A Hodgkin

B Cazelles

CR Laing

DR Chialvo

EM Izhikevich

JL Hindmarsh

JM Beggs

M Copelli

Marcelo HR Tragtenberg

Mauricio Girardi-Schappo

NF Rulkov

O Kinouchi

Osame Kinouchi

SM Kuva

TL Ribeiro

V Priesemann

BMC Neuroscience

English

PubMed

Springer - Publisher Connector

POSTER PRESENTATION Open Access
Signal propagation and neuronal avalanches
analysis in networks of formal neurons
Mauricio Girardi-Schappo1*, Marcelo HR Tragtenberg1, Osame Kinouchi2
From Twentieth Annual Computational Neuroscience Meeting: CNS*2011
Stockholm, Sweden. 23-28 July 2011
To study neurons with computational tools, one may
call upon, at least, two different approaches: (i) Hodg-
kin-Huxley like neurons [1] (i.e. biological neurons) and
(ii) formal neurons (e.g. Hindmarsh-Rose (HR) model
[2], Kinouchi-Tragtenberg (KT) model [3], etc). Formal
neurons may be represented by ordinary differential
equations (e.g. HR), or by maps, which are dynamical
systems with continuous state variables and discrete
time dynamics (e.g. KT). A few maps had been proposed
to describe neurons [3-10]. Such maps provide one with
a number of computational advantages [10], since there
is no need to set any precision on the integration vari-
able, which leads to better performance in the
calculations.
An extended KT neuron model, here called KTz
model, has been studied in [4] and [5], may be supplied
with a Chemical Synapse Map (CSM) in order to study
interacting neurons in a lattice, in the framework of
coupled map lattices. KTz model presents most of the
standard behavior of excitable cells like fast spiking, reg-
ular spiking, bursting, plateau action potentials and
adaptation phenomena, and the CSM is in good agree-
ment with some standard functions used to model post-
synaptic currents, like the alpha function or the double-
exponential function [4]. Preliminary results indicate
antiferromagnetic oscillatory behavior or plane wave
behavior in KTz neurons coupled with inhibitory CSM
on a square lattice.
Besides, many systems in nature are characterized by
complex behavior where large cascades of events,
named avalanches, unpredictably alternate with periods
of little activity (e.g. snow avalanches, earthquakes, etc).
Avalanches are described by power law distributions
and when the branching parameter equals to unity, the
system is said to be a self-organized critical (SOC) sys-
tem [13]. These have been observed for neuronal activity
in vitro [11,12]. And since both SOC systems and neu-
ronal activity show large variability, long-term stability
and memory capabilities, networks of neurons have
been proposed to be SOC systems. This hypothesis was
tested in [13], where they made comparisons among in
vivo recordings using Local Field Potentials in three
macaque monkeys performing a short term memory
task and three different well-established subsampled
SOC models (e.g. Sandpile model, Random Neighbour
Sandpile model and Forest Fire model). Some similar
comparison has been done in [14] with in vivo data
from fourteen rats and a cellular automaton developed
by the authors.
We claim that still no simulation has been made to
detect whether formal or realistic neuron models can
evolve naturally to a SOC state, in a full or subsampled
network. Our simulations are made with KTz model,
which is a formal neuron, but keeps the usual behaviors
of living cells, connected through CSM on a square lat-
tice. We divided the work into two parts: (i) the analysis
of network itself and how it evolves with time from a
given initial state, varying its parameters and (ii) the
analysis of the data generated by a network of silent
cells, stimulated at random sites, trying to resemble the
SOC models above. We compare these second part
results with the experimental ones presented in [11-13].
Author details
1Departamento de Física, Universidade Federal de Santa Catarina,
Florianópolis, SC, 88040-970, Brazil. 2Faculdade de Filosofia, Ciências e Letras
de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, SP, Brazil.
Published: 18 July 2011* Correspondence: girardi.s@gmail.com
1Departamento de Física, Universidade Federal de Santa Catarina,
Florianópolis, SC, 88040-970, Brazil
Full list of author information is available at the end of the article
Girardi-Schappo et al. BMC Neuroscience 2011, 12(Suppl 1):P172
http://www.biomedcentral.com/1471-2202/12/S1/P172
© 2011 Girardi-Schappo et al; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
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doi:10.1186/1471-2202-12-S1-P172
Cite this article as: Girardi-Schappo et al.: Signal propagation and
neuronal avalanches analysis in networks of formal neurons. BMC
Neuroscience 2011 12(Suppl 1):P172.
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Page 2 of 2


Signal propagation and neuronal avalanches analysis in networks of formal neurons

Crossref

AC: A minimal model for excitable and bursting elements. Neurocomputing

Anti-phase regularization. Europhys Lett

Generic excitable dynamics on a two-dimensional map. Chaos Solit Fract

Hoppensteadt F: Classification of bursting mappings.

Huxley A: A quantitative description of membrane current.

Longtin A: A two variable model of somaticdendritic interactions.

Modeling of spiking-bursting neuronal behavior using twodimensional map. Phys Rev E

Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures.

Plenz D: Neuronal avalanches in neocortical circuits.

RM: A model of neuronal bursting.

Stability diagrams for bursting neurons. Physica A

Subsampling effects in neuronal avalanche.

Tragtenberg MHR: Modeling neurons by simple maps.

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Signal propagation and neuronal avalanches analysis in networks of formal neurons

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