The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread.

Despite the importance and frequent use of Bayesian frameworks in brain network modeling for parameter inference and model prediction, the advanced sampling algorithms implemented in probabilistic programming languages to overcome the inference difficulties have received relatively little attention in this context. In this technical note, we propose a probabilistic framework, namely the Bayesian Virtual Epileptic Patient (BVEP), which relies on the fusion of structural data of individuals to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. To invert the individualized whole-brain model employed in this study, we use the recently developed algorithms known as No-U-Turn Sampler (NUTS) as well as Automatic Differentiation Variational Inference (ADVI). Our results indicate that NUTS and ADVI accurately estimate the degree of epileptogenicity of brain regions, therefore, the hypothetical brain areas responsible for the seizure initiation and propagation, while the convergence diagnostics and posterior behavior analysis validate the reliability of the estimations. Moreover, we illustrate the efficiency of the transformed non-centered parameters in comparison to centered form of parameterization. The Bayesian framework used in this work proposes an appropriate patient-specific strategy for estimating the epileptogenicity of the brain regions to improve outcome after epilepsy surgery.

Differences in MEG and EEG power-law scaling explained by a coupling between spatial coherence and frequency: a simulation study.

Electrophysiological signals (electroencephalography, EEG, and magnetoencephalography, MEG), as many natural processes, exhibit scale-invariance properties resulting in a power-law (1/f) spectrum. Interestingly, EEG and MEG differ in their slopes, which could be explained by several mechanisms, including non-resistive properties of tissues. Our goal in the present study is to estimate the impact of space/frequency structure of source signals as a putative mechanism to explain spectral scaling properties of neuroimaging signals. We performed simulations based on the summed contribution of cortical patches with different sizes (ranging from 0.4 to 104.2 cm2). Small patches were attributed signals of high frequencies, whereas large patches were associated with signals of low frequencies, on a logarithmic scale. The tested parameters included i) the space/frequency structure (range of patch sizes and frequencies) and ii) the amplitude factor c parametrizing the spatial scale ratios. We found that the space/frequency structure may cause differences between EEG and MEG scale-free spectra that are compatible with real data findings reported in previous studies. We also found that below a certain spatial scale, there were no more differences between EEG and MEG, suggesting a limit for the resolution of both methods.Our work provides an explanation of experimental findings. This does not rule out other mechanisms for differences between EEG and MEG, but suggests an important role of spatio-temporal structure of neural dynamics. This can help the analysis and interpretation of power-law measures in EEG and MEG, and we believe our results can also impact computational modeling of brain dynamics, where different local connectivity structures could be used at different frequencies.

The Virtual Epileptic Patient: Individualized whole-brain models of epilepsy spread.

Individual variability has clear effects upon the outcome of therapies and treatment approaches. The customization of healthcare options to the individual patient should accordingly improve treatment results. We propose a novel approach to brain interventions based on personalized brain network models derived from non-invasive structural data of individual patients. Along the example of a patient with bitemporal epilepsy, we show step by step how to develop a Virtual Epileptic Patient (VEP) brain model and integrate patient-specific information such as brain connectivity, epileptogenic zone and MRI lesions. Using high-performance computing, we systematically carry out parameter space explorations, fit and validate the brain model against the patient's empirical stereotactic EEG (SEEG) data and demonstrate how to develop novel personalized strategies towards therapy and intervention.

Anatomical connectivity and the resting state activity of large cortical networks.

This paper uses mathematical modelling and simulations to explore the dynamics that emerge in large scale cortical networks, with a particular focus on the topological properties of the structural connectivity and its relationship to functional connectivity. We exploit realistic anatomical connectivity matrices (from diffusion spectrum imaging) and investigate their capacity to generate various types of resting state activity. In particular, we study emergent patterns of activity for realistic connectivity configurations together with approximations formulated in terms of neural mass or field models. We find that homogenous connectivity matrices, of the sort of assumed in certain neural field models give rise to damped spatially periodic modes, while more localised modes reflect heterogeneous coupling topologies. When simulating resting state fluctuations under realistic connectivity, we find no evidence for a spectrum of spatially periodic patterns, even when grouping together cortical nodes into communities, using graph theory. We conclude that neural field models with translationally invariant connectivity may be best applied at the mesoscopic scale and that more general models of cortical networks that embed local neural fields, may provide appropriate models of macroscopic cortical dynamics over the whole brain.

