Brain metabolic-functional (de)coupling from health to glioma dysfunction

Abstract

The interplay between brain metabolism and function supports the brain’s adaptive capacity in cognitively demanding processes. Prior work has linked glucose metabolism to resting-state fMRI activity, but often overlooks both hemodynamic confounders in the BOLD signal and the brain’s dynamic nature. To address this, we employed a novel effective connectivity decomposition, separating symmetric partial covariance, capturing “true” statistical dependencies between regions, from antisymmetric differential covariance, reflecting directional brain flow. In 42 healthy subjects, we show that partial covariance corresponds to metabolic connectivity across regions, while node directionality relates to standardized uptake value ratio, a proxy for local glucose consumption. We subsequently tested the sensitivity of detected couplings in 43 glioma patients, identifying disruptions in both local and network-level effective–metabolic interactions that varied with tumor anatomical location. Our findings provide novel insights into the coupling between brain metabolism and functional dynamics at rest, advancing understanding of healthy and pathological brain states.

Introduction

Contemporary cognitive neuroscience aims to understand how the human brain, fueled by its significant metabolic budget¹, interacts with the environment during rest, interpreting, responding to, and predicting external demands^2,3. This states transition results in a flow that facilitates the information transfer between brain regions, which is intricately linked to the energy consumption required to drive cerebral functions, through the so-called neurometabolic coupling, delineating the delicate balance between heightened metabolic demand, blood flow, and neural function⁴. Consequently, thought-provoking questions emerge: what is the link between brain function, i.e., the dynamic flow and transition between cerebral states, and large-scale brain metabolism? Could investigating potential alterations in this coupling in clinical settings significantly enhance our understanding of the multimodal effects of focal brain lesions?

Previous research has examined, both in physiological and pathophysiological conditions, the large-scale relationship between the brain’s functional activity, assessed through spontaneous oscillations in the blood oxygen level-dependent (BOLD) signal captured with resting-state functional magnetic resonance imaging (fMRI), and glucose metabolism, utilizing [¹⁸F]fluorodeoxyglucose ([¹⁸F]FDG) positron emission tomography (PET), based on the assumption that the brain relies on glucose as energy to facilitate synaptic transmission⁵. These studies examined the relationship between local metabolic activity, such as the standardized uptake value ratio (SUVR), i.e., semi-quantitative measure of [¹⁸F]FDG uptake in each brain region, as well as measures of network metabolic activity, i.e., metabolic connectivity (MC), which describes the relationships between the metabolic measurements of different brain areas, alongside functional metrics, i.e., functional connectivity (FC), from BOLD-fMRI signal, expressed as pairwise statistical dependencies between observed brain activity, or its derived measures^6,7,8,9,10. However, BOLD-fMRI is significantly influenced by local hemodynamic confounders¹¹, introducing temporal delays and high interindividual and interregional variability^12,13. Effective connectivity (EC), expressing the directed and causal influence that one brain region exerts over another, offer a potential solution to overcome these limitations by disentangling neuronal activity from the undesired impact of hemodynamic component¹⁴. To date, the only attempt to bridge EC and glucose metabolism was proposed by Riedl and collegues¹⁵, who put forward a method to estimate EC based on regional glucose metabolism, associated with postsynaptic functional activity. This approach uses the spatial correlation between FC and glucose metabolism measured by [¹⁸F]FDG PET, but does not account for differences in blood vessel distribution, leading to potential inaccuracies. Moreover, the method treats EC as a static counterpart to FC. In contrast, large-scale EC inferred from dynamic causal modelling (DCM) not only provides a vascular-independent depiction of whole-brain networks—thanks to the observation model that accounts for hemodynamic coupling¹⁶—but also offers mechanistic insight through its generative modelling framework. Framed within a Bayesian framework, DCM can model brain functional activity as a linear dynamic process evolving over time in a state space, thereby enabling the interpretation of intrinsic brain network emergence in terms of critical dynamics¹⁷.

Given these premises, we aim to compare, via Partial Least Squares Correlation (PLSC)¹⁸, the large-scale EC dynamic patterns of functional activity with glucose metabolism, evaluated by [¹⁸F]FDG PET, in healthy controls (HCs).

By employing a thermodynamic analogy, we devised a novel decomposition method for the EC matrix, separating it into two distinct components¹³: a symmetric partial covariance matrix $(\widehat{{\mbox{FC}}}),$ and an antisymmetric differential cross-covariance matrix (S). While $\widehat{{\mbox{FC}}}$ shapes the geometry of the steady-state potential energy landscape—relating to the “surprise” (or free energy) of observing the brain in any functional state¹⁷—the antisymmetric component S captures the irreversible, directional aspects of brain dynamics. While $\widehat{{\mbox{FC}}}$ captures genuine symmetric functional dependencies between regions in the information flow, effectively filtering out any spurious correlations^19,20, S encodes the asymmetry between forward and backward functional flows, thus establishing a time arrow²¹ and reflecting nonequilibrium steady-state dynamics. In this framework, the node strength of S (i.e., the sum over each column) can be interpreted as a marker of causal role—identifying a node as a source (if positive) or a sink (if negative) of information flow¹³.

From a metabolic standpoint, we incorporated both local metabolism (SUVR) and network information (within-individual MC)^6,22.

Subsequently, we validated the effective-metabolic relationships identified in HCs by examining a group of glioma patients to elucidate whether the expected dysfunctions induced by a localized brain lesion could be captured by an alteration of these relationships. Gliomas, the most prevalent type of primary brain tumors, are known to induce both localized and widespread functional and metabolic dysfunctions^22,23,24. Therefore, we hypothesize that the functional-metabolic interplay would also be disrupted in glioma patients, making them an ideal model not only for validation of detected couplings but also for gaining new insights into the underlying pathophysiological mechanisms.

Our findings reveal two neurometabolic coupling patterns during rest: a local-level association between regional glucose uptake and node directional flow, and a network-level relation between metabolic and functional regional interactions. In glioma patients, a differential sensitivity of effective-metabolic coupling to the anatomical location of the lesion is revealed: local decoupling is prominent in temporo-parietal tumors, while network disruption stems from fronto-parietal lesions, where widespread connectivity reductions are expected given the high density of tracts in these areas²⁵, which have been identified as hub regions for functional communication^26,27. These findings reinforce the interpretability of our effective-metabolic coupling results and the validity of our method, suggesting that the interaction between brain function and metabolism is crucial in understanding the brain’s adaptive or maladaptive responses to gliomas, potentially shedding light on how these changes influence brain information transfer and cognitive functions.

Results

Effective-metabolic coupling

To explore multivariate correlation patterns between effective and metabolic measures from 42 HCs (mean age 58.2 ± 14.5 years, 19 males/23 females), we employed PLSC analysis (pipeline summarized in Supplementary Fig. 1 and detailed in Methods section). PLSC is a statistical method used to explore the relationship between two features (e.g., metabolic and functional measures), by projecting the original variables onto a reduced-dimensional (latent) space, producing weight patterns called PLSC salience maps. When applied to original features, these maps are optimized to maximize the covariance between the corresponding latent variables, named scores, which quantify the associative effects across the sample^18,28.

