Ponente
Descripción
Mesoscopic Neural Mass Models (NMMs) allow biophysical modeling and understanding of network properties and their reflection in EEG, MEG, or fMRI. This work deals with three critical aspects of this type of modeling
• We avoid numerical methods that destroy the dynamical properties of networks, employing the Local Linearization method (LLM) instead.
• We show that by drastically increasing simulation sampling frequency, inputs to each neural mass may be treated as already available, decoupling the integration of each neural mass.
• Our differential algebraic formulation creates the present input to each NMM by an efficient tensor product between the past outputs of all masses and the Connectome Tensor (CT).
• We can model any configuration of connectivities and delays, including distributed delays, which to our knowledge, have not been included in the previous NMM frameworks.
We illustrate the formulation by simulating different configurations of the Zetterberg-Jansen and Rit (ZJR) NMM, comprising three coupled second-order nonlinear random differential equations (RDEs). Each component is integrated symbolically with the LLM using MATLAB. We simulate a single classical ZJR cortical column and then scale the number of cortical columns up to 1000 (eZJR). A 3D sparse CT specifies the emitter neural masses projecting to receiver masses with different time lag distributions. Within each ZJR cortical column, we adopt canonical connections. For the eZJR NMM, we test different topologies: the Nearest Neighbor (NN), the Small World (SW), and the Full Connected (FC) networks. We additionally implement three delays: the standard simple zero lag Dirac delta, the Dirac delta delays with a time lag, and the Distributed delays. All pyramidal cells are averaged, and the spectrum is reported.
Large-scale NMM simulations are shown to be susceptible to changes in CT. We note that oscillatory activity is quenched for SE and FC networks with Delta Dirac delays, presenting alpha oscillations only for the NN case. Distributed delays restrict quenching only to the FC case. However, oscillation and harmonics are now shifted to theta range. Simulation for the eZJR model only took 2.4h on a PC without parallel computing. We estimate that traditional methods scale proportional to (NmxNe)^2 while ours does it linearly. An open-source toolbox with algorithms for enhancing brain simulation and allowing more realistic modeling is presented.
We provide a very efficient NM simulator that is an order of magnitude faster than traditional implementations using correct integration technique for RDEs, allowing, for the first time, encoding distributed transmission delays between neural masses.
