Disturbed functional connectivity in brain tumour patients: Evaluation by graph analysis of synchronization matrices

Clinical Neurophysiology 117 (2006) 2039–2049 www.elsevier.com/locate/clinph

Disturbed functional connectivity in brain tumour patients: Evaluation by graph analysis of synchronization matrices Fabrice Bartolomei a,b,*, Ingeborg Bosma c, Martin Klein d, Johannes C. Baayen f, Jaap C. Reijneveld c, Tjeerd J. Postma c, Jan J. Heimans c, Bob W. van Dijk e, Jan C. de Munck e, Arent de Jongh e, Keith S. Cover e, Cornelis J. Stam a b

a Department of Clinical Neurophysiology1, VU University Medical Center, Amsterdam, The Netherlands Department of Clinical Neurophysiology and Epileptology, CHU Timone, INSERM U 751 Marseille, France c Department of Neurology, VU University Medical Center, Amsterdam, The Netherlands d Department of Medical Psychology, VU University Medical Center, Amsterdam, The Netherlands e MEG Center, VU University Medical Center, Amsterdam, The Netherlands f Department of Neurosurgery, VU University Medical Center, Amsterdam, The Netherlands

Accepted 18 May 2006 Available online 21 July 2006

Absract Objective: Cerebral functions are based on the functional interactions between multiple distinct specialized regions of the brain. Functional interactions require anatomical connections as well as the synchronization of brain oscillations. The present work aims at evaluating the impact of brain tumours on spatial patterns of functional connectivity of the brain measured at rest by MEG. Methods: We analyzed the statistical dependency (by computing the synchronization likelihood (SL, a measure of generalized synchronization)) between MEG signals at rest, in 17 patients with a brain tumour and in 15 healthy controls. Following an approach that derives from graph theory, we also analyzed the architectural properties of the networks by computing two parameters from the SL matrix, the cluster coefficient C and the characteristic path length L. Results: Alterations in synchronization levels were found in the patients and were not focal but involved intra-hemispheric connectivity. Effects were different considering the frequencies sub-bands, predominating in a decrease in high frequencies bands for long-distance connections and an increase in slower bands for local connectivity. In addition, graph analysis reveals changes in the normal ‘‘small-world’’ network architecture in addition to changes in synchronization levels with some differences according to the studied frequency sub-bands. Conclusions: Brain tumours alter the functional connectivity and the ‘‘network’’ architecture of the brain. These alterations are not focal and effects are different considering the frequencies sub-bands. Significance: These neurophysiological changes may contribute to the cognitive alterations observed in patients with brain tumours.  2006 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. Keywords: Brain tumour; MEG; Synchronization; Epilepsy; ‘‘Small-world’’ networks

1. Introduction

* Corresponding author. Present address: Department of Clinical Neurophysiology and Epileptology, CHU Timone, Marseille, France, 264 rue Saint-Pierre, 13012 Marseille, France. Tel.: +33491385826; fax: +33491385828. E-mail address: [email protected] (F. Bartolomei). 1 Where the work was done.

A traditional reasoning in neurology is to correlate a focal lesion to a ‘‘focal’’ clinical deficit. Historically, this approach gave important insights into our knowledge of the localization of brain functions and their alterations in neurological diseases. Thus, the notion of localized brain functions has emerged from these classical anatomo-clinical works. However it is not rare that a patient with a

1388-2457/$32.00  2006 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.clinph.2006.05.018

