Characteristics of patients with brain tumors.

<p>Characteristics of patients with brain tumors.</p

An anatomically-constrained network of phase oscillators approximates the empirically observed phase statistics.

<p>The empirical statistics (black) were compared to the statistics generated by the anatomically connected heterogeneous model (model 1, <i>red</i>) and three control models: 100 realizations of the heterogeneous model with shuffled connectivity (model 2, <i>gray</i>, mean ± 95% confidence interval across realizations (gray area)), the anatomically connected homogeneous model (model 3, <i>green</i>), and the anatomically connected homogeneous stochastic model (model 4, <i>yellow</i>), with noise amplitude σ = 0.2. <b>a)</b> Averaged value of the order parameter, <<i>R</i>>. <b>b)</b> Similarity (1/<i>D</i>_<i>KL</i>) between the phase differences distribution, Pr(Δφ), of the empirical data and of each model. All similarity values were normalized to the maximum similarity for model 1. <i>Inset</i>: Pr(Δφ) from the empirical data (<i>black</i>) and from model 1 (<i>red</i>) generated with the best-fit parameter. <b>c)</b> Similarity (1/<i>D</i>_<i>KL</i>) between the distribution of the number <i>N</i> of synchronized pairs, Pr(<i>N</i>), of the empirical data and each model (normalized by the maximum similarity for model 1). <i>Inset</i>: Pr(<i>N</i>) distribution from the empirical data (<i>black</i>) and from model 1 (<i>red</i>) generated with the best-fit parameter. <b>d)</b> Agreement (correlation) between the empirical PLV matrix and the models’ PLV matrices. Red area: 95% confidence interval of the sample Pearson correlation coefficient. <i>Insets</i>: PLV matrix from the empirical data and from model 1 generated with the best-fit parameter. <b>e)</b> Peak of the power spectrum of <i>R</i>. The color code represents the empirical frequency power of <i>R</i> and the white line represents the empirical peak frequency. <b>f)</b><i>Top</i>: time evolution of <i>R</i> for one single fMRI session. <i>Bottom</i>: time evolution of the <i>R</i> of model 1 for <i>G</i> = 0.2. Note different time-scales (x-axis).</p

Spatiotemporal synchronization patterns.

<p>A synchronization matrix <b>Q</b> was built at each time step <i>t</i> (<i>t</i> = 1, .., <i>T</i>) by calculating the phase difference of each pair of empirical analytic signals and imposing a synchronization threshold: Q_<i>ij</i>(<i>t</i>) = 1 if |<i>φ</i>_<i>j</i>(<i>t</i>)-<i>φ</i>_<i>i</i>(<i>t</i>)|<π/6 and Q_<i>ij</i>(<i>t</i>) = 0 otherwise (1 <i>≤ i</i>, <i>j ≤ n</i>). The temporal evolution of the synchronization matrix <b>Q</b> is shown for an example scanning session (session #3) and for selected time periods; entries equal to one are represented in black, null entries are represented in white. The synchronization patterns framed in <i>blue</i> and <i>red</i> last several seconds and reoccur during disjointed time periods.</p

Relation between the T₁W and between MRS and histological outcomes respectively.

a,b<p>for Pearson's and Spearman's correlation respectively.</p><p><i>Abbreviations</i>: T₁-WI TSE = T₁-weighted Image Turbo-Spin-Echo; STIR = Short Time Inversion Recovery sequences; ¹H-MRS = Proton MR Spectroscopy (¹H-MRS).</p

Dynamical range of the anatomically-constrained phase oscillators’ network.

<p><b>a)</b> Time evolution of the phase difference between two nodes of the anatomically-connected heterogeneous Kuramoto model, for three values of the global coupling <i>G</i>. <i>Left</i>: in the weakly connected case (<i>G</i> = 0.025) the phases run almost independently; <i>middle</i>: with moderate coupling (<i>G</i> = 0.25) the phases tend to lock for short periods of time, as revealed by the deflections in the trajectory of the relative phase, indicating the presence of metastability; <i>right</i>: with strong coupling (<i>G</i> = 1.25) the phases are locked. <b>b)</b> Corresponding oscillations of the two nodes, for the three dynamical regimes.</p

Quantitative analysis of arteriole density in the limbs of diabetic and non-diabetic rats.

<p>Quantitative analysis of arteriole density from non-ischemic limbs or limbs with femoral artery ligation of diabetic (n = 7) and non-diabetic (n = 6) rats.</p><p>Data are presented as mean ± SD,</p>*<p>p<0.05, versus non-ischemic limbs.</p

Community structure of spatiotemporal synchronization patterns.

