Neuroinformatic tool to study high dimensional dynamics with distributed delays in Neural Mass Models
Presenting author:
A vital tool at this moment in neuroscience is the construction of mesoscopic Neural Mass (NMM) that allows understanding neural mechanisms at large scales, the generation of images as well as inside into pathophysiology. One of NMM most famous is the one formulated by Jansen and Rit-Zetterberg (JR-Zetterberg) through three coupled second-order nonlinear differential equations.
Here, a Random Delay Differential Equation formulation enables integrating the neural masses step by step for more efficiency and a reasonable time scale. We deal with an algebraic interpretation of NMM, then the solution of a cortical column is explicitly calculated, making numerical integration more accessible and faster. To numerical calculations was used the Local Linearization Method, which provides, unlike the other discretization methods, non-explosive discrete-time dynamical systems. Due to the relevance of transmission delays in NMM and its influence on oscillatory behavior, it was introduced a new interpretation for time delays. It is an exponential distribution instead of using a Dirac-delta function and compared between them. The connectome is a full tensor adding transmission delay info. Three structural levels (cortical unit, population and system) at the mesoscopic level were defined to study the brain's organization and generate more complex dynamics.
We found the model is susceptible to changes to transmission delays reflected in the system stability and shows better properties under the distributed delays introduced in this study, making the temporal dimension well-defined. The algebraic formulation joined to the LLM provides efficient calculations performed in a Live Script by MATLAB Symbolic Toolbox.
This work provides a public toolbox to be disseminated for a distributed time-delay NMM, simulating several types of EEG activities at three levels of complexity at the mesoscopic level and also offers basic algorithms to increase the dimensionality of brain simulations. The temporal dimension was extended, representing the interaction between neurons through a connectivity tensor via specific connection weight and time delays.
Keywords: Neural Mass Model, time-delays, connectivity matrix, Local Linearization Method
Here, a Random Delay Differential Equation formulation enables integrating the neural masses step by step for more efficiency and a reasonable time scale. We deal with an algebraic interpretation of NMM, then the solution of a cortical column is explicitly calculated, making numerical integration more accessible and faster. To numerical calculations was used the Local Linearization Method, which provides, unlike the other discretization methods, non-explosive discrete-time dynamical systems. Due to the relevance of transmission delays in NMM and its influence on oscillatory behavior, it was introduced a new interpretation for time delays. It is an exponential distribution instead of using a Dirac-delta function and compared between them. The connectome is a full tensor adding transmission delay info. Three structural levels (cortical unit, population and system) at the mesoscopic level were defined to study the brain's organization and generate more complex dynamics.
We found the model is susceptible to changes to transmission delays reflected in the system stability and shows better properties under the distributed delays introduced in this study, making the temporal dimension well-defined. The algebraic formulation joined to the LLM provides efficient calculations performed in a Live Script by MATLAB Symbolic Toolbox.
This work provides a public toolbox to be disseminated for a distributed time-delay NMM, simulating several types of EEG activities at three levels of complexity at the mesoscopic level and also offers basic algorithms to increase the dimensionality of brain simulations. The temporal dimension was extended, representing the interaction between neurons through a connectivity tensor via specific connection weight and time delays.
Keywords: Neural Mass Model, time-delays, connectivity matrix, Local Linearization Method