2040

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

‘‘focal’’ lesion presents with more important alterations than expected by the localization of the lesion. This is typically the case of patients with brain tumours. These patients often suffer from diffuse alteration of cognitive functions that cannot be explained by a focal alteration of their brain functions (Taphoorn and Klein, 2004). In this situation, it is probable that the brain tumour interferes with widespread functional networks in the brain rather than only the site of the lesion itself. A new way to explore the consequences of a lesion on the brain is to evaluate its impact on the functional interactions (‘functional connectivity’) taking place between brain regions (Lowe et al., 1998; Quigley et al., 2001; Salvador et al., 2005; Stam et al., 2002). Modern neuroscience research has shown that the notion of ‘‘localized’’ brain functions is – at least in part – erroneous, especially when dealing with higher brain functions. Indeed, cognitive functions in the brain require the functional interactions between multiple distinct neural networks (Bressler, 2002). In this respect, EEG and MEG recordings represent a way to study the functional connectivity between different brain regions (Schnitzler and Gross, 2005; Varela et al., 2001). The measure of statistical interdependencies between signals of brain activity is a tentative index of functional interactions and is referred to as ‘functional connectivity’ (for review see: (Lee et al., 2003)). The underlying assumption is that such correlations reflect, at least in part, functional interactions between different brain areas. For example, this approach enabled to demonstrate alterations in functional connectivity in Alzheimer’s disease (Stam et al., 2002) multiple sclerosis (Cover et al., 2004; Cover et al., 2005) or brain tumours (Bartolomei et al., 2006). Recently, a new way to characterize the topographical properties of complex networks has been proposed using the ‘Graph’ theory approach (Sporns et al., 2004; Strogatz, 2001). A graph is a basic representation of a network, which is essentially reduced to nodes (‘vertices’) and connections (‘edges’) (Albert and Barabasi, 2002). Graphs are characterized by a cluster coefficient C and a characteristic path length L. The cluster coefficient is a measure of the local interconnectedness of the graph, whereas the path length is an indicator of its overall connectedness or level of integration. Watts and Strogatz (1998) have shown that graphs with many local connections and a few random long-distance connections are characterized by a high cluster coefficient and a short path length; such near optimal networks are designated ‘small-world’ networks. Since then many types of real networks have been shown to have small-world features (Strogatz, 2001). Patterns of anatomical connectivity in neuronal networks are particularly characterized by high clustering and a small path length (Watts and Strogatz, 1998). It has been suggested that a small-world like network architecture may be optimal for synchronizing neural activity between different brain regions (Barahona and Pecora, 2002; Latora and

Marchiori, 2001) Networks of functional connectivity based upon recordings in animals, fMRI BOLD signals or MEG recordings have also been shown to have smallworld characteristics (Lahaye et al., 2003; Salvador et al., 2005; Stam, 2004). The present work aims at evaluating the impact of brain tumours on spatial patterns of functional connectivity of the brain measured at rest by MEG. In a previous study (Bartolomei et al., 2006) we showed that patients with brain tumours have more alterations in synchronization, particularly in the gamma band. This study extends and completes the aforementioned one. We addressed the question whether brain tumours may alter local or/and long-distance connectivity in the five frequency bands and whether the connectivity ‘‘architecture’’, estimated from graph analysis, may be modified. Here we predict that brain tumours will interfere with the ‘optimal’ architecture of brain functional networks. 2. Methods 2.1. Subjects The 17 patients (age mean 41 ± 12, 9 females) who entered the study were recruited from previous studies done in our center (Baayen et al., 2003; de Jongh et al., 2003). All patients had brain tumours and underwent surgery at the Department of Neurosurgery, VU University Medical Center [H.B.]. The histopathological diagnosis was determined according to the WHO Classification of Tumours affecting the central nervous system (Kleihues et al., 2002) (Table 1). MEG recordings from 15 healthy control subjects (age 31 ± 8, 7 females) were also analyzed. Healthy controls were mainly recruited from the staff of the department from various MEG prospective studies. Table 1 Summarized characteristics of the patients Patients

Gender

Age

Side

Localization

Histology

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

F M F F F M F M F F M M M F F M F

66 34 30 27 49 54 50 38 40 38 33 31 38 41 39 63 27

R R R R R R R L L L L L L L L L L

T T Pc F T T T P F T Pc F F Pc F Pc Pc

Me AIII AI AII AII Me AIV AIII AIII AIII AII AIV AIV OC OD AIV OB

T, temporal; F, frontal; PC, parieto-central; Me, meningioma; AI-IV, astrocytoma grade I-IV; OB, oligodendroglioma grade B; OC, oligodendroglioma grade C; OD, oligodendroglioma grade D.

