Electroencephalographic derived network differences in Lewy body dementia compared to Alzheimer’s disease patients

Dementia with Lewy bodies (DLB) and Alzheimer’s disease (AD) require differential management despite presenting with symptomatic overlap. Currently, there is a need of inexpensive DLB biomarkers which can be fulfilled by electroencephalography (EEG). In this regard, an established electrophysiological difference in DLB is a decrease of dominant frequency (DF)—the frequency with the highest signal power between 4 and 15 Hz. Here, we investigated network connectivity in EEG signals acquired from DLB patients, and whether these networks were able to differentiate DLB from healthy controls (HCs) and associated dementias. We analysed EEG recordings from old adults: HCs, AD, DLB and Parkinson’s disease dementia (PDD) patients. Brain networks were assessed with the minimum spanning tree (MST) within six EEG bands: delta, theta, high-theta, alpha, beta and DF. Patients showed lower alpha band connectivity and lower DF than HCs. DLB and PDD showed a randomised MST compared with HCs and AD in high-theta and alpha but not in DF. The MST randomisation in DLB and PDD reflects decreased brain efficiency as well as impaired neural synchronisation. However, the lack of network topology differences at the DF between all dementia groups and HCs may indicate a compensatory response of the brain to the neuropathology.

groups did not show significant differences in terms of age and gender. All patient groups were matched for global cognitive impairment by their CAMCOG and MMSE scores, although the AD group showed a trend of lower cognitive impairment compared with the other dementia groups. The memory domain in the CAMCOG was significantly lower in the AD group than in PDD and DLB. Complex visual hallucinations (NPI hall) and cognitive fluctuations (CAF) were, as expected, higher in both Lewy body dementias compared to AD patients. In relation to their medications, PDD patients were on higher doses of dopaminergic therapy than the DLB group, but there were not significant differences between the dementia groups in terms of use of cholinesterase inhibitor medications.

Dominant frequency and network measures.
The one-way ANOVA tests were significant for differences in DF across the four participant groups; F(85,3) = 6.75, p-value = 0.0004. Post-hoc tests showed that DLBs had a significantly lower DF (DLB: mean = 6.8 Hz, SD = 0.91) than ADs (mean = 7.5 Hz, SD = 1.21) and HCs (mean = 8.6 Hz, SD = 0.82) but not when compared against the PDD group (PDD: mean = 6.2 Hz, SD = 0.56). The AD group showed a lower DF than HCs but it was higher than in the PDD group, Fig. 1. The one-way ANOVA for the dominant frequency variability (DFV) also showed significant differences; F(85,3) = 4.59, p-value = 0.005. The AD group presented with significantly higher variability (AD: mean = 1.67 Hz, SD = 0.79) compared with the other groups, and DLBs showed significantly lower DFV (DLB: mean = 1.027 Hz, SD = 0.3) when compared with AD, Fig. 1.
The two-way four-group ANOVA tests (group and frequency band effects) for the network structure measures within the six frequency bands, showed significant differences for the maximum nodal degree (degree max ), leaf ratio, eccentricity, network diameter and radius (see Methods for a full description of MST measures); these measures were significant for the group effect. The global effects for these measures showed a decreased degreemax and leaf ratio in the three dementia groups compared with HCs, predominantly in the alpha band, while diameter, eccentricity and radius were higher in the dementia groups compared with HCs, predominantly in the high-theta band and with a trend for differences in the means of HC < AD < DLB < PDD, see Fig. 2 upper row. However, when analysing the post-hoc between-group differences in network topology for the DF band, none of the post-hoc tests were significant, with uncorrected p-values > 0.05, Fig. 2 bottom row.
The MST-PLI related measures (PLI mean, leaf, root and height) were significant for both mean and variability but mainly for the interaction effect of group and frequency band-see Fig. 3. Differences between groups were found predominantly in the theta, high-theta and alpha bands. Specifically, the HC group was significantly different when compared against the dementia groups for PLI measures in the alpha band. PLI height was significantly different between DLB and AD in the beta band.
