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Borges RR, Borges FS, Lameu EL, Batista AM, Iarosz KC, Caldas IL, Antonopoulos CG, Baptista MS. Spike timing-dependent plasticity induces non-trivial topology in the brain. Neural Netw 2017; 88:58-64. [PMID: 28189840 DOI: 10.1016/j.neunet.2017.01.010] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Revised: 01/14/2017] [Accepted: 01/24/2017] [Indexed: 10/20/2022]
Abstract
We study the capacity of Hodgkin-Huxley neuron in a network to change temporarily or permanently their connections and behavior, the so called spike timing-dependent plasticity (STDP), as a function of their synchronous behavior. We consider STDP of excitatory and inhibitory synapses driven by Hebbian rules. We show that the final state of networks evolved by a STDP depend on the initial network configuration. Specifically, an initial all-to-all topology evolves to a complex topology. Moreover, external perturbations can induce co-existence of clusters, those whose neurons are synchronous and those whose neurons are desynchronous. This work reveals that STDP based on Hebbian rules leads to a change in the direction of the synapses between high and low frequency neurons, and therefore, Hebbian learning can be explained in terms of preferential attachment between these two diverse communities of neurons, those with low-frequency spiking neurons, and those with higher-frequency spiking neurons.
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Affiliation(s)
- R R Borges
- Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil; Departamento de Matemática, Universidade Tecnológica Federal do Paraná, 86812-460, Apucarana, PR, Brazil
| | - F S Borges
- Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil
| | - E L Lameu
- Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil
| | - A M Batista
- Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil; Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil; Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil.
| | - K C Iarosz
- Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil
| | - I L Caldas
- Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil
| | - C G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, UK
| | - M S Baptista
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, SUPA, Aberdeen, UK
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Popovych OV, Tass PA. Control of abnormal synchronization in neurological disorders. Front Neurol 2014; 5:268. [PMID: 25566174 PMCID: PMC4267271 DOI: 10.3389/fneur.2014.00268] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2014] [Accepted: 11/28/2014] [Indexed: 11/13/2022] Open
Abstract
In the nervous system, synchronization processes play an important role, e.g., in the context of information processing and motor control. However, pathological, excessive synchronization may strongly impair brain function and is a hallmark of several neurological disorders. This focused review addresses the question of how an abnormal neuronal synchronization can specifically be counteracted by invasive and non-invasive brain stimulation as, for instance, by deep brain stimulation for the treatment of Parkinson’s disease, or by acoustic stimulation for the treatment of tinnitus. On the example of coordinated reset (CR) neuromodulation, we illustrate how insights into the dynamics of complex systems contribute to successful model-based approaches, which use methods from synergetics, non-linear dynamics, and statistical physics, for the development of novel therapies for normalization of brain function and synaptic connectivity. Based on the intrinsic multistability of the neuronal populations induced by spike timing-dependent plasticity (STDP), CR neuromodulation utilizes the mutual interdependence between synaptic connectivity and dynamics of the neuronal networks in order to restore more physiological patterns of connectivity via desynchronization of neuronal activity. The very goal is to shift the neuronal population by stimulation from an abnormally coupled and synchronized state to a desynchronized regime with normalized synaptic connectivity, which significantly outlasts the stimulation cessation, so that long-lasting therapeutic effects can be achieved.
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Affiliation(s)
- Oleksandr V Popovych
- Institute of Neuroscience and Medicine - Neuromodulation, Jülich Research Center , Jülich , Germany
| | - Peter A Tass
- Institute of Neuroscience and Medicine - Neuromodulation, Jülich Research Center , Jülich , Germany ; Department of Neurosurgery, Stanford University , Stanford, CA , USA ; Department of Neuromodulation, University of Cologne , Cologne , Germany
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Kalitzin S, Lopes da Silva F. Predicting the unpredictable: The challenge or mirage of seizure prediction? Clin Neurophysiol 2014; 125:1930-1. [DOI: 10.1016/j.clinph.2014.02.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2014] [Revised: 02/24/2014] [Accepted: 02/24/2014] [Indexed: 11/25/2022]
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KALITZIN STILIYAN, KOPPERT MARCUS, PETKOV GEORGE, DA SILVA FERNANDOLOPES. MULTIPLE OSCILLATORY STATES IN MODELS OF COLLECTIVE NEURONAL DYNAMICS. Int J Neural Syst 2014; 24:1450020. [DOI: 10.1142/s0129065714500208] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In our previous studies, we showed that the both realistic and analytical computational models of neural dynamics can display multiple sustained states (attractors) for the same values of model parameters. Some of these states can represent normal activity while other, of oscillatory nature, may represent epileptic types of activity. We also showed that a simplified, analytical model can mimic this type of behavior and can be used instead of the realistic model for large scale simulations. The primary objective of the present work is to further explore the phenomenon of multiple stable states, co-existing in the same operational model, or phase space, in systems consisting of large number of interconnected basic units. As a second goal, we aim to specify the optimal method for state control of the system based on inducing state transitions using appropriate external stimulus. We use here interconnected model units that represent the behavior of neuronal populations as an effective dynamic system. The model unit is an analytical model (S. Kalitzin et al., Epilepsy Behav. 22 (2011) S102–S109) and does not correspond directly to realistic neuronal processes (excitatory–inhibitory synaptic interactions, action potential generation). For certain parameter choices however it displays bistable dynamics imitating the behavior of realistic neural mass models. To analyze the collective behavior of the system we applied phase synchronization analysis (PSA), principal component analysis (PCA) and stability analysis using Lyapunov exponent (LE) estimation. We obtained a large variety of stable states with different dynamic characteristics, oscillatory modes and phase relations between the units. These states can be initiated by appropriate initial conditions; transitions between them can be induced stochastically by fluctuating variables (noise) or by specific inputs. We propose a method for optimal reactive control, allowing forced transitions from one state (attractor) into another.