Towards the virtual brain: network modeling of the intact and the damaged brain.

Neurocomputational models of large-scale brain dynamics utilizing realistic connectivity matrices have advanced our understanding of the operational network principles in the brain. In particular, spontaneous or resting state activity has been studied on various scales of spatial and temporal organization including those that relate to physiological, encephalographic and hemodynamic data. In this article we focus on the brain from the perspective of a dynamic network and discuss the role of its network constituents in shaping brain dynamics. These constituents include the brain's structural connectivity, the population dynamics of its network nodes and the time delays involved in signal transmission. In addition, no discussion of brain dynamics would be complete without considering noise and stochastic effects. In fact, there is mounting evidence that the interaction between noise and dynamics plays an important functional role in shaping key brain processes. In particular, we discuss a unifying theoretical framework that explains how structured spatio-temporal resting state patterns emerge from noise driven explorations of unstable or stable oscillatory states. Embracing this perspective, we explore the consequences of network manipulations to understand some of the brain's dysfunctions, as well as network effects that offer new insights into routes towards therapy, recovery and brain repair. These collective insights will be at the core of a new computational environment, the Virtual Brain, which will allow flexible incorporation of empirical data constraining the brain models to integrate, unify and predict network responses to incipient pathological processes.

The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

Cortical network dynamics with time delays reveals functional connectivity in the resting brain.

In absence of all goal-directed behavior, a characteristic network of cortical regions involving prefrontal and cingulate cortices consistently shows temporally coherent fluctuations. The origin of these fluctuations is unknown, but has been hypothesized to be of stochastic nature. In the present paper we test the hypothesis that time delays in the network dynamics play a crucial role in the generation of these fluctuations. By tuning the propagation velocity in a network based on primate connectivity, we scale the time delays and demonstrate the emergence of the resting state networks for biophysically realistic parameters.

Noise during rest enables the exploration of the brain's dynamic repertoire.

Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.

Local and global stabilization of coordination by sensory information.

In studies of rhythmic coordination, where sensory information is often generated by an auditory stimulus, spatial and temporal variability are known to decrease at points in the movement cycle coincident with the stimulus, a phenomenon known as anchoring (Byblow et al. 1994). Here we hypothesize that the role of anchoring may be to globally stabilize coordination under conditions in which it would otherwise undergo a global coordinative change such as a phase transition. To test this hypothesis, anchoring was studied in a bimanual coordination paradigm in which either inphase or antiphase coordination was produced as auditory pacing stimuli (and hence movement frequency) were scaled over a wide range of frequencies. Two different anchoring conditions were used: a single-metronome condition, in which peak amplitude of right finger flexion coincided with the auditory stimulus; and a double-metronome condition, in which each finger reversal (flexion and extension) occurred simultaneously with the auditory stimuli. Anchored reversal points displayed lower spatial variation than unanchored reversal points, resulting in more symmetric phase plane trajectories in the double- than the single-metronome condition. The global coordination dynamics of the double-metronome condition was also more stable, with transitions from antiphase to inphase occurring less often and at higher movement frequencies than in the single-metronome condition. An extension of the Haken-Kelso-Bunz model of bimanual coordination is presented briefly which includes specific coupling of sensory information to movement through a process we call parametric stabilization. The parametric stabilization model provides a theoretical account of both local effects on the individual movement trajectories (anchoring) and global stabilization of observed coordination patterns, including the delay of phase transitions.

Theory of the relation between human brain activity (MEG) and hand movements.