Significant multiple linear regressions between the clinical variables and the network measures are shown in Table 2 and Fig. 4. None of the measures of variability related with the clinical variables, and we also tested these without the log-transformation with same results. For dominant frequency, the most significant relation ScIeNtIfIc REPORtS | (2018) 8:4637 | DOI:10.1038/s41598-018-22984-5 was found between it and verbal fluency in all dementia groups with a positive correlation, and in AD and DLB for the within-group correlations, see Table 2. Dominant frequency was also significantly related to animal naming, CAMCOG, MMSE and Trail A test, and showed a positive relation between DF and cognitive impairment by these clinical measures. PLI tree measures in the theta band significantly related to cognitive variables. The network mean PLI in the high-theta band significantly related to the frequency and severity of complex visual hallucinations (NPI hall) in the DLB group, see Fig. 4. We also tested whether changing the reference group in the multiple linear regressions altered the results, which it did not. Additionally, we tested if Levodopa presented with a significant effect on the EEG features for the DLB and PDD groups. No effect was found between Levodopa medication and significant network measures. However, there was a significant group effect as result of the higher Levodopa doses in the PDD group (Supplementary Table S7).

Diagnostic analysis.
MST measures that showed significant differences for the diagnostic scenarios including DF and DFV, were used in the classification analysis; the receiver operating characteristic curves for this analysis are shown in Fig. 5  sensitivity was 76% (0.27-0.83 CI) and specificity was also 76% (0.58-0.88 CI); 0.77 AUC. Classification between HC and AD + DLB reached 0.96% sensitivity (0.78-1.0 CI) and 77% specificity (0.58-0.90 CI), 0.93 AUC. The step-wise multiple linear regression showed that for the AD vs DLB separation, the DFV was the best discriminant between both dementias (p-value = 0.0083) followed by PLI height in the beta band (p-value = 0.027). When diagnosing both combined groups AD + DLB versus the HC group, the step wise linear regression showed that the best discriminants were the PLI leaf mean in the alpha band (p-value < 0.0001) followed by DF (p-value < 0.0039). For the classification between DLB and PDD the PLI mean in the alpha band was the best discriminant between both groups (p-value = 0.0012).

Discussion
Our analysis showed significant differences between the dementia groups and HCs for DF and PLI network measures. We confirmed the well-established finding that there is a slowing of DF in the Lewy body dementias-DLB and PDD-compared with AD and HCs in the occipital regions 9,16,24,25 . Additionally, we explored the variability of DF between the studied groups and we demonstrated that DFV is higher in AD compared with HCs and both Lewy body dementia groups. Differences between the MST measures were significant at several frequency bands; theta, high-theta and alpha. However, PLI height scores in the beta band were shown to be lower in DLB compared with AD patients. PLI height is a measure of focused synchronisation in the root node (high PLI values and degree max ) and to be higher requires the existence of leaves far away from the root with low PLI connections, these latter lower than the root node connections 26 . A decrease in PLI height will therefore occur in two scenarios: (1) a star-like topology where the majority of edges connecting the root and leaf nodes are the same or (2) a PLI random connectivity matrix, where there are not significant differences in PLI strength between leaf edges and root edges. Our results suggests the latter case, i.e. that our DLB and PDD groups present with a randomisation of the MST. This is observed by the global effects of the network measures; the lower degree max and leaf ratio in the alpha band combined with higher network diameter, eccentricity and radius in the high-theta band indicate network randomisation, and a decrease in global efficiency of the MST. Similar results were reported by Olde Dubbelink, et al. 27 and Utianski, et al. 28 who showed than in PD and PDD respectively, there exists a less "star-like" network topology or as Yu, et al. 22 reported, a "line-like" topology in dementia patients. Specifically, Utianski, et al. 28 reported decreased number of MST leaves in PD patients. A more line-like network topology suggests a desynchronization of neural communication, where the brain network of dementia patients fails to engage in focused regional synchronisations which may happen at different locations depending on the brain's dynamics. Visualisation of these MST network characteristics in four representative participants is shown in Fig. 6, for the alpha and DF bands. The star-like topology can be easily observed in the HC participant where two highly connected nodes comprise the centre of the star. The randomised tree or line-like topology can be observed easier in the DLB patient in the dominant frequency example (bottom row); nodes here are not highly connected (low degree max ) and several nodes are connected within the same path in a sequence, i.e. lines.