Four multivariate combinations were assessed: $\widehat{{\mbox{FC}}}$–SUVR, S–SUVR, $\widehat{{\mbox{FC}}}$–MC and S–MC. Supplementary Fig. 2 reports a qualitative overview of the group-average matrices (MC, S and $\widehat{{\mbox{FC}}}$), alongside corresponding node strength distributions and average region-level SUVR. In the case of combinations involving SUVR, the nodal strength of $\widehat{{\mbox{FC}}}$ (i.e., the sum of functional correlations of each node with all the remaining nodes) or S (along the columns, providing insights into the node’s behavior as a sink or source) was used. These values were then stacked as participant-by-strength on one side and participant-by-SUVR value on the other, using these matrices as input for the PLSC. On the other hand, for combinations including comparisons between MC versus $\widehat{{\mbox{FC}}}$ and S matrices, the upper triangle of the connectivity matrices were vectorized and stacked as participant-by-connection to assess the metabolic-effective coupling across the whole brain network.

To address potential overfitting in PLSC due to limited sample size²⁸, model generalizability was evaluated via K-fold cross-validation. Supplementary Table 1 and Supplementary Fig. 3 show the results. Only the $\widehat{{\mbox{FC}}}$–MC (correlation between metabolic and effective scores r = 0.7435, p-value < 0.001; first latent dimension) and S–SUVR (r = 0.6375, p-value < 0.001; second latent dimension) pairs showed generalizability (Pearson’s correlation between original and test scores > 0.5²⁹ for both effective and metabolic pairs), while the other combinations did not.

Distinct PLSC salience patterns emerge when comparing effective and metabolic features, as illustrated in Fig. 1. Details on statistical significance assessment and reliability evaluation for nonzero PLSC salience values are detailed in the Methods section. Specifically, for the S-strength variable (Fig. 1a, upper panel), positive weights tend to increase when transitioning from sensory-attentive (Vis, SomMot, DorsAttn) to transmodal networks (DMN, Cont, SalVentAttn, Limbic)³⁰, reaching high levels in DMN regions. This pattern is accompanied by a concurrent inversion trend, i.e., a shift from positive to negative values (with higher absolute magnitude for transmodal areas), in the weighting model of the SUVR salience (Fig. 1a, lower panel). Latent scores represent how closely an individual’s original data aligns with the PLSC salience patterns: a positive score indicates strong similarity, while a negative score shows an inverse relationship. Therefore, by analyzing the scores sign and the PLSC saliences pattern, it is possible to infer the subjects’ metabolic and functional characteristics. Figure 1c (left panel) reports the latent scores for S–SUVR, suggesting that two groups of subjects primarily contribute to the component variance. The first group (with negative latent scores for both S-strength and SUVR, i.e., the III quadrant) is characterized by a predominantly negative S-strength profile (nodes’ behaviour primarily as sinks), coupled with high SUVR in cognitive networks and low SUVR in sensory-attentive areas. The second group (with positive latent scores for both S-strength and SUVR, i.e., the I quadrant) comprises individuals exhibiting an overall positive S-strength across the entire brain (nodes primarily functioning as sources), associated with high SUVR in sensory-attentive networks and low SUVR in higher-order areas. Figure 2 confirms these insights based directly on original data. The upper panel displays the scatter plot of S–SUVR scores, with each dot color representing the median of S-strength values (significant, according to the PLSC salience map) in subject’s transmodal and sensory-attentive areas separately. For both cases, a clear trend is evident, transitioning from negative values (for subjects with negative scores) to progressively positive values (for subjects with positive scores). Furthermore, comparing the S-strength across different RSNs for two individuals exhibiting contrasting coupling behaviors reveals a significant reversal in the sign of these values. The scatter plot in the lower panel shows S–SUVR scores, with dots colored based on the difference between median SUVR significant values in sensory-attentive and transmodal areas. This highlights a hierarchical inversion of networks during the transition from negative scores, indicating a prevalence of higher values in transmodal areas, to positive scores, suggesting higher SUVR in sensory-attentive networks. Additionally, the marker sizes are proportional to the median values in transmodal areas: negative SUVR scores generally exhibit a greater magnitude than positive SUVR scores, suggesting higher glucose consumption. As in the upper panel, the same two representative subjects are depicted, with SUVR values reported in each RSN and bar plots ordered by their median value, illustrating the inversion between sensory-attentive and transmodal areas accompanying the observed shift of S-strength values.

Fig. 1: PLSC results: Saliences and Scores.

a S and SUVR PLSC saliences, over the bootstrap samples, only the PLSC salience weights significantly different from zero are reported. b $\widehat{{\mbox{FC}}}$ and MC network-wise PLSC salience pattern. These matrices are obtained by averaging the entries values in each block, considering zero the non-significant entries. c Scatter dots plotted in the latent space for both S–SUVR (left) and $\widehat{{\mbox{FC}}}$–MC (right), where each point corresponds to a healthy control’s score, alongside the least-square best-fitting line. The colored boxes highlight the subjects who primarily contribute to defining the variance of the component, exhibiting distinct metabolic-functional characteristics. Vis, visual network; SomMot, somatosensory motor network; DorsAttn, dorsal attention network; SalVentAttn, saliency/ventral attentional network; Limbic, limbic network; Cont, control network; DMN, default mode network, Subcortical, subcortical regions: thalamus proper, caudate, putamen, pallidum, cerebellum, and hippocampus.

Fig. 2: Evaluation of the S–SUVR patterns on the original data, with reference to the scores model (single-subject analysis).

(Upper panel) S–SUVR scores with each dot color determined by the median of S-strength values in subject’s transmodal and sensory-attentive areas separately, alongside the S-strength values in each RSNs (sensory-attentive RSNs in red) for two individuals exhibiting contrasting coupling behaviors (right and left insets). In the boxplots, the central line represents the median value, the box limits indicate the interquartile range (IQR; 25th–75th percentiles), the whiskers extend to 1.5×IQR, and outliers are shown as individual points. Only the significant S-strength values, according to the PLSC salience map, are considered. (Central panel) Recall the meaning of the S-strength value: a positive value for a node (region) indicates that it primarily behaves as a source node, while a negative value suggests that the node primarily acts as a sink. (Lower panel) S–SUVR scores with each dot colored according to the corresponding difference between the median SUVR values in sensory-attentive and transmodal areas, alongside the SUVR values in each RSNs for two individuals exhibiting contrasting coupling behaviors (sensory-attentive RSNs in red). Only the significant SUVR values, according to the PLSC salience map, are considered. Additionally, the marker sizes are proportional to the median SUVR values in transmodal areas.

