The relationship between pathological brain activity and functional network connectivity in glioma patients

PURPOSE

Glioma is associated with pathologically high (peri)tumoral brain activity, which relates to faster progression. Functional connectivity is disturbed locally and throughout the entire brain, associating with symptomatology. We, therefore, investigated how local activity and network measures relate to better understand how the intricate relationship between the tumor and the rest of the brain may impact disease and symptom progression.

METHODS

We obtained magnetoencephalography in 84 de novo glioma patients and 61 matched healthy controls. The offset of the power spectrum, a proxy of neuronal activity, was calculated for 210 cortical regions. We calculated patients' regional deviations in delta, theta and lower alpha network connectivity as compared to controls, using two network measures: clustering coefficient (local connectivity) and eigenvector centrality (integrative connectivity). We then tested group differences in activity and connectivity between (peri)tumoral, contralateral homologue regions, and the rest of the brain. We also correlated regional offset to connectivity.

RESULTS

As expected, patients' (peri)tumoral activity was pathologically high, and patients showed higher clustering and lower centrality than controls. At the group-level, regionally high activity related to high clustering in controls and patients alike. However, within-patient analyses revealed negative associations between regional deviations in brain activity and clustering, such that pathologically high activity coincided with low network clustering, while regions with 'normal' activity levels showed high network clustering.

CONCLUSION

Our results indicate that pathological activity and connectivity co-localize in a complex manner in glioma. This insight is relevant to our understanding of disease progression and cognitive symptomatology.

The longitudinal relation between executive functioning and multilayer network topology in glioma patients

Many patients with glioma, primary brain tumors, suffer from poorly understood executive functioning deficits before and/or after tumor resection. We aimed to test whether frontoparietal network centrality of multilayer networks, allowing for integration across multiple frequencies, relates to and predicts executive functioning in glioma. Patients with glioma (n = 37) underwent resting-state magnetoencephalography and neuropsychological tests assessing word fluency, inhibition, and set shifting before (T1) and one year after tumor resection (T2). We constructed binary multilayer networks comprising six layers, with each layer representing frequency-specific functional connectivity between source-localized time series of 78 cortical regions. Average frontoparietal network multilayer eigenvector centrality, a measure for network integration, was calculated at both time points. Regression analyses were used to investigate associations with executive functioning. At T1, lower multilayer integration (p = 0.017) and epilepsy (p = 0.006) associated with poorer set shifting (adj. R2 = 0.269). Decreasing multilayer integration (p = 0.022) and not undergoing chemotherapy at T2 (p = 0.004) related to deteriorating set shifting over time (adj. R2 = 0.283). No significant associations were found for word fluency or inhibition, nor did T1 multilayer integration predict changes in executive functioning. As expected, our results establish multilayer integration of the frontoparietal network as a cross-sectional and longitudinal correlate of executive functioning in glioma patients. However, multilayer integration did not predict postoperative changes in executive functioning, which together with the fact that this correlate is also found in health and other diseases, limits its specific clinical relevance in glioma.

Multimodal multilayer network centrality relates to executive functioning

Executive functioning (EF) is a higher order cognitive process that is thought to depend on a network organization facilitating integration across subnetworks, in the context of which the central role of the fronto-parietal network (FPN) has been described across imaging and neurophysiological modalities. However, the potentially complementary unimodal information on the relevance of the FPN for EF has not yet been integrated. We employ a multilayer framework to allow for integration of different modalities into one 'network of networks.' We used diffusion MRI, resting-state functional MRI, MEG, and neuropsychological data obtained from 33 healthy adults to construct modality-specific single-layer networks as well as a single multilayer network per participant. We computed single-layer and multilayer eigenvector centrality of the FPN as a measure of integration in this network and examined their associations with EF. We found that higher multilayer FPN centrality, but not single-layer FPN centrality, was related to better EF. We did not find a statistically significant change in explained variance in EF when using the multilayer approach as compared to the single-layer measures. Overall, our results show the importance of FPN integration for EF and underline the promise of the multilayer framework toward better understanding cognitive functioning.

P01.10.B The relation between executive functioning and MEG multilayer network centrality in glioma patients

Background

Many patients with glioma suffer from deficits in executive functioning (EF), regardless of tumor location and size. While some patients experience improving EF after tumor resection, others deteriorate over time. This variability in cognitive trajectories is still poorly understood, but neuroscientific approaches that view the brain as a network may bear correlative and predictive value in this respect. Particularly integrative network connectivity of the fronto-parietal network are crucial for EF, but studies so far have only investigated isolated neural frequency bands of interest. Here, we synergize fronto-parietal network connectivity across frequency bands and test its explanatory power for EF at diagnosis and 1 year after tumor resection.

Material and Methods

Patients with diffuse glioma (n=37) underwent neuropsychological assessments, including three tests for EF, and resting-state magnetoencephalography (MEG) at both time points. Patients’ EF performance was standardized to z-scores using validated norm scores, adjusting for age, sex and education. MEG was source-reconstructed using patients’ MRI in combination with a beamformer approach and time series were filtered into six classical frequency bands. Band-specific functional connectivity between 78 cortical regions was estimated, after which an interconnected multilayer, multi-frequency network was created per patient. Multilayer centrality was then calculated as a measure of integrative network connectivity per region, and averaged over all fronto-parietal network regions to yield a single value reflecting integrative, multi-frequency network connectivity per patient at each time point.

Results

At diagnosis, eight patients had z-scores <-1.5, indicating clinically relevant cognitive deficits. Preoperatively, poorer performance on the Concept Shifting Task was associated with lower multilayer centrality (p=.017), while improving performance on this task from diagnosis to 1 year after resection was associated with an increase in multilayer centrality (p=.022). Multilayer centrality at diagnosis did not significantly predict EF at follow-up.