In a previous investigation, van Dellen, et al. 23 reported a PLI decrease in the alpha band of DLB patients compared to AD and HCs. This contrasts somewhat with our investigation where PLI alpha was not significantly different between AD and DLB, although we demonstrated that it was lower in both dementias when compared with HCs. Instead we found that there are PLI differences in the high-theta and beta band between AD and DLB. PLI  alpha band differences in our study occurred when comparing HCs against all dementia groups but not between the dementia groups. This suggests that PLI in the alpha band is a marker of healthy brain but that it is not specific enough to differentiate between dementias 9 .
Exploratory diagnostic classification between AD and DLB was achieved by MST-PLI measures in the high-theta and beta bands as well as DF and DFV with high sensitivity and specificity of 80% and 85% respectively, and which is comparable to FP-CIT SPECT imaging 29 . For this classification analysis, the most significant discriminant was the larger DFV in the AD group followed by the lower PLI height in beta band in the DLB group. This contrasts with the results by Bonanni, et al. 17 who reported higher DFV in DLB patients compared to AD ones and higher DFV than HCs for both dementia groups 17 . This result disagreement may be driven by cohort specific differences or by the estimating method for DFV; here DFV was defined as the standard deviation of the DF throughout the EEG segments, while in Bonanni, et al. 17 DFV was defined using a visual rating of DF range on sequential EEG segments. Previous investigations using EEG features have reported similar or higher classification rates when differentiating Lewy body dementias and AD groups. For instance, Garn, et al. 30 reported 100% accuracy separating AD from a group of DLB-PDD patients using 25 EEG features, and Snaedal, et al. 31 reported an accuracy of 91% in a similar group set-up using 37 EEG features. It is difficult to compare the performance between these investigations and ours due to differences in adopted approaches (the latter focussed on canonical spatial-temporal EEG features compared to our work which additionally used graph theory derived metrics/features) and number of features used for classification (nine features in our investigation). Additionally, these two previous reports 30,31 used a collated DLB-PDD group which may have biased the group classification as PDD patients may be closer to PD in the Lewy body spectrum 5,32 and neuropathologically further away from AD in contrast to DLB. In this investigation, we decided to keep our PDD and DLB groups separated since there is a clinical interest on the correct diagnosis of DLB versus AD, but not so much between AD and PDD given PDD . Minimum spanning tree measures that showed significant differences across the groups of interests; ANOVA tests' p-values are shown Bonferroni adjusted, i.e. multiplied by a correction factor that accounts for the 72 post-hoc one-way ANOVA tests. Significant multiple unpaired t-tests, p-value < 0.05, within each one-way ANOVA test are shown with line markers (in magenta colour) for the two groups with different means. For each plot, the line crosses the group means and the error bars span the first and third quartiles; mean and standard deviation are given in Supplementary Table S4. Bottom-right: Minimum spanning tree example comprising nine nodes and eight edges, where five of them connect leaf nodes. A(i, j) is the network adjacency matrix where an edge between nodes i and j is indicated with 1, and 0 otherwise. PLI(i, j) is the PLI score between nodes i and j. M is the total number of electrode nodes. See Supplementary Table S3 for variable  meaning. patients are diagnosed with PD prior to the onset of dementia 33 . Related to this, a recent report by Babiloni, et al. 9 showed a 69.7% accuracy differentiating AD from DLB (64.7% sensitivity, 73.8% specificity) using only three EEG features associated with occipital alpha and delta power. However, higher diagnostic classification can be achieved by combining neuroimaging modalities. For instance, Colloby, et al. 13 reported 86% sensitivity and 93% specificity (90% accuracy) classification for DLB versus AD, using a combined EEG-structural MRI approach. Forward projection of the MST-PLI and DF measures presented here, onto independent EEG samples will be required to clarify the robustness of these measures as diagnostic tools for DLB.
