Dissertations / Theses on the topic 'Excitable media'
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Theisen, Bjørn Bjørge. "Waves in Excitable Media." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19373.
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This thesis is dedicated to the study of Barkley's equation, a stiff diffusion-reaction equation describing waves in excitable media. Several numerical solution methods will be derived and studied, range from the simple explicit Euler method to more complex integrating factor schemes. A C++ application with guided user interface created for performing several of the numerical experiments in this thesis will also be described.
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Sailer, Franz-Xaver. "Controlling excitable media with noise." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980114284.
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Armstrong, Gavin Robert. "Chemical waves in excitable media." Thesis, University of Leeds, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427767.
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Courtemanche, Marc. "Reentrant waves in excitable media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186311.
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This dissertation presents a study of instabilities in the propagation of excitation pulses within spatially-distributed models of cardiac reentry. In one-dimensional closed rings, I study the onset of oscillations in the dynamics of circulating pulses as the ring length is decreased. In two-dimensional sheets, I analyze the spontaneous breakup of rotating spiral waves. In both cases, numerical results illustrating the instability phenomena are obtained using simulations of a partial differential equation (PDE) that models cardiac electrical activity using the Beeler-Reuter (BR) equations. The properties of the PDE model are summarized using the restitution and dispersion curves. The restitution curve gives the dependence of the pulse duration on the recovery time, defined as the elapsed time between the onset of an excitation pulse and the end of the previous excitation pulse. The dispersion curve gives the dependence of the pulse speed on the recovery time. I use these two properties to construct simplified models aimed at capturing the essence of the instabilities observed in the PDE. On the ring, I derive an integral-delay equation for the evolution of the recovery time as a function of the distance along the ring that incorporates the restitution and the dispersion curves. Numerical simulations and bifurcation analysis of the delay equation explain and predict the dynamics of the PDE. In two-dimensions, I extend early work that presented the first clear demonstration of spiral wave breakup in a reasonable discretization of a continuous PDE model of cardiac propagation. Spiral breakup can be observed in the BR model, depending on the value of a parameter controlling the duration of the electrical pulses. I study the appearance of spiral wavebreaks and relate it to the change in restitution properties of the BR equations as the parameter is varied. Finally, the effects of restitution and dispersion in two dimensions are examined in a discrete space/continuous time model of cardiac propagation. Results about the dependence of the propagation speed on the excitation threshold and on the excitation front curvature are obtained analytically. Inclusion of restitution relations derived from the BR equations into this simple model can give rise to spiral wavebreaks.
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Weimar, Jörg Richard. "Cellular automata models for excitable media /." This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-03032009-040651/.
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Weimar, Jörg Richard. "Cellular automata models for excitable media." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/41365.
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A cellular automaton is developed for simulating excitable media. First, general "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature" relation with slope given by the predicted diffusion coefficient. The utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation is assessed. Then, a cellular automaton model for wave propagation in reaction diffusion systems is constructed based on these "masks" for the diffusion component and on singular perturbation analysis for the reaction component. The cellular automaton is used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral waves and the movement of the spiral tip are analyzed. By comparing these results to solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient replacement for the standard numerical solution of the PDE's.
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Beato, Valentina. "Noise-induced pattern formation in excitable media." [S.l.] : [s.n.], 2006. http://opus.kobv.de/tuberlin/volltexte/2007/1419.
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Xu, Jinshan. "Dynamics and synchronization in biological excitable media." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00776373.
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This thesis investigates the origin of spontaneous activity in the uterus. This organ does not show any activity until shortly before delivery, where fast and efficient contractions are generated. The aim of this work is to provide insight into the origin of spontaneous oscillations and into the transition from asynchronous to synchronized activity in the pregnant uterus. One intriguing aspect in the uterus is the absence of any pacemaker cell. The organ is composed of muscular cells, which are excitable, and connective cells, whose behavior is purely passive; None of these cells, taken in isolation, spontaneously oscillates. We develop an hypothesis based on the observed strong increase in the electrical coupling between cells in the last days of pregnancy. The study is based on a mathematical model of excitable cells, coupled to each other on a regular lattice, and to a fluctuating number of passive cells, consistent with the known structure of the uterus. The two parameters of the model, the coupling between excitable cells, and between excitable and passive cells, grow during pregnancy.Using both a model based on measured electrophysiological properties, and a generic model of excitable cell, we demonstrate that spontaneous oscillations can appear when increasing the coupling coefficients, ultimately leading to coherent oscillations over the entire tissue. We study the transition towards a coherent regime, both numerically and semi-analytically, using the simple model of excitable cells. Last, we demonstrate that, the realistic model reproduces irregular action potential propagation patterns as well as the bursting behavior, observed in the in-vitro experiments.
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Borek, Bartlomiej. "Dynamics of heterogeneous excitable media with pacemakers." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107795.
