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A simulation model for the spread and control of lesions in the brain is constructed using a planar network (graph) representation for the Central Nervous System (CNS). The model is inspired by the lesion structures observed in the case of…
The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto's equations. In this article, we build such neural-oscillator models, partly based on…
We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of…
Background: Mathematical modeling approaches are becoming ever more established in clinical neuroscience. They provide insight that is key to understand complex interactions of network phenomena, in general, and interactions within the…
Brain cancer can be very fatal, but chances of survival increase through early detection and treatment. Doctors use Magnetic Resonance Imaging (MRI) to detect and locate tumors in the brain, and very carefully analyze scans to segment brain…
A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations…
Dynamic functional connectivity is an effective measure for the brain's responses to continuous stimuli. We propose an inferential method to detect the dynamic changes of brain networks based on time-varying graphical models. Whereas most…
Deep learning methods are actively used for brain lesion segmentation. One of the most popular models is DeepMedic, which was developed for segmentation of relatively large lesions like glioma and ischemic stroke. In our work, we consider…
We demonstrate that chimera behavior can be observed in nonlocally coupled networks of excitable systems in the presence of noise. This phenomenon is distinct from classical chimeras, which occur in deterministic oscillatory systems, and it…
The emergence and nature of amplitude mediated chimera states, spatio-temporal patterns of co-existing coherent and incoherent regions, are investigated for a globally coupled system of active and inactive Ginzburg-Landau oscillators. The…
The characterisation of the brain as a "connectome", in which the connections are represented by correlational values across timeseries and as summary measures derived from graph theory analyses, has been very popular in the last years.…
Cognition is supported by neurophysiological processes that occur both in local anatomical neighborhoods and in distributed large-scale circuits. Recent evidence from network control theory suggests that white matter pathways linking…
We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model of coupling which is implemented by smooth…
Cancer of the brain is deadly and requires careful surgical segmentation. The brain tumors were segmented using U-Net using a Convolutional Neural Network (CNN). When looking for overlaps of necrotic, edematous, growing, and healthy tissue,…
In this paper, we propose a framework to control brain-wide functional connectivity by selectively acting on the brain's structure and parameters. Functional connectivity, which measures the degree of correlation between neural activities…
Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in…
There is growing interest in understanding how the structural interconnections among brain regions change with the occurrence of neurological diseases. Diffusion weighted MRI imaging has allowed researchers to non-invasively estimate a…
Today the human brain can be modeled as a graph where nodes represent different regions and links stand for statistical interactions between their activities as recorded by different neuroimaging techniques. Empirical studies have lead to…
Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available…
Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding…