A mathematical model of dysfunction of the thalamo-cortical loop in schizophrenia.

Nils Rosjat,Svitlana Popovych,Silvia Daun-Gruhn

doi:10.1186/1742-4682-11-45

Nils Rosjat, Svitlana Popovych + Show 1 more

Open Access

https://doi.org/10.1186/1742-4682-11-45

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Abstract

BackgroundRecent experimental results suggest that impairment of auditory information processing in the thalamo-cortical loop is crucially related to schizophrenia. Large differences between schizophrenia patients and healthy controls were found in the cortical EEG signals.MethodsWe derive a phenomenological mathematical model, based on coupled phase oscillators with continuously distributed frequencies to describe the neural activity of the thalamo-cortical loop. We examine the influence of the bidirectional coupling strengths between the thalamic and the cortical area with regard to the phase-locking effects observed in the experiments. We extend this approach to a model consisting of a thalamic area coupled to two cortical areas, each comprising a set of nonidentical phase oscillators. In the investigations of our model, we applied the Ott-Antonsen theory and the Pikovsky-Rosenblum reduction methods to the original system.ResultsThe results derived from our mathematical model satisfactorily reproduce the experimental data obtained by EEG measurements. Furthermore, they show that modifying the coupling strength from the thalamic region to a cortical region affects the duration of phase synchronization, while a change in the feedback to the thalamus affects the strength of synchronization in the cortex. In addition, our model provides an explanation in terms of nonlinear dynamics as to why brain waves desynchronize after a given phase reset.ConclusionOur model can explain functional differences seen between EEG records of healthy subjects and schizophrenia patients on a system theoretic basis. Because of this and its predictive character, the model may be considered to pave the way towards an early and reliable clinical detection of schizophrenia that is dependent on the interconnections between the thalamic and cortical regions. In particular, the model parameter that describes the strength of this connection can be used for a diagnostic classification of schizophrenia patients.

Highlights

Schizophrenia is a severe and complex mental illness causing disability [1,2,3]
In the present study we extended this mathematical model such that each area of the thalamo-cortical loop is represented by a large population of phase oscillators
In section “Mathematical model”, we present the general structure of the thalamo-cortical loop and set up a mathematical model which we use to analyze first the behavior of two coupled brain regions, the thalamus and one cortical region, and that of three coupled ones, the thalamus and two cortical regions

Summary

Introduction

Schizophrenia is a severe and complex mental illness causing disability [1,2,3]. It has been conceptualized as a disconnectivity syndrome concerning the interplay of the brain areas involved. As information on the activity of some of the deeply localized involved brain areas, such as the thalamus is not accessible to noninvasive electroencephalography (EEG) measurement, alternative methods, like mathematical models, need to be developed in order to deepen our understanding of the fundamental neural processes underlying schizophrenia, and to detect dysfunctions in the interactions between the participating brain areas. Such methods aim at deriving reliable criteria that indicate the progress of the disease at an early stage. Large differences between schizophrenia patients and healthy controls were found in the cortical EEG signals

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