Andreas Spiegler

Functional connectivity dynamics: Modeling the switching behavior of the resting state

Functional connectivity (FC) sheds light on the interactions between different brain regions. Besides basic research, it is clinically relevant for applications in Alzheimers disease, schizophrenia, presurgical planning, epilepsy, and traumatic brain injury. Simulations of whole-brain mean-field computational models with realistic connectivity determined by tractography studies enable us to reproduce with accuracy aspects of average FC in the resting state. Most computational studies, however, did not address the prominent non-stationarity in resting state FC, which may result in large intra- and inter-subject variability and thus preclude an accurate individual predictability. Here we show that this non-stationarity reveals a rich structure, characterized by rapid transitions switching between a few discrete FC states. We also show that computational models optimized to fit time-averaged FC do not reproduce these spontaneous state transitions and, thus, are not qualitatively superior to simplified linear stochastic models, which account for the effects of structure alone. We then demonstrate that a slight enhancement of the non-linearity of the network nodes is sufficient to broaden the repertoire of possible network behaviors, leading to modes of fluctuations, reminiscent of some of the most frequently observed Resting State Networks. Because of the noise-driven exploration of this repertoire, the dynamics of FC qualitatively change now and display non-stationary switching similar to empirical resting state recordings (Functional Connectivity Dynamics (FCD)). Thus FCD bear promise to serve as a better biomarker of resting state neural activity and of its pathologic alterations.

Mathematical framework for large-scale brain network modeling in The Virtual Brain.

In this article, we describe the mathematical framework of the computational model at the core of the tool The Virtual Brain (TVB), designed to simulate collective whole brain dynamics by virtualizing brain structure and function, allowing simultaneous outputs of a number of experimental modalities such as electro- and magnetoencephalography (EEG, MEG) and functional Magnetic Resonance Imaging (fMRI). The implementation allows for a systematic exploration and manipulation of every underlying component of a large-scale brain network model (BNM), such as the neural mass model governing the local dynamics or the structural connectivity constraining the space time structure of the network couplings. Here, a consistent notation for the generalized BNM is given, so that in this form the equations represent a direct link between the mathematical description of BNMs and the components of the numerical implementation in TVB. Finally, we made a summary of the forward models implemented for mapping simulated neural activity (EEG, MEG, sterotactic electroencephalogram (sEEG), fMRI), identifying their advantages and limitations.

Transcranial direct current stimulation changes resting state functional connectivity: A large-scale brain network modeling study

Transcranial direct current stimulation (tDCS) is a noninvasive technique for affecting brain dynamics with promising application in the clinical therapy of neurological and psychiatric disorders such as Parkinsons disease, Alzheimers disease, depression, and schizophrenia. Resting state dynamics increasingly play a role in the assessment of connectivity-based pathologies such as Alzheimers and schizophrenia. We systematically applied tDCS in a large-scale network model of 74 cerebral areas, investigating the spatiotemporal changes in dynamic states as a function of structural connectivity changes. Structural connectivity was defined by the human connectome. The main findings of this study are fourfold: Firstly, we found a tDCS-induced increase in functional connectivity among cerebral areas and among EEG sensors, where the latter reproduced empirical findings of other researchers. Secondly, the analysis of the network dynamics suggested synchronization to be the main mechanism of the observed effects. Thirdly, we found that tDCS sharpens and shifts the frequency distribution of scalp EEG sensors slightly towards higher frequencies. Fourthly, new dynamic states emerged through interacting areas in the network compared to the dynamics of an isolated area. The findings propose synchronization as a key mechanism underlying the changes in the spatiotemporal pattern formation due to tDCS. Our work supports the notion that noninvasive brain stimulation is able to bias brain dynamics by affecting the competitive interplay of functional subnetworks.

Systematic approximations of neural fields through networks of neural masses in the virtual brain

Full brain network models comprise a large-scale connectivity (the connectome) and neural mass models as the networks nodes. Neural mass models absorb implicitly a variety of properties in their constant parameters to achieve a reduction in complexity. In situations, where the local network connectivity undergoes major changes, such as in development or epilepsy, it becomes crucial to model local connectivity explicitly. This leads naturally to a description of neural fields on folded cortical sheets with local and global connectivities. The numerical approximation of neural fields in biologically realistic situations as addressed in Virtual Brain simulations (see http://thevirtualbrain.org/app/ (version 1.0)) is challenging and requires a thorough evaluation if the Virtual Brain approach is to be adapted for systematic studies of disease and disorders. Here we analyze the sampling problem of neural fields for arbitrary dimensions and provide explicit results for one, two and three dimensions relevant to realistically folded cortical surfaces. We characterize (i) the error due to sampling of spatial distribution functions; (ii) useful sampling parameter ranges in the context of encephalographic (EEG, MEG, ECoG and functional MRI) signals; (iii) guidelines for choosing the right spatial distribution function for given anatomical and geometrical constraints.

How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models?

Recent efforts to model human brain activity on the scale of the whole brain rest on connectivity estimates of large-scale networks derived from diffusion magnetic resonance imaging (dMRI). This type of connectivity describes white matter fiber tracts. The number of short-range cortico-cortical white-matter connections is, however, underrepresented in such large-scale brain models. It is still unclear on the one hand, which scale of representation of white matter fibers is optimal to describe brain activity on a large-scale such as recorded with magneto- or electroencephalography (M/EEG) or functional magnetic resonance imaging (fMRI), and on the other hand, to which extent short-range connections that are typically local should be taken into account. In this article we quantified the effect of connectivity upon large-scale brain network dynamics by (i) systematically varying the number of brain regions before computing the connectivity matrix, and by (ii) adding generic short-range connections. We used dMRI data from the Human Connectome Project. We developed a suite of preprocessing modules called SCRIPTS to prepare these imaging data for The Virtual Brain, a neuroinformatics platform for large-scale brain modeling and simulations. We performed simulations under different connectivity conditions and quantified the spatiotemporal dynamics in terms of Shannon Entropy, dwell time and Principal Component Analysis. For the reconstructed connectivity, our results show that the major white matter fiber bundles play an important role in shaping slow dynamics in large-scale brain networks (e.g. in fMRI). Faster dynamics such as gamma oscillations (around 40 Hz) are sensitive to the short-range connectivity if transmission delays are considered.