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The heart is a heterogeneous excitable tissue embedded with pacemakers. To understand the fundamental rules governing its behaviour it is useful to investigate the interplay between structure and dynamics in simplified experimental and mathematical models. This thesis examines FitzHugh-Nagumo type reaction-diffusion equation models motivated by experiments with engineered cardiac tissue culture. The aim is to relate how the design properties of these systems determine the underlying spatiotemporal dynamics. First, a functional relation between randomly distributed heterogeneities and conduction velocity is proposed in two dimensional heterogeneous excitable media. The transitions to wave break are studied for two types of heterogeneities related to fibroblasts and collagen deposits. The effects of pacemakers are next considered with a theoretical study of the transitions in one-dimensional wave patterns of a pacemaker reset by a stimulus pulse from a distance. Reflected wave solutions are found near the apparent discontinuity in the phase transition curve of the system, and they grow into more multi-reflected trajectories for a coarser spatial discretization of the model. Finally, the dynamical regimes arising from the interaction of two pacemakers in heterogeneous excitable media are investigated. A novel chick culture is developed to exhibit dominant pacemaker dynamics. This stable rhythm undergoes transitions to more complex reentrant patterns following induction of new pacemakers by the application of the potassium channel blocker, E-4031. The dynamics are reproduced by the FitzHugh-Nagumo model, which further demonstrates the effects of pacemaker size and heterogeneity density on the transition to wave break and reentry. These findings may contribute to our understanding of the generic mechanisms governing the dynamics of wave propagation through heterogeneous excitable media with pacemakers, including healthy and diseased hearts.Le coeur est un tissu hétérogène excitable qui contient des générateurs de rythme. Pour comprendre les règles fondamentales qui dirigent son comportement, il est utile d'étudier l'interaction entre la structure et la dynamique des modèles expérimentaux et mathématiques simplifiés. Dans cette thèse, j'utilise des modèles d'équations de FitzHugh-Nagumo. Ces modèles sont motivés par l'expérimentation avec des tissus cardiaques modifiés pour étudier comment les propriétés des conceptions influencent la dynamique d'ondes. Tout d'abord, une relation fonctionelle entre la densité des hétérogénéités distribuées au hasard et la vitesse de conduction est proposée dans un modèle numérique de deux dimensions de média hétérogènes excitables. Les transitions à l'onde rupturée sont différentes pour deux types de substrats hétérogènes. Les effets des régions automatiques sont alors considérés avec une étude théorique des transitions dans les ondes unidimensionelles des générateurs de rythme réinitialisés par une seule impulsion d'une distance. Des solutions d'ondes réfléchies se trouvent près de la discontinuité apparente de la courbe de transition de phase du système et deviennent des trajectoires plus complexes pour une discrétisation spatiale plus grossière du modèle. Enfin, les modèles d'ondes résultant de l'interaction de deux générateurs de rythme dans des médias hétérogènes excitables sont étudiés. Une nouvelle culture de tissu cardiaque de poussin est développée pour présenter la dynamique dominante déterminée par un générateur de rythme. Ce rythme stable subit des transitions à des modèles d'ondes réentrants plus complexes suivant l'induction de nouveaux générateurs de rythme, par l'application du bloqueur des canaux potassiques, E-4031. La dynamique est reproduite par le modèle FitzHugh-Nagumo, prévoyant l'effet de la taille du générateur de rythme et la densité de l'hétérogèneité sur la transition de l'onde rupturée et à la réentrée. Ces résultants contribuent à notre compréhension des mécanismes de média hétérogènes excitables avec des générateurs de rythme, dont les coeurs sains et malades.
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Henze, Christopher Ernest. "Vortex filaments in three dimensional excitable media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186300.
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An "excitable medium", such as nerve fiber or heart tissue, can be locally provoked by a relatively small stimulus to execute a relatively large transient response, followed by recovery to the original rest state. In one-, two-, or three-dimensional excitable media, such episodes of excitation can propagate as nondecrementing pulses, until they are extinguished at the domain boundaries. In two- or three-dimensional excitable media, these travelling wavefronts of excitation can become arranged in self-perpetuating spirals (in 2D) or "scrolls" (in 3D), which rotate indefinitely, organizing the entire medium with periodic wavetrains. In three dimensions, the pivot of the scroll, around which the sheetlike wavefront unfurls, is a one-dimensional space curve, a "vortex filament", which may end only on domain boundaries, or close into rings, and which may be knotted or linked. Vortex filaments and their associated scroll waves are of interest as periodic solutions to the underlying reaction-diffusion equations, and they may also play a role in understanding the behavior of certain natural systems, perhaps most prominently the disintegration of normal coordinated activity in large mammalian hearts known as ventricular fibrillation. Analytic or experimental approaches to investigating vortex filaments have met with limited success, and in any case stand in need of testing. This thesis presents the results of four largescale numerical investigations of vortex filaments, using supercomputers. Starting with various carefully contrived initial conditions, three-dimensional volumes of excitable media are simulated by numerical integration of partial differential equation models. During the run, the form and behavior of the simulated vortex filaments are monitored by means of a "differential geometry toolkit". Emphasis is given to two fronts. First, I tried to establish the existence and properties of stable filament configurations. This resulted in the discovery of half a dozen stable organizing centers, more than doubling the number of previously known periodic solutions. Second, I attempted to discern the factors and rules which govern filament dynamics. This effort is largely guided by and aims to test the so-called "local geometry hypothesis", which supposes that local filament dynamics are determined by local filament geometry.