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Affiliation(s)
- STILIYAN KALITZIN
- Foundation Epilepsy Institute in The Netherlands (SEIN), Achterweg 5, Heemstede, The Netherlands
| | - MARCUS KOPPERT
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon EX4 4QF, UK
| | - GEORGE PETKOV
- Foundation Epilepsy Institute in The Netherlands (SEIN), Achterweg 5, Heemstede, The Netherlands
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon EX4 4QF, UK
| | - FERNANDO LOPES DA SILVA
- Swammerdam Institute for Life Sciences, Center of Neuroscience, University of Amsterdam, Amsterdam, The Netherlands
- Department of Bioengineering, Instituto Superior Técnico, Lisbon Technical University, Lisbon, Portugal
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Wu JJS, Chang WP, Shih HC, Yen CT, Shyu BC. Cingulate seizure-like activity reveals neuronal avalanche regulated by network excitability and thalamic inputs. BMC Neurosci 2014; 15:3. [PMID: 24387299 PMCID: PMC3893465 DOI: 10.1186/1471-2202-15-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Accepted: 12/30/2013] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Cortical neurons display network-level dynamics with unique spatiotemporal patterns that construct the backbone of processing information signals and contribute to higher functions. Recent years have seen a wealth of research on the characteristics of neuronal networks that are sufficient conditions to activate or cease network functions. Local field potentials (LFPs) exhibit a scale-free and unique event size distribution (i.e., a neuronal avalanche) that has been proven in the cortex across species, including mice, rats, and humans, and may be used as an index of cortical excitability. In the present study, we induced seizure activity in the anterior cingulate cortex (ACC) with medial thalamic inputs and evaluated the impact of cortical excitability and thalamic inputs on network-level dynamics. We measured LFPs from multi-electrode recordings in mouse cortical slices and isoflurane-anesthetized rats. RESULTS The ACC activity exhibited a neuronal avalanche with regard to avalanche size distribution, and the slope of the power-law distribution of the neuronal avalanche reflected network excitability in vitro and in vivo. We found that the slope of the neuronal avalanche in seizure-like activity significantly correlated with cortical excitability induced by γ-aminobutyric acid system manipulation. The thalamic inputs desynchronized cingulate seizures and affected the level of cortical excitability, the modulation of which could be determined by the slope of the avalanche size. CONCLUSIONS We propose that the neuronal avalanche may be a tool for analyzing cortical activity through LFPs to determine alterations in network dynamics.
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Affiliation(s)
| | | | | | | | - Bai Chuang Shyu
- Institute of Biomedical Sciences, Academia Sinica, Taipei 11529, Taiwan.
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KOPPERT MARC, KALITZIN STILIYAN, VELIS DEMETRIOS, DA SILVA FERNANDOLOPES, VIERGEVER MAXA. REACTIVE CONTROL OF EPILEPTIFORM DISCHARGES IN REALISTIC COMPUTATIONAL NEURONAL MODELS WITH BISTABILITY. Int J Neural Syst 2012; 23:1250032. [DOI: 10.1142/s0129065712500323] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We aim to derive fully autonomous seizure suppression paradigms based on reactive control of neuronal dynamics. A previously derived computational model of seizure generation describing collective degrees of freedom and featuring bistable dynamics is used. A novel technique for real-time control of epileptogenicity is introduced. The reactive control reduces practically all seizures in the model. The study indicates which parameters provide the maximal seizure reduction with minimal intervention. An adaptive scheme is proposed that optimizes the stimulation parameters in nonstationary situations.
