63 research outputs found
Dynamics of biologically informed neural mass models of the brain
This book contributes to the development and analysis of computational models that help brain function to be understood. The mean activity of a brain area is mathematically modeled in such a way as to strike a balance between tractability and biological plausibility. Neural mass models (NMM) are used to describe switching between qualitatively different regimes (such as those due to pharmacological interventions, epilepsy, sleep, or context-induced state changes), and to explain resonance phenomena in a photic driving experiment. The description of varying states in an ordered sequence gives a principle scheme for the modeling of complex phenomena on multiple time scales. The NMM is matched to the photic driving experiment routinely applied in the diagnosis of such diseases as epilepsy, migraine, schizophrenia and depression. The model reproduces the clinically relevant entrainment effect and predictions are made for improving the experimental setting.Die vorliegende Arbeit stellt einen Beitrag zur Entwicklung und Analyse von
Computermodellen zum Verständnis von Hirnfunktionen dar. Es wird die
mittlere Aktivität eines Hirnareals analytisch einfach und dabei
biologisch plausibel modelliert. Auf Grundlage eines Neuronalen
Massenmodells (NMM) werden die Wechsel zwischen Oszillationsregimen (z.B.
durch pharmakologisch, epilepsie-, schlaf- oder kontextbedingte
Zustandsänderungen) als geordnete Folge beschrieben und Resonanzphänomene
in einem Photic-Driving-Experiment erklärt. Dieses NMM kann sehr komplexe
Dynamiken (z.B. Chaos) innerhalb biologisch plausibler Parameterbereiche
hervorbringen. Um das Verhalten abzuschätzen, wird das NMM als Funktion
konstanter Eingangsgrößen und charakteristischer Zeitenkonstanten
vollständig auf Bifurkationen untersucht und klassifiziert. Dies
ermöglicht die Beschreibung wechselnder Regime als geordnete Folge durch
spezifische Eingangstrajektorien. Es wird ein Prinzip vorgestellt, um
komplexe Phänomene durch Prozesse verschiedener Zeitskalen darzustellen.
Da aufgrund rhythmischer Stimuli und der intrinsischen Rhythmen von
Neuronenverbänden die Eingangsgrößen häufig periodisch sind, wird das
Verhalten des NMM als Funktion der Intensität und Frequenz einer
periodischen Stimulation mittels der zugehörigen Lyapunov-Spektren und der
Zeitreihen charakterisiert. Auf der Basis der größten Lyapunov-Exponenten
wird das NMM mit dem Photic-Driving-Experiment überein gebracht. Dieses
Experiment findet routinemäßige Anwendung in der Diagnostik verschiedener
Erkrankungen wie Epilepsie, Migräne, Schizophrenie und Depression. Durch
die Anwendung des vorgestellten NMM wird der für die Diagnostik
entscheidende Mitnahmeeffekt reproduziert und es werden Vorhersagen für
eine Verbesserung der Indikation getroffen
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
timescales. For the fast subsystem we use the planar unfolding of a high
codimension singularity. In its bifurcation diagram, we locate paths that
underly 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 subsystems. 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.Comment: 22 pages, 15 figure
Selective activation of resting state networks following focal stimulation in a connectome- based network model of the human brain
Imaging studies suggest that the functional connectivity patterns of resting
state networks (RS-networks) reflect underlying structural connectivity (SC).
If the connectome constrains how brain areas are functionally connected, the
stimulation of specific brain areas should produce a characteristic wave of
activity ultimately resolving into RS-networks. To systematically test this
hypothesis, we use a connectome-based network model of the human brain with
detailed realistic SC. We systematically activate all possible thalamic and
cortical areas with focal stimulation patterns and confirm that the stimulation
of specific areas evokes network patterns that closely resemble RS-networks.
For some sites, one or no RS-network is engaged, whereas for other sites more
than one RS-network may evolve. Our results confirm that the brain is operating
at the edge of criticality, wherein stimulation produces a cascade of
functional network recruitments, collapsing onto a smaller subspace that is
constrained in part by the anatomical local and long-range SCs. We suggest that
information flow, and subsequent cognitive processing, follows specific routes
imposed by connectome features, and that these routes explain the emergence of
RS-networks. Since brain stimulation can be used to diagnose/treat neurological
disorders, we provide a look-up table showing which areas need to be stimulated
to activate specific RS-networks.Comment: 25 pages (in total), 7 figures, 2 table
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
Linking Molecular Pathways and Large-Scale Computational Modeling to Assess Candidate Disease Mechanisms and Pharmacodynamics in Alzheimer's Disease
Introduction: While the prevalence of neurodegenerative diseases associated with dementia such as Alzheimer's disease (AD) increases, our knowledge on the underlying mechanisms, outcome predictors, or therapeutic targets is limited. In this work, we demonstrate how computational multi-scale brain modeling links phenomena of different scales and therefore identifies potential disease mechanisms leading the way to improved diagnostics and treatment. Methods: The Virtual Brain (TVB; thevirtualbrain.org) neuroinformatics platform allows standardized large-scale structural connectivity-based simulations of whole brain dynamics. We provide proof of concept for a novel approach that quantitatively links the effects of altered molecular pathways onto neuronal population dynamics. As a novelty, we connect chemical compounds measured with positron emission tomography (PET) with neural function in TVB addressing the phenomenon of hyperexcitability in AD related to the protein amyloid beta (Abeta). We construct personalized virtual brains based on an averaged healthy connectome and individual PET derived distributions of Abeta in patients with mild cognitive impairment (MCI, N = 8) and Alzheimer's Disease (AD, N = 10) and in age-matched healthy controls (HC, N = 15) using data from ADNI-3 data base (http://adni.loni.usc.edu). In the personalized virtual brains, individual Abeta burden modulates regional Excitation-Inhibition balance, leading to local hyperexcitation with high Abeta loads. We analyze simulated regional neural activity and electroencephalograms (EEG). Results: Known empirical alterations of EEG in patients with AD compared to HCs were reproduced by simulations. The virtual AD group showed slower frequencies in simulated local field potentials and EEG compared to MCI and HC groups. The heterogeneity of the Abeta load is crucial for the virtual EEG slowing which is absent for control models with homogeneous Abeta distributions. Slowing phenomena primarily affect the network hubs, independent of the spatial distribution of Abeta. Modeling the N-methyl-D-aspartate (NMDA) receptor antagonism of memantine in local population models, reveals potential functional reversibility of the observed large-scale alterations (reflected by EEG slowing) in virtual AD brains. Discussion: We demonstrate how TVB enables the simulation of systems effects caused by pathogenetic molecular candidate mechanisms in human virtual brains
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