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

Anisleidy González Mitjans; Deirel Paz Linares; Carlos López Naranjo; Ariosky Areces Gonzalez; Min Li; Ying Wang; Ronaldo Garcia Reyes; Maria L Bringas-Vega; Ludovico Minati; Alan C Evans; Pedro A Valdes-Sosa

doi:10.1016/j.neuroimage.2023.120137

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

Neuroimage. 2023 Jul 1:274:120137. doi: 10.1016/j.neuroimage.2023.120137. Epub 2023 Apr 26.

Affiliations

¹ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China; Department of Mathematics, University of Havana, Havana, Cuba. Electronic address: anisleidy@neuroinformatics-collaboratory.org.
² The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China; Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba. Electronic address: deirel.paz@neuroinformatics-collaboratory.org.
³ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China. Electronic address: clopez@neuroinformatics-collaboratory.org.
⁴ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China; Department of Informatics, University of Pinar del Rio, Pinar del Rio, Cuba. Electronic address: ariosky@neuroinformatics-collaboratory.org.
⁵ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China. Electronic address: min.li@neuroinformatics-collaboratory.org.
⁶ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China. Electronic address: rigel.wang@neuroinformatics-collaboratory.org.
⁷ Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba. Electronic address: ronaldo@neuroinformatics-collaboratory.org.
⁸ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China; Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba. Electronic address: maria.bringas@neuroinformatics-collaboratory.org.
⁹ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China; Center for Mind/Brain Sciences (CIMeC), University of Trento, 38100 Trento, Italy. Electronic address: lminati@neuroinformatics-collaboratory.org.
¹⁰ McGill Centre for Integrative Neuroscience, Ludmer Centre for Neuroinformatics and Mental Health, Montreal Neurological Institute, Canada. Electronic address: alan.evans@mcgill.ca.
¹¹ The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China; Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba. Electronic address: pedro.valdes@neuroinformatics-collaboratory.org.

PMID: 37116767
DOI: 10.1016/j.neuroimage.2023.120137

Abstract

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 they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Keywords: Connectome Tensor; Local Linearization Method; Neural Mass Model; brain dynamics; time-delay.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Axons
Computer Simulation
Connectome*
Electroencephalography* / methods
Humans