A Phenomenological Deep Oscillatory Neural Network Model to Capture the Whole Brain Dynamics in Terms of BOLD Signal

Abstract

A large-scale model of brain dynamics, as it is manifested in functional neuroimaging data, is presented in this study. The model is built around a general trainable network of Hopf oscillators, the dynamics of which are described in the complex domain. It was shown earlier that when a pair of Hopf oscillators are coupled by power coupling with a complex coupling strength, it is possible to stabilize the normal phase difference at a value related to the angle of the complex coupling strength. In the present model, the magnitudes of the complex coupling weights are set using the Structural Connectivity information obtained from Diffusion Tensor Imaging (DTI). The complex-valued outputs of the oscillator network are transformed by a complex-valued feedforward network with a single hidden layer. The entire model is trained in 2 stages: in the $1^{st}$ stage, the intrinsic frequencies of the oscillators in the oscillator network are trained, whereas in the $2^{nd}$ stage, the weights of the feedforward network are trained using the complex backpropagation algorithm. The Functional Connectivity Matrix (FCM) obtained from the network’s output is compared with empirical Functional Connectivity Matrix, a comparison that resulted in a correlation of 0.99 averaged over 5 subjects.

Supported by DBT,Govt. of India, Centre of Computational System and Dynamics, IIT Madras.