DF and MST-PLI frequency scores significantly related with cognitive variables in our patients, suggesting a pathological relation with dementia. The verbal fluency test, which measures executive function, was highly positively correlated with DF in the dementia groups. Complex visual hallucinations (severity and frequency) was related with PLI mean in high-theta band, and significantly correlated within the DLB group, see Table 2. To date, we are not aware of previous investigations reporting a relation between complex visual hallucinations and resting state EEG features in DLB; this core symptom is frequently studied with event related responses 34,35 or transcranial stimulations 36 . However, previous EEG investigations in the Charles Bonnet syndrome (CBS) which is characterised by complex visual hallucinations in people with partial or severe blindness, have reported alterations in alpha and theta power 37,38 and this agrees with our results. Nevertheless, we must also take into account that our multiple linear regression results are uncorrected, and thus these findings must be taken with caution.
None of the MST measures were significantly different between groups for the individualised DF band in measures related to network structure such as diameter, radius and eccentricity; see Fig. 2 bottom row. This suggests that in dementia, the EEG network which is present at lower dominant frequencies and whilst these dominant frequencies are pathological, it is still a network which would have been present in the premorbid state with normal structural neural communications, and thus may represent a reactive or compensation state 39 . A recent EEG investigation on brain connectivity by Frantzidis et al. 39 reported compensation in participants with mild cognitive impairment (MCI), a condition that often preludes the onset of AD. They demonstrated the presence of densely connected regions in the networks of MCI participants but not in healthy controls, which the authors attributed to a compensation mechanism at early disease stages. Brain compensation is a phenomenon reported as well in functional magnetic resonance imaging (fMRI) research 40 . In fMRI, compensation is expressed and interpreted as an over-recruitment of neural circuits in order to maintain cognitive levels or motor processes in the presence of disease. In this regard, computational models of cortical activity have proven that the resonance frequency-dominant frequency-of neural circuits is inversely proportional to the size of the excited tissue 41 , i.e. larger networks communicate at lower frequencies 42 . These investigations thus suggest that the decrease of dominant frequency observed in our Lewy body dementia and Alzheimer's disease participants may be an effect of over-recruitment of neural tissue in order to maintain a dynamic network structure similar to healthy controls; or in other words, recruitment of larger neural circuits needed for compensation is implemented by the brain at lower frequencies. It is suggested that the slowing of DF is driven by neurodegeneration of the cholinergic system not only in parkinsonian diseases 43 but also in AD 44 . Evidence for this comes from EEG investigations analysing the effect of cholinesterase inhibitors and the partial restoration of alpha band power after medication 45,46 . Our results then propose a complementary perspective of these previous findings for the relation between cholinergic dysfunction in dementia and DF slowing as a compensatory mechanism. Our investigation has some limitations. First, all patients were medicated at the time of assessment and potentially on agents which are known to alter EEG and could, for example, partially restore alpha power in patients. Despite this, we were able to find robust differences between patients and healthy controls and our results were in agreement with previous work in the field. Also, eyes-open EEG was not investigated in the current report which may offer higher diagnostic ratios if combined with features from eye-closed EEG. We were also unable to test our studied network features for disease progression, since we do not have longitudinal patient data. Ideally, EEG biomarkers for DLB should be investigated in the prodromal phase of the disease when clinical diagnosis is uncertain 47 , and with follow-up patient assessments; certainly early and distinct EEG changes are evident in MCI patients who go on to develop dementia 7 . Finally, the MST approach followed in the current investigation does not provide regional measures of network connectivity which may offer as well other important features for diagnostic classification and disease progression 27 . Future research will be needed to investigate all these possibilities including external validation of biomarkers. This work represents a first step in biomarker discovery and further investigations to evaluate cost-effectiveness, increased patient benefits in comparison with the current diagnostic standard, and feasibility of introduction of such biomarkers in the current care pathway are needed before these indexes can be proposed as validated biomarkers.  Table 2 for all significant results. Model: Clinical variable ~β 1 *network variable + β 2 *D DLB + β 2 *D PDD + Intercept, where D is a dichotomous vector for each of the Lewy body dementia groups. In conclusion, we found that the alpha band and its related MST network measures are markers of healthy brain as compared with dementia, while DLB and AD patients differentiated in DFV and PLI height in the beta band, and that these measures resulted of higher utility as potential diagnostic biomarkers. We demonstrated that DLB as well as PDD present with a randomised or line-like MST network compared to HCs, and this suggests a decrease in focused neuronal synchronisation in these patients for the high-theta and alpha bands. In contrast, we found potential evidence of compensation in the functional network within the dominant frequency band, where no differences were found between our dementia groups and healthy controls for the topology of their MSTs.