Earlier research established that spontaneous changes in human sensorimotor coordination are accompanied by qualitative changes in the spatiotemporal dynamics of neural activity measured by multisensor electroencephalography and magnetoencephalography. More recent research has demonstrated that a robust relation exists between brain activity and the movement profile produced. In particular, brain activity has been shown to correlate strongly with movement velocity independent of movement direction and mode of coordination. Using a recently developed field theoretical model of large-scale brain activity itself based on neuroanatomical and neurophysiological constraints we show here how these experimental findings relate to the field theory and how it is possible to reconstruct the movement profile via spatial and temporal integration of the brain signal. There is a unique relation between the quantities in the theory and the experimental data, and fit between the shape of the measured and the reconstructed time series for the movement is remarkably good given that there are no free parameters.

Recruitment of degrees of freedom stabilizes coordination.

By showing that transitions may be obviated by recruiting degrees of freedom in the coupled pendulum paradigm, the authors reveal a novel mechanism for coordinative flexibility. In Experiment 1, participants swung pairs of unconstrained pendulums in 2 planes of motion (sagittal and frontal) at 8 movement frequencies starting from either an in-phase or antiphase mode. Few transitions were observed. Measures of spatial trajectory showed recruitment effects tied to the stability of the initial coordinative pattern. When the motion of the pendulums was physically restricted to a single plane in Experiment 2, transitions were more common, indicating that recruitment delays--or even eliminates--transitions. Such recruitment complements transitions as a source of coordinative flexibility and is incorporated in a simple extension of the Haken-Kelso-Bunz (1985) model.

Parametric stabilization of biological coordination: a theoretical model.

In human coordination studies information from the environment may not only pace rhythmic behavior, but also contribute to the observed dynamics, e.g. aphenomenon known as anchoring in the literature. For the paradigmatic caseof bimanual coordination we study these contributions mathematically and develop a model of the interaction between the limb's intrinsic dynamics and environmental signals from a metronome in terms of oscillator equations. We discuss additive versus multiplicative metronomeimpact and show the latter to be more appropriate.Our model describes single limb-metronome interaction, as well as multilimb-metronome interaction. We establish a parametricstabilization term which preserves the characteristicsof bimanual coordination and additionally explains the varyingstability of movement under different metronome conditions, the frequency dependence of the amplitudes of finger movements, anchoring phenomena andgeometries of phase space trajectories. Predictions of our model are tested against experimental observations.

Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies.

Biological systems like the human cortex show homogeneous connectivity, with additional strongly heterogeneous projections from one area to another. Here we report how such a dynamic system performs a macroscopically coherent pattern formation. The connection topology is used systematically as a control parameter to guide the neural system through a series of phase transitions. We discuss the example of a two-point connection, and its destabilization mechanism.

Connecting cortical and behavioral dynamics: bimanual coordination.

For the paradigmatic case of bimanual coordination, we review levels of organization of behavioral dynamics and present a description in terms of modes of behavior. We briefly review a recently developed model of spatiotemporal brain activity that is based on short- and long-range connectivity of neural ensembles. This model is specified for the case of motor and sensorimotor units embedded in the neural sheet. Focusing on the cortical left-right symmetry, we derive a bimodal description of the brain activity that is connected to behavioral dynamics. We make predictions of global features of brain dynamics during coordination tasks and test these against experimental magnetoencephalogram (MEG) results. A key feature of our approach is that phenomenological laws at the behavioral level can be connected to a field-theoretical description of cortical dynamics.

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies.

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.

A theoretical model of phase transitions in the human brain.

An experiment using a multisensor SQUID (superconducting quantum interference device) array was performed by Kelso and colleagues (1992) which combined information from three different sources: perception, motor response, and brain signals. When an acoustic stimulus frequency is changed systematically, a spontaneous transition in coordination occurs at a critical frequency in both motor behavior and brain signals. Qualitatively analogous transitions are known for physical and biological systems such as changes in the coordination of human hand movements (Kelso 1981, 1984). In this paper we develop a theoretical model based on methods from the interdisciplinary field of synergetics (Haken 1983, 1987) and nonlinear oscillator theory that reproduces the main experimental features very well and suggests a formulation of a fundamental biophysical coupling.