Regarding the $\widehat{{\mbox{FC}}}$–MC pair (Fig. 1b), we only reported the network matrices, i.e., obtained by averaging the entries in each network-to-network block, while full-entries matrices are provided in the Supplementary Materials. $\widehat{{\mbox{FC}}}$ PLSC salience map exhibits a uniform positive pattern across functional networks, favoring between-network interaction over within-network links, where the entries are not significant (explaining lower values in the within-network blocks, as non-significant entries are set to zero). Conversely, the association with the metabolic counterpart is predominantly characterized by positive weights in the sensory-attentive networks and their connections with transmodal areas, as well as in the cerebellar links (see Supplementary Fig. 5a). Negative weights are primarily observed within-DMN, while for the SalVenAttn and DorsAttn, they mainly correspond to interactions either between these networks or with the Limbic network. Similarly to the S–SUVR case, two groups of subjects primarily contribute to defining the variance of the component (Fig. 1c). The group primarily characterized by negative latent scores (III quadrant) comprises individuals exhibiting negative $\widehat{{\mbox{FC}}}$ links, particularly those associated with between-network dependencies, while predominantly low MC links are found within sensory-attentive areas and in their connections with transmodal ones, accompanied by elevated within-DMN links. Conversely, individuals with positive latent scores (I quadrant) are primarily distinguished by higher $\widehat{{\mbox{FC}}}$ inter-networks links and predominantly strong MC connections within sensory-attentive networks, along with their integration with transmodal areas, accompanied by a reduction in DMN segregation. These deductions from the PLSC results are corroborated by the findings on the original data, reported in Fig. 3. In the upper panel, the $\widehat{{\mbox{FC}}}$–MC scores are presented, with each dot color corresponding to the median of the entries (significant according to the PLSC salience map) in the subjects’ $\widehat{{\mbox{FC}}}$ matrix. A progressive increase in connection values is evident, and since the significant entries mainly pertain to inter-network links, this analysis showcases a progressive enhancement in network integration, transitioning from subjects with negative scores to those with positive scores. This transition in $\widehat{{\mbox{FC}}}$ is associated with different MC characteristics. To enhance comprehension, we divided the analysis of the MC entries based on those presenting negative or positive PLSC salience values, focusing the attention on the associated areas. Therefore, the dot color in Fig. 3 (lower panel) is according to the median value of the MC entries for the selected areas. As previously mentioned, negative PLSC salience values are predominantly associated with intra-DMN and SalVentAttn, DorsAttn areas. From the median of the corresponding entries, a clear shift in trend emerges, transitioning from very high values for subjects with negative scores to lower values for those with positive scores. On the other hand, analyzing the positive PLSC salience values, namely the sensory-attentive RSNs and their connections with transmodal regions, a change in direction is noticeable: the transition from negative to positive scores indicates a progression from low MC values within sensory-attentive and between sensory-attentive and transmodal areas to a gradual increase integration between these regions, accompanied by a metabolic activation of sensory-attentive areas. Representative subjects for both $\widehat{{\mbox{FC}}}$ and MC are portrayed, each showcasing contrasting behaviors that illuminate the observed patterns, underscoring the correlation between functional integration shifts and distinct metabolic trends.

Fig. 3: Evaluation of the $(\widehat{FC})$–MC patterns on the original data, with reference to the scores model (single-subject analysis).

(Upper panel) $\widehat{{\mbox{FC}}}$–MC scores with each dot color determined by the median of $\widehat{{\mbox{FC}}}$ entries across the subject’s brain, alongside the $\widehat{{\mbox{FC}}}$ matrices for two individuals exhibiting contrasting coupling behaviors (right and left insets). Only the significant $\widehat{{\mbox{FC}}}$ entries, according to the salience map, are considered, and the network matrices are obtained by averaging the remaining entries in each block. (Lower panel) $\widehat{{\mbox{FC}}}$–MC scores with each dot colored according to the median of MC entries across the subject’s brain, alongside the MC matrices for two individuals exhibiting contrasting coupling behaviors (right and left insets). Particularly the MC entries are analysed separating those presenting positive or negative salience values, to focus attention on the associated areas. Only the significant MC entries, according to the PLSC salience map, are considered, and the network matrices are obtained by averaging the remaining entries in each block.

Effective-metabolic (de)coupling in glioma

MC, $\widehat{{\mbox{FC}}}$, S, and SUVR were extracted from 43 glioma patients (mean age 58.8 ± 14.9 years, 24 males/19 females), and mapped onto the maximizing-covariance latent spaces identified for the HCs. As depicted in Fig. 4 (upper panels), in both S–SUVR and $\widehat{{\mbox{FC}}}$–MC cases, certain patients notably deviate from the expected effective-metabolic coupling. Figure 4 (lower panels) reports the weighted tumor frequency maps referring to patients’ falling outside the “normality-band” (outlier patients), revealing that the S–SUVR pair is predominantly altered in temporo-parietal tumors, while $\widehat{{\mbox{FC}}}$–MC mainly in patients with fronto-parietal lesions. The statistical comparison reported in Supplementary Fig. 9 allows us to localize the regions where tumor occurrence significantly differs between the two groups, beyond visual inspection. Therefore, moving beyond qualitative visual comparison, the analysis confirms a spatial dissociation: as hypothesized, S–SUVR outliers show significantly greater lesion occurrence in temporo-parietal regions, while $\widehat{{\mbox{FC}}}$–MC outliers are predominantly associated with frontal areas. These findings support the presence of anatomically distinct lesion distributions underlying the two coupling disruptions.

Fig. 4: Glioma patients’ effective-metabolic decoupling.

(Upper panel) Projection of patient’s latent scores onto the latent space for S–SUVR (left), $\widehat{{\mbox{FC}}}$–MC (right). Colored dots represent glioma patients, while black dots depict healthy controls. For patients the marker size is proportional to the tumor volume (TM, includes tumor core, i.e., contrast agent enhancing and non-enhancing regions). The shaded area represents the “normality-band” for the expected healthy coupling. (Lower panel) Corresponding tumor-weighted frequency map for outlier patients.

No significant correlation emerges between the patients’ distance from the regression line and tumor volume (S–SUVR r = 0.21, p-value = 0.11, $\widehat{{\mbox{FC}}}$–MC r = 0.19, p-value = 0.21).

We then examined how the spatial location of the tumor relates to the nature of the observed deviation, by comparing the outlier patients’ and HCs’ PLSC loadings. Loadings provide the degree of contribution of each original variable to the PLSC latent score (statistical significance assessment and reliability evaluation for nonzero loading values are in the Methods section). From Fig. 5a, S-strength and SUVR loadings generally exhibit higher absolute magnitudes for outlier patients compared to HCs. Moreover, a contribution from sensory-attentive areas (SomMot and DorsAttn), previously absent in controls, emerges in patients, particularly a positive S-strength loadings trend is here associated with negative SUVR loadings pattern.

Fig. 5: S-strength and SUVR, $(\widehat{FC})$ and MC loadings (healthy controls vs outlier patients).

a Stem plot illustrating S-strength loadings in the HC sample and in the group of outlier patients, together with the stem plot illustrating SUVR loadings in the HC sample and in the group of outlier patients. Healthy controls are in black, while outlier patients in red. Only the loadings significantly different from zero are reported. b Network matrices illustrating $\widehat{{\mbox{FC}}}$ and MC loadings computed in the HC sample (upper triangular portions) and the group of outlier patients (lower triangular portion). The network matrices are obtained by averaging the entries in each block (including as zero the non-significant entries).

$\widehat{{\mbox{FC}}}$–MC network matrices loadings are reported in Fig. 5b (full-entries matrices in Supplementary Fig. 5b). $\widehat{{\mbox{FC}}}$ loadings have higher magnitude in outlier patients compared to HCs, particularly in the relationships between sensory-attentive and transmodal networks. However, many entries lose significance compared to healthy cases, resulting in reduced mean values in each network matrix block. The combined interpretation of scores and loadings suggests that inter-network entries contribute more intensely negatively for those with negative $\widehat{{\mbox{FC}}}$ scores, compared to HCs. The metabolic counterpart, on the other hand, is characterized by a loss of significance of the entries compared to the HCs, with inter-network links involving DorsAttn and Subcortical areas slightly remaining relative to other RSNs.

The original features, i.e., S-strength and SUVR values as well as $\widehat{{\mbox{FC}}}$ and MC matrices, for all outlier patients are reported in Supplementary Fig. 6 and Supplementary Fig. 7, respectively.

