Generative Embeddings of Brain Collective Dynamics Using Variational Autoencoders

Abstract

We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We use variational autoencoders (VAEs) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wakesleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations results in an embedding that encodes the repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first follow this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two end points of this trajectory; then, we show that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology.

Nonequilibrium brain dynamics as a signature of consciousness

“…We applied this optimization procedure to reproduce the empirical observables for wakefulness, for all human non-rapid eye movement (NREM) sleep stages (N1, N2, N3), and for propofol-induced sedation and loss of consciousness. We then used the optimal parameters to enhance the BOLD signal lengths of each subject (n=15) up to 30.000 samples for each region of interest [16,17], allowing us to estimate entropy production as done with the ECoG data (Fig. 2).…”

Data-driven discovery of canonical large-scale brain dynamics

“…in recent years to simulate different physiological and pathological brain states, as well as to study in silico their behavior under multiple forms of external perturbations 13,[24][25][26][27] . Thus, our results can be interpreted as a hypothesis-free validation of the Hopf model (also known as Stuart-Landau oscillator), although in our case the oscillations were not always harmonic.…”

“…Thus, the core capacity of a model to capture whole-brain dynamics can be characterized by its repertoire of bifurcations and their classification. For instance, noise-driven models close to a bifurcation (such as the Stuart-Landau oscillator) have been extensively explored and characterized in recent publications 13,[24][25][26][27] . Even though more realistic models offer advantages in terms of interpretability, they cannot escape the fact that most of the time, if not always, the model parameters must be posed next to a bifurcation to adequately reproduce empirical observables 22 .…”

Whole-Brain Models to Explore Altered States of Consciousness from the Bottom Up

“…The same concept could apply to the development and in silico testing of new pharmaceuticals to treat psychiatric conditions, where whole-brain models could be used to reverse-engineer the optimal receptor affinity profiles required to restore statistical signatures of healthy brain dynamics. Finally, the combination of data produced by whole-brain models and machine learning classifiers could be useful for data augmentation in the context of automated diagnosis of rare neurological diseases [165] and to generate input for deep learning architectures (e.g., variational autoencoders) capable of representing altered states of consciousness as trajectories within a low dimensionality latent space [166].…”