test our hypothesis, we reconstructed functional networks from resting-state EEG recordings in 21 ALS patients and 16 age-matched healthy controls using the phase lag index (PLI) 18 , a widely used and robust measure of phase synchronization that is relatively insensitive to the effects of volume conduction. The topologies of frequency specific minimum spanning trees (MSTs) were subsequently characterised and compared between groups as it has been shown 19,20 that it avoids important methodological biases that would otherwise limit a meaningful comparison between the groups 21 . Moreover, a correlation analysis was performed between the MST parameters and disability.

Results and Discussion
Age-matching. No significant group differences were observed in age (W = 145.5, p = 0.499).
Functional Connectivity. No significant group differences were observed for the global mean PLI in any frequency band (both with and without FDR correction for number of frequency bands). Descriptive results and statistics are summarized in Table 1. No significant correlation was observed between the patients' global mean PLI and the disability score for any frequency band (see Table 2).
MST dissimilarity. A significant MST dissimilarity between ALS patients and healthy controls was found in the beta band using Mann-Whitney U test (W = 68.00, p = 0.008) after FDR correction.
MST topology. A significant difference between groups was observed for MST leaf fraction in the beta band (W = 87.5, p = 0.014). Results from Mann-Whitney U test statistics are summarized in Table 3. Individual values for each MST parameter in the beta band are shown in Fig. 1. Significant correlations were observed between some MST parameters (leaf, hierarchy and kappa) and disability score in the beta band (scatterplots for individual MST parameters and disability scores are reported in Fig. 2). Plots and correlations at single epoch level are also reported (see Fig. 3).
Power analysis. No significant differences were observed in any frequency band.

Discussion
In summary, by applying the PLI and the MST analysis in EEG recordings, this study shows large-scale changes in the functional brain network organization in ALS patients as identified using MST dissimilarity. Post-hoc analysis revealed that this difference in network topology between patients and controls was due to a difference in leaf fraction, and that the patients' network organization in terms of MST parameters significantly correlated with disability, which is of clinical relevance. These results were observed in the beta band (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), where the MST topology was characterized by a significantly lower leaf fraction in the patients. Together with the significant negative correlation between disability score and leaf fraction, as well as a positive correlation with the diameter (even though not significant), indicates the tendency to deviate from a more centralized (star-like topology) towards a more decentralized organization (line-like topology). The negative correlation between tree hierarchy and disability score suggests that there is a sub-optimal balance between hub overload and functional integration in the network. Moreover, the negative correlation between disability and kappa, a measure that captures the broadness of the degree distribution, reflects the detrimental effect of a network topology with a reduced ease of synchronization (i.e., decreased spread of information across the tree) 22 . Furthermore, it is also important to note that the correlation analysis is still valid when using data from every single epoch (see Fig. 3). This further analysis suggests that even when using MST parameters extracted from single epochs it is possible to characterise the association between network topology and patients disability score. As hypothesized, these findings suggest that ALS alters the brain network topology, which thus tends to deviate from the normal, presumably optimal, organization, and suggest that the correlation between MST parameters and the ASLFRS-R scale maybe be useful in monitoring the progression of the disease. These findings indicate that also at macroscopic scale (as measured by EEG functional networks), in accordance with previous studies on structural and functional neuroimaging 2 , ALS seems to affect extramotor brain regions, a result that is in line with the idea that pathological perturbations are rarely confined to a single locus 23 .
Moreover, it is of interest to note that a similar shift towards a more decentralized topology has been previously observed in multiple sclerosis 24 and Parkinson's disease 25 , and that functional networks in epilepsy patients that respond to vagal nerve stimulation re-organize towards a more centralized topology 26 . Together, these findings suggest that there is a possible common pathway in neurological disorders, as has been hypothesised  Table 3. Group differences in the beta band.

