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

Recent 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.

We 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.

The 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.

Our 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.