Patterned functional network disruption in amyotrophic lateral sclerosis

Abstract Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease primarily affecting motor function, with additional evidence of extensive nonmotor involvement. Despite increasing recognition of the disease as a multisystem network disorder characterised by impaired connectivity, the precise neuroelectric characteristics of impaired cortical communication remain to be fully elucidated. Here, we characterise changes in functional connectivity using beamformer source analysis on resting‐state electroencephalography recordings from 74 ALS patients and 47 age‐matched healthy controls. Spatiospectral characteristics of network changes in the ALS patient group were quantified by spectral power, amplitude envelope correlation (co‐modulation) and imaginary coherence (synchrony). We show patterns of decreased spectral power in the occipital and temporal (δ‐ to β‐band), lateral/orbitofrontal (δ‐ to θ‐band) and sensorimotor (β‐band) regions of the brain in patients with ALS. Furthermore, we show increased co‐modulation of neural oscillations in the central and posterior (δ‐, θ‐ and γl‐band) and frontal (δ‐ and γl‐band) regions, as well as decreased synchrony in the temporal and frontal (δ‐ to β‐band) and sensorimotor (β‐band) regions. Factorisation of these complex connectivity patterns reveals a distinct disruption of both motor and nonmotor networks. The observed changes in connectivity correlated with structural MRI changes, functional motor scores and cognitive scores. Characteristic patterned changes of cortical function in ALS signify widespread disease‐associated network disruption, pointing to extensive dysfunction of both motor and cognitive networks. These statistically robust findings, that correlate with clinical scores, provide a strong rationale for further development as biomarkers of network disruption for future clinical trials.