Heterogeneity of time delays determines synchronization of coupled oscillators.

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

Fast–Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes

Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system. In this work, we propose a model that, appropriately tuned, can display several types of bursting behaviors. The model contains two subsystems acting at different time scales. For the fast subsystem we use the planar unfolding of a high codimension singularity. In its bifurcation diagram, we locate paths that underlie the right sequence of bifurcations necessary for bursting. The slow subsystem steers the fast one back and forth along these paths leading to bursting behavior. The model is able to produce almost all the classes of bursting predicted for systems with a planar fast subsystem. Transitions between classes can be obtained through an ultra-slow modulation of the model’s parameters. A detailed exploration of the parameter space allows predicting possible transitions. This provides a single framework to understand the coexistence of diverse bursting patterns in physical and biological systems or in models.

Ebbinghaus figures that deceive the eye do not necessarily deceive the hand

In support of the visual stream dissociation hypothesis, which states that distinct visual streams serve vision-for-perception and vision-for-action, visual size illusions were reported over 20 years ago to ‘deceive the eye but not the hand’. Ever since, inconclusive results and contradictory interpretations have accumulated. Therefore, we investigated the effects of the Ebbinghaus figure on repetitive aiming movements with distinct dynamics. Participants performed a Fitts’ task in which Ebbinghaus figures served as targets. We systematically varied the three parameters which have been shown to influence the perceived size of the Ebbinghaus figure’s target circle, namely the size of the target, its distance to the context circles and the size of the context circles. This paper shows that movement is significantly affected by the context size, but, in contrast to perception, not by the other two parameters. This is especially prominent in the approach phase of the movement towards the target, regardless of the dynamics. To reconcile the findings, we argue that different informational variables are used for size perception and the visual control of movements irrespective of whether certain variables induce (perceptual) illusions.

Effects of multimodal distribution of delays in brain network dynamics

Large-scale modeling of the brain is defined by the local oscillatory dynamics that are superimposed on an architecture based on a comprehensive map of neural connections in the brain - connectome [1]. Besides coupling strengths, time-delays due to transmissions via tracts are crucial features of a connectome. They represent a proxy of the spatial structure (the tract lengths) to the temporal dynamics. Thus, the most straightforward approach to model brain dynamics in space and time is to concatenate oscillatory nodes to a connectome-based network. The analysis that we performed on the experimentally derived connectome suggests that the tract lengths - distances between different brain nodes, thus the time delays, follow a multimodal distribution. Here, we investigated the conceptual implementation of multimodal distributions of discrete time delays of network links, and its effects on the mean-field dynamics. Because of the analytical tractability, the Kuramoto oscillator describes the temporal dynamics of each node, and the links between the nodes are symmetric but heterogeneous. Hence, we analyze synchronization in populations of phase oscillators [2], which have the same distribution of natural frequencies and coupling strengths, but their structure is defined solely by their different intra- and inter-population delays. Assuming a same overall distribution of time delays, several cases are investigated: from fully random distribution, to two delays-imposed structures of subpopulations, Figure ​Figure11. Figure 1 Schematic representation of the delay-imposed structure of population of oscillators: with different inter and same intra delays in A; same inter and intra delays in B; and random distribution of the delays, in C. For all scenarios, mean-field dynamics are analytically obtained [3] and numerically confirmed. Moreover, boundaries and stabilities of different low-dimensional solutions are also investigated. These reveal a split of phase dynamics in different clusters, which can be phase shifted, or even non-stationary with different time-varying frequencies of synchronization and order parameters for the clusters. In summary, the large-scale spatial organization of the brain is integrated in a network model. Using this model, we present the effects of the multimodal distribution of time delays and the structure that they impose on the network dynamics such as synchronization. Hence, we stress the role of the spatial organization of the brain that is reflected through the different time-delays between different parts of the brain in the formation of spatiotemporal dynamics.

Spatiotemporal dynamics in the human brain during rest:a virtual brain study

Over the past years the ongoing human brain activity at rest came into focus, emphasizing the role of the rest-state activity for brain functions such as planning and perception in both healthy and diseased brains. For instance, it has been shown that the alpha rhythm during rest can be affected (e.g., resetting, entrainment) using stimulations such as sensory or Transcranial Magnetic Stimulations (TMS). However, the origin and the mechanisms underlying the rest-state activity are not yet well understood. In this study, we focus on the propagation of largescale brain responses to stimulations such as TMS to identify sub-networks involved in the rest-state. Using The Virtual Brain [1] we model the dynamics of the human cortex as a network of 16,384 neural masses (NMs), each representing nearly 16 mm of the cortical surface. A sub-threshold Hopf oscillator with a Van der Pol term describes the temporal behavior of each NM and a Gaussian kernel defines the spatial interactions among the NMs. We also consider the connections through the white matter extracted from a combination of diffusion spectrum MRI tractography and the CoCoMac database. We systematically stimulate different brain areas and analyze the spatiotemporal responses of the model, using Principal Component Analysis. The results provide evidence for the existence of a low dimensional set of networks during rest. Stimulations of brain areas involved in resting-state networks produce stronger and longer lasting responses than stimulations