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Stochastic resonance induced by external factor is considering to investigate the complex dynamics of tumor. The surrounding environment and the treatment effects on the tumor growth are considered as additive and multiplicative noises in…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
We offer a general theoretical framework for brain and behavior that is evolutionarily and computationally plausible. The brain in our abstract model is a network of nodes and edges. Although it has some similarities to standard neural…
Neuro-oncological surgery is the primary brain cancer treatment, yet it faces challenges with gliomas due to their invasiveness and the need to preserve neurological function. Hence, radical resection is often unfeasible, highlighting the…
The relation between EEG rhythms, brain functions, and behavioral correlates is well-established. Some mechanisms underlying rhythm generation are understood, enabling the replication of brain rhythms $in\; silico$. This allows to explore…
While phase oscillators are often used to model neuronal populations, in contrast to the Kuramoto paradigm, strong interactions between brain areas can be associated with loss of synchrony. Using networks of coupled oscillators described by…
Abnormal cortical folding patterns may be related to neurodevelopmental disorders such as lissencephaly and polymicrogyria. In this context, computational modeling is a powerful tool to provide a better understanding of the early brain…
Chimera states, which consist of coexisting synchronous and asynchronous domains in networks of coupled oscillators, are in the focus of attention for over a decade. Although chimera morphology and properties have been investigated in a…
We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
Uncontrolled cell division in the brain is what gives rise to brain tumors. If the tumor size increases by more than half, there is little hope for the patient's recovery. This emphasizes the need of rapid and precise brain tumor diagnosis.…
Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…
In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors with radiotherapy influence. Under certain assumptions on the given data in the model, we prove existence and uniqueness of a weak…
When chaotic oscillators are coupled in complex networks a number of interesting synchronization phenomena emerge. Notable examples are the frequency and amplitude chimeras, chimera death states, solitary states as well as combinations of…
Gliomas are the most common malignant brain tumourswith intrinsic heterogeneity. Accurate segmentation of gliomas and theirsub-regions on multi-parametric magnetic resonance images (mpMRI)is of great clinical importance, which defines…
Neural oscillations are considered to be brain-specific signatures of information processing and communication in the brain. They also reflect pathological brain activity in neurological disorders, thus offering a basis for diagnoses and…
Deep learning motivated by convolutional neural networks has been highly successful in a range of medical imaging problems like image classification, image segmentation, image synthesis etc. However for validation and interpretability, not…
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…
We analyse the possible dynamical states emerging for two symmetrically pulse coupled populations of leaky integrate-and-fire neurons. In particular, we observe broken symmetry states in this set-up: namely, breathing chimeras, where one…
The neural networks of the human brain act as very efficient parallel processing computers co-ordinating memory related responses to a multitude of input signals from sensory organs. Information storage, update and appropriate retrieval are…