Discussion

Effective-metabolic coupling

Through a comprehensive examination of both local and network metrics of brain metabolism alongside directed and undirected patterns of functional information flow, our investigation unveils the emergence of a dual effective-metabolic coupling. On one front, the association between the column-wise S-strength (node signal directionality) and regional SUVR (proxy of local glucose consumption) suggests that localized energy resources play a crucial role in supporting the directionality of signalling, specifically in terms of temporal irreversibility²¹, akin to chemical changes facilitating unidirectional transitions between molecular states³¹. Notably, for both S-strength and SUVR, PLSC salience weights exhibit dominance in higher-order RSNs, as better elucidated by the loading profiles (Fig. 5) where the regional contributions to the score are mainly driven by the transmodal networks, suggesting that these areas significantly influence the observed coupling. This aligns with previous studies^32,33 that reported a linear relationship between regional metabolism and the degree of functional interaction between regions, with stronger association in DMN areas. However, our study provides additional insights by elucidating each node’s role as either a source or a sink¹³, thereby suggesting a relationship between metabolism and functional activity, even in the context of directional links. Going further into the details of this coupling through both PLSC salience (Fig. 1a) and direct data analysis (Fig. 2), a precise link between S-strength and SUVR is revealed, suggesting that a change in the functional-directional role of the node is associated with a subsequent change in glucose consumption. In this view, when the nodes predominantly act as sinks, an intra-subject hierarchy emerges, with increased SUVR in transmodal areas compared to sensory-attentive ROIs. Additionally, a trend across subjects, transitioning progressively from sink to source nodes, reveals a progressive reduction in glucose consumption in transmodal areas (Fig. 2, marker size). Suggesting that transmodal areas play a key role in driving the coupling, with this connection being more pronounced (loading profile in Fig. 5a), these findings reinforce and extend the observations made by Riedl and colleagues¹⁵. Recognizing that a substantial portion—up to 75%—of signalling-related energy is expended at the postsynaptic level (i.e., within the target neurons), they postulated that an increase in large-scale local metabolism corresponds to an augmentation in afferent effective connectivity from source regions. Nonetheless, our findings mitigate the confounding influence of hemodynamic heterogeneity, yielding more robust and reliable coupling results.

On another front, PLSC analysis brings to light a significant association between metabolic and functional networks measures: the magnitude of functional interactions relies on metabolic synchronization regulated at the network level, potentially facilitating the reversible exchange of balancing forces as predicted by the fluctuation-dissipation theorem³⁴. This outcome resonates with a recent study by Jamadar and collegues⁸, revealing a significant shared variance between MC and fMRI-FC with a notable tendency towards stronger connectivity in the frontal cortex. Additionally, the coupling between glucose metabolism and fMRI-FC was shown to be limited when considering only local metabolic measures such as SUVR¹⁰, but strengthens significantly when both PET and rs-fMRI are analyzed within a broader, large-scale connectivity framework⁶. However, our results provide a more nuanced analysis by examining coupling patterns across individuals rather than relying solely on average matrices, thus facilitating more detailed inferences about different across-subject relationships that might otherwise be obscured by group-level analyses. Additionally, by employing $\widehat{{\mbox{FC}}}$ to capture the genuine statistical dependencies between regions, the reliability of the findings is further strengthened. The exploration of the intricacies of this coupling through both PLSC salience (Fig. 1b) and direct data analysis (Fig. 3) unveils a precise link between $\widehat{{\mbox{FC}}}$ and MC, indicating that changes in the brain’s functional architecture result in a subsequent reorganization of the metabolic network, suggesting that glucose metabolism can modulate oscillatory dynamics and, consequently, the functional connectivity of neural ensembles^35,36. Notably, our results indicate that greater $\widehat{{\mbox{FC}}}$ integration is accompanied by increased MC activation of sensory-attentive areas, along with stronger communication with transmodal networks, particularly the DMN, while also highlighting the significance of cerebellar metabolic activation. Therefore, the DMN not only plays a crucial role in high-level interoceptive tasks, but also in dynamically integrating metabolic information exchanged within functional networks. Furthermore, the metabolic activation of the cerebellum in the case of strong functional integration parallels the theory that suggests the cerebellum primarily expends energy on upholding potential sensory-motor associations in real-time, favouring its functional connections with both motor- and cognitive-related regions³⁷. On the other side, when the DMN appears metabolically active and synchronized, exhibiting positive connections with the Cont and SalVentAttn networks, and to a lesser extent with sensory-attentive networks, the functional counterpart manifests lower inter-network connections, indicating that reduced metabolic integration leads to decreased functional integration. Our findings align with works^38,39 which emphasizes that central nodes within the DMN strategically modulate crosstalk between sensory-attentive networks. Moreover, Zhang et al.⁴⁰ reveal a coupled relationship between network segregation and glucose metabolism in the SalVenAttn employing simultaneous PET/fMRI acquisition. Here, we demonstrate that such dual functional state must be supported by specific metabolic configurations. Moreover, the degree of arousal and internally- versus externally-driven attention might in particular be related to the axes of effective-metabolic coupling seen here, which warrants further investigation⁴¹.

Overall, both local and network coupling suggest a high baseline necessity for cerebral blood flow and metabolic activity especially required for the nonstop coherent activity of cognitive regions during resting state⁴².

Effective-metabolic (de)coupling in gliomas

To strengthen the reliability of our coupling results, we tested their sensitivity in detecting potential disruptions in local or network effective-metabolic interplay in glioma patients.

Upon analysing weighted tumour frequency maps (Fig. 4 and Supplementary Fig. 9), a distinctive pattern emerged: the decoupling of both pairs (S–SUVR and $\widehat{{\mbox{FC}}}$–MC) was contingent on lesion location. Notably, patients with disrupted local coupling predominantly manifested temporo-parietal lesions, situating in brain areas characterized by prevalent sensory-attentive functions. In contrast, deviations from expected network coupling were in patients with fronto-parietal lesions, in regions typically associated with the DMN and devoted to cognitive functions. Crucially, this divergence from the expected pattern is not contingent on the tumor’s volume, emphasizing a dependence on glioma location rather than its size. To quantitatively assess whether lesion location differs between the two outlier groups, we performed a voxel-wise statistical comparison of their tumor-weighted frequency maps; full details and results are provided in Supplementary Information.

To further probe the variables contributing to the observed decoupling, an assessment of the loadings’ profile (Fig. 5) was conducted for each pair in both the outlier patient cohort and HCs (i.e., reference baseline for understanding the degree of contribution from each variable to the scores). In the S–SUVR analysis, the loadings reveal a notable discrepancy between outlier patients and HCs, especially in the contributions of sensory-attentive areas and DMN, suggesting these RSNs as the primary networks involved in the decoupling. We hypothesize that the decoupling is linked to a dual action. Sensory-attentive areas, such as SomMot and DorsAttn, are often involved in lesions (see Supplementary Fig. 6), potentially resulting in their significant contribution to the scores (absent in HCs) with disrupted S–SUVR coupling. Indeed, analyzing the tracts involved in the tumor for outlier patients (Supplementary Fig. 8), it is interesting to note that the Arcuate Posterior Segment Right, mainly responsible for temporo-parietal connections and dedicated to visual and language processes⁴³, as well as the Frontal Aslant Tract Left, also involved in language functions⁴⁴, are primarily implicated, mostly differentiating outlier patients from the patients within the “normality-band”. On the other hand, the latter group of patients primarily involves the Frontal Commissure, a tract that connects the two cerebral hemispheres and facilitates information transfer between them, causing significant repercussions on cerebral network communication⁴⁵, demonstrating that it is precisely the involvement of more local and sensory-attentive tracts that causes an alteration in the S–SUVR coupling. Concerning DMN loadings, while parietal areas are involved in the lesion for some patients, frontal regions may exert a more pronounced effect due to possible compensatory mechanisms. Liu and colleagues⁴⁶ had already examined the role of the DMN in temporal tumors, showing that graph metrics derived from structural connectivity showed higher values for areas like the medial and superior frontal gyrus, located within the DMN.

