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Reliability of unstable periodic orbit based control strategies in biological systems

Nagender Mishra, Maria Hasse, B. Biswal, Harinder P. Singh
2015 Chaos  
Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos .  ...  A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control  ...  Unstable periodic orbits (UPOs) analysis has now become an established tool for detecting determinism in biological systems.  ... 
doi:10.1063/1.4916899 pmid:25933652 fatcat:od5agrslmzeahcacbou73mu3cu

Periodic Orbits: A New Language for Neuronal Dynamics

Paul So, Joseph T. Francis, Theoden I. Netoff, Bruce J. Gluckman, Steven J. Schiff
1998 Biophysical Journal  
The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs).  ...  UPOs are rigorously identified in data sets representative of three different levels of organization in mammalian brain.  ...  Period-1 UPO extraction from dynamics of neuronal ensemble in a hippocampal slice (8.5 mM [K ϩ ]).  ... 
doi:10.1016/s0006-3495(98)77985-8 pmid:9635732 pmcid:PMC1299619 fatcat:66di5yywdfegjhcazh7bezas2m

Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy

Marc W. Slutzky, Predrag Cvitanovic, David J. Mogul
2001 Annals of Biomedical Engineering  
Epileptiform bursting was induced in transverse rat hippocampal slices using three experimental methods.  ...  The existence of chaos and determinism was assessed using two different analytical techniques: unstable periodic orbit ͑UPO͒ analysis and a new technique for estimating Lyapunov exponents.  ...  We also wish to thank David Ferster for his comments and criticisms in preparing this manuscript. This work was supported by NIH Grant No. NS31764 and the Whitaker Foundation.  ... 
doi:10.1114/1.1380419 pmid:11501625 fatcat:invgfjny5beg3gdrgguxpeh67e

Stochastic neural network model for spontaneous bursting in hippocampal slices

B. Biswal, C. Dasgupta
2002 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
periodic orbits ͑UPOs͒ of systems exhibiting deterministic chaos.  ...  Estimation of the statistical significance of UPOs through surrogate data analysis also leads to results that resemble those of similar analysis of data obtained from slice experiments and human epileptic  ...  significant UPOs in human epileptic activity.  ... 
doi:10.1103/physreve.66.051908 pmid:12513524 fatcat:vtw2svrq3zgpvm5mm3imibna4i

Fiber tract stimulation can reduce epileptiform activity in an in-vitro bilateral hippocampal slice preparation

Sheela Toprani, Dominique M. Durand
2013 Experimental Neurology  
We tested low-frequency stimulation (LFS) of a novel target that enables simultaneous targeting of bilateral hippocampi: the ventral hippocampal commissure (VHC) with a novel in-vitro slice preparation  ...  The goal of this study is to understand the role of hippocampal interplay in seizure propagation and reduction by commissural fiber tract stimulation.  ...  An explanation for this interictal-ictal interplay may be that the interictal events force the hippocampal network to spike at a particular interval or unstable periodic orbit (UPO), thereby making the  ... 
doi:10.1016/j.expneurol.2012.10.022 pmid:23123405 pmcid:PMC3552029 fatcat:ugypkhk2abdxlk4wmvlhg5h2we

The Control of Seizure-Like Activity in the Rat Hippocampal Slice

Houman Khosravani, Peter L. Carlen, Jose L. Perez Velazquez
2003 Biophysical Journal  
This perturbation results in the stabilization of an interictal-like low-frequency firing pattern in the hippocampal slice.  ...  Using an in vitro model of recurrent spontaneous seizures in the rat horizontal hippocampal slice preparation, we present an approach to characterize the dynamics of the transition to seizure, and to use  ...  FIGURE 3 Perturbation of the spontaneous activity in hippocampal slices. Periodic forcing at 0.5 Hz stops the transition to seizure.  ... 
doi:10.1016/s0006-3495(03)74888-7 pmid:12524321 pmcid:PMC1302649 fatcat:fz4vezlf4rerdjg5cva5kevwkm

Controlled transition from chaos to periodic oscillations in a neural network model

Sitabhra Sinha
1996 Physica A: Statistical Mechanics and its Applications  
On imposition of control, transition of the network behavior from chaos to periodicity was observed.  ...  ., during epileptic seizures) as well as a more dynamic interpretation of associative recall performed by neural network models.  ...  [433][434][435][436][437][438][439][440][441][442][443][444][445][446] I am grateful to the organizers of the conference on "Dynamics of Complex Systems" for giving me the opportunity to take part in  ... 
doi:10.1016/0378-4371(95)00328-2 fatcat:whf45adcenghpmfaqhcwpszfjy

An investigation of EEG dynamics in an animal model of temporal lobe epilepsy using the maximum Lyapunov exponent

Sandeep P. Nair, Deng-Shan Shiau, Jose C. Principe, Leonidas D. Iasemidis, Panos M. Pardalos, Wendy M. Norman, Paul R. Carney, Kevin M. Kelly, J. Chris Sackellares
2009 Experimental Neurology  
These results indicate that a rat TLE model demonstrates several important dynamical signal characteristics similar to those found in human TLE and support future use of the model to study epileptic state  ...  Also, the T-index values corresponding to the preictal period were lower than those during the interictal period (p < 0.05).  ...  We confirm that we have read the Journal's position on issues involved in ethical publication and affirm that this report is consistent with those guidelines.  ... 
doi:10.1016/j.expneurol.2008.11.009 pmid:19100262 pmcid:PMC2643305 fatcat:a5bfywyab5h4xgr22r27grpcme