Methods
Participants and clinical assessments. A total of 98 old adult participants were recruited within the North East of England. Dementia patients were recruited from a population referred to old age psychiatry and neurology services: 32 patients with AD (22 male, 10 female), 26 patients with DLB (21 male, 5 female), and 22 patients diagnosed with PDD (20 male, 2 female). Additionally, 18 healthy controls (HC) were recruited for group comparisons (11 male, 7 female). Patient groups were diagnosed by two experienced clinicians according to the clinical diagnosis criteria for these dementias: The dementia with Lewy bodies consensus criteria 1,15 , the diagnostic criteria for PDD 33 , and the National Institute on Aging-Alzheimer's Association criteria for AD 48 .
All participants underwent comprehensive neurological and neuropsychiatric examinations. Specific tests relevant to the present study included the Mini-mental state examination (MMSE), the Cambridge cognitive battery tests (CAMCOG) as measures of global cognition as well as trail making test A, animal naming, FAS verbal fluency and visual perception (angle discrimination task). The latter tests, representative of executive and visuo-perceptual function, are often disproportionately affected in LBD and thus considered as key additional cognitive measures for correlation against our MST metrics. To assess whether MST alterations were associated with other core symptoms of LBD such as motor parkinsonism, cognitive fluctuations and visual hallucinations, the Unified Parkinson's Disease rating scale part III (UPDRS III), cognitive assessment of fluctuations (CAF) 49 scale, and the neuropsychiatric inventory test subscale for the severity and frequency of hallucinations (NPI hallucinations) were assessed; for the latter, carers were specifically asked about visual hallucinations rather than hallucinations in other modalities 50 . For patients that were on dopaminergic therapy, the Levodopa equivalent daily dose (LEDD) was estimated 51 . A MMSE score <8 for patients and <26 for the HC group was used as exclusion criteria. None of the recruited healthy participants had a history of neurological or psychiatric conditions and neither did the patients outside their core dementia. Figure 6. EEG minimum spanning tree examples from representative participants. Each participant was chosen as representative for being the median of their respective groups according to the leaf ratio mean in the alpha band. Similarly, the dominant frequency tree is also shown for the same participants. Notice the distinguishable "star-like" topology for the alpha-band network tree of the healthy control (HC) with two nodes with high nodal degree, and the more random tree in Lewy body dementia patients with a "line-like" topology; dementia with Lewy bodies (DLB) and Parkinson's disease dementia (PDD). The Alzheimer's disease (AD) patient also shows a star-like topology, although not as evident as the HC, suggesting impaired network. At the top of each network tree, the same network is shown on an EEG 10-5 system layout; here the diameter of the EEG electrodes is proportional to their nodal degree. Patients with Parkinsonism and on dopaminergic therapy were studied in the "ON" state. Ethical approval for this study was given by the Northumberland Tyne and Wear NHS Trust and Newcastle University ethics committee, and all methods in this study followed approved research guidelines by the mentioned ethics committee. All participants gave written informed consent prior study participation.
Electroencephalography and signal processing. Resting EEG recordings were acquired with Waveguard caps (ANT Neuro, The Netherlands) comprising 128 sintered Ag/AgCl electrodes placed in a 10-5 positioning system 52 . Channels were recorded with a sampling frequency of 1024 Hz and electrode impedance of <5 KΩ. At recording, all electrodes were referenced to Fz channel and the ground electrode was attached to the right clavicle. 150 seconds of continuous EEG resting state eyes closed were stored for off-line data processing, participants were seated throughout the recording and instructed to remain awake and as still as possible.