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

Results (linear interhemispheric correlations) of this control group were previously reported (Cover et al., 2004; Cover et al., 2005). 2.2. MEG recordings Magnetic fields were recorded while subjects were seated inside a magnetically shielded room (Vacuumschmelze GmbH, Hanau, Germany) using a 151-channel whole-head MEG system (CTF Systems Inc., Port Coquitlam, BC, Canada). A third-order software gradient (Vrba et al., 1999) was used with a recording passband of 0.25–125 Hz. Fields were measured during a no-task eyes-closed condition. At the beginning and at the end of each recording the head position relative to the coordinate system of the helmet was recorded by leading small alternating currents through three head position coils attached to the left and right preauricular points and the nasion on the subject’s head. Head position changes during a recording condition up to approximately 1.5 cm were accepted. During the MEG recording, the patients were instructed to close their eyes to reduce artefact signals due to eye movements. 2.3. Synchronization likelihood The synchronization likelihood is a general measure of the statistical interdependencies between two time series. A technical description of the synchronization likelihood can be found in (Stam and Dijk, 2002) and will be briefly summarized here. We assume two dynamic systems, for instance neural networks, designated X and Y. From both systems time series xi and yi, for instance EEG or MEG signals, are recorded. The general problem is to infer functional interactions between X and Y from xi and yi. Usually it is assumed that the more xi and yi ‘‘resemble’’ each other, the stronger X and Y interact. This ‘‘resemblance’’ can be quantified for instance by the cross-correlation. When this is done as a function of frequency, the coherency is determined, which is the most commonly used tool for this purpose. However it has been shown that X and Y can interact, even when xi and yi do not ‘‘resemble’’ each other in a simple way. This more general concept, aptly called generalized synchronization, implies that the state of Y is a function of the state of X (Rulkov et al., 1995). Here xi and yi do not have to resemble each other, as long as recurrent patterns of xi coincide (in time) with recurrent patterns of yi. The synchronization likelihood is a way to quantify this ‘‘generalized synchronization.’’ It ranges from a small value close to 0 (no synchronization) to 1 (complete synchronization). The synchronization likelihood can be studied at different levels of temporal and spatial detail (for extensive simulation studies see (Stam and Dijk, 2002)). For the present analysis, 149 of the 151 channels could be used. MEG recordings were converted to ASCII files and down-sampled from 625 to 312.5 Hz. From these ASCII files artifact free epochs of 4096 samples (13.083 s)

2041

were carefully selected by visual analysis. Digital, zero-phase shift filtering of the MEG in the gamma band (26–60 Hz), beta band (13–25 Hz), alpha band (9–12 Hz), theta band (4–8 Hz) and delta band (0.5–4 Hz), computation of synchronization likelihood and graph theoretical measures, were done off-line with the DIGEEGXP software developed at the department (DIGEEGXP; CS).The parameter setting of the SL computation in the present study were as follows: lag L = 10; embedding dimension m = 10; Pref = 0.01. 2.4. Computation of the cluster coefficient C and characteristic path length L Computation of the cluster coefficient C and the characteristic path length L were done as described in Stam et al. (2006): The first step in applying graph theoretical analysis to synchronization matrices is to convert the N · N synchronization matrix into a binary (unweighted) graph. A binary graph is a network that consists of elements (also called ‘vertices’) and undirected connections between elements (called ‘edges’). Edges between vertices either exist or do not exist; they do not have graded values. The synchronization matrix can be converted to a graph by considering a threshold T. If the SL between a pair of channels i and j exceeds T an edge is said to exist between i and j; otherwise no edge exists between i and j. Now we choose T such that for each individual graph we get a number of connections per vertex K (with K the same for all subjects and filters); in this way all graphs studied have the same number of connections, and only the distribution of the connections over the networks is considered. In the present study we used K = 10. The choice of K is arbitrary. We followed the suggestion of Watts and Strogatz (Watts and Strogatz, 1998) of the minimal K value for a network with size N (here 149) such that a random network generated from it will still be guaranteed to be fully connected: N P k P Ln(N). Here a k number greater than 5 fulfills these conditions. Once the synchronization matrix has been converted to a graph, the next step is to characterize the graph in terms of its cluster coefficient C and its characteristic path length L. To compute the cluster coefficient of a certain vertex, we first determine to which other vertices it is directly connected; these other vertices (one edge away) are called neighbours. Now the cluster coefficient is the ratio of all existing edges between the neighbours and the maximum possible number of edges between the neighbours; it ranges between 0 and 1. This cluster coefficient is computed for all vertices of the graph and then averaged. It is a measure for the tendency of network elements to form local clusters. The characteristic path length L is the average shortest path connecting any two vertices of the graph; the length of a path is indicated by the number of edges of which it exists. The path length L is an emergent property of the graph which indicates how well its elements are integrated/interconnected.

