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Echo state networks (ESN) are recurrent neural networks where the hidden layer is replaced with a fixed reservoir of neurons. Unlike feed-forward networks, neuron training in ESN is restricted to the output neurons alone thereby providing a computational advantage. We demonstrate the use of such ESNs in our mutual connectivity analysis (MCA) framework for recovering the primary motor cortex network associated with hand movement from resting state functional MRI (fMRI) data. Such a framework consists of two steps - (1) defining a pair-wise affinity matrix between different pixel time series within the brain to characterize network activity and (2) recovering network components from the affinity matrix with non-metric clustering. Here, ESNs are used to evaluate pair-wise cross-estimation performance between pixel time series to create the affinity matrix, which is subsequently subject to non-metric clustering with the Louvain method. For comparison, the ground truth of the motor cortex network structure is established with a task-based fMRI sequence. Overlap between the primary motor cortex network recovered with our model free MCA approach and the ground truth was measured with the Dice coefficient. Our results show that network recovery with our proposed MCA approach is in close agreement with the ground truth. Such network recovery is achieved without requiring low-pass filtering of the time series ensembles prior to analysis, an fMRI preprocessing step that has courted controversy in recent years. Thus, we conclude our MCA framework can allow recovery and visualization of the underlying functionally connected networks in the brain on resting state fMRI.

Functional connectivity analysis in resting state fMRI with echo-state networks and non-metric clustering for network structure recovery