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Affiliation(s)
- MARC KOPPERT
- Stichting Epilepsie Instellingen Nederland, Achterweg 5, 2103 SW Heemstede, The Netherlands
| | - STILIYAN KALITZIN
- Stichting Epilepsie Instellingen Nederland, Achterweg 5, 2103 SW Heemstede, The Netherlands
| | - DEMETRIOS VELIS
- Stichting Epilepsie Instellingen Nederland, Achterweg 5, 2103 SW Heemstede, The Netherlands
- Department of Neurosurgery, Free University Medical Centre (VUmc), De Boelelaan 1117, 1081 HV Amsterdam, The Netherlands
| | - FERNANDO LOPES DA SILVA
- Swammerdam Institute for Life Sciences, University of Amsterdam, 1098 SM Amsterdam, The Netherlands
- Department Bioengineering, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal
| | - MAX A. VIERGEVER
- Image Sciences Institute, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht, The Netherlands
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Chakravarthy N, Sabesan S, Iasemidis L, Tsakalis K. CONTROLLING SYNCHRONIZATION IN A NEURON-LEVEL POPULATION MODEL. Int J Neural Syst 2011; 17:123-38. [PMID: 17565508 DOI: 10.1142/s0129065707000993] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We have studied coupled neural populations in an effort to understand basic mechanisms that maintain their normal synchronization level despite changes in the inter-population coupling levels. Towards this goal, we have incorporated coupling and internal feedback structures in a neuron-level population model from the literature. We study two forms of internal feedback — regulation of excitation, and compensation of excessive excitation with inhibition. We show that normal feedback actions quickly regulate/compensate an abnormally high coupling between the neural populations, whereas a pathology in these feedback actions can lead to abnormal synchronization and "seizure"-like high amplitude oscillations. We then develop an external control paradigm, termed feedback decoupling, as a robust synchronization control strategy. The external feedback decoupling controller acts to achieve the operational objective of maintaining normal-level synchronous behavior irrespective of the pathology in the internal feedback mechanisms. Results from such an analysis have an interesting physical interpretation and specific implications for the treatment of diseases such as epilepsy. The proposed remedy is consistent with a variety of recent observations in the human and animal epileptic brain, and with theories from nonlinear systems, adaptive systems, optimization, and neurophysiology.
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Koppert MMJ, Kalitzin S, Lopes da Silva FH, Viergever MA. Plasticity-modulated seizure dynamics for seizure termination in realistic neuronal models. J Neural Eng 2011; 8:046027. [DOI: 10.1088/1741-2560/8/4/046027] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Connor D, Shanahan M. A computational model of a global neuronal workspace with stochastic connections. Neural Netw 2010; 23:1139-54. [DOI: 10.1016/j.neunet.2010.07.005] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2008] [Revised: 07/09/2010] [Accepted: 07/12/2010] [Indexed: 10/19/2022]
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Kalitzin SN, Velis DN, da Silva FHL. Stimulation-based anticipation and control of state transitions in the epileptic brain. Epilepsy Behav 2010; 17:310-23. [PMID: 20163993 DOI: 10.1016/j.yebeh.2009.12.023] [Citation(s) in RCA: 73] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/25/2009] [Accepted: 12/28/2009] [Indexed: 12/01/2022]
Abstract
We focus on the implications that the underlying neuronal dynamics might have on the possibility of anticipating seizures and designing an effective paradigm for their control. Transitions into seizures can be caused by parameter changes in the dynamic state or by interstate transitions as occur in multi-attractor systems; in the latter case, only a weak statistical prognosis of the seizure risk can be achieved. Nevertheless, we claim that by applying a suitable perturbation to the system, such as electrical stimulation, relevant features of the system's state may be detected and the risk of an impending seizure estimated. Furthermore, if these features are detected early, transitions into seizures may be blocked. On the basis of generic and realistic computer models we explore the concept of acute seizure control through state-dependent feedback stimulation. We show that in some classes of dynamic transitions, this can be achieved with a relatively limited amount of stimulation.
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Affiliation(s)
- Stiliyan N Kalitzin
- Medical Physics Department, Epilepsy Institute of The Netherlands Foundation (SEIN), Heemstede, The Netherlands.
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Rutishauser U, Douglas RJ. State-dependent computation using coupled recurrent networks. Neural Comput 2009; 21:478-509. [PMID: 19431267 DOI: 10.1162/neco.2008.03-08-734] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Although conditional branching between possible behavioral states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem, we demonstrate by theoretical analysis and simulation how networks of richly interconnected neurons, such as those observed in the superficial layers of the neocortex, can embed reliable, robust finite state machines. We show how a multistable neuronal network containing a number of states can be created very simply by coupling two recurrent networks whose synaptic weights have been configured for soft winner-take-all (sWTA) performance. These two sWTAs have simple, homogeneous, locally recurrent connectivity except for a small fraction of recurrent cross-connections between them, which are used to embed the required states. This coupling between the maps allows the network to continue to express the current state even after the input that elicited that state is withdrawn. In addition, a small number of transition neurons implement the necessary input-driven transitions between the embedded states. We provide simple rules to systematically design and construct neuronal state machines of this kind. The significance of our finding is that it offers a method whereby the cortex could construct networks supporting a broad range of sophisticated processing by applying only small specializations to the same generic neuronal circuit.
