Assimilating Seizure Dynamics

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.Author Summary: To understand a complex system such as the weather or the brain, one needs an exhaustive detailing of the system variables and parameters. But such systems are vastly undersampled from existing technology. The alternative is to employ realistic computational models of the system dynamics to reconstruct the unobserved features. This model based state estimation is referred to as data assimilation. Modern robotics use data assimilation as the recursive predictive strategy that underlies the autonomous control performance of aerospace and terrestrial applications. We here adapt such data assimilation techniques to a computational model of the interplay of excitatory and inhibitory neurons during epileptic seizures. We show that incorporating lower scale metabolic models of potassium dynamics is essential for accuracy. We apply our strategy using data from simultaneous dual intracellular impalements of inhibitory and excitatory neurons. Our findings are, to our knowledge, the first validation of such data assimilation in neuronal dynamics.