frontal (δ-and γ l -band) regions, as well as decreased synchrony in the temporal and frontal (δ-to β-band) and sensorimotor (β-band) regions. Factorisation of these complex connectivity patterns reveals a distinct disruption of both motor and nonmotor networks.
The observed changes in connectivity correlated with structural MRI changes, functional motor scores and cognitive scores. Characteristic patterned changes of cortical function in ALS signify widespread disease-associated network disruption, pointing to extensive dysfunction of both motor and cognitive networks. These statistically robust findings, that correlate with clinical scores, provide a strong rationale for further development as biomarkers of network disruption for future clinical trials.  (Hardiman, Van Den Berg, & Kiernan, 2011). Although originally considered a disease exclusively of the motor system (Achi & Rudnicki, 2012), widespread nonmotor (Bede et al., 2013) and subcortical (Bede et al., 2018) structural changes are now recognised (Douaud, Filippini, Knight, Talbot, & Turner, 2011). Clinical and neuroimaging evidence confirms extensive involvement of motor (Douaud et al., 2011;Nasseroleslami et al., 2019;Proudfoot, van Ede, et al., 2018) and cognitive (Iyer et al., 2015;McMackin, Dukic, et al., 2019) pathways and networks. These network impairments manifest as measurable changes in cortical connectivity, informing altered dynamics within different networks, which may lead to widespread changes in neural signalling beyond the regions of direct disease pathology.
Functional magnetic resonance imaging (fMRI) studies have identified increased connectivity in the sensorimotor networks of ALS patients (Agosta et al., 2011;Douaud et al., 2011) based on blood oxygen-level-dependent signal. However, network impairment can also be interrogated using neuroelectric signals captured with electroencephalography (EEG). These signals appear in varying frequency bands and can differ substantially across networks (Siegel, Donner, & Engel, 2012). This variability is due to the complex hierarchal organisation of projections between different granular layers forming connections between different areas (Barbas, 2015;Kopell, Kramer, Malerba, & Whittington, 2010), which oscillate at either lower or higher frequencies (Jensen, Bonnefond, Marshall, & Tiesinga, 2015). These spectral signatures of connectivity require high temporal resolution and cannot be captured by fMRI (Hipp, Hawellek, Corbetta, Siegel, & Engel, 2012;Laufs, 2008).
Previous EEG studies have shown altered patterns, such as increased frontal-to-parietal connectivity in ALS (Blain-Moraes, Mashour, Lee, Huggins, & Lee, 2013;Iyer et al., 2015;Nasseroleslami et al., 2019). To date, however, there have been limited attempts to localise abnormal EEG patterns to specific brain regions. A recent magnetoencephalography study in ALS has focussed on slow/broadband fMRI-like activity, and has demonstrated widespread changes within the posterior brain regions . However, because network interactions are often marked by narrow band cortical oscillations (Buzsáki & Draguhn, 2004), it has not been possible to address the spectral aspects of ALS-specific changes in brain networks using broadband signals. Moreover, although source-space studies that use frequency-specific analysis have also been performed in ALS (Fraschini et al., 2018;Sorrentino et al., 2018), the phase-and amplitude-based connectivity profiles of specific brain networks affected by ALS remain to be established.
The majority of the commonly used EEG connectivity measures falls into two categories: amplitude-based and phase-based indices.
Within a given frequency-band, these two different groups of measures reflect two conceptually different aspects of the cortical communication. Amplitude-based measures are predominantly used to quantify co-modulation of the oscillatory activity in distinct brain areas at infra-slow rates (<0.1 Hz), which are shown to resemble slow co-modulations observed in resting-state fMRI (Brookes et al., 2011;Tagliazucchi, von Wegner, Morzelewski, Brodbeck, & Laufs, 2012).
These fluctuations seem to emerge from the regulation and coordination of the network activity for an (upcoming) functionally distinct task in the brain at larger temporal and spatial scales; therefore, reflecting the functional organisation of the brain networks (Leopold, Murayama, & Logothetis, 2003;Munk, Roelfsema, König, Engel, & Singer, 1996;Siegel et al., 2012). Phase-based coupling likely informs on facilitation and regulation of communication between distinct brain areas on faster timescales (Engel, Gerloff, Hilgetag, & Nolte, 2013;Siegel et al., 2012). In principle, these two measures are independent of one another (Bruns, Eckhorn, Jokeit, & Ebner, 2000). For instance, the activity in two brain regions can strongly co-vary, albeit their phase values being randomly distributed. However, these two types of measures and their corresponding underlying mechanisms seem to interact and work together; with the amplitude-based coupling indicating the priming of the activation of brain areas needed for an upcoming task, and the phase-based coupling indicating the instantaneous synchronous influences in the networks (Engel et al., 2013).
Nevertheless, exploring brain dynamics exclusively using either amplitude-or phase-based connectivity measure provides limited insights into the underlying functional changes and ALS pathophysiology in general.
To date, evidence of correlation between the brain network impairments in ALS observed from neuroelectric signals and clinical scores of motor and cognitive function has been limited. In addition to this, the observed changes have not discriminated between the traditionally defined clinical ALS subgroups (e.g., bulbar-vs. spinal-onset ALS or ALS with the presence or absence of the pathologic hexanucleotide expansion in the C9ORF72 gene) Nasseroleslami et al., 2019).
Here, we have reconstructed resting-state brain activity and performed functional connectivity analysis using both amplitude-and phasebased measures in a large group of ALS patients and healthy controls. Our findings correlate with clinical measures, providing robust evidence that measurement of functional connectivity can be used as a complementary investigative tool to interrogate ALS-associated changes in brain networks. St. James's Hospital, Dublin, Ireland. The experimental procedure conformed to the Declaration of Helsinki. All participants provided written informed consent before taking part in the experiments.

| Patient recruitment
Patients with ALS were recruited from the National ALS clinic in Beaumont Hospital, Dublin. Healthy controls were recruited from an existing control cohort of a neuropsychology study in ALS .

| Inclusion criteria
All ALS patients were within the first 18 months of their diagnosis and fulfilled the revised El Escorial diagnostic criteria for possible, probable, or definite ALS (Ludolph et al., 2015).

| Exclusion criteria
Patients diagnosed with primary lateral sclerosis, progressive muscular atrophy, flail arm/leg syndromes, prior transient ischemic attacks, multiple sclerosis, stroke, epilepsy, seizure disorder, brain tumours, structural brain abnormalities, other neurodegenerative conditions and other medical morbidities, such as human immunodeficiency virus, were excluded.