Electrogenic properties of the Na+/K+ ATPase control transitions between normal and pathological brain states

Giri P. Krishnan, Gregory Filatov, Andrey Shilnikov, Maxim Bazhenov
2015 Journal of Neurophysiology  
Abstract 28 29 Ionic concentrations fluctuate significantly during epileptic seizures.  ...  It was suggested that a reduction in the performance of glial Na + /K + pumps 69 would result in dysregulation of the extracellular potassium concentration ([K + ] o ), which in turn 70 leads to seizures  ...  Indeed we found in experiments 638 with mice hippocampal slices that application of the Na + /K + pump antagonist strophanthidin 639 (STDN) to the slice preparation exhibiting recurrent periodic  ... 
doi:10.1152/jn.00460.2014 pmid:25589588 pmcid:PMC4443608 fatcat:75uprahk2fedfb33r5t36jcmlu

Is there chaos in the brain? II. Experimental evidence and related models

Henri Korn, Philippe Faure
2003 Comptes rendus. Biologies  
The second part explores the more recent period during which surrogate-testing, definition of unstable periodic orbits and period-doubling bifurcations have been used to establish more firmly the nonlinear  ...  The first concerns the early attempts by several pioneer authors to demonstrate chaos in experimental material such as the olfactory system or in human recordings during various forms of epilepsies, and  ...  orbits) to (i) single cell and (ii) network burst firing activity recorded in rat hippocampal slices as well as to (iii) digitized human EEG, collected from return maps with a family of period-2 (left  ... 
doi:10.1016/j.crvi.2003.09.011 pmid:14694754 fatcat:5hl2srannrai3pnsie7672puai

Extracellular Potassium Dynamics and Epileptogenesis [chapter]

Flavio Fröhlich, Igor Timofeev, Terrence J. Sejnowski, Maxim Bazhenov
2008 Computational Neuroscience in Epilepsy  
in cats and in human patients with the Lennox-Gastaut syndrome.  ...  In particular, relatively small changes in extracellular potassium concentration ( K + o ) mediate substantial changes in neuronal excitability and intrinsic firing patterns.  ...  Before merging with the unstable fixed point P u in a saddle homoclinic orbit bifurcation at point O 4 , the unstable limit cycle with larger amplitude in the V D dimension becomes stable in a narrow range  ... 
doi:10.1016/b978-012373649-9.50029-6 fatcat:k33mcagnv5fa7fqola55fewnsa

Mitochondria, oxidative stress, and temporal lobe epilepsy

Simon Waldbaum, Manisha Patel
2010 Epilepsy Research  
Although certain inherited epilepsies are associated with mitochondrial dysfunction, little is known about its role in acquired epilepsies such as temporal lobe epilepsy.  ...  of epilepsy increases with age, and mitochondrial oxidative stress is a leading mechanism of aging and age-related degenerative disease, suggesting a further involvement of mitochondrial dysfunction in  ...  hippocampal slices from rats and mice.  ... 
doi:10.1016/j.eplepsyres.2009.09.020 pmid:19850449 pmcid:PMC3236664 fatcat:g7s6rzoznnh3xmatv2ouivp4du

Extracting unstable periodic orbits from chaotic time series data

Paul So, Edward Ott, Tim Sauer, Bruce J. Gluckman, Celso Grebogi, Steven J. Schiff
1997 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
A general nonlinear method to extract unstable periodic orbits from chaotic time series is proposed.  ...  Thus, one can extract unstable periodic orbits from a chaotic time series by simply looking for peaks in a finite grid approximation of the distribution function of the transformed data.  ...  A detailed report on the first identification of periodic orbit structures in the rat hippocampus slice and in electroencephalogram signals from a human epileptic focus will appear in Ref. ͓31͔ .͒  ... 
doi:10.1103/physreve.55.5398 fatcat:limfbdkd5vbylcygyocmlahabe

Modeling Focal Epileptic Activity in the Wilson–Cowan Model with Depolarization Block

Hil G. E. Meijer, Tahra L. Eissa, Bert Kiewiet, Jeremy F. Neuman, Catherine A. Schevon, Ronald G. Emerson, Robert R. Goodman, Guy M. McKhann, Charles J. Marcuccilli, Andrew K. Tryba, Jack D. Cowan, Stephan A. van Gils (+1 others)
2015 Journal of Mathematical Neuroscience  
Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an  ...  We examined the effect of such a saturation in the Wilson-Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function.  ...  This periodic orbit emerges from a Hopf bifurcation H 2 of the symmetric steady state at α ≈ 0.083.  ... 
doi:10.1186/s13408-015-0019-4 pmid:25852982 pmcid:PMC4385301 fatcat:uinaxil5prcuxgycznt5tjf25m

Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a nonlinear model of neuronal dynamics

Michael Breakspear, John R. Terry, Karl J. Friston
2003 Neurocomputing  
We study dynamical synchronization in a model of a neural system constituted by local networks of densely interconnected excitatory and inhibitory neurons.  ...  This may facilitate adaptive brain function by engendering a diverse repertoire of dynamics and contribute to the genesis of complexity in the EEG.  ...  The evolution equations are adapted from a study of epileptic seizures in hippocampal slices [6] consisting of coupled di erential equations, which in turn are derived from the model of Morris and Lecar  ... 
doi:10.1016/s0925-2312(02)00740-3 fatcat:lmsoxgcxqjah7ll4wpyk7fq4de
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