A stimulation-based measurement paradigm is proposed that can provide a biomarker, which we call “separatrix proximity marker”, able to assess how close is a neural system from an epileptic transition. We use a distributed network of potentially multi-stable local systems that can have different levels of susceptibility for transitions to oscillatory states, considered surrogates of epileptic seizures. The simplest computational model of the bistable system is the complex-valued polynomial model, also called z6 model that has been developed by our group. A two-dimensional grid of (9 x 9) z6 units connected with non-linear aperture based interactions is generated for 1000 random sets of parameters, including local parameters and connectivity weights resulting in various degrees of epileptic condition. We investigated an “active” closed-loop protocol where stimulation sequences of increasing amplitudes were delivered to the model system. We found that the separatrix proximity can be used to estimate the relative closeness of the system to the state transition. In this way, our model prescribes a universal biomarker based on the single assumption that the epileptic state is caused by bistable dynamics and does not rely on the specific level of model detail. We also show that the only spatial information needed to do the analysis is the location of the stimulated area and therefore no locally acquired signals are necessary. The findings in this work can be exploited to increase the efficiency and accuracy of pre-surgical epileptogenic zone localisation in cases of focal epileptic seizure onsets or to determine the effective dose and discriminate responsiveness to anti-epileptic drugs.
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