Parameter Identifiability and Non-Uniqueness in connectome based neural mass models

The spatial-temporal patterns of neuronal dynamics emerge from the network of coordinated brain regions, this structure-function relationship of the brain can be described mathematically by biophysical models of coupled brain regions connected by white matter tractography. Implementations of such models have focused on reproducing functional connectivity extracted from functional magnetic resonance imaging (fMRI), but these efforts are limited by the temporal resolution of fMRI data and the reduction of time course recordings into phenomenological functional connectivity maps. Here, we optimize parameters of a neural mass model (NMM) to best fit region-wise power spectra across the whole brain estimated from source localized electroencephalography (EEG). NMM models with global parameters were not able to fully reproduce region-wise power spectra, with or without the inclusion of structural connectivity information. In contrast, without the inclusion of structural connectivity information, independent oscillators at each brain region are able to reproduce region-wise power spectra. But the addition of structural connectivity and transmission delays to the NMM does not improve overall power spectra fit. Connectome-based NMM implementations with regional parameters lead to high dimensional network models that produce non-unique results. Inherent parameter identifiability problem in network models poses challenges for using such models as diagnostic tools for neurological diseases.