PhD Student, The School of Physics, University of Sydney, NSW-2006, Australia
Modal analysis of corticothalamic dynamics, electroencephalographic spectra, coherence, correlation
The brain is the most complex organ in the body, and the most important. Understanding the brain activity is a broad problem and much progress has been made towards understanding the structure and functioning of the brain.
Do you have any idea about the Electroencephalogram (EEG)? It is a measure that records electrical patterns in our brain. It is very useful to diagnose different diseases such as seizures, epilepsy, head injuries, dizziness, headaches, brain tumors and sleeping problem. In our brain we have billions of nerve cells. These cells produce very small electrical signals that forms patterns called brain waves. Electroencephalographic (EEG) measurements are commonly made using multiple electrodes and wires, are attached to our brain. The brain waves which detected by electrodes and the EEG machine amplifies the signals and records them in a wave pattern.
In our model we use established corticothalamic neural field theory (NFT), which has successfully explained a wide variety of phenomena, ranging from EEG spectra and evoked potentials to nonlinear phenomena such as seizures and Parkinsonian oscillations. NFT has also been used to understand brain connectivities and interelating brain structural and functional connectivity. We adapt this model to spherical harmonics, modelling the cortex as a thin spherical shell. Aside from the fact that the cortex is curved, this model is motivated by the fact that the eigenmodes of the neural field model resemble those of the spherical eigenmodes and we need to understand how the discreteness of these modes affects observable quantities.
Here, corticothalamic NFT is analyzed on a sphere and the power spectrum, the correlation function, and the cross spectrum are expressed in terms of spherical harmonics. The results are analyzed and compared with planar NFT in both finite and infinite geometries. The results of spherical and finite planar geometries converge to the infinite planar geometry in the limit of large brain size. The main effects of the spherical modal structure are explored, particularly to understand the number of modes that contribute significantly to these observable quantities and the effects of the finite spatial extent of the cortex.
The analysis for the spherical geometry will enable more realistic modeling and analysis of experimental brain signals in future.
Abstract: This paper examines nonlinear effects in a neural field model of the corticothalamic system to predict the EEG power spectrum of sleep spindles. Nonlinearity in the thalamic relay nuclei gives rise to a spindle harmonic visible in the cortical EEG. By deriving an analytic expression for nonlinear spectrum, the power in the spindle harmonic is predicted to scale quadratically with the power in the spindle oscillation. By isolating sleep spindles from background sleep in experimental EEG data, the spindle harmonic is directly observed.
Pub.: 03 Dec '13, Pinned: 30 Oct '17
Abstract: Plasticity is crucial to neural development, learning, and memory. In the common in vivo situation where postsynaptic neural activity results from multiple presynaptic inputs, it is shown that a widely used class of correlation-dependent and spike-timing dependent plasticity rules can be written in a form that can be incorporated into neural field theory, which enables their system-level dynamics to be investigated. It is shown that the resulting plasticity dynamics depends strongly on the stimulus spectrum via overall system frequency responses. In the case of perturbations that are approximately linear, explicit formulas are found for the dynamics in terms of stimulus spectra via system transfer functions. The resulting theory is applied to a simple model system to reveal how collective effects, especially resonances, can drastically modify system-level plasticity dynamics from that implied by single-neuron analyses. The simplified model illustrates the potential relevance of these effects in applications to brain stimulation, synaptic homeostasis, and epilepsy.
Pub.: 20 Jul '11, Pinned: 30 Oct '17
Abstract: A physiologically based model of corticothalamic dynamics is used to investigate the electroencephalographic (EEG) activity associated with tumors of the thalamus. Tumor activity is modeled by introducing localized two-dimensional spatial non-uniformities into the model parameters, and calculating the resulting activity via the coupling of spatial eigenmodes. The model is able to reproduce various qualitative features typical of waking eyes-closed EEGs in the presence of a thalamic tumor, such as the appearance of abnormal peaks at theta ( approximately 3Hz) and spindle ( approximately 12Hz) frequencies, the attenuation of normal eyes-closed background rhythms, and the onset of epileptic activity, as well as the relatively normal EEGs often observed. The results indicate that the abnormal activity at theta and spindle frequencies arises when a small portion of the brain is forced into an over-inhibited state due to the tumor, in which there is an increase in the firing of (inhibitory) thalamic reticular neurons. The effect is heightened when there is a concurrent decrease in the firing of (excitatory) thalamic relay neurons, which are in any case inhibited by the reticular ones. This is likely due to a decrease in the responsiveness of the peritumoral region to cholinergic inputs from the brainstem, and a corresponding depolarization of thalamic reticular neurons, and hyperpolarization of thalamic relay neurons, similar to the mechanism active during slow-wave sleep. The results indicate that disruption of normal thalamic activity is essential to generate these spectral peaks. Furthermore, the present work indicates that high-voltage and epileptiform EEGs are caused by a tumor-induced local over-excitation of the thalamus, which propagates to the cortex. Experimental findings relating to local over-inhibition and over-excitation are discussed. It is also confirmed that increasing the size of the tumor leads to greater abnormalities in the observable EEG. The usefulness of EEG for localizing the tumor is investigated.
Pub.: 28 Dec '04, Pinned: 30 Oct '17
Abstract: The mechanisms underlying pathologically synchronized neural oscillations in Parkinson's disease (PD) and generalized epilepsies are explored in parallel via a physiologically-based neural field model of the corticothalamic-basal ganglia (CTBG) system. The basal ganglia (BG) are approximated as a single effective population and their roles in the modulation of oscillatory dynamics of the corticothalamic (CT) system and vice versa are analyzed. In addition to normal EEG rhythms, enhanced activity around 4 Hz and 20 Hz exists in the model, consistent with the characteristic frequencies observed in PD. These rhythms result from resonances in loops formed between the BG and CT populations, analogous to those that underlie epileptic oscillations in a previous CT model, and which are still present in the combined CTBG system. Dopamine depletion is argued to weaken the dampening of these loop resonances in PD, and network connections then explain the significant coherence observed between BG, thalamic, and cortical population activity around 4-8 Hz and 20 Hz. Parallels between the afferent and efferent connection sites of the thalamic reticular nucleus (TRN) and BG predict low dopamine to correspond to a reduced likelihood of tonic-clonic (grand mal) seizures, which agrees with experimental findings. Furthermore, the model predicts an increased likelihood of absence (petit mal) seizure resulting from pathologically low dopamine levels in accordance with experimental observations. Suppression of absence seizure activity is demonstrated when afferent and efferent BG connections to the CT system are strengthened, which is consistent with other CTBG modeling studies. The BG are demonstrated to have a suppressive effect on activity of the CTBG system near tonic-clonic seizure states, which provides insight into the reported efficacy of current treatments in BG circuits. Sleep states of the TRN are also found to suppress pathological PD activity in accordance with observations. Overall, the findings demonstrate strong parallels between coherent oscillations in generalized epilepsies and PD, and provide insights into possible comorbidities.
Pub.: 22 Jun '17, Pinned: 30 Oct '17
Abstract: Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory.
Pub.: 02 Jun '12, Pinned: 27 Sep '17
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