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This paper introduces methods and a novel toolbox that efficiently integratesany high-dimensional Neural Mass Models (NMMs) specified by two essentialcomponents. The first is the set of nonlinear Random Differential Equations ofthe dynamics of each neural mass. The second is the highly sparsethree-dimensional Connectome Tensor (CT) that encodes the strength of theconnections and the delays of information transfer along the axons of eachconnection. Semi-analytical integration of the RDE is done with the LocalLinearization scheme for each neural mass model, which is the only schemeguaranteeing dynamical fidelity to the original continuous-time nonlineardynamic. It also seamlessly allows modeling distributed delays CT with anylevel of complexity or realism, as shown by the Moore-Penrose diagram of thealgorithm. This ease of implementation includes models with distributed-delayCTs. We achieve high computational efficiency by using a tensor representationof the model that leverages semi-analytic expressions to integrate the RandomDifferential Equations (RDEs) underlying the NMM. We discretized the stateequation with Local Linearization via an algebraic formulation. This approachincreases numerical integration speed and efficiency, a crucial aspect oflarge-scale NMM simulations. To illustrate the usefulness of the toolbox, wesimulate both a single Zetterberg-Jansen-Rit (ZJR) cortical column and aninterconnected population of such columns. These examples illustrate theconsequence of modifying the CT in these models, especially by introducingdistributed delays. We provide an open-source Matlab live script for thetoolbox.

Accurate and efficient Simulation of very high-dimensional Neural Mass Models with distributed-delay Connectome Tensors