Concearing the $\widehat{{\mbox{FC}}}$–MC pair, the $\widehat{{\mbox{FC}}}$ scores are uniformly negative for outlier patients. Combining these findings with the loadings analysis suggests a greater negative contribution of inter-network links compared to healthy individuals, indicative of reduced integration (Supplementary Fig. 7 reports $\widehat{{\mbox{FC}}}$ matrices for the outlier patients). Interestingly, such extensive functional disruption mirrors findings from Cai et al.⁴⁷, which highlighted a profound impairment of interhemispheric communication and vulnerability of long-range functional connections in frontal gliomas. Similarly, Zhang and collegues⁴⁸ emphasized that frontal gliomas not only impact local brain function but also diminish the functional capacity of the entire brain, with even posterior brain regions without tumor infiltration showing decreased strength of functional connectivity. Conversely, MC loadings map appear quite sparse, suggesting a non-significant deviation from controls (see Supplementary Fig. 7), with few significant positive entries primarily concentrated in Subcortical and DorsAttn links with other RSNs. Similarly, Cai et al.⁴⁷ reported a strong role of structural and functional remodeling of subcortical nuclei in the case of frontal gliomas, which could justify the parallel metabolic involvement characterizing such areas. In addition, the functional activation of DorsAttn⁴⁹ has been reported, which may stem from its tendency to connect functionally to the tumor-infiltrated cortex⁵⁰, potentially explaining its observed metabolic activation. The analysis of the involved tracts (Supplementary Fig. 8) revealed that outlier patients (compared to within-band patients) exhibit a strong involvement of the Frontal Commissure, confirming that the $\widehat{{\mbox{FC}}}$–MC decoupling serves as a proxy for alterations in network communication. Accordingly, diffuse gliomas—particularly those localized within this core frontoparietal network—have been shown to profoundly disrupt brain hub architecture, driving widespread reorganization of large-scale brain connectivity²⁷.

Additionally, since frontal regions are distinguished by their high glucose consumption and BOLD activity, such high metabolic demands could contribute to a more elevated cell turnover, enhancing the likelihood of a cell acquiring an oncogenic mutation during mitosis⁵¹. This could lead to heightened interactions between the neural system and malignant cells, which have been proven to exist not only near the tumor site but also at a distance, with glioneuronal synapses that enable gliomas to integrate into functionally active brain circuits⁵², also resulting in long-range network communication alterations.

In summary, temporo-parietal and fronto-parietal gliomas seem to involve distinct metabolic and functional mechanisms, offering valuable insights into how gliomas reshape brain function by perturbing large-scale network dynamics as well as local metabolic-functional coupling. This dual disruption may reflect unique patterns of neural plasticity and response to tumor presence⁴⁶.

Study limitations

While PET and fMRI acquisitions were performed simultaneously in patients with glioma, they were not in healthy subjects, which could partially influence the results. However, the relationship between brain metabolism and function has already been explored in previous studies using this same dataset^6,10. Additionally, while our results suggest differences between frontal and temporal gliomas, we recognize that tumor histology may also contribute to these findings. Due to the sample composition, we were not able to systematically assess the interaction between tumor location, histology and effective-metabolic (de)coupling. Therefore, future studies with larger and more balanced cohorts are needed to further investigate this aspect.

Conclusions

This study represents a pioneering effort to comprehensively characterize the mechanisms underlying brain metabolism and the associated functional trajectories during resting state. Moreover, our investigation underscores that the nature of effective-metabolic (de)coupling is intricately tied to the anatomical location of brain tumours. This observation supports the idea that the pathophysiological mechanisms of gliomas may drive multimodal dysfunctions, potentially fostering adaptive neuroplasticity processes in response to tumor presence.

Methods

Participants

In this study, we included 42 healthy controls (HCs), mean age 58.2 ± 14.5 years, 19 males/23 females, as a control group from the Adult Metabolism & Brain Resilience (AMBR) study⁵³. The patient cohort comprised pre-surgical data from 43 patients, mean age 58.8 ± 14.9 years, 24 males/19 females, with de novo brain tumors collected at the University Hospital of Padova between June 2016 and April 2021. The lesion frequency maps (Supplementary Fig. 4) and the table containing demographic characteristics (Supplementary Table 2) are provided in the Supplementary Information.

The diagnosis was made according to the criteria of the WHO classification system, 2016 version⁵⁴. The dataset includes 6 low-grade gliomas (LGG), 34 high-grade (HGG) and 3 for whom the information is not available because no biopsy was performed; as to IDH1 mutation status, 26 are wild-type, 7 mutated and 10 undefined. All participants regularly received anticonvulsants for seizure control, and corticosteroids. The protocol has been approved by the local Ethics Committee of the University Hospital of Padova and conducted in accordance with the 1964 Declaration of Helsinki and its subsequent amendments. Written informed consent was obtained from all participants. All ethical regulations relevant to human research participants were followed.

Data acquisition

For HCs, high-resolution T1-weighted (T1w) MRI and T2*-weighted gradient-echo echo planar imaging (GE-EPI) resting state functional MRI (rs-fMRI) scans were performed on a Siemens Magnetom Prisma^fit scanner, while [¹⁸F]FDG scans were acquired on a Siemens 962 ECAT EXACT HR + PET (Siemens/CTI) scanner. The GE-EPI sequences (repetition time (TR) = 800 ms, echo time (TE)  =  33 ms, flip angle (FA) = 52°, voxel size 2.4 × 2.4 × 2.4 mm³, multi-band acceleration factor (MBAccFactor) = 6, 375 volumes for total scan time of 5 min) are acquired together with two spin-echo (SE) acquisitions (TR/TE  =  6000/60 ms, FA 90°) with opposite phase encoding directions (AP, PA). Dynamic PET data (60-minute acquisition) were reconstructed as 128 × 128 × 63 matrices with a 2.0 × 2.0 × 2.4 mm³ voxel size in 52 frames (24 × 5 s, 9 × 20 s, 10 × 60 s, 9 × 300 s).

Glioma patients underwent simultaneous PET/MR acquisitions on a Siemens 3 T Biograph mMR scanner (Siemens, Erlangen, Germany). Functional imaging comprised rs-fMRI scans acquired with a T2*-weighted GE-EPI sequence (TR/TE  =  1260/30, FA  =  68°, voxel size 3×3×3 mm³, MBAccFactor = 2, 750 volumes for total scan time of 16:03 min, phase encoding direction antero-posterior) and two SE acquisitions with reverse phase encoding (TR/TE  =  4200/70 ms, FA  =  90°) for EPI distortion correction purposes. Dynamic PET data (60-minute acquisition) were reconstructed as 256×256×127 matrices with a 2.8 × 2.8 × 2.0 mm³ voxel size, in 39 frames with increasing duration (10 × 6 s, 8 × 15 s, 9 × 60 s, 12 × 240 s).