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Affiliation(s)
- Ueli Rutishauser
- Computation and Neural Systems, California Institute of Technology, Pasadena, CA 91225, USA.
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Hsu D, Tang A, Hsu M, Beggs JM. Simple spontaneously active Hebbian learning model: homeostasis of activity and connectivity, and consequences for learning and epileptogenesis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:041909. [PMID: 17995028 DOI: 10.1103/physreve.76.041909] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2007] [Revised: 08/13/2007] [Indexed: 05/25/2023]
Abstract
A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that connectivity is maintained at a state that is optimal for information transmission and storage. This state is referred to as the critical state. We present a simple stochastic computational Hebbian learning model that incorporates both firing rate and critical homeostasis, and we explore its stability and connectivity properties. We also examine the behavior of our model with a simulated seizure and with simulated acute deafferentation. We argue that a neural system that is more highly connected than the critical state (i.e., one that is "supercritical") is epileptogenic. Based on our simulations, we predict that the postseizural and postdeafferentation states should be supercritical and epileptogenic. Furthermore, interventions that boost spontaneous activity should be protective against epileptogenesis.
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Affiliation(s)
- David Hsu
- Department of Neurology, University of Wisconsin, Madison, Wisconsin 53792, USA.
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Smolen P. A model of late long-term potentiation simulates aspects of memory maintenance. PLoS One 2007; 2:e445. [PMID: 17505541 PMCID: PMC1865388 DOI: 10.1371/journal.pone.0000445] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2007] [Accepted: 04/25/2007] [Indexed: 11/21/2022] Open
Abstract
Late long-term potentiation (L-LTP) denotes long-lasting strengthening of synapses between neurons. L-LTP appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing ongoing activity and biochemical pathways important for L-LTP. In this study, ongoing activity was incorporated into two such models – a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction simply and intuitively, and the detailed model adds activation of essential kinases by Ca2+. Ongoing activity was modeled as continual brief elevations of Ca2+. In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca2+ transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low basal weight to a high weight that is stabilized by ongoing activity. Bistability was robust to parameter variations in both models. Simulations illustrated that prolonged periods of decreased activity reset synaptic strengths to low values, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength. Further investigations that examine the dynamics of activity and synaptic maintenance can be expected to help in understanding how memories are preserved for up to a lifetime in animals including humans.
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Affiliation(s)
- Paul Smolen
- Department of Neurobiology and Anatomy, W.M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas Medical School at Houston, Houston, Texas, United States of America.
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Ohayon EL, Kalitzin S, Suffczynski P, Jin FY, Tsang PW, Borrett DS, Burnham WM, Kwan HC. Charting epilepsy by searching for intelligence in network space with the help of evolving autonomous agents. ACTA ACUST UNITED AC 2005; 98:507-29. [PMID: 16290117 DOI: 10.1016/j.jphysparis.2005.09.018] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The problem of demarcating neural network space is formidable. A simple fully connected recurrent network of five units (binary activations, synaptic weight resolution of 10) has 3.2 *10(26) possible initial states. The problem increases drastically with scaling. Here we consider three complementary approaches to help direct the exploration to distinguish epileptic from healthy networks. [1] First, we perform a gross mapping of the space of five-unit continuous recurrent networks using randomized weights and initial activations. The majority of weight patterns (>70%) were found to result in neural assemblies exhibiting periodic limit-cycle oscillatory behavior. [2] Next we examine the activation space of non-periodic networks demonstrating that the emergence of paroxysmal activity does not require changes in connectivity. [3] The next challenge is to focus the search of network space to identify networks with more complex dynamics. Here we rely on a major available indicator critical to clinical assessment but largely ignored by epilepsy modelers, namely: behavioral states. To this end, we connected the above network layout to an external robot in which interactive states were evolved. The first random generation showed a distribution in line with approach [1]. That is, the predominate phenotypes were fixed-point or oscillatory with seizure-like motor output. As evolution progressed the profile changed markedly. Within 20 generations the entire population was able to navigate a simple environment with all individuals exhibiting multiply-stable behaviors with no cases of default locked limit-cycle oscillatory motor behavior. The resultant population may thus afford us a view of the architectural principles demarcating healthy biological networks from the pathological. The approach has an advantage over other epilepsy modeling techniques in providing a way to clarify whether observed dynamics or suggested therapies are pointing to computational viability or dead space.
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Affiliation(s)
- Elan L Ohayon
- University of Toronto Epilepsy Research Program, Institute of Medical Science, Medical Sciences Building, University of Toronto, Ont., Canada.
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