Abstracts

Rationale: It is widely accepted that epilepsies are complex syndromes, due to their multi-factorial cellular origins and their intricate behavioral and electrophysiological manifestations. These qualitative and intuitive appreciations are consistent with different mathematical and computational descriptions of these diseases. We can divide these theoretical approaches in two major categories: stochastic and deterministic. Both approaches can help understand the manifold underlying characteristics of epilepsy. Here we present two models, each based on one of these approaches, which shed light on the quantitative aspects of the complexity inherent to epilepsy. Methods: For the stochastic approach, we used flowchart and graph theory to characterize the neuroethological and functional neuroimaging manifestations of seizures in temporal-lobe epileptic patients. Analyzed variables were the duration, frequency and interactions of observed behaviors and the intensity and localization of brain SPECT signals. For the deterministic method, we used a compartment model that reproduced specific membrane features, in this case the electrophysiological properties of newborn dentate gyrus granular cells after pilocarpine-induced status epilepticus. Results: The stochastic analysis, an up-down approach, was used to establish indexes that allowed to characterize seizures, and identify important factors related with the neural substrates of the epileptic seizures, including the anatomical epileptogenic zone and recruited spread pathways. The bottom-up deterministic approach demonstrated how subtle changes in the form and function of specific cells affect network responses to exogenous stimulation. At the same time, we evaluated possible effects produced by different changes that have not yet been observed in experimental conditions, but that are plausible to occur. Conclusions: While both models offer insights into epilepsy, integration of our results with the current literature is challenging. Considering this, we point out the necessity of a common framework for analyzing and modeling pathophysiological phenomena in the context of epilepsy research. For stochastic techniques, we propose graph theory as a potential common frame of reference, due to its wide user base and relatively simple mathematical foundation. There are currently various open source software projects that can be adapted for the graphical representation of multiple variables and thus be applied to this purpose. Finding a common framework for deterministic modeling is much more challenging, as current models are being constructed under a huge variety of theoretical guidelines and computational languages. At the very least, we encourage the publication of the code behind each model in an open online database and the usage, as far as possible, of open source software, which will permit the development of global standards and potentially offer a common theoretical structure for the sharing and combination of models. Financial support: FAPESP, FAPESP-Cinapce, PROEX-CAPES, CNPQ and FAEPA.