For a comprehensive description of the acquisition protocols see Supplementary Methods.

Structural MRI preprocessing

T1w structural images of both HCs and patients underwent similar preprocessing procedures, involving N4 bias field correction⁵⁵, skull-stripping using Multi-Atlas Skull Stripping⁵⁶, tissue segmentation obtained using Statistical Parametric Mapping tool (SPM12, v7219 https://www.fil.ion.ucl.ac.uk/spm/) and non-linear registration to the MNI152 standard space. Next, regions of interest (ROIs) were defined according to a clustered cortical parcellation that comprises 74 regions derived from the Yan’s 100-area atlas⁵⁷ detailed in the Supplementary Methods section. Specifically, it categorizes each parcel into one of seven resting-state networks (RSNs)⁵⁸: Visual network (Vis) with 5 parcels, Somatomotor network (SomMot) with 13 parcels, Dorsal attention network (DorsAttn) with 9 parcels, Saliency/Ventral attention network (SalVenAttn) with 10 parcels, Limbic network (Limbic) with 5 parcels, Control network (Cont) with 13 parcels, and Default mode network (DMN) with 19 parcels. To ensure a comprehensive analysis, 12 subcortical and cerebellar regions were added, aligning with the AAL2 segmentation by Rolls and collegues⁵⁹. This extension included, for each hemisphere, 6 regions: thalamus, caudate, putamen, pallidum, cerebellum, and hippocampus.

For glioma patients, two lesion segmentations were defined²⁴: specifically, the tumor (TM) mask includes tumor core (contrast agent enhancing and non-enhancing regions) and necrosis, while the lesion mask (TM + E) also includes the area of edema (E).

The atlas was then registered to individual T1w image using the Advanced Normalization Tools (ANTs, v2.4.3)⁶⁰, specifically, diffeomorphic non-linear registration (utilizing the ANTs SyN algorithm) was employed to register the T1w volumes to the MNI152 FSL standard space⁶¹. Notably, the registration in glioma patients was employed excluding the TM + E area⁶² to ensure accurate normalization⁶³.

Functional MRI preprocessing

For the preprocessing of rs-fMRI data, both controls and patients underwent analogous steps. fMRI volumes were corrected for slice timing disparities⁶⁴ and magnetic field distortions⁶⁵. A realignment to the median volume was performed⁶⁶. We used ICA-based approach for the removal of spurious variance associated with scanner artifacts. For healthy controls, we applied ICA-AROMA, which automatically identifies and removes motion-related components^67,68. Our analysis was executed within a singularity container for reproducibility, and we set 150 ICA components to ensure stability. In glioma patients, the identification and removal of motion-related components were done manually to better align with the specific characteristics of the data, given the more heterogeneous motion patterns observed due to the presence of tumors. This manual approach has been shown to be effective in mitigating the impact of both motion and scanner artifacts in clinical populations, as demonstrated in Silvestri et al.²⁴. For both groups, a regression analysis was employed to eliminate motion-related artifacts, incorporating motion parameters and their first-order derivatives. Additionally, the first 5 temporal principal components, derived from principal component analysis of white matter (WM) and cerebrospinal fluid (CSF) EPI signals⁶⁹, were regressed out from all brain voxels in the native EPI space. Subsequently, each subject was assigned a binary temporal mask to identify brain volumes affected by head motion (FD > 0.4 mm). This binary temporal mask was utilized to account for the reliability of temporal frames in the sDCM estimation process, with high-motion frames receiving less weight than normal frames. Volume despiking was applied to the time series using the icatb_despike_tc function of the GIFT toolbox. Furthermore, the temporal traces underwent band-pass filtering (0.0078 to 0.2 Hz) to retain frequencies typically supported by the canonical HRF in the DCM framework^70,71, facilitating accommodation of potential hemodynamic alterations in oncological patients.

In the case of patients, ROIs were carefully extracted by excluding voxels within the lesion mask (TM + E). This approach aimed to eliminate grey matter (GM) areas in close proximity to the tumour, where fMRI signals are susceptible to significant distortions in neurovascular uncoupling due to tumour angiogenesis^72,73,74 that may not be effectively captured by the HRF prior.

Effective connectivity analysis

For both HCs and patients, individual-level fMRI timeseries were demeaned and rescaled, following the recommendations in Zeidman and collegues⁷⁵. The effective connectivity (EC) matrix, alongside other model variables, was then individually estimated using sDCM⁷⁶. In the case of patients, recent studies have shown that cerebral gliomas induce vascular dysfunction in peritumoral areas and excessive synchronization of vascular activity in the contralesional hemisphere, both of which are malignancy-specific^73,77. To address these considerations, we appropriately adjusted the variance scale of the HRF parameter priors used by sDCM during the inference procedure to account for potential abnormal vascular properties induced by the lesion. Further information about the hemodynamic prior settings for oncological patients is provided in⁷⁸.

Once the EC matrices were obtained, following the framework proposed by Friston et al.¹⁷, they can be decomposed into two key matrices: a steady-state differential cross-covariance matrix (S), which introduces time irreversibility, and a partial covariance matrix ($\widehat{{\mbox{FC}}}$), which captures genuine symmetric functional dependencies between regions while accounting for and discounting the influence of mediators. Specifically, $\widehat{{\mbox{FC}}}$ is mathematically equivalent to $-{\Sigma }^{-1}$, where ${\Sigma }^{-1}$ is extracted as detailed in¹³ and represents a surrogate for a precision matrix that is free of spurious correlations^19,20. Further details regarding sDCM application and matrices extraction are provided in the Supplementary Methods section with specific reference to the methodology established in the work of Benozzo et al¹³.

PET preprocessing

The dynamic PET data of both patients and HCs underwent motion correction using FSL’s mcflirt algorithm⁷⁹, and to minimize partial volume effects (PVEs), the data were processed without applying any additional spatial smoothing, in agreement with many recent studies⁸⁰. For each participant, a static PET image was generated by summing the motion-corrected late PET frames (40–60 min). The T1w image was registered to the static PET using ANTs (v2.4.3)⁶⁰. Subsequently, the TM and TM + E masks, atlas parcellations, and individual GM and WM tissue segmentations—obtained using SPM12 (v7219 https://www.fil.ion.ucl.ac.uk/spm/)—were mapped from T1w to PET space by applying the previously estimated transformations. Subsequently, SUVR maps were obtained by dividing the static PET image of each participant by the average [¹⁸F]FDG uptake in the cerebellum WM (as further described in the Supplementary Methods)⁸¹. In the case of healthy individuals and bilateral gliomas, the reference region comprises the entire cerebellum WM. For glioma patients, the reference region encompasses the cerebellum WM ipsilateral to the lesion. This choice was motivated by the fact that the incidence of glioma is very low in the cerebellum (4.5% of all gliomas) and crossed cerebellar diaschisis is not infrequent in glioma patients^82,83. For each patient/control, the SUVR maps were parceled using the clustered cortical parcellation plus 12 subcortical and cerebellar regions, as done for fMRI data, and the average SUVR value was extracted for each ROI. As detailed in the Supplementary Methods and suggested in recent PET analysis works^6,84, the parcellation was filtered with the individual GM mask to minimize the partial volume effect. Additionally, in the patient cohort, as for fMRI data, the lesion voxels (TM + E mask) were excluded from the computation. This approach is typically followed in studies on gliomas to ensure that possible alterations were not simply due to tumor-associated tissue loss and dysfunction^23,85.

