Julian Tejada

The epilepsies: Complex challenges needing complex solutions

It is widely accepted that epilepsies are complex syndromes due to their multi-factorial origins and manifestations. Different mathematical and computational descriptions use appropriate methods to address nonlinear relationships, chaotic behaviors and emergent properties. These theoretical approaches can be divided into two major categories: descriptive, such as flowcharts, graphs and other statistical analyses, and explicative, which include both realistic and abstract models. Although these modeling tools have brought great advances, a common framework to guide their design, implementation and evaluation, with the goal of future integration, is still needed. In the current review, we discuss two examples of complexity analysis that can be performed with epilepsy data: behavioral sequences of temporal lobe seizures and alterations in an experimental cellular model. We also highlight the importance of the creation of model repositories for the epileptology field and encourage the development of mathematical descriptions of complex systems, together with more accurate simulation techniques.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains.

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal. It consists of a plus-shaped maze with two open and two closed arms elevated 50cm from the floor. The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms. In this work, we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions: normal and under the effects of anxiogenic and anxiolytic drugs. The spatial structure of the elevated plus-maze is divided into squares, which are associated with states of a Markov chain. By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze, we constructed stochastic matrices for the three conditions studied. The stochastic matrices show specific patterns, which correspond to the observed behaviors of the rat under the three different conditions. For the control group, the stochastic matrix shows a clear preference for places in the closed arms. This preference is enhanced for the anxiogenic group. For the anxiolytic group, the stochastic matrix shows a pattern similar to a random walk. Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze.

Mathematical methods to model rodent behavior in the elevated plus-maze

The elevated plus maze is a widely used experimental test to study anxiety-like rodent behavior. It is made of four arms, two open and two closed, connected at a central area forming a plus shaped maze. The whole apparatus is elevated 50 cm from the floor. The anxiety of the animal is usually assessed by the number of entries and duration of stay in each arm type during a 5-min period. Different mathematical methods have been proposed to model the mechanisms that control the animal behavior in the maze, such as factor analysis, statistical inference on Markov chains and computational modeling. In this review we discuss these methods and propose possible extensions of them as a direction for future research.

Use of Evolutionary Robots as an Auxiliary Tool for Developing Behavioral Models of Rats in an Elevated Plus-Maze

This work proposes the use of evolutionary robots as an auxiliary tool for the development of models to describe rats’ behavior. Evolutionary robots can be useful to test hypothesis and models of behavior, what is demonstrated here in experiments where a mobile robot is trained to reproduce the behavior of the rat in an elevated plus-maze (EPM). A recurrent Elman multilayer perceptron is used to control the robot. Due to the impossibility of knowing each desired output of the neural network, the weight optimization is made by a genetic algorithm. In this way, each individual of the genetic algorithm represents a set of weights of the neural network. Experiments where the fitness of each individual was computed based on the difference between the trajectories of the evolutionary robot on a EPM replica and of the rats behavior on a real EPM are presented.

Computational models of dentate gyrus with epilepsy-induced morphological alterations in granule cells

Temporal lobe epilepsy provokes a number of different morphological alterations in granule cells of the hippocampus dentate gyrus. These alterations may be associated with the hyperactivity and hypersynchrony found in the epileptic dentate gyrus, and their study requires the use of different kinds of approaches including computational modeling. Conductance-based models of both normal and epilepsy-induced morphologically altered granule cells have been used in the construction of network models of dentate gyrus to study the effects of these alterations on epilepsy. Here, we review these models and discuss their contributions to the understanding of the association between alterations in neuronal morphology and epilepsy in the dentate gyrus.

Role of morphological changes in newly born granule cells of hippocampus after status epilepticus induced by pilocarpine in hyperexcitability

Newly born dentate gyrus (DG) granule cells (GCs) after Status Epilecticus induced by pilocarpine (PILO) exhibit morphological changes including narrower arborizations, greater number of branches and more endings in the inner molecular layer (IML) [1]. The increased concentration of dendrites in the IML where granule cell axons (mossy fibers) sprout in epileptic animals and make extensive recurrent excitatory synapses may contribute to enhance the DG hyperexcitability. A previous DG network model has shown that mossy fiber sprouting has a crucial role on hyperexcitability with only 10% sprouting being enough to generate spread of activity to all GCs in the network [2]. However, the additional effect of GC morphological changes on DG hyperexcitability is as yet unknown. Here we used the DG model [2] to evaluate the effect of different GC morphologies on the network activity. We replaced all reduced GC models of [2] with morphologically detailed models coming from tridimensional reconstructions of newly born doublecortin-positive DG GCs [1]. The scheme of the network connections is shown in Figure ​Figure1A.1A. Our sample of morphologically reconstructed GCs includes 20 from PILO-treated rats and 20 from control rats. Our cell models were constructed in NEURON and their ionic channels and maximum conductance distributions were the same as [2] taking into consideration the shorter arborizations of the PILO-treated cells. Our “control” network model is exactly the same as the topographic ring network of [2] with 10% sprouting available in ModelDB with the 500 original GC models replaced by morphologically reconstructed cells randomly chosen from our control sample. From our control network model we constructed two other models: one with 10% of the GCs (chosen randomly) replaced by cells chosen randomly from our PILO-treated sample and the other with the fraction of PILO-treated GC cells increased to 50%. The networks were submitted to focal perforant-path stimulations as in [2] and to obtain averages we ran 100 simulations for each network (connections between cells were created anew before each run). Our control network model produced a response similar to the one of the original model [2], showing that the insertion of GCs with realistic morphologies did not affect the 10% sprouting DG hyperexcitability (Figure 1 B, 100% C). In contrast, when a few amount of PILO-treated GCs were inserted the excitability of the network increased (Figure ​(Figure1B1B , 90% C – 10% P) and the increase was higher when the amount of PILO-treated GCs was larger (Figure 1 B, 50% C – 50% P). However, the effect of the insertion of PILO-treated GCs was only visible in combination with mossy fiber sprouting. Our results suggest that changes in GC morphology alone are not enough to affect the DG hyperexcitability but when these changes occur in the presence of other alterations such as mossy fiber sprouting they could enhance the DG hyperexcitability. Figure 1 Basic circuit diagram and effect of PILO-treated GC morphological changes on the average GCs response. A. Schematic view of the network (adapted from [1]). GC: granule cell; BC: basket cell; HC: HIPP cell; MC: mossy cell. DD: distal dendrites; MD: medial ...