All pre-processing steps were carried out blinded to group membership and implemented with EEGLAB 53 MATLAB functions (R2012; MathWorks, Natick Massachusetts). 1) EEG channels had their baseline component subtracted and were band pass filtered between 0.3 Hz and 54 Hz with a second order Butterworth filter. 2) Bad channels were deleted including the reference electrode Fz; mean of four channels, with minimum one and maximums of 10 channels deleted. 3) Independent component analysis (ICA) with the FastICA 54 algorithm using default parameters was run for the entire EEG recording and up to 12 artefactual independent components were deleted. At this step special interest was put on identifying eye blink, cardiac and the 50 Hz power line components, i.e. components that were noisy throughout the EEG recording. 4) If after component deletion artefactual components were still identified, FastICA algorithm was run again and up to 6 artefactual components were deleted. 5) Noisy EEG segments with artefacts affecting all channels (e.g. muscle artefacts) were deleted. 6) EEG components were remixed to the sensor domain. 7) Previously deleted bad channels were spatially interpolated with EEGLAB using spherical interpolation. 8) As final step, the electrode montage was modified to average montage 55 . Participants with less than 50 seconds of continuous EEG after artefact cleaning were excluded from the remaining of the analysis. Curated and raw 50-second EEGs signals as well as anonymised clinical data are available upon request from the senior author (J-PT).
Dominant Frequency and its variability. Dominant frequency (DF) was estimated for the 50 second EEG segments. First, occipital channels (PO and O channels) were averaged to obtain a representative signal from this region, see Supplementary Fig. S1. Power spectral density was then estimated with Welch's periodogram; 2048 sample segments tapered with a Hamming window, 50% overlap between segments and a fast Fourier transform size of 2^13; these parameters led to a frequency resolution of 0.125 Hz. We defined DF as the frequency bin in the power spectrum with highest power between 4 and 15 Hz. DF for each participant was then estimated as the mean dominant frequency across the 49 windowed segments and DF variability (DFV) was defined as the standard deviation (SD) across the segments.
Phase lag index. Phase lag index (PLI) was chosen to measure the regional relation among all electrode pairs 56 .
Minimum spanning tree. The minimum spanning tree (MST) in EEG networks is a subgraph which encompasses the strongest edges within the connectivity matrices, and reaches all nodes without creating cycling paths 19 . Here the edges of the network are represented by their connectivity strength given by the PLI scores and the nodes of the network are the electrodes. The Prim's algorithm 59 was used to estimate the MST with one minus the PLI score as input. Then, 10 MST measures and their variability (mean and SD; thus providing a total of 20 measures) were estimated for each frequency and participant. These measures are: Maximum betweenness centrality (BC max ). Is a measure of hubness or centrality 60 and it is proportional to the number of shortest paths that crosses a node in the tree 61 . A node with high BC indicates high reachability of that node throughout the network. BC max then represents the node with highest BC in the MST 62 , and decreased BC max suggests that the MST has decreased global efficiency 19 .
Diameter. This is the largest distance or number of edges between any two nodes in the tree. An increased diameter indicates decreased network efficiency 28 .
Eccentricity. Is the maximum distance or number of edges between a node and any other node in the tree. Here we summarised this measure as the average eccentricity across all nodes in the tree 62  Radius. The smallest node eccentricity in the tree.
Maximum degree (degree max ). The degree of a node equals the number of edges connected to that node. The degree max is the highest degree in the MST and belongs to the most connected node in the network 62 . This is a measure of focused synchronisation, and the highest possible degree max score would correspond to a MST that has a "star" topology 19 with only one central node connected.
Leaf ratio. The number of nodes connected to the MST by only one edge divided by the maximum number of possible leaves (M-1), where M equals 128 electrode nodes in this investigation.
PLI mean. The mean PLI score across the entire MST network.
PLI leaf. The mean PLI for all the edges connected to the leaf nodes.
PLI root. The mean PLI for the root node of the MST. Here the root is defined as node with the highest degree. Hence, PLI root is the mean PLI score for the edges connected to the node with highest degree in the MST.