<p><b>a)</b> The temporal evolution of the synchronization matrix is represented in a <i>n×n×T</i> tensor <b>T</b>. The tensor can be factorized as a sum of <i>K</i> rank-one tensors, each one being an outer product of three vectors, <b><i>a</i></b>_{<b><i>k</i></b>}, <b><i>b</i></b>_{<b><i>k</i></b>}, <b><i>c</i></b>_{<b><i>k</i></b>}, of dimension equal to <i>n</i>, <i>n</i>, and <i>T</i>, respectively (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004100#pcbi.1004100.e009" target="_blank">Equation 8</a>). The network communities are contained in the vectors <b><i>a</i></b>_{<b><i>k</i></b>}, the elements of which give the participation weight of each node (i.e., brain region) in the community <i>k</i>. The temporal activation <i>s</i>_<i>k</i>(<i>t</i>) of each community <i>k</i> is related to <b><i>c</i></b>_{<b><i>k</i></b>} and to the participation weights as: <i>s</i>_<i>k</i>(<i>t</i>) = <i>c</i>_<i>k</i>(<i>t</i>)Σ_<i>j</i><i>a</i>_<i>k</i>(<i>j</i>). <b>b)</b> Detected community patterns (<b><i>a</i></b>_{<b><i>k</i></b>}. <b><i>a</i></b>_{<b><i>k</i></b>}^{<b><i>T</i></b>}) for the example session #1. <b>c)</b><i>Top</i>: temporal activation strength of each community, for the scanning session #1 (same colors as in (b)). <i>Bottom</i>: temporal evolution of both the order parameter <i>R</i>(<i>t</i>) (left y-axis) and the total activation strength [<i>S</i>(<i>t</i>) = Σ_<i>k</i><i>s</i>_<i>k</i>(<i>t</i>)] (right y-axis), for session #1. <b>d-e)</b> same as (b-c) but for session #7. <b>f)</b> Correlation matrix between all detected communities from all scanning sessions (<i>top</i>), re-arranged according to cluster membership. <i>Bottom</i>: corresponding dendrogram based on correlation coefficients.</p

Topology of the synchronization communities.

<p><b>a)</b> Spatial organization of the communities obtained with the first half of the sessions (<i>top</i>) and the second half of the sessions (<i>bottom</i>). For each community, the brain regions with the highest participation weights are presented (yellow: 0.1<<i>a</i>_<i>k</i>(<i>i</i>)<0.2; orange: <i>a</i>_<i>k</i>(<i>i</i>)>0.2). The community patterns of the second half of the sessions were matched to the ones of the first half of the sessions (below each panel the correlation between the community <i>i</i> from the first half-dataset and the community <i>i</i> from the second half-dataset is presented; <i>r</i>_<i>c</i>: correlation coefficient; <i>p</i>: p-value). <b>b)</b> The synchronization communities were compared to the resting-state networks obtained using ICA. As a measure of similarity we used the Jaccard index. The Jaccard similarity matrix between ICA-based components and synchronization communities is shown for the first half of the data (<i>left</i>) and the second half of the data (<i>right</i>). The spatial patterns given by the synchronization communities include: the default mode network (DMN, community 1), the somato-motor network (2), the visual network (3), the auditory/somato-motor network (4), the self-referencial/DMN network (5), the right cognitive control network (6), and other networks (7–14) that are overlaps of the previous ones and other functional networks detected using ICA.</p

Emergence of transient synchronization patterns.

<p><b>a)</b> Temporal evolution of activation strengths of the communities of the anatomically connected heterogeneous Kuramoto model (<i>G</i> = 0.2 and <i>K</i> = 10). <b>b)</b> Temporal evolution of the total community activation strength <i>S</i> (<i>top</i>) and the order parameter <i>R</i> (<i>bottom</i>) of the model anatomically connected heterogeneous Kuramoto model (<i>G</i> = 0.2 and <i>K</i> = 10). The correlation coefficient between <i>S</i>(<i>t</i>) and <i>R</i>(<i>t</i>) is 0.82 (p<10^–3). <b>c)</b><i>Top</i>: The largest correlation coefficient <i>r</i>_<i>max</i> (and 95% confidence interval) between the model communities and the empirical communities was calculated for various number of components (<i>K</i> = 2, …, 16) as a function of the global coupling. <i>Middle</i>: <i>r</i>_<i>max</i> was compared to the expected upper 95% confidence bound of the largest correlation coefficient (<i>r</i>_{<i>max</i>, <i>perm</i>}) between the model communities and 10³ random permutations of the <i>n</i> elements of each empirical communities, for each <i>K</i> and each <i>G</i>. <i>Bottom</i>: Probability that <i>r</i>_<i>max</i>> <i>r</i>_{<i>max</i>, <i>perm</i>}.</p

Frequency map of the spatial distribution of high (A) and low (B) grade tumors superimposed on a standard anatomical template, in radiological convention.

<p>An overlap between tumor volume and DMN was present in 4 patients: one with low grade (overlap of 230 mm³) and three with high grade (maximum overlap of 10930 mm³) tumors.</p