Tissue time activity curves (TACs) were extracted for each atlas ROI from pre-processed dynamic [¹⁸F]FDG PET images by averaging the voxel activities within the GM mask. Again, in the calculation of the patients’ ROI TACs, lesion voxels (TM + E mask) were excluded. Regional TACs were then interpolated on a uniform virtual grid (one-second step) and wi-MC matrices were calculated for both HCs and patients, using the Euclidean similarity (ES)-based method, detailed in Volpi et al.⁶ and summary reported in the Supplementary Methods. Importantly, this ES approach determines similarity based on the amplitude and shape of the time-activity curves, which are biologically informative and typically used in kinetic modeling, rather than on their fluctuations, which are more likely to reflect physical and statistical noise (measurement error) than biologically relevant variability^6,22. Additionally, as reported by Volpi et al.⁶, the strong correlation between MC computed from full TACs and that obtained from the second compartment curves of the Sokoloff model⁸⁶, and even more so from the late phase of the curves (i.e., 40–60 min), indicates that this approach is particularly sensitive to metabolic processes such as glucose trapping and phosphorylation. From a methodological perspective, this aligns with the observation that the tail of the TACs generally exhibits higher amplitudes, which contribute most to between-region similarity in the Euclidean framework.

Partial Least Squares Correlation analysis

To investigate the interconnected relationships between effective and metabolic metrics within the control group, we utilized Partial Least Squares Correlation analysis (PLSC). This is an advanced unsupervised multivariate statistical technique designed to uncover and quantify the shared information between two distinct datasets (X and Y). The core objective of PLSC is to extract orthogonal latent variables, referred to as scores, that maximize the covariance between the two datasets. These latent variables are linear combinations of the original data variables that best capture the common variance present in both datasets. In the PLSC framework, the linear combinations of the original variables are weighted by what are known as PLSC salience maps. Additionally, the PLSC loadings represent the degree to which each original variable contributes to the latent scores. This contribution is quantified through Pearson’s correlation between the original variables and the derived latent variables.

In the following section, we delve deeper into the methodological details of the PLSC analysis. For each latent dimension, the PLSC analysis produced effective and metabolic PLSC salience maps, i.e., the left and right singular vectors of the data covariance matrix (i.e., correlation matrix when X and Y are normalized and centered) obtained through singular value decomposition:

$$R={Y}^{T}X$$

(1)

$$R=U\Delta {V}^{T}$$

(2)

Where $R$ is the correlation matrix, while $U$ and $V$ represent the effective and metabolic saliences, respectively.

Additionally, it produced the sets of brain and cognitive latent scores ${L}_{x}$ and ${L}_{y}$, corresponding to data projections onto the brain and cognitive saliences, such that the covariance between each pair of latent vectors (i.e., the l-th column of ${L}_{x}$ and ${L}_{y}$) is maximized:

$${L}_{x}={XV}$$

(3)

$${L}_{y}={YU}$$

(4)

$${\max }_{{u}_{l},{v}_{l}}\,{cov}({l}_{X,l},{l}_{Y,l})$$

(5)

where ${l}_{X,l}=X{v}_{l}$ and ${l}_{Y,l}=Y{u}_{l}$, while ${v}_{l}$ and ${u}_{l}$ are the l^th of $V$ and $U$, respectively¹⁸.

Moreover, the PLSC analysis yielded a collection of effective and metabolic loadings:

$${{Load}}_{X}={corr}(X,\,{L}_{X})$$

(6)

$${{Load}}_{Y}={corr}(Y,\,{L}_{Y})$$

(7)

To quantify the amount of functional measure variance explained by the metabolic counterpart within the new latent space, Pearson’s correlation between the latent scores of each PLSC pair was used. Additionally, before applying PLSC functional measures were normalized to the range [-1, 1], while metabolic measures were scaled to the range [0, 1]. Furthermore, to ensure consistency in the variability range across participants and features, thus facilitating meaningful comparisons during the analysis, we applied z-score scaling across both directions.

Effective-metabolic coupling

We focused on four principal multivariate pairings (X–Y): $\widehat{{\mbox{FC}}}$–SUVR, S–SUVR, $\widehat{{\mbox{FC}}}$–MC, and S–MC. For combinations involving SUVR, the nodal strength of $\widehat{{\mbox{FC}}}$ (i.e., the sum of functional correlations of each node with all the remaining nodes) or S (along the columns, providing insights into the node’s behavior as a sink or source) was computed for each individual. These measures were subsequently organized into matrices structured as participant-by-strength and participant-by-SUVR value, which served as inputs for the PLSC. Conversely, for comparisons between MC and $\widehat{{\mbox{FC}}}$ or S matrices, the upper triangle of the connectivity matrices was vectorized and arranged as participant-by-connection to evaluate metabolic-effective coupling across the entire brain network. Additionally, we performed intra-individual normalization on features within each modality to ensure comparability of the variability range across participants and features.

Significance of multivariate correlation patterns was evaluated using permutation testing (200 permutations, critical α = 0.01)^87,88. The reliability of nonzero PLSC salience and loading values was determined through a bootstrapping procedure (100 random samples), with standard scores computed relative to the bootstrap distributions, following the procedure of Griffa and collegues²⁹. The decision to restrict the number of random permutations and bootstrapping samples was driven by the necessity to maintain computational efficiency at reasonable levels, particularly when dealing with edgewise features. Given the exploratory nature of this process, no corrections for multiple comparisons were applied during the bootstrapping process, as it focuses on identifying reliable experimental effects rather than conducting traditional hypothesis tests⁸⁷. The significance of PLSC salience and loading vectors was assessed by examining the inclusion of zero in the corresponding 95% confidence interval distribution²⁹. Meanwhile, PLSC salience and loading matrices were deemed reliable for absolute standard scores >3, with the threshold set higher compared to the previous case due to the increased number of variables⁸⁹.

Given the possibility of overfitting in PLSC models due to the small sample size relative to the considered number of imaging variables²⁸, it is necessary to ensure generalizability of the multivariate correlation models obtained²⁹. Therefore, we employed a K-fold cross-validation procedure (K = 7, resulting in folds containing 6 subjects each), where 14% of subjects were held out for testing in each iteration. Subsequently, PLSC salience maps were derived from the training set after excluding the test individuals, and the test data were projected onto these saliences to obtain test latent scores. The alignment between the original and test latent scores along the identity line was evaluated using Pearson’s correlation to assess the generalizability of the multivariate correlation patterns⁹⁰. The pair will be considered generalizable if the correlation values exceed 0.5 for both effective and metabolic pairs.

Each PLSC analysis resulted in a pair of individual-level latent scores, corresponding to each significant latent dimension. To quantify the relationship of each effective-metabolic pair in the new latent space, we utilized Pearson’s correlation between the latent scores.

