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Although the electroencephalogram (EEG) activity of Autism Spectrum Disorder (ASD) has extremely complicated dynamics, the basic research on its dynamic modeling remains unexplored. This paper aims to investigate the mechanisms underlying EEG abnormalities in ASD from the perspective of dynamic modeling, and delve into the therapeutic principles of neuromodulation. First, by adjusting the average inhibitory synaptic gain and the average excitatory synaptic connection strength in the Wendling model, we reproduce clinical EEG characteristics of ASD, including Interictal Epileptiform Discharges (IEDs), increased relative power of the $\delta +𝜃$ band, decreased relative power of the $\alpha$ band, and reduced EEG complexity. This indicates that Excitation–Inhibition (EI) imbalance is potentially the trigger of abnormal EEG in ASD. Then, we demonstrate that both monophasic and biphasic repetitive Transcranial Magnetic Stimulation (rTMS) effectively control pathological discharges in ASD, with biphasic rTMS showing a reduced risk of over-control at the same frequency and intensity, consistent with clinical findings. Additionally, we show that Deep Brain Stimulation (DBS) plays a similar role to rTMS in the treatment of ASD, which proves the low-frequency DBS to be more effective in enhancing the complexity of brain activity, suggesting that DBS may hold promise as an innovative neuromodulation strategy for ASD. Our work helps to promote the development of dynamic modeling for ASD and to inspire therapeutic approaches for regulating the EI balance.

A neural mass model for the memorization of sequences is presented. It exploits three layers of cortical columns that generate a theta/gamma rhythm. The first layer implements an auto-associative memory working in the theta range; the second segments objects in the gamma range; finally, the feedback interactions between the third and the second layers realize a hetero-associative memory for learning a sequence. After training with Hebbian and anti-Hebbian rules, the network recovers sequences and accounts for the phase-precession phenomenon.

Recent work presented a framework for space-time-resolved neurophysiological process imaging that augments existing electromagnetic source imaging techniques. In particular, a nonlinear Analytic Kalman filter (AKF) has been developed to efficiently infer the states and parameters of neural mass models believed to underlie the generation of electromagnetic source currents. Unfortunately, as the initialization determines the performance of the Kalman filter, and the ground truth is typically unavailable for initialization, this framework might produce suboptimal results unless significant effort is spent on tuning the initialization. Notably, the relation between the initialization and overall filter performance is only given implicitly and is expensive to evaluate; implying that conventional optimization techniques, e.g. gradient or sampling based, are inapplicable. To address this problem, a novel efficient framework based on blackbox optimization has been developed to find the optimal initialization by reducing the signal prediction error. Multiple state-of-the-art optimization methods were compared and distinctively, Gaussian process optimization decreased the objective function by 82.1% and parameter estimation error by 62.5% on average with the simulation data compared to no optimization applied. The framework took only 1.6h and reduced the objective function by an average of 13.2% on 3.75min 4714-source channel magnetoencephalography data. This yields an improved method of neurophysiological process imaging that can be used to uncover complex underpinnings of brain dynamics.

We propose a neural mass model for anatomically-constrained effective connectivity among neuronal populations residing in four layers (L2/3, L4, L5 and L6) within a cortical column. Eight neuronal populations in a given column — an excitatory population and an inhibitory population per layer — are assumed to be coupled via effective connections of unknown strengths that need to be estimated. The effective connections are constrained to anatomical connections that have been shown to exist in previous anatomical studies. The neural input to a cortical column is directed into the two populations in L4. The anatomically-constrained effective connectivity is captured by a system of 16 stochastic differential equations. Solving these equations yields the average postsynaptic potentials and transmembrane currents generated in each population. The current source density (CSD) responses in each layer, which serve as the model observations, are equated in the model to the sum of all currents generated within that layer. The model is implemented in a continuous-discrete state-space framework, and the innovation method is used for estimating the model parameters from CSD data. To this end, local field potential (LFP) responses to forepaw stimulation were recorded in rat area S1 using multi-channel linear probes. LFPs were converted to CSD signals, which were averaged within each layer, yielding one CSD response per layer. To estimate the effective strengths of connections between all cortical layers, the model was fitted to these CSD signals. The results show that the pattern of effective interactions is strongly influenced by the pattern of strengths of the anatomical connections; however, these two patterns are not identical. The estimated anatomically-constrained effective connectivity matrix and the anatomical connectivity matrix shared five of their six strongest connections, although rankings according to connection strength differed. The strongest effective connections were from excitatory neurons in layer 4 to excitatory neurons in layer 2/3. Our study shows the feasibility of estimating anatomically-constrained effective connectivity within a cortical column, and indicates that there is a strong influence of anatomical connectivity on effective connectivity between cortical layers.

We analyze the neurodynamics attributed by a model proposed by Wendling and co-workers (2002) [Wendling, F., Bartolomei, F., Bellanger, J.J. & Chauvel, P. (2002) Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur. J. Neurosci., 15, 1499.] to explain several different types of electroencephalographic activities. We could find three principal types of steady states when the system parameters change slowly: (i) the model produce a constant output when it is under a state of stable equilibrium point with a constant input. If a small perturbation is introduced (e.g., noisy input), the output changes into noise without oscillatory components, which is related to the normal background activity or low-voltage rapid activity, (ii) Hopf bifurcations lead to stable limit cycles, which we call Hopf cycles. The model generates a rhythmic oscillating output when it is under a state of Hopf cycles, which is related to slow rhythmic activity or slow quasi-sinusoidal activity, (iii) global bifurcations lead to homoclinic limit cycles that appear suddenly at high amplitude, which we call spike cycles. In general, the spike cycles are not harmonic but they have a spike-like appearance (anharmonic oscillation). The model produces a spike-like output when it is under a state of spike cycles, which is related to the sustained discharge of spikes. Finally, the bifurcation analysis demonstrates the influence of the interaction between the excitatory and inhibitory synaptic gains on the dynamics.

Deterministic and stochastic methods for online state and parameter estimation for neural mass models are presented and applied to synthetic and real seizure electrocorticographic signals in order to determine underlying brain changes that cannot easily be measured. The first ever online estimation of neural mass model parameters from real seizure data is presented. It is shown that parameter changes occur that are consistent with expected brain changes underlying seizures, such as increases in postsynaptic potential amplitudes, increases in the inhibitory postsynaptic time-constant and decreases in the firing threshold at seizure onset, as well as increases in the firing threshold as the seizure progresses towards termination. In addition, the deterministic and stochastic estimation methods are compared and contrasted. This work represents an important foundation for the development of biologically-inspired methods to image underlying brain changes and to develop improved methods for neurological monitoring, control and treatment.