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

Rosjat N, Popovych S, Daun-Gruhn S - Theor Biol Med Model (2014)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Heisenberg Research Group of Computational Biology, Department of Animal Physiology, Institute of Zoology, University of Cologne, Zülpicher Str, 47b, 50674 Cologne, Germany. rosjatn@uni-koeln.de.

ABSTRACT

Background: 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.

Methods: 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.

Results: 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.

Conclusion: 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.

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Related in: MedlinePlus

Dynamic behavior of cortical regions. An example of the desynchronization in the two cortical areas of the non-reduced system (only 200 of N=1000 oscillators are shown);  Hz  Hz,  Hz, , , , . The max SLI is shown in black. Frequency of coupled oscillators in the phase-locking interval: 6 Hz for θ-population and 9.4 Hz for α-population.
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Fig9: Dynamic behavior of cortical regions. An example of the desynchronization in the two cortical areas of the non-reduced system (only 200 of N=1000 oscillators are shown); Hz Hz, Hz, , , , . The max SLI is shown in black. Frequency of coupled oscillators in the phase-locking interval: 6 Hz for θ-population and 9.4 Hz for α-population.

Mentions: Figure 9 shows the behaviour of the θ- and α-populations in the case of schizophrenia patients, i.e. the coupling parameters are , , . The cosine of the phases of 200 oscillators is shown (in total we calculated N=1000 oscillators in each population). The system was stimulated at t=0. The black lines indicate the max SLI. Before the stimulation, i.e. t∈[ -100,0], we have a uniform distribution of the phases, which means that the oscillators in each population are desynchronized, i.e. max SLI = 0. Directly after the stimulation at t=0 a phase reset occurs and the phases of the oscillators synchronize (thin blue waves), hence now max SLI >0. After a certain time, they desynchronize again: the desynchronization in the α-population happens earlier (at ≈250 ms) followed by that in the θ-population (at ≈400 ms). These simulation results fully agree with the experimental data [12].Figure 9


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

Rosjat N, Popovych S, Daun-Gruhn S - Theor Biol Med Model (2014)

Dynamic behavior of cortical regions. An example of the desynchronization in the two cortical areas of the non-reduced system (only 200 of N=1000 oscillators are shown);  Hz  Hz,  Hz, , , , . The max SLI is shown in black. Frequency of coupled oscillators in the phase-locking interval: 6 Hz for θ-population and 9.4 Hz for α-population.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4216834&req=5

Fig9: Dynamic behavior of cortical regions. An example of the desynchronization in the two cortical areas of the non-reduced system (only 200 of N=1000 oscillators are shown); Hz Hz, Hz, , , , . The max SLI is shown in black. Frequency of coupled oscillators in the phase-locking interval: 6 Hz for θ-population and 9.4 Hz for α-population.
Mentions: Figure 9 shows the behaviour of the θ- and α-populations in the case of schizophrenia patients, i.e. the coupling parameters are , , . The cosine of the phases of 200 oscillators is shown (in total we calculated N=1000 oscillators in each population). The system was stimulated at t=0. The black lines indicate the max SLI. Before the stimulation, i.e. t∈[ -100,0], we have a uniform distribution of the phases, which means that the oscillators in each population are desynchronized, i.e. max SLI = 0. Directly after the stimulation at t=0 a phase reset occurs and the phases of the oscillators synchronize (thin blue waves), hence now max SLI >0. After a certain time, they desynchronize again: the desynchronization in the α-population happens earlier (at ≈250 ms) followed by that in the θ-population (at ≈400 ms). These simulation results fully agree with the experimental data [12].Figure 9

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Heisenberg Research Group of Computational Biology, Department of Animal Physiology, Institute of Zoology, University of Cologne, Zülpicher Str, 47b, 50674 Cologne, Germany. rosjatn@uni-koeln.de.

ABSTRACT

Background: 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.

Methods: 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.

Results: 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.

Conclusion: 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.

Show MeSH
Related in: MedlinePlus