| MRI data
Magnetic resonance data were available for 37 ALS patients (Schuster, Elamin, Hardiman, & Bede, 2016). Structural T1-weighted MRI data were acquired on a 3 T Philips Achieva system with a gradient strength of 80 mT/m and slew rate of 200 T/m/s using an eight-channel receive-only head coil. They were obtained using a three-dimensional inversion recovery prepared spoiled gradient recalled echo sequence with field-of-view = 256 × 256 × 160 mm 3 , spatial resolution = 1 mm 3 (Schuster et al., 2016;Schuster, Hardiman, & Bede, 2017). MRI scans were individually screened for the presence of vascular alterations on fluid-attenuated inversion recovery (FLAIR) and diffusion-weighted imaging (DWI) sequences and patients with co-morbid vascular white matter lesions were not included (Bede, Iyer, Finegan, Omer, & Hardiman, 2017).

| EEG source localisation
EEG data were source reconstructed using the linearly constrained minimum variance beamformer (Van Veen, Van Drongelen, Yuchtman, & Suzuki, 1997) to obtain time-varying signals originating from the brain.
An atlas-based approach was applied to estimate signals from 90 brain regions (see Supporting Information). The included regions of interest (ROIs) were from the automated anatomical labelling atlas (Tzourio-Mazoyer et al., 2002), excluding the cerebellum and including the subcortical regions (see Figure S2, Supporting Information).

| Estimating spectral power
For each ROI, spectral power was calculated using the autospectrum: where x(t) is a time-domain signal corresponding to brain region and FT{Á} is a Fourier transformation. Spectral power was estimated in six frequency bands, as the sum of the auto-spectrum values within each frequency band.

| Estimating functional connectivity
For each pair of ROIs, functional connectivity was calculated from two different perspectives to inform on different aspects of connectivity between brain regions.
An amplitude-based measure, the 'amplitude envelope correlation' (AEC) (Brookes et al., 2011) measures the correlation between the power envelopes of two oscillatory time series. It reflects the simultaneous presence and co-modulation of the intensity of the oscillatory activity in two regions. The phase synchrony of the oscillations in the two ROIs is not reflected in AEC. This amplitude-based measure was chosen because of its capability to mirror the functional networks obtained in fMRI studies (Hipp & Siegel, 2015).
A phase-based measure, the 'imaginary coherence' (iCoh) (Nolte et al., 2004), captures the extent to which two signals have a constant relative nonzero phase. This measure reflects the neuronal communication between the brain regions that contribute to synchronous neural oscillations, even though the intensity of the activities in the two ROIs may behave differently.
Estimating the functional connectivity in source-space requires caution, since signals beamformed at spatially separate cortical locations are not necessarily independent (Schoffelen & Gross, 2009). This signal leakage can lead to spurious zero-lagged connectivity between reconstructed signals (Palva et al., 2018). Hence, removing instantaneous relationships between pairs of projected signals would mitigate the problem, albeit at the expense of removing true instantaneous interactions between them. The implementation of the connectivity measures in this study corrects for this zero-lag leakage.

| Amplitude envelope correlation
To mitigate the problem of spurious connectivity caused by source localisation methods, we performed time-domain orthogonalisation of the reconstructed time series (Brookes, Woolrich, & Barnes, 2012) between each pair of ROIs before estimating the power envelopes, as follows: where x(t) and y(t) are time-domain signals representing two brain regions and filtered to a specific frequency band, and HT{Á} is a Hilbert transformation. Estimated power envelopes were then downsampled to 0.5 Hz.
As a measure of association, an absolute value of Pearson's correlation was used on the entire log-transformed power time series, as follows:

| Imaginary coherence
Unlike AEC, iCoh is not affected by the limitation of source localisation methods (Palva et al., 2018). It is defined as follows: where J m S xy f g denotes the imaginary part of cross-spectral density between the signal x(t) and y(t), whereas S x and S y are the autospectral densities calculated for those signals. iCoh was estimated from 2 s long epochs.
These two measures were calculated for all possible pairs of estimated ROI signals, resulting in two symmetric 90 × 90 connectivity matrices for each subject. This was carried out for six separate frequency bands: δ (2-4 Hz), θ (5-7 Hz), α (8-13 Hz), β (14-30 Hz) and γ (γ l : 31-47 Hz, γ h : 53-97 Hz). Frequencies of 48-52 Hz were excluded from the analysis due to the potential power-line noise. This resulted in 12 connectivity matrices per subject which are referred to as 'point-to-point connectivity'. These matrices can be seen as weighted network matrices with elements representing link weights between network nodes. Additionally, each matrix was averaged using algebraic mean across ROIs to estimate the average connectivity of each brain region. This resulted in one value per ROI, representing mean node strength (average link weight), from each connectivity matrix.

