Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

• Published in: NeuroImage (Orlando, Fla.) Fla.), 2023-07, Vol.274, p.120137-120137, Article 120137
• Main Authors: Mitjans, Anisleidy González, Linares, Deirel Paz, Naranjo, Carlos López, Gonzalez, Ariosky Areces, Li, Min, Wang, Ying, Reyes, Ronaldo Garcia, Bringas-Vega, Maria L., Minati, Ludovico, Evans, Alan C., Valdes-Sosa, Pedro A.
• Format: Article
• Language: English
• Subjects: Algorithms; Axons; brain dynamics; Computer Simulation; Connectome; Connectome Tensor; Electroencephalography - methods; Humans; Inverse problems; Local Linearization Method; Medical imaging; Neural Mass Model; Neural networks; Neuroimaging; Oscillations; time-delay; Velocity
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2023.120137

•This paper introduces the Distributed-Delay Connectome Tensor Neural Mass Model.•The DD-NMM Toolbox allows modeling networks with arbitrary connectivities and realistic transmission delays.•Compared to more traditional methods, an order-of-magnitude reduction in the computation time is possible.•Feasible explorations of extensive networks are possible to investigate physiological phenomena such as the splitting alpha peak of the EEG spectrum.•Our software can be used stand-alone or integrated into other platforms such as The Virtual Brain (TVB). This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen and Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since t