To translate the information obtained from the PLSC analysis on the original data (normalized, as the input in the PLSC) to make the results clearer, we individually evaluated relevant features of S, SUVR, $\widehat{{\mbox{FC}}}$, and MC at the single-subject level. For S, we calculated the median column-wise strength values of S across sensory-attentive and transmodal networks for each subject. For SUVR, we calculated the difference between the median values in sensory-attentive and transmodal areas for each subject. For $\widehat{{\mbox{FC}}}$ and MC (analyzing separately the entries associated with positive or negative PLSC saliences to focus the attention on the corresponding areas), we evaluated the median of the single-subject matrix entries. Only significant values of S strength, SUVR, $\widehat{{\mbox{FC}}}$, and MC according to the PLSC salience map were considered.

Effective-metabolic (de)coupling in gliomas

For each effective-metabolic pairing demonstrating generalizability (i.e., correlation values between original and test latent scores > 0.5), we identified the least squares line that optimally captured the relationship between variables X and Y within the relevant latent plane. Subsequently, we computed the distance of each individual latent point from the least squares line, providing insight into the distribution of distances within the HC sample. The 90^th percentile of this distribution was then determined to establish the range of “normality” for pairing distances.

Following features normalization, using mean and standard deviation of HC features, we projected the effective and metabolic variables of patients onto the corresponding HC’s latent plane. This involved determining latent scores for patients by summing the original variables weighted by the salience values previously calculated for the HC group⁹¹. Subsequently, these latent scores were projected onto the latent plane of the control sample, enabling the identification of patients who deviate from the expected healthy range (outside the “normality-band”), termed outlier patients.

It is worth pointing that rather than conducting a direct multivariate comparison between groups, we adopted a deviation-based framework inspired by normative modeling principles. The approached used allowed us to assess individual deviations from normative patterns, rather than symmetric statistical comparison between healthy controls and glioma patients. To exclude potential confounds from acquisition differences, we performed group-wise quality control analyses on both PET and fMRI signals (see Supplementary Results and Supplementary Fig. 10 and 11). A distinct PLSC analysis on oncological patients was omitted at this stage due to the heterogeneous divergence in growth dynamics and remodelling processes of lesions⁹², potentially hindering the identification of a common dimension of effective-metabolic association. To investigate the potential association between outlier patients’ deviation from the expected healthy range and tumour anatomical location, we examined the corresponding tumour frequency maps for each effective–metabolic coupling. Each individual spatial tumour mask was weighted according to its latent point’s distance from the corresponding least squares line, in order to reduce the sensitivity of outlier identification to the threshold used for defining the “normality band”.

Additionally, potential associations between the degree of outlier patient deviations (distance from the line) and the volume of both the lesion (TM + E) and tumour (TM) were tested. Ultimately, to pinpoint the effective and metabolic features contributing significantly to the extent of deviation of latent scores from the regression line, we computed the corresponding loadings for the outlier patients, providing valuable insights into each variable’s contribution to the PLSC-derived latent scores. Statistical significance was evaluated through bootstrap sampling, similar to that implemented for HCs, and the outlier patient loadings were compared with those obtained for HCs, serving as baseline correlation values. Statistical thresholds were set at the same values used to assess the significance of PLSC salience weights.

Analysis of Involved White Matter Tracts in the glioma group

To assess which tracts are primarily involved in the lesions of “outlier patients” (outside the normal range) compared to “pseudo-healthy patients” (within the expected range) for each coupling, we used the probabilistic tract maps provided by the BCBToolkit⁹³.

We applied an 80% threshold to the probabilistic maps to ensure a conservative assessment of tract presence. Next, we evaluated the potential overlap between the patient’s tumor map and the thresholded tract map. A tract was considered involved if more than 20% of the tumor mask intersected with the tract mask. Finally, we calculated for each tract the percentage of outlier patients and pseudo-healthy patients having that tract involved.

Voxel-wise statistical analysis for the comparison of the tumor frequency maps

Here we performed a formal voxel-wise statistical analysis based on non-parametric permutation testing for the comparison of the tumor frequency maps derived from the two groups of outlier patients (S–SUVR, $\widehat{{\mbox{FC}}}$–MC), to objectively assess whether glioma location differs between them beyond visual inspection.

To focus on spatially relevant areas, each tumor-weighted frequency map for outlier patients was thresholded at its 80^th percentile, and values above this threshold were rescaled to the [0–1] range to allow voxel-wise comparison focused on spatial distribution rather than differences in their absolute magnitude. We then computed the voxel-wise signed difference between the two normalized maps: positive values indicated voxels more frequently lesioned in the $\widehat{{\mbox{FC}}}$–MC outliers, while negative values indicated voxels more frequent in the S–SUVR outliers.

To test the significance of these differences, we used a permutation-based approach (100 permutations). Specifically, we randomly permuted the patients’ distances (separately for the two latent spaces), reidentified outlier patients using the same percentile criterion, and recalculated the frequency maps and their difference as in the real case. This generated a voxel-wise null distribution of difference values under the null hypothesis of no group effect. We then computed two-sided p-values by comparing the real observed difference to the empirical null distribution:

$$p=(1\,+{{{\rm{\#}}}}\left(\left|{permuted\; difference}\right|\,\ge \,\left|{observed\; difference}\right|\,\right))\,/\,101$$

Resulting p-values were corrected for multiple comparisons using the false discovery rate (FDR), and voxels with ${p}_{{FDR}} < 0.05$ were considered statistically significant. To retain directionality in the final result, we constructed a signed statistical map where each voxel was labeled as:

• +1 if the difference was significant and positive (more frequent in $\widehat{{\mbox{FC}}}$–MC outliers),

• –1 if significant and negative (more frequent in S–SUVR outliers),

• 0 otherwise.

Statistics and Reproducibility

All statistical analyses were performed in MATLAB R2021b using custom scripts and publicly available toolboxes, including the myPLS toolbox (https://github.com/danizoeller/myPLS). PLSC analyses were used to assess multivariate associations between effective connectivity and metabolic measures. Significance of latent correlations was determined through permutation testing (200 permutations, α = 0.01), and reliability of salience and loading values was assessed by bootstrap resampling (100 iterations). PLSC components were considered significant if their 95% confidence interval excluded zero and the absolute standard score exceeded 3. Model generalizability was verified using a seven-fold cross-validation procedure (K = 7), requiring Pearson correlation coefficients >0.5 between training and test latent scores.

Voxel-wise statistical comparisons of tumor frequency maps were conducted using non-parametric permutation tests (100 permutations) with false discovery rate (FDR) correction (p_FDR < 0.05). To evaluate potential scanner effects, non-parametric Mann–Whitney rank-sum tests (α = 0.01, Holm–Bonferroni corrected) were repeated across 1000 random subsamplings for both fMRI temporal signal-to-noise ratio (tSNR) and PET contrast-to-noise ratio (CNR).

Each participant (42 healthy controls and 43 glioma patients) represented a unique biological replicate; no technical replicates were performed. Sample sizes reflected the available eligible data, and no statistical method was used to predetermine sample size. Replicability of all analyses was ensured through standardized preprocessing pipelines and fixed algorithmic parameters to maintain computational consistency.

For reproducibility of model-based measures, effective connectivity was estimated using the sparse Dynamic Causal Modeling (sDCM) framework with automated sparsity-inducing regularization and motion-weighted likelihood estimation. Model fit was evaluated through normalized root mean squared error (NRMSE) and correlations between empirical and simulated functional connectivity. The cortical atlas used for all analyses was derived from a consensus-clustered version of the Yan 100-area atlas, optimized for spatial homogeneity and computational reproducibility. Full implementation details are provided in the Methods and Supplementary Methods to facilitate independent replication.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.