| Connectivity modules
To extract and compare the connectivity modules/networks affected in ALS, we used non-negative matrix factorisation (NMF) (Paatero & Tapper, 1994). This method factorises a given matrix V, such that  (Schwarz, 1978).

| Correlates of EEG with MRI, neuropsychology and disease severity
We correlated the signal analysis findings with the structural MRI data, motor disease severity (ALSFRS-R) and cognitive scores derived from a neuropsychological battery.
In all cases, except in correlations with cognitive scores, the Spearman's partial correlation was used to test the presence of the hypotheses, and at the same time to correct for the age of patients. In the case of correlations with cognitive scores, the Spearman's correlation was used, since the cognitive scores were z-scored, already accounting for age.

| Statistical analysis
Statistical analysis of high-dimensional measures suffers from high rates of false positive findings, which necessitates the use of advanced statistics to mitigate the problem. To determine the statistical significance of the observed differences in each of the three highdimensional measures (spectral power, AEC and iCoh), we used frequentist statistics together with an implementation of the empirical Bayesian inference (EBI) (Efron, 2007;Efron, Tibshirani, Storey, & Tusher, 2001) suited to neuroelectric signal analysis (Nasseroleslami, 2018). EBI provides major benefits, such as reliable estimation of FDR, calculation of statistical power and the posterior Bayesian probability, which are not afforded by alternative methods.
We used the area under the curve (AUC) of the receiver operating characteristics curve to make the between-group comparisons (Zhou, McClish, & Obuchowski, 2011). To further infer statistical significance in a high-dimensional space, EBI is applied on the test statistics (i.e., AUC), which exploits both the original (non-null) observations and null-permuted data to estimate the probability density function of the data and null, respectively. We then estimated the posterior probability (P 1 ) and the statistical power (1-β). The statistical analysis was performed separately for each of the three measures and for each frequency band in the case of point-to-point connectivity, while in the case of spectral power and average connectivity the analysis was done on the concatenated data across frequencies. False discovery rate (FDR) was set to 10%. This selection was based on careful inspection of curves that explain the relationship between FDR and power (or between Type I and Type II errors) as a function of thresholds (Nasseroleslami, 2018).
To assess the statistical significance and statistical power of the connectivity modules from the NMF analysis and the correlations between EEG connectivity and other measures, a null and non-null bootstrapping resampling (n = 10,000) approach was applied (Nasseroleslami, 2018;Nasseroleslami et al., 2019). In the former case, the resampling was applied on the NMF weights, whereas in the latter case, it was applied on the data used in the correlation analysis. Here, to control for multiple comparisons, rejection of null hypothesis was additionally checked using adaptive FDR (aFDR) (Benjamini, Krieger, & Yekutieli, 2006) set to 5%.
In the analysis of ALS subgroups, two-way ANOVA was applied on all three EEG measures (spectral power, AEC and iCoh) in two frequency bands that showed the most prominent changes in ALS patients compared to healthy controls. The analysis was performed on each measure and frequency band separately, with the C9ORF72 status (presence/absence of the gene mutation) and the site of symptom onset (bulbar/spinal) chosen as independent variables. Data used were averaged from selected brain regions that had the highest discriminatory power between healthy controls and ALS patients in each measure and frequency band separately. Prior to the ANOVA analysis, data were transformed to standard normal distributions using the inverse normal transformation (Beasley, Erickson, & Allison, 2009;Efron, 2007).

