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Institute of Neuroscience and Medicine

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Mathematical Neuroscience

AG Sasha

Employing mathematical models for the investigation of the brain dynamics and behavior in health and disease could significantly contribute to the progress in the fields of neuroimaging, psychology and translational medicine. Such a model-based approach complements the classical data analysis and is aimed at suggesting and explaining the background mechanisms of the phenomena reported and studied by the data-driven research. The emerging interdisciplinary field that combines mathematical modeling with neuroimaging data analytics can help to go a step further towards our understanding of the brain structure and function and their relation to behavior.

The group “Mathematical Neuroscience” led by Oleksandr Popovych primarily aims to derive, validate and investigate mathematical models of neuronal networks based on empirical data. Doing so, the anatomical architecture of brain networks, i.e., their structural connectivity (SC), can be inferred from diffusion weighted magnetic resonance imaging (dwMRI) data, where the reconstructed fiber tracts can serve as physical connections between brain regions. These physical connections constitute the underlying structure of the model on top of which the time dynamics of neuronal activity can emerge. The latter can be measured by indirect, blood flow-based methods such as functional MRI (fMRI). Based on this, the model dynamics is simulated and compared with empirical dynamics, so that the model is adapted to the measured activity of the neuronal networks. The model parameters (like time delay in coupling, global coupling strength, etc.) are calibrated in such a way that the model dynamics closely replicates that of the brain networks extracted from the empirical data.

Mathematical Neuroscience

For the functional interrelations between brain nodes used in the data-driven and model-based approaches, the directionality, weight and type of connections are important, which is addressed by an intrinsically model-based approach of dynamic causal modeling (DCM) providing an estimation of effective connectivity reflecting causal interactions. Another topic of research of the group concerns the investigation of behavioral models for the time representation in the brain and modeling the learning principles underlying temporal preparation process when speeded reactions to external events are required.

A thorough exploration of the model parameter space and possible dynamical repertoires that the validated models can support can help to formulate predictions and hypotheses and test their relationship to the phenomena observed in the empirical data. The derived conclusions can thus serve as a basis for further experimental verification and data analysis. The models can provide an initial test bed for different methods and parameters of the data processing and signal extraction, which leads in such a way to incorporation of the mathematical models in the neuroimaging data processing and analysis pipelines. Furthermore, a model-based mathematical description allows to compare and differentiate brain structure and dynamics in health and disease, such that the model parameters and dynamical regimes may serve as additional biomarkers of brain states and behavioral modes.