PLI height. The difference between PLI root minus PLI leaf. PLI root equals the PLI leaf score if the MST has a star configuration 19 .
MST measures were computed using functions from the Brain Connectivity 63 and the Network Analysis 64 toolboxes, as well as in-house functions in MATLAB.

Statistics. Statistical tests for the clinical and demographic variables were implemented in SPSS (Statistical
Package for the Social Sciences v22, IBM) and these are defined in Table 1. All EEG scores of variability, standard deviations and DFV, were log-transformed to approximate their distribution to a Gaussian. Differences in DF and DFV were investigated with a one-way ANOVA for the four groups and post-hoc unpaired t-tests for between group comparisons. Significance of MST measures was assessed in three steps. First, significant differences were investigated with two-way four-group ANOVAs for each MST measure as dependant variable and the following factors as independent variables: group (HC, AD, DLB, and PDD), frequency (delta, theta, high-theta, alpha, beta, and DF) and their interaction (group and frequency). Null hypotheses were rejected if either the diagnosis or the interaction effects were significant at a p-value < 0.0025 thus accounting for the 20 MST measures assessed, i.e. Bonferroni correction. Secondly, for the significant two-way ANOVAs, post-hoc multiple one-way ANOVAs at each frequency band were evaluated and their significance was again Bonferroni corrected by the number of post-hoc tests, leading to an uncorrected p-value threshold of <0.0007 (since 12 two-way ANOVAs survived the first stage of tests). Finally, group differences were assessed with multiple unpaired t-tests. For this latter step we were interested in three exploratory diagnostic scenarios of significant difference: AD vs DLB, DLB vs PDD and HC vs both AD and DLB (AD + DLB). Notice that differences in DF is a hypothesized test based on previous literature and as such the post-hoc tests of the one-way ANOVA are uncorrected, while the two-way four-group ANOVA tests for the multiple network measures are corrected for multiple tests or comparisons.
In order to assess relations of network measures with the clinical variables in our dementia patients, we implemented a multiple linear regression for the three dementia groups with clinical variable as the dependant variable and the network measure as the independent variable. Additionally, we included two dichotomous regressors for the DLB and PDD groups, in order to account for the group effects. The AD group was left as the reference group for being the largest group in our investigation. Before regression analysis, all measures of variability including DFV were log-transformed to approximate their distribution to Gaussian. The regression was considered significant if the first coefficient of the model (β 1 for the network measure) was significant at a p-value < 0.05. The effect of Levodopa medication (LEDD) was assessed with multiple regression for the DLB and PDD groups, with one dichotomous variable to account for the group effect.
To assess the diagnostic accuracy of the studied measures in the three diagnostic scenarios, we implemented a logistic regression classification (Matlab functions glmfit.m and glmval.m); sensitivity, specificity and area under the curve (AUC) were computed for each scenario; confidence intervals were estimated by statistical bootstrapping with 5000 iterations (Matlab function perfcurve.m). For the DLB vs AD case, scores from the PLI mean, PLI leaf mean, PLI root mean in the high-theta band, PLI mean, PLI root mean, PLI height mean in the beta band, DF and DFV were used as regressors. For DLB vs PDD, scores from the PLI mean, PLI root mean and PLI height mean in the alpha band were used in the logistic regression. The HC vs AD + DLB diagnostic scenario used twelve network features as regressors which also showed significant differences, Supplementary Table S6. Diagnostic classification of HC vs PDD was not implemented. In order to find the most significant discriminants for the three diagnostic scenarios a stepwise multiple linear regression was implemented.
Network display and layout. In order to observe network topology characteristics within our studied groups, participants at the group median for the leaf ratio mean in the alpha band were selected as representative of each group. Leaf ratio mean scores were chosen for being consistently higher in the HCs compared with the dementia groups but not between the dementias. For each selected participant, the 49 PLI connectivity matrices were averaged. From the mean connectivity matrix, the MST was extracted and displayed using a forced-directed graph layout 64 , which facilitates graph visualisation by minimising edge crossings. This procedure was also repeated for the DF band for the same participants.