| Spectral power revealed similar decrease across low-and mid-frequency bands
Spectral power in ALS was significantly decreased and widespread from δto β-band (Figure 1). The most notable changes were found in the occipital and temporal (from δto β-band), lateral/orbitofrontal (δand θ-band) and sensorimotor (β-band) regions.
3.2 | Average connectivity reflects frequencydependent changes in co-modulation and synchrony 3.2.1 | Changes in the AEC revealed increased comodulation at δ, θ and γ l bands ALS patients showed a significant and widespread increase in AEC connectivity compared to healthy controls ( Figure 2), with most notable changes in the central and posterior (δ-, θand γ l -band), and frontal (δ-and γ l -band) regions.

| Changes in iCoh revealed decreased synchrony at δ and β bands
ALS patients showed significant decrease in iCoh connectivity across multiple frequency bands compared with healthy controls (Figure 3).
The changes were observed in temporal and frontal lobes from δto β-band, while in β-band, the decreased connectivity was additionally observed in the sensorimotor cortex. For an overview of results from the statistical analysis of spectral power, and average co-modulation and synchrony, see Figure S3, Supporting Information.

| Changes in point-to-point connectivity patterns are widespread
Significant widespread increase in the point-to-point co-modulation of the neural activity was found in ALS patients compared with healthy controls in θand γ l -band (Figure 4, upper). The θ-band comodulation was observed within the regions encompassing the central, parietal and occipital lobe, as well as between these regions and the remainder of the brain; whereas the γ l -band co-modulation was present in the whole brain, but to a lesser extent within the frontal, between frontal and subcortical, and within and between temporal and subcortical regions. Conversely, we detected significant decreases in the point-topoint synchrony in ALS patients compared with healthy controls in δand β-band (Figure 4, lower). As it was the case for co-modulation, the changes in synchrony were widespread-the δ-band synchrony was decreased within the frontal regions, between the frontal and the occipital, temporal and subcortical regions, as well as between and within the temporal and subcortical regions; the β-band synchrony was primarily decreased between and within the central and parietal regions and the rest of the brain (except the frontal region), and to a lesser extent within the occipital and subcortical regions.

| EEG differences between ALS patients and controls do not discriminate between ALS subgroups
To assess the differences between ALS subgroups based on site of onset (spinal, bulbar) and the presence or absence of the pathologic hexanucleotide expansion in C9ORF72, we used EEG measures that discriminated between ALS patients and healthy controls ( Figure 6). Brain Although these measures showed difference between ALS patients and healthy controls, they did not discriminate between F I G U R E 2 In amyotrophic lateral sclerosis (ALS), the average co-modulation is significantly increased in the δ, θ and γ frequency bands. Notice the increase of amplitude envelope correlation (AEC) in the central and posterior regions (δ-, θand γ l -band) and frontal regions (δand γ l -band). Statistical difference between healthy controls (n = 47) and ALS patients (n = 74) was assessed in the six defined frequency bands using empirical Bayesian inference (EBI). False discovery rate (FDR) was set to 10%, yielding an estimated statistical power of 1-β = .93 and posterior probability of P 1 = .71 (across all frequency bands). AUC, area under the receiver operating characteristic curve. β-band (p 1 = .484; p 2 = .301); co-modulation in δ-band (p 1 = .554; p 2 = .445) and θ-band (p 1 = .708; p 2 = .267); synchrony in δ-band (p 1 = .826; p 2 = .35) and β-band (p 1 = .409; p 2 = .717)].