Archetypes and Outliers in the Neuromorphological Space

Neuromorphology has a long history of meticulous analysis and fundamental studies about the intricacies of neuronal shape. These studies converged to a plethora of information describing in detail many neuronal characteristics, as well as comprehensive data about cell localization, animal type, age, among others. Much of this information has notably been compiled through efforts of the Computational Neuroanatomy Group at the Krasnow Institute for Advanced Study, George Mason University, thus originating the NeuroMorpho.org repository, a resource that incorporates a large set of data and related tools. In the current work we present a methodology that can be used to search for novel relationships in cell morphology contained in databases such as the NeuroMorpho.org. More specifically, we try to understand which morphological characteristics can be considered universal for a given cell type, or to what extent we can represent an entire cell class through an archetypal shape. This analysis is done by taking a large number of characteristics from cells into account, and then applying multivariate techniques to analyze the data. The neurons are then classified as archetypes or outliers according to how close they are to the typical shape of the class. We find that granule and medium spiny neurons can be associated with a typical shape, and that different animals and brain regions show distinct distributions of shapes.

A model for the rat exploratory behavior in the elevated plus-maze

Address: 1Department of Psychology and Education, School of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, 14040901 Ribeirão Preto, SP, Brazil, 2Computational and Experimental Neuroplasticity Laboratory, Krasnow Institute, George Mason University, Rockfish Creek Lane, Fairfax, VA 22030-4444, USA, 3Department of Morphology, Stomatology and Physiology, School of Odontology of Ribeirão Preto, University of São Paulo, 14040-901 Ribeirão Preto, SP, Brazil and 4Department of Physics and Mathematics, School of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, 14040-901 Ribeirão Preto, SP, Brazil

A novel anxiety index for the rat behavior in the elevated plus-maze

The elevated plus-maze (EPM) is a widely used anxiety animal model [1]. It consists of a plus-shaped maze elevated 50 cm from the floor. The maze is composed of two open arms and two closed arms crossing at right angles at a central area. The usual anxiety measures are the percentages of open or closed arm entries and the percentages of time spent on open or closed arms [2]. Recently, we have proposed a graph representation of the EPM in which the maze floor is divided into 21 squares that are treated as nodes of a directed graph [3], i.e. transitions between connected nodes can occur in both directions. Using the directed graph representation we have shown that the displacements of the rat in the EPM during a 5 min trial can be well modeled by a first-order homogeneous Markov chain [4]. Moreover, we have shown that the estimated stochastic matrix, which gives the transition probabilities between nodes, is sensitive to the pharmacological condition of the animal, i.e. if it belongs to the control group or was treated with an anxiogenic or anxiolytic drug [4]. The stochastic matrices for the different drug treatment types are interesting to compare different groups of rats but they are not practical as succinct indexes of their anxiety level. Here we propose a new anxiety index for the rat behavior in the EPM based on measures from the stochastic matrix. The stochastic matrices were estimated from the recorded behaviors of 107 rats submitted to the EPM test under different pharmacological conditions. Twenty-five of the rats were control animals, 44 received anxiogenic drugs (pentylenetetrazol, 10, 20, and 30 mg/kg; semicarbazide, 20 mg/kg), and 38 received anxiolytic drugs (midazolam, 1 µg/kg; chlordiazepoxide, 5 mg/kg). From these matrices, the mean number of transitions until the rat reaches for the first time one of the nodes in the open or closed arms, starting from the central node at time 0, is calculated for all graph nodes. These mean values are called average absorption times of the nodes, which can be grouped in different ways. In this work, we considered the ratio of the average absorption time of a closed arm node to the average absorption time of the symmetrical node on the open arm. For high doses of anxiogenic drugs not all graph nodes are reached by the rat. These nodes were discarded from our calculations. Our results show that for each pharmacological condition the ratios determined as explained above are approximately the same for any distance from the center. This invariance suggests that only one of the average absorption time ratios can be used to characterize the pharmacological condition of the animal. Based on this finding we propose that the average absorption time ratio can be used as an additional index to characterize the anxiety-related behavior of the rat in the EPM.