Conclusion

Our results establish a significant relationship between poorer and decreasing EF with lower and decreasing multilayer, multi-frequency integrative connectivity of the fronto-parietal network in glioma patients. Studies with larger and more homogeneous samples may further explore the relevance of this multilayer approach in understanding and particularly predicting postoperative decline in EF in these patients, as our sample was characterized by large heterogeneity in cognitively relevant patient and tumor characteristics.

Fock-space approach to stochastic susceptible-infected-recovered models

We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock-space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system's states defined by SIR occupation numbers. In the Fock-space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N. We present small- and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock-space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.

Cellular Substrates of Functional Network Integration and Memory in Temporal Lobe Epilepsy

Temporal lobe epilepsy (TLE) patients are at risk of memory deficits, which have been linked to functional network disturbances, particularly of integration of the default mode network (DMN). However, the cellular substrates of functional network integration are unknown. We leverage a unique cross-scale dataset of drug-resistant TLE patients (n = 31), who underwent pseudo resting-state functional magnetic resonance imaging (fMRI), resting-state magnetoencephalography (MEG) and/or neuropsychological testing before neurosurgery. fMRI and MEG underwent atlas-based connectivity analyses. Functional network centrality of the lateral middle temporal gyrus, part of the DMN, was used as a measure of local network integration. Subsequently, non-pathological cortical tissue from this region was used for single cell morphological and electrophysiological patch-clamp analysis, assessing integration in terms of total dendritic length and action potential rise speed. As could be hypothesized, greater network centrality related to better memory performance. Moreover, greater network centrality correlated with more integrative properties at the cellular level across patients. We conclude that individual differences in cognitively relevant functional network integration of a DMN region are mirrored by differences in cellular integrative properties of this region in TLE patients. These findings connect previously separate scales of investigation, increasing translational insight into focal pathology and large-scale network disturbances in TLE.

Geometry and molecular dynamics of the Hamiltonian mean-field model in a magnetic field

The Hamiltonian mean-field model is investigated in the presence of a field. The self-consistent equations for the magnetization and the energy per particle are derived, and the field effect on the caloric curve is presented. The analytical geometric approach to Hamiltonian dynamics, under the hypothesis of quasi-isotropy, allows us to calculate the field effect on the energy-dependent microcanonical mean Ricci curvature and its fluctuations. Notably, the method proved suitable to identify that stable and metastable solutions of the Lyapunov exponent exhibit intriguing distinct curvature behavior very close to the critical point at extremely low field values. In addition, finite-size molecular dynamics (MD) simulations are used to observe the evolution of the magnetization and their components, including the stability properties of the solutions. Most importantly, comparison of finite-size MD calculations of the Lyapunov exponent and related properties with those via the geometric approach unveil the sensible dependence of these microcanonical quantities on energy, number of particles, and field, before a quasisaturation behavior at high fields. Finally, relaxation properties from out-of-equilibrium initial conditions are discussed in light of MD simulations.

Fock-space methods for diffusion: Capturing volume exclusion via fermionic statistics

Volume exclusion and single-file diffusion play an important role at very small scales, such as those associated with molecular machines, ion channels, and transport in zeolites, while introducing fundamental differences compared to Brownian motion, such as changes to the power-law relation between the mean square displacement and time. In this work we map the chemical master equation for excluded diffusion onto a Schrödinger equation via annihilation and creation ladder operators with fermionic statistics, together with linear and symbolic algebra with the resulting Fock-space representation to describe the effect of volume-exclusion processes in finite one-dimensional chains. We contrast the dynamics with the nonexclusive (bosonic) diffusion for crowded, intermediate, and dilute particle populations. Motivated by shuttling in molecular machines, we proceed to investigate differences in exit time distributions introduced by volume exclusion, incorporating the presence of transport bias. More generally, this study demonstrates how one can analyze volume-excluded transport for small stochastic systems, without the need for stochastic simulation and ensemble averaging, simply by considering anticommutation relations and fermionic statistics in a Fock-space representation of the stochastic dynamics.

Topological phase transitions in functional brain networks

Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. The geometric nature of the transitions can be interpreted, under certain hypotheses, as an extension of percolation to high-dimensional objects. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives toward establishing reliable topological and geometrical markers for group and possibly individual differences in functional brain network organization.

Fock space, symbolic algebra, and analytical solutions for small stochastic systems

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Topology, symmetry, phase transitions, and noncollinear spin structures

We use a topological approach to describe the frustration- and field-induced phase transitions exhibited by the infinite-range XY model on the AB2 chain, including noncollinear spin structures. For this purpose, we have computed the Morse number and the Euler characteristic, as well as other topological invariants, which are found to behave similarly as a function of the energy level in the context of Morse theory. In particular, we use a method based on an analogy with statistical mechanics to compute the Euler characteristic, which proves to be quite feasible. We also introduce topological energies which help us to clarify several properties of the transitions, both at zero and finite temperatures. In addition, we establish a nontrivial direct connection between the thermodynamics of the systems, which have been solved exactly under the saddle-point approach, and the topology of their configuration space. This connection allows us to identify the nondegeneracy condition under which the divergence of the density of Jacobian's critical points [jl(E)] at the critical energy of a topology-induced phase transition, proposed by Kastner and Schnetz [Phys. Rev. Lett. 100, 160601 (2008)] as a necessary criterion, is suppressed. Finally, our findings and those available in the literature suggest that the cusplike singularity exhibited both by the Euler characteristic and the topological contribution for the entropy at the critical energy, put together with the divergence of jl(E) , and emerge as necessary and sufficient conditions for the occurrence of the finite-temperature topology-induced phase transitions examined in this work. The general character of this proposal should be subject to a more rigorous scrutiny.