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Absence epilepsy is characterized by a sudden paroxysmal loss of consciousness accompanied by oscillatory activity propagating over many brain areas. Although primary generalized absence seizures are supported by the global corticothalamic system, converging experimental evidence supports a focal theory of absence epilepsy. Here a physiology-based corticothalamic model is investigated with spatial heterogeneity due to focal epilepsy to unify global and focal aspects of absence epilepsy. Numeric and analytic calculations are employed to investigate the emergent spatiotemporal dynamics as well as their underlying dynamical mechanisms. They can be categorized into three scenarios: suppressed epilepsy, focal seizures, or generalized seizures, as summarized from a phase diagram vs focal width and characteristic axon range. The corresponding temporal frequencies and spatial extents of cortical waves in generalized seizures and focal seizures agree well with experimental observations of global and focal aspects of absence epilepsy, respectively. The emergence of the spatiotemporal dynamics corresponding to focal seizures provides a biophysical explanation of the temporally higher frequency but spatially more localized cortical waves observed in genetic rat models that display characteristics of human absence epilepsy. Predictions are also presented for further experimental test.

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.