Paula Sanz-Leon, Leonardo L Gollo, James A Roberts
**Background.** Neural activity organizes in constantly evolving spatiotemporal patterns of activity, also known as brain waves (Roberts et al., 2019). Indeed, wave-like patterns have been observed across multiple neuroimaging modalities and across multiple spatiotemporal scales (Muller et al., 2016; Contreras et al. 1997; Destexhe et al. 1999). However, due to experimental constraints most attention has thus far been given to localised wave dynamics in the range of micrometers to a few centimeters, rather than at the global or large-scale that would encompass the whole brain. Existing toolboxes (Muller et al., 2016; Townsend et al., 2018) are geared particularly for 2D spatial domains (e.g., LFPs or VSDs on structured rectangular grids). No tool exists to study spatiotemporal waves naturally unfolding in 3D+t as recorded with different non-invasive neuroimaging techniques (e.g, EEG, MEG, and fMRI). In this work, we present results of using our toolbox neural flows (shown in Fig. 1).
**Methods and Results.** Our toolbox handles irregularly sampled data such as those produced via brain network modelling (Sanz-Leon et al., 2015; Breakspear, 2017) or source-reconstructed M/EEG, and regularly sampled data such as voxel-based fMRI. The toolbox performs the following steps: 1) Estimation of neural flows (Destexhe et al. 1999; Townsend et al., 2018; Sanz- Leon et al. 2020). 2) Detection of 3D singularities (i.e., points of vanishing flow). 3) Classification of 3D singularities. In that regard, the key flow singularities detected so far had been sources and sinks (from where activity emerges and vanishes, respectively), but no methods or tools existed to detect 3D saddles (around which activity is redirected to other parts of the brain). 4) Quantification of singularity statistics. 5) Finally, modal decomposition of neural flow dynamics. This decomposition allows for the detection and prediction of the most common spatiotemporal patterns of activity found in empirical data.
**Conclusions.** Representation of neural activity based on singularities (commonly known as critical points) is essentially a dimensionality reduction framework to understand large-scale brain dynamics. The distribution of singularities in physical space allows us to simplify the complex structure of flows into areas with similar dynamical behavior (e.g., fast versus slow, stagnant, laminar, or rotating). For modelling work, this compact representation allows for an intuitive and systematic understanding of the effects of various parameters in brain network dynamics such as spatial heterogeneity, lesions and noise. For experimental work, neural flows enable a rational understanding of large-scale brain dynamics directly in anatomical space which facilitates the interpretation and comparison of results across multiple modalities. Toolbox capabilities are presented in the accompanying figure. Watch this space for the open-source code: [ https://github.com/brain- modelling-group](https://github.com/brain-modelling-group)
References
Contreras et al. 1997 _J. Neurosci. 17, 1179-1196. _ Destexhe et al. 1999 J. Neurosci. _19 (11) 4595-4608. _ Muller et al., 2016 _eLife 5:e17267. _ Roberts et al., 2019 _Nat. Commun. 5;10(1):1056. _ Townsend et al., 2018 _PLoS Comput Biol_. 2018;14(12):e1006643. Sanz-Leon et al. 2020 _Neuroimage toolbox_ \- in preparation