| The EEG measures of connectivity change reflect the neurodegeneration and functional impairment in both motor and cognitive domains
The changes in cortico-cortical EEG connectivity were correlated with the changes captured by other modalities in both cognitive and motor domain; namely, the identified discriminant measures correlated with structural degeneration as captured by MRI, as well as the functional scores (ALSFRS-R for motor function and neuropsychological battery scores for cognitive function). Figure 7 shows the significant correlations in each domain and for functional and structural measures. For EEG-MRI (Figure 7a-b), these correlations were between the altered connectivity of motor and frontal networks with the grey matter volume of those networks. In the case of the motor network, the average motor network β-band iCoh was correlated with the average cortical volume (Figure 7a), whereas in the case of the frontal network, the average δ-band iCoh connectivity was correlated with average cortical volume (Figure 7b). We also found correlations between altered EEG connectivity and functional scores (Figure 7c-e).
In the motor domain, the correlation was between the ALSFRS-R scores with the average β-band iCoh connectivity changes in the motor network (Figure 7c). In the cognitive domain, we found correlations between the neuropsychological battery scores and the alter- F I G U R E 3 In amyotrophic lateral sclerosis (ALS), the average synchrony is significantly decreased in the δ and β frequency bands. Notice the decrease of imaginary coherence (iCoh) in temporal and frontal lobes (δ-, θand α-band), and in the sensorimotor cortex (β-band). Statistical difference between healthy controls (n = 47) and ALS patients (n = 74) was assessed in the six defined frequency bands using empirical Bayesian inference (EBI). False discovery rate (FDR) was set to 10%, yielding an estimated statistical power of 1-β = .55 and posterior probability of P 1 = .77 (across all frequency bands). AUC, area under the receiver operating characteristic curve. No changes were detected in the γ frequency bands; therefore, they are not shown. Frequency bands: δ (2-4 Hz), θ (5-7 Hz), α (8-13 Hz) and β (14-30 Hz) [Color figure can be viewed at wileyonlinelibrary.com]

| DISCUSSION
This study demonstrates that neuroelectric signal analysis can capture and quantify important changes that occur in functional networks in ALS. Using spectral power and two conceptually different measures of connectivity that reflect co-modulation (AEC) and synchrony (iCoh), we have demonstrated statistically robust neurophysiological evidence of a multisystem disruption of networks in ALS patients. These disruptions correlate with functional impairment as detected using ALSFRS-R and neuropsychological assessment, as well as with structural changes captured by MRI.

| Spectral power changes in ALS disease
The observed changes in spectral power are consistent with previously described θand α-band power decrease above the sensorimotor F I G U R E 4 The increase of point-to-point co-modulation and the decrease of point-to-point synchrony have a widespread pattern in amyotrophic lateral sclerosis (ALS) patients. Note that the widespread patterns of increased co-modulation [amplitude envelope correlation (AEC)] are predominantly in the θand γ l -bands, while synchrony [imaginary coherence (iCoh)] patterns were predominantly in the δand β-bands. Statistical difference between healthy controls (n = 47) and ALS patients (n = 74) was assessed separately in the six defined frequency bands using empirical Bayesian inference (EBI). False discovery rate (FDR) was set to 10% (in each frequency band), yielding an estimated statistical power of 1-β = .96 and posterior probability of P 1 = .56 in the θ-band AEC and an estimated statistical power of 1-β = .89 and posterior probability of P 1 = .7 in the γ l -band AEC. For synchrony measures, the 10% FDR threshold yielded an estimated statistical power of 1-β = .39 and posterior probability of P 1 = .8 in the δ-band iCoh and an estimated statistical power of 1-β = .16 and posterior probability of P 1 = .83 in the β-band iCoh. AUC, area under the receiver operating characteristic curve. No changes were detected in the other frequency bands; therefore, they are not shown. The abbreviations 'Front', 'Cntr/Prtl', 'Occp', 'Tmp' and 'Subcort' stand for frontal, central/parietal, occipital, temporal and subcortical, respectively. For the order of ROIs used in the connectivity matrix, see Figure S2, Supporting Information. Frequency bands: δ (2-4 Hz), θ (5-7 Hz), β (14-30 Hz) and γ l (31-47 Hz) [Color figure can be viewed at wileyonlinelibrary.com] network (Bizovi car, Dreo, Koritnik, & Zidar, 2014;Nasseroleslami et al., 2019). Other studies in ALS have similarly identified decreased postmovement β-band power above motor cortices (Proudfoot et al., 2017;Riva et al., 2012), which is considered a reflection of idling and/or an active inhibition of the motor network (Cassim et al., 2001).
Different frequency bands are mediated by complex neurochemistry and oscillations of frequencies 12-80 Hz are linked to pyramidal neurons, regulated by GABA A inhibitory interneurons (Khanna & Carmena, 2015). Loss of GABAergic interneurons, together with pyramidal neurons, has been observed in both motor and nonmotor areas in ALS (Nihei, McKee, & Kowall, 1993); consequently, the decrease in the lower frequency spectral power can be attributed to structural degeneration of pyramidal cells and/or loss of interneurons that entrain them. These changes in spectral power observed beyond motor network (Bede et al., 2018;McMackin, Dukic, et al., 2019;Nasseroleslami et al., 2019) across multiple frequency bands, support the evolving recognition of significant involvement of nonmotor networks in ALS.