2042

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

2.5. Statistical analysis Local synchrony was estimated by averaging the SL values obtained from all the pair-wise combinations of channels calculated in each MEG sector (Central, Frontal, Temporal, Parietal and Occipital), and in each hemisphere. Long distance synchrony was estimated by averaging the values of all pair-wise combinations between MEG sectors. Four inter-regional interactions were considered: Frontal– Parietal (FP), Frontal–Temporal (FT), Temporo–Occipital (TO) and Parieto–Occipital (PO) (Fig. 1). A repeated Analysis of Variance (ANOVA) was used to evaluate differences in SL values between healthy controls and brain tumour patients in each frequency sub-band. Values were first normalized according to the following equation w = (LN[(1 + r)/(1 r)])/2 (Bendat and Piersol, 1971). A Bonferroni correction was used to adjust p values when necessary. A p value <0.05 was considered to be statistically significant. 3. Results 3.1. Local and long-distance synchrony 3.1.1. Differences between controls and brain tumours patients Brain tumour patients and healthy controls disclosed significantly different values for local and long-distance

couplings (F(1,4) = 6.63, p < 0.0001 long-distance, F(1,4) = 6.78, p < 0.0001 local). For local couplings, significant increase in alpha, theta and delta bands were found and for long-distance couplings, a significant decrease in beta and an increase in alpha and delta bands was observed in patients when compared to controls (Fig. 2). Differences were found between right-sided and left-sided tumours for local or long-distance couplings (Fig. 3). For local coupling, the interaction Subjects*SL values in the 5 sub-band was also significant (F2,8 = 6.2, p < 0.0001). An increase in SL values in comparison with controls was found in alpha band for right and left sided tumours (p < 0.0001 left, p = 0.002 right), in theta band (p < 0.0001 left and right) and in delta band (p = 0.0003 left, p = 0.0002 right). For long-distance couplings, the interaction Subjects *SL values in the 5 sub-band was significant (F2,8 = 5.2, p < 0.0001). Mean SL values were lower in the left tumour group in comparison with controls for gamma (p = 0.006), beta (p = 0.004) and higher for the alpha band (p = 0.004). No significant differences were found between controls and right-sided tumours. Taken as a whole, results indicate that patients with right or left-sided tumours presented with different alterations in the synchronization levels affecting both local and long-distance connections. For long-distance synchrony, the main effect is a decrease of gamma and beta coupling, significant for the left-sided tumours subjects. For

Fig. 1. (a) Schematic representation of the location of the CTF magnetoencephalographic sensors. (b) Long distance synchrony is estimated by averaging the values of all pair-wise combinations between MEG sectors from several inter-regional interactions: Frontal–Parietal (FP), Frontal–Temporal (FT), Temporo–Occipital (TO) and Parieto–Occipital (PO). (c) Local synchrony was estimated by averaging the SL values obtained from all the pair-wise combinations of channels calculated in 5 MEG sectors (Central (C), Frontal (F), Temporal (T), Parietal (P) and Occipital (O)).

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

2043

Fig. 2. Local (a) and long-distance (b) couplings estimated by the computation of synchronization likelihood (SL) in five frequency bands in controls and in tumour patients. A asterisk indicates a statistically significant difference (p < 0.05, ANOVA).

Fig. 3. Local (a) and long-distance (b) couplings estimated in controls and in right or left-sided brain tumour patients.

