Spectral and Non-linear Analysis of Thalamocortical Neural Mass Model Oscillatory Dynamics

Abstract

The chapter is organised in two parts: In the first part, the focus is ona combined power spectral and non-linear behavioural analysis of a neural massmodel of the thalamocortical circuitry. The objective is to study the effectivenessof such ‘multi-modal’ analytical techniques in model-based studies investigatingthe neural correlates of abnormal brain oscillations in Alzheimer’s disease (AD).The power spectral analysis presented here is a study of the ‘slowing’ (decreasingdominant frequency of oscillation) within the alpha frequency band (8 – 13 Hz),a hallmark of Electroencephalogram (EEG) dynamics in AD. Analysis of the nonlineardynamical behaviour focuses on the bifurcating property of the model. Theresults show that the alpha rhythmic content is maximal at close proximity to thebifurcation point — an observation made possible by the ‘multi-modal’ approachadopted herein. Furthermore, a slowing in alpha rhythm is observed for increasinginhibitory connectivity — a consistent feature of our research into neuropathologicaloscillations associated with AD. In the second part, we have presented powerspectral analysis on a model that implements multiple feed-forward and feed-backconnectivities in the thalamo-cortico-thalamic circuitry, and is thus more advancedin terms of biological plausibility. This study looks at the effects of synaptic connectivityvariation on the power spectra within the delta (1 – 3 Hz), theta (4 – 7 Hz),alpha (8 – 13 Hz) and beta (14 – 30 Hz) bands. An overall slowing of EEG with decreasing synaptic connectivity is observed, indicated by a decrease of power withinalpha and beta bands and increase in power within the theta and delta bands. Thus,the model behaviour conforms to longitudinal studies in AD indicating an overallslowing of EEG.