Figure 1. MST parameters for the patients and controls in the beta band.
Horizontal bars indicate mean and standard deviation. Each dot or square represents a single ALS patients or healthy control, respectively. recently 5 . Group differences and significant correlations between network topology and disability were found in the beta band, which may not be surprising given its link with motor function 27 and that changes in beta activity can occur with ageing, sensorimotor disorders and amyotrophic lateral sclerosis 28,29 . It should also be noted that the observed differences in network topology are unlikely to be due to differences in beta-band power, since no significant power differences were observed between the groups. Even though this latest finding seems in contrast with a recent MEG study 30 that reported an intensified cortical beta desynchronization in ALS patients, other studies have not reported the same finding 28,31 . Differences in protocol design, for example the use of different tasks, or resting-state data, or differences in characteristics of the patient population, may explain these differences across studies. From a theoretical point of view, it is also unlikely that changes in the topology of PLI-based MSTs are due to power changes, because the PLI is a phase-based measure that is not directly affected by power, and the MST is based on the ranking of connections, not on their absolute values. Noteworthy in this respect is that we also observed that the mean PLI was not different between the groups.
Despite the observed differences between healthy controls and ALS patients in terms of MST dissimilarity and leaf fraction, and clinically relevant correlations between disability and network topology, we found that the detection of distinctive EEG network properties still remains a difficult task during the early stages of the disease. This is in contrast with the study by Iyer and colleagues 14 , who used a set of connectivity metrics in combination with network analysis. In contrast to their work, we used different methods of functional connectivity (PLI) and network reconstruction (MST), as well as a conservative statistical approach. Indeed, the PLI has been shown to be an index of phase synchronization that is robust to biases introduced by volume conduction and field spread. Moreover, the MST represents a network approach that, although still providing network characteristics that can be related to conventional graph measures 20 , is not biased by common methodological issues arising when reconstructing and comparing networks using traditional approaches (i.e. the use of arbitrary thresholds) 21 .
Previous studies have shown a direct relation between disability and disease progression 32 . Interestingly, the observed correlation between network organization and disease disability suggests that it might be possible to track disease progression on the basis of EEG network analysis. However, a longitudinal study is needed to confirm this idea. The difference between groups in terms of overall MST topology (i.e. the MST dissimilarity results), in combination with the change in leaf fraction, suggests that ALS affects the brain networks at a global level. However, it could be that the networks were reconstructed at a level that was too coarse, and/or without enough anatomical precision. The study of source-reconstructed time-series would be of help in investigating the role of specific brain regions, and in identifying whether certain regions are more affected than others.
Despite the limits of EEG analysis, the proposed approach has several advantages over other techniques. In particular, in comparison with fMRI, EEG is a direct measure of neuronal activity, allows time-frequency analysis of this activity, is less affected by head motion, can more readily be used with challenging patient populations (such as ALS), and the hardware costs are significantly lower. Furthermore, the high temporal resolution enables the study of dynamic processes involved in brain diseases such as ALS. Even though MEG has comparable temporal and spectral resolutions, and typically a higher spatial resolution, the costs of installment and maintenance, as well as the limited number of installed systems, still represent important obstacles. EEG has therefore still an important role in the study of ALS.
In conclusion, this study shows that EEG functional network re-organization in ALS patients, as computed by the PLI and MST approach, is associated with the patient disability. This finding suggests that resting-state EEG networks analysis may play an important role in evaluating the status of ALS patients and monitoring disease progression.

Methods
Subjects. Twenty-one patients (7 female; mean age 66, standard deviation 9 years) diagnosed with ALS according to the revised El Escorial criteria 33 , who attended the ALS Centre of the Azienda Ospedaliera Universitaria of Cagliari (Italy), were included in the study. A control group, consisting of sixteen age-and gender-matched healthy subjects (9 female; mean age 65, standard deviation 7 years), was also included. Informed consent was obtained from all participants. Local ethics committee from University of Cagliari approved the study protocol (NP/2013/1496) and all procedures were carried out in accordance with the approved protocol. The clinical ALSFRS-R score 32 , a validated rating instrument for monitoring the progression of disability in patients with ALS, was evaluated at the time of EEG recording. This score was converted to a disability score by subtracting it from the maximum obtainable score, i.e. 48 -ALSFRS-R. That is, a disability score of 0 means that you are healthy.
Functional connectivity. The phase lag index (PLI) 18 , which evaluates the asymmetry of the distribution of instantaneous phase differences between pairs of channels, was used to estimate functional connectivity (FC). Computing FC between all pair wise combinations of EEG time-series resulted in a weighted adjacency matrix of 58 × 58 entries (after excluding bad channels form both patients and healthy subjects) for each epoch. Mean PLI was also computed across epochs and channels.
MST reconstruction. The MST is an acyclic sub-network, which connects all nodes minimizing the link weights (for the computation of the MST, the link weight is defined as 1-PLI). The MST was obtained using Kruskal algorithm 35 . The topology of the MST was characterised using several measures: the diameter, the normalized leaf fraction, kappa (or degree divergence) and the tree hierarchy. The diameter, which is the largest distance between any two nodes, is defined as the longest shortest path in the network. The normalized leaf fraction is calculated as the number of nodes with degree of 1 divided by the total number of nodes, and is a measure of integration in the network 19,20 . It has been shown that both these MST descriptors are important network parameters during development 36 , that they capture network alterations in multiple sclerosis 24 , in Parkinson disease 25 , in epileptic patients implanted with VNS 26 and in aging 37 . Kappa, or degree divergence, is a measure of the broadness of the degree distribution. It is related to resilience against attack, epidemic spreading and synchronizability 20 . Furthermore, it has been shown that Kappa is high in networks with a scale-free degree distribution 4 . The tree hierarchy captures the balance between a small diameter and overload of hub nodes. This MST parameter ranges from 0 to 1 and an optimal tree configuration is thought to correspond to hierarchy values around 0.5 (intermediate between a line-like and star-like topology, i.e. a compromise between hub-overload and weak integration) 19 .
MST dissimilarity. MST dissimilarity, which assesses the overlap between MSTs 38 , was estimated between MSTs of ALS patients and healthy controls. In this study the MST reconstructed from the average connectivity matrix of all healthy subjects was used as reference in order to compute MST dissimilarities for both patients and controls 24 . Power analysis. Power analysis was performed using Welch's averaged modified periodogram method. The power spectral density (PSD) was computed separately for each epoch and subject. The relative power for each frequency band was successively evaluated and averaged over the epochs.
Statistical analysis. Statistical differences in age, mean PLI, and MST dissimilarity between groups were evaluated using the non-parametric Mann-Whitney test. The value used for significance was set to p < 0.05 and a correction for multiple comparisons was performed by the false discovery rate (FDR), correcting for the four frequency bands 39 . In case we found significant MST dissimilarity, post-hoc analysis was performed to find out which MST parameters were different. Moreover, a Spearman's rank correlation coefficient was computed to assess the relationship between the network topology (in terms of mean PLI and MST parameters) and disease severity (in terms of the disability score). Statistical analysis was performed using JASP (version 0.7.5 beta 2 for Mac OS X) 40 .