2044

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

Fig. 4. Schematic graph representation of results obtained for local synchronization estimated from SL computation in five sub-bands (delta, theta, alpha, beta, gamma). Significant changes (ANOVA with Bonferoni correction) are indicated in green dotted lines for a decrease in SL values and in red continuous line for increase in synchrony. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

2045

Fig. 5. Schematic graph representation of results obtained for long-distance synchronization estimated from SL computation in five sub-bands (delta, theta, alpha, beta, gamma). Significant changes (ANOVA, Bonferoni correction) are indicated in green dotted lines for a decrease in SL values and in red continuous line for increase in synchrony. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

2046

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

Fig. 6. Mean and SD values for Cp/Cp-s and Lp/Lp-s in gamma, beta and theta bands for controls.

local synchrony, the main effect is (for right an left sided tumours) an increase in the synchrony of slower frequency bands (alpha, theta and delta). 3.1.2. Analysis of regional variation in synchrony In the following sections, we separately analyzed the changes for patients with a tumour in the right of left hemisphere. To study the regional changes observed for local or long-distance couplings a two-way repeatedmeasures ANOVA was applied with one independent factor (patients and controls) and dependant factors (SL values in local (left C,F,T,O,P right C, F, T, O,P)) or in long-distance interactions (left FP, FT, PO,TO right FP, FT, PO, TO). Figs. 4 and 5 show the significant results that were obtained for each subbands frequency. These figures deserve several comments. First alterations affect the lesioned hemisphere but also the contralateral hemisphere and are not restricted to a focal brain region. Long distance connectivity seems to be altered mainly between frontal and parietal channels, with a significant decrease in gamma and beta couplings in both right-sided an left-sided brain tumour patients and a increase in the delta band. Increase in long-distance coupling is observed mainly in slower bands with a predominance for left-sided tumours.

Decrease in local synchrony in gamma band is particularly marked in left-sided tumours. Obviously the more important changes are observed in the slower bands with an increase of synchrony in alpha, theta and delta bands, that predominate in the lesioned hemisphere. These results suggest that brain tumours induce (mostly opposite) changes in both local and long-distance couplings in the brain. Long distance couplings seem to be more affected in the higher frequencies, and particularly in the fronto–parietal interactions. Local connectivity is marked by important changes predominating in the slower bands and within the affected hemisphere. 3.2. Changes in graph configurations: application to beta and theta bands 3.2.1. Controls Graph analysis was applied to data obtained from the computation of SL in the three bands particularly involved in cognitive process (Gamma, beta and theta bands). After filtering, a matrix of connection strengths obtained after computing the SL for all pairs of 149 MEG channels, was obtained. From this matrix C and L were determined as described in the method section, using an individually adapted threshold T which resulted for all subjects in a value of K = 10. The values were compared to the mean and SD of 10 random surrogate matrices (referred as C-s and L-s), in which all entries pi,j were shuffled randomly while preserving the number of connections as well as the degree distribution (Sporns and Zwi, 2004). The comparison with random graphs is a way to determine how change may occur, independently from the changes in absolute SL values. For the three bands, values in controls were characterized by a cluster coefficient (C) of the real data that was much higher (the ratio C/C-s is 4) than that of a random network (where C/C-s is expected to be around 1). In contrast the path length L of the MEG matrices was only slightly higher than that of random networks (L/L-s 1.5). The overall pattern (cluster coefficient larger than random networks, relative low values for path length) is

Fig. 7. Mean and SD values of Cp/Cp-s and Lp/Lp-s in theta bands for controls (C), left tumours (LT) and right tumours (RT). Significant changes are indicated by * (ANOVA with Bonferoni correction).

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

2047

Fig. 8. Mean and SD values of Cp/Cp-s and Lp/Lp-s in beta bands for controls, left tumours and right tumours.

suggestive of small-world like characteristics of resting state MEG (Fig. 6). 3.2.2. Brain tumours In theta band, we observed a significant decrease in patients compared to controls of both Cp/Cp-s (F(5,10) = 4.6, p = 0.03; right tumours p = 0.01, left tumours p = 0.003) and Lp/Lp-s ratios (F(5,10)=58, p < 0.001, RT p < 0.001, LT p < 0.001) (Fig. 7). In the beta band and in comparison with random graphs, no significant changes in Cp/Cp-s ratio was observed (F(5,10) = 0.58, p = 0.57). A significant decrease in Lp/Lp-s values were found (F(5,10) = 16, p = 0.0008) significant only for left tumours (p = 0.004) (Fig. 8). In the gamma band, significant decrease in Cp/Cp-s ratios were found F(6,12 = 4,2 p = 0.04), reaching significant values for right tumours (p = 0.005). Lp/Lp-s values were found to be decreased in comparison with controls (F(6,12) = 13, p = 0.001), but reaching significant values only for right tumours (p = 0.0002) (Fig. 9). Thus alterations in graph architecture were found in the three studied bands affecting both Cp (except in beta band) and Lp. These results may be interpreted as a tendency to a change in the normal configuration observed in control subjects and a tendency for the networks to be closer to a random configuration. This change may be related to the preferential loss of short connections.