| Correlating connectivity changes in networks affected by ALS with structural MRI and clinical scores
Our AEC connectivity findings are consistent with resting-state fMRI findings of increased connectivity changes in the cingulate (Agosta et al., 2011;Douaud et al., 2011) and parietal cortices (Agosta et al., 2013), and prefrontal (Douaud et al., 2011), temporal and parahippocampal (Abrahams et al., 2004;Heimrath et al., 2014) regions in ALS patients. Factorised AEC networks from NMF analysis, showing increased connectivity in the θand γ l -band, resemble the frontoparietal and frontotemporal networks, respectively.
The frontoparietal network is required for active maintenance of information relevant for successful performance in working memory (Ptak, 2012). Functional connectivity within this network (Blain-Moraes et al., 2013;Iyer et al., 2015;Nasseroleslami et al., 2019), as well as the white matter volumes of association fibres within the frontal brain regions and cingulum are known to be affected in ALS, while the latter changes show correlation with memory impairments in ALS patients F I G U R E 5 The connectivity modules reveal the (sub-)network with frequency-specific increase of co-modulation and decrease of synchrony in amyotrophic lateral sclerosis (ALS). The factorised (sub-)networks resemble the occipital network (a), motor loops of basal ganglia and/or thalamus (b), frontal network (c), sensorimotor network (d), frontoparietal network (e), frontotemporal network (f) and combined occipitofrontal and uncinate fasciculus (g). The connectivity modules from non-negative matrix factorisation analysis of the affected co-modulation or synchrony in ALS reveal the altered brain networks, while the changes in module's weights show the increase or decrease in the activity of these networks. Statistical analysis between ALS patients and healthy controls (n c = 47 and n p = 47) of the weights corresponding to the connectivity modules reached significance in all cases (marked with asterisk) as controlled by adaptive false discovery rate (aFDR) at q = 0.05. Frequency bands: δ (2-4 Hz), θ (5-7 Hz), β (14-30 Hz) and γ l (31-47 Hz) [Color figure can be viewed at wileyonlinelibrary.com] (Abrahams et al., 2005). In addition, degeneration of neurons in frontal and temporal regions (Bede et al., 2013) and associated tracts (Abrahams et al., 2005) is linked to language impairment (Neary et al., 1998) in ALS.
We have identified significant correlations between our observed neurophysiological changes in the frontoparietal and frontotemporal network and composite scores of executive and language function, respectively.

| Spectral EEG measures as a marker of ALS disease
Numerous studies in neurodegenerative diseases, particularly in demen- The observed electroencephalography (EEG) spectral power and connectivity changes are not different between amyotrophic lateral sclerosis (ALS) subgroups. The comparison shows the differences between healthy controls and ALS subgroups. Statistical difference between healthy controls and pooled ALS patients was assessed using Mann-Whitney U test, whereas statistical difference between patient subgroups was assessed using two-way analysis of variance (ANOVA) in all three measures, each in two frequency bands with the most prominent changes (see Figures 1-3). None of the measures showed statistically significant difference among ALS subgroups. Spectral power data were log-transformed for plotting purposes.

| CONCLUSIONS
This study is the first to simultaneously interrogate power activity, comodulation and synchrony of brain networks in ALS to decipher the nature of change in network function caused by the disease using standard 128-channel EEG recordings. In doing so, we have identified increased comodulation and decreased synchrony in both motor and nonmotor networks. Taken together, these data provide a compelling argument for the development of quantitative EEG, a noninvasive and inexpensive technology, as a robust data-driven tool for measuring network disruption in ALS. Finally, the authors thank all the patients and their families who contributed their time for this research.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request and subject to the approvals by Data Protection Officer and Technology Transfer Office in Trinity College Dublin.