4. Discussion The main results of this study are: (i) brain tumours alter the functional connectivity of the brain, (ii) these alterations are not focal but may involve intra-hemispheric connectivity, (iii) the effects are different considering the frequencies sub-bands, predominating in a decrease in high frequencies bands for long-distance connections and an increase in slower bands for local connectivity, (iv) Graph analysis reveals changes in network architecture of functional connectivity in gamma, beta and theta bands. Pair-wise estimations of SL, as used in the present paper, may fail to reveal higher order correlations between brain sites. Such correlation could be captured by a more multivariate approach. However, for the graph analysis we intended to perform the first step, the construction of a simple matrix of pair-wise correlations. While we cannot exclude that some of these correlations might be influenced by common sources/volume conduction, we consider it unlikely that such effects could explain the group differences in the graph measures. These results demonstrate that brain tumours induce important changes in functional connectivity that may contribute to explain cognitive dysfunction, which is very common in patients with brain tumours (Tucha et al., 2000). It is generally assumed that cognitive dysfunction in these patients depends on several factors, including the tumour itself, the associated epilepsy and the treatments (Taphoorn

Fig. 9. Mean and SD values of Cp/Cp-s and Lp/Lp-s in gamma bands for controls, left tumours and right tumours.

2048

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049

and Klein, 2004). Most of the patients have global cognitive deficits that can hardly be explained by a focal effect of the tumour. They indeed suffer from attentional deficits, working memory problems, reduced psychomotor speed and problems with executive functions (Klein et al., 2001). In particular, patients with tumours in the left hemisphere disclosed the most important deficit in all the reported series (Hahn et al., 2003; Scheibel et al., 1996; Taphoorn et al., 1992). Our results showing alterations affecting several brain regions are in agreement with these ‘‘diffuse’’ alterations. It is also relevant to note that the most affected long-distance couplings involve fronto–parietal interactions with both decrease in gamma and beta synchrony and abnormal hypersynchrony in delta band. Alterations in fronto–parietal synchrony could be an important factor contributing to working memory and executive function since in normal subject working memory or direct attentional task involve the transient synchronization between these two regions (Halgren et al., 2002; von Stein and Sarnthein, 2000). Results extend our previous analysis, that showed alterations in functional connectivity estimated in a broad frequency band and in the gamma band (Bartolomei et al., 2006). In addition, in the present study, we analyzed the architectural properties of the networks in gamma, beta and theta band following a recent proposed approach that derive from graph theory analysis. Following the seminal work of Watts et Strogatz (Watts and Strogatz, 1998), it is possible to calculate two coefficients that are aimed at evaluating two properties of the network, the cluster coefficient (C) and the path length (L). Using this two parameters, and according to simulation studies, it has been proposed that a network can have properties ranging from an ordered mode (characterized by high values of C and L) to a random one (characterized by low C and L values). An intermediate situation, characterized by a high value of C but low values of L is the ‘‘small word’’ configuration, a situation that could characterized many real networks. One reason for the interest in ‘smallworld’ networks is the fact that this type of architecture may be optimal for information processing in complex networks (Strogatz, 2001). Several studies attempted to apply graph analysis to functional networks in the brain (Dodel et al., 2002; Eguiluz et al., 2005; Stam, 2004). This was done by considering a matrix of interaction strengths of recordings of brain activity from different regions, and by applying a threshold to convert the matrix to a conventional, binary graph. In this way small-world features have been reported for fMRI data (Dodel et al., 2002; Salvador et al., 2005) and for magneto encephalographic recordings (Stam, 2004). Using this approach, we observed that alteration of graph configuration could be found in patients with brain tumours. A loss of architecture configuration was observed in theta and gamma band networks, less important in beta network configuration. In addition to the changes in the strength of couplings, this effect could modify the functioning of underlying neu-

ral networks. Modeling studies have indeed shown that neural networks with small-world characteristics are optimal in facilitating synchronous firing and rapid information transfer (Lago-Fernandez et al., 2000; Latora and Marchiori, 2001; Masuda and Aihara, 2004). The decrease in both C and L values indicate that the networks here could function in a more random mode. However if this effect is deleterious or positive is uncertain. The decrease in L values could indeed favor the speed of information process and thus be a compensatory mechanism to the changes in synchronization and/or anatomical alterations. Alternatively, a very low L might also be responsible for a tendency to excessive synchronization and epileptic seizures which occur commonly in brain tumour patients. Acknowledgments We thank J. Verbunt, P.J. Ris, I. Manshanden, G. de Vos for technical assistance. The original data were collected in a study supported by a grand from the National Epilepsy Foundation of the Netherlands (Grant n99-05). References Albert R, Barabasi A. Statistical mechanic of complex networks. Rev Mod Phys 2002;74:47–97. Baayen JC, de Jongh A, Stam CJ, de Munck JC, Jonkman JJ, Trenite DG, et al. Localization of slow wave activity in patients with tumorassociated epilepsy. Brain Topogr 2003;16:85–93. Barahona M, Pecora LM. Synchronization in small-world systems. Phys Rev Lett 2002;89:054101. Bartolomei F, Bosma I, Klein M, Baayen JC, Reijneveld JC, Postma TJ, et al. How do brain tumors alter functional connectivity? A magnetoencephalography study. Ann Neurol 2006;59:128–38. Bendat J, Piersol A. Random data: analysis and measurement procedures. New York: Wiley-Interscience; 1971. Bressler S. Understanding cognition through large-scale cortical networks. Curr Direct Psych Sci 2002;11:58–61. Cover KS, Stam CJ, van Dijk BW. Detection of very high correlation in the alpha band between temporal regions of the human brain using MEG. Neuroimage 2004;22:1432–7. Cover KS, Vrenken H, Geurts JJ, van Oosten BW, Jelles B, Polman CH, Stam CJ, van Dijk BW. Multiple sclerosis patients show a highly significant decrease in alpha band interhemispheric synchronization measured using MEG. Neuroimage 2006;29(3):783–8. de Jongh A, Baayen JC, de Munck JC, Heethaar RM, Vandertop WP, Stam CJ. The influence of brain tumor treatment on pathological delta activity in MEG. Neuroimage 2003;20:2291–301. Dodel S, Hermann JM, Geisel T. Functional connectivity by crosscorrelation clustering. Neurocomputing 2002;44-46:1065–70. Eguiluz V, Chialvo D, Cecchi G, Baliki M, Apkarian A. Scale-free brain functional networks. Phys Rev Lett PRL 2005;94:018102. Hahn CA, Dunn RH, Logue PE, King JH, Edwards CL, Halperin EC. Prospective study of neuropsychologic testing and quality-of-life assessment of adults with primary malignant brain tumors. Int J Radiat Oncol Biol Phys 2003;55:992–9. Halgren E, Boujon C, Clarke J, Wang C, Chauvel P. Rapid distributed fronto-parieto-occipital processing stages during working memory in humans. Cereb Cortex 2002;12:710–28. Kleihues P, Louis DN, Scheithauer BW, Rorke LB, Reifenberger G, Burger PC, et al. The WHO classification of tumors of the nervous system. J Neuropathol Exp Neurol 2002;61:215–25, discussion 226–9.

F. Bartolomei et al. / Clinical Neurophysiology 117 (2006) 2039–2049 Klein M, Taphoorn MJ, Heimans JJ, van der Ploeg HM, Vandertop WP, Smit EF, et al. Neurobehavioral status and health-related quality of life in newly diagnosed high-grade glioma patients. J Clin Oncol 2001;19:4037–47. Lago-Fernandez L, Huerta R, Corbacho F, Siguenza J. Fast response and temporal coherent oscillations in small-world networks. Phys Rev Lett 2000;84:2758–61. Lahaye PJ, Poline JB, Flandin G, Dodel S, Garnero L. Functional connectivity: studying nonlinear, delayed interactions between BOLD signals. Neuroimage 2003;20:962–74. Latora V, Marchiori M. Efficient behavior of small-world networks. Phys Rev Lett 2001;87:198701. Lee L, Harrison LM, Mechelli A. The Functional Brain Connectivity Workshop: report and commentary. Network 2003;14:R1–R15. Lowe MJ, Mock BJ, Sorenson JA. Functional connectivity in single and multislice echoplanar imaging using resting-state fluctuations. Neuroimage 1998;7:119–32. Masuda N, Aihara K. Global and local synchrony of coupled neurons in small-world networks. Biol Cybern 2004;90:302–9. Quigley M, Cordes D, Wendt G, Turski P, Moritz C, Haughton V, et al. Effect of focal and nonfocal cerebral lesions on functional connectivity studied with MR imaging. AJNR Am J Neuroradiol 2001;22:294–300. Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HD. Generalized synchronization of chaos in directionally coupled chaotic systems. Physical Review. E. Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 1995;51:980–94. Salvador R, Suckling J, Coleman MR, Pickard JD, Menon D, Bullmore E. Neurophysiological Architecture of Functional Magnetic Resonance Images of Human Brain. Cereb Cortex 2005. Scheibel RS, Meyers CA, Levin VA. Cognitive dysfunction following surgery for intracerebral glioma: influence of histopathology, lesion location, and treatment. J Neuro-oncol 1996;30:61–9. Schnitzler A, Gross J. Normal and pathological oscillatory communication in the brain. Nat Rev Neurosci 2005;6:285–96. Sporns O, Chialvo DR, Kaiser M, Hilgetag CC. Organization, development and function of complex brain networks. Trends Cogn Sci 2004;8:418–25.

2049

Sporns O, Zwi JD. The small world of the cerebral cortex. Neuroinformatics 2004;2:145–62. Stam C, Dijk BV. Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets. Physica D 2002;163:236–41. Stam C, Nolte G, Breakspear M, Jones B, P S. Small-world networks and functional connectivity in Alzheimer’s disease. Cerebral Cortex 2006, Feb 1; [Epub ahead of print]. Stam CJ. Functional connectivity patterns of human magnetoencephalographic recordings: a ‘small-world’ network? Neurosci Lett 2004;355:25–8. Stam CJ, van Cappellen van Walsum AM, Pijnenburg YA, Berendse HW, de Munck JC, Scheltens P, et al. Generalized synchronization of MEG recordings in Alzheimer’s Disease: evidence for involvement of the gamma band. J Clin Neurophysiol 2002;19:562–74. Strogatz SH. Exploring complex networks. Nature 2001;410:268–76. Taphoorn MJ, Heimans JJ, Snoek FJ, Lindeboom J, Oosterink B, Wolbers JG, et al. Assessment of quality of life in patients treated for low-grade glioma: a preliminary report. J Neurol Neurosurg Psychiatry 1992;55:372–6. Taphoorn MJ, Klein M. Cognitive deficits in adult patients with brain tumours. Lancet Neurol 2004;3:159–68. Tucha O, Smely C, Preier M, Lange KW. Cognitive deficits before treatment among patients with brain tumors. Neurosurgery 2000;47:324–33, discussion 333–4. Varela F, Lachaux JP, Rodriguez E, Martinerie J. The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2001;2:229–39. von Stein A, Sarnthein J. Different frequencies for different scales of cortical integration: from local gamma to long range alpha/theta synchronization. Int J Psychophysiol 2000;38:301–13. Vrba J, Anderson G, Betts K, Burbank M, Cheung T, Cheyne D, et al. 151-Channel whole-cortex MEG system for seated or supine positions. In: Yoshimoto T, Kotani M, Kuriki S, Karibe H, Nakasato N, editors. Recent Advances in Biomagnetism. Sendai, Japan: Tohoku University Press; 1999. p. 93–6. Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature 1998;393:440–2.