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Chirila, Florin. "Feedback control of wave propagation patterns in excitable media." Morgantown, W. Va. : [West Virginia University Libraries], 2003. http://etd.wvu.edu/templates/showETD.cfm?recnum=2820.
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Thesis (Ph. D.)--West Virginia University, 2003.Title from document title page. Document formatted into pages; contains xii, 156 p. : ill. (some col.) + MPEG video files. Includes MPEG video files. Includes abstract. Includes bibliographical references.
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Guo, Hongjun. "Transition fronts and propagation speeds in diffusive excitable media." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0216.
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Cette thèse porte sur les fronts de transition pour des équations de réaction-diffusion dans différents milieux. Les fronts de transition généralisent les notions habituelles de fronts progressifs ou pulsatoires. Les principaux résultats sont les suivants. Pour des réactions bistables, nous prouvons la monotonie en temps de tous les fronts de transition avec vitesse globale moyenne non nulle. Pour des réactions bistables périodiques en temps ou pour des réactions de type combustion, nous prouvons l’existence et l’unicité de la vitesse globale moyenne d’un front. De plus, nous montrons que les fronts presque plans sont en réalité plans et nous montrons l’existence de fronts de transitions non standard. Pour des réactions bistables périodiques en espace, nous montrons la continuité et la différentiabilité des vitesses et des profils de ces fronts pulsatoires par rapport à la direction e en supposant l’existence de fronts pulsatoires à vitesse non nulle dans toutes les directions $e$. Ensuite, nous prouvons que la vitesse de propagation d’un front de transition quelconque est comprise entre les vitesses minimales et maximales des fronts pulsatoires. Enfin, nous étudions les vitesses globales moyennes des fronts de transition bistables dans des domaines non bornés : domaines extérieurs ou domaines à branches multiples cylindriques. Dans ces deux types de domaines, nous prouvons l’existence et l’unicité de la vitesse globale moyenne de tous les fronts de transition sous certaines hypothèsesThis dissertation is concerned with transition fronts in various media, which generalize the standard notions of traveling fronts. The main results are as following. For bistable reaction, we prove the time monotonicity of all transition fronts with non-zero global mean speed, whatever shape their level sets may have. For time-periodic bistable reaction and combustion-type reaction, we prove the existence and the uniqueness of the global mean speed. Meantime, we show that almost-planar fronts are actually planar and we show the existence of non-standard transitions fronts in $\mathbb{R}^N$. For spatially periodic bistable reaction, we show some continuity and differentiability properties of the front speeds and profiles with respect to the direction $e$ by providing the existence of pulsating fronts with nonzero speed in all directions $e$. Then, we prove that the propagating speed of any transition front is bounded by the minimal speed and the maximal speed of pulsating fronts. Finally, we study the mean speed of bistable transition fronts in unbounded domains: exterior domains and domains with multiple cylindrical branches. In both domains, we prove the existence and uniqueness of the global mean speed of any transition front under some assumptions
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Zhao, Yifan. "System Identification for Cellular Automata with Applications to Excitable Media." Thesis, University of Sheffield, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485082.
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As an important class of spatia-temporal systems, cellular automata (CA) have attracted more and more attention from researchers, but only a few have studied how to extract the CA rules directly from observed data, especially from real data. This thesis therefore centres around an investigation into the identification of CA and the application to real data with the aim of building a link connecting the behaviour of real spatia-temporal systems with CA model realizations. Some basic concepts associated with the developments of CA and the corresponding identification are reviewed initially in a literature survey to provide the motivation and background for this study. The applications of four modified orthogonalleast squares (OL8) methods in the identification of CA are then investigated to select one as the core algorithm for use in this thesis. After a discussion on the improvement of all methods, a group of tests is conducted to compare the feasibility, speed and accuracy of each algorithm when dealing with CA data. The main contribution in theoretical research of this thesis has been the intraduction of a new neighbourhood detection method using mutual information. This has important advantageous over existing methods because it can detect an exact or slightly large neighbourhood without any a prior information. With excellent approximation properties and easy implementation, the new method is well-suited for deterministic CA, probabilistic CA, and even highly noise corrupted systems. By combining the new neighbourhood detection method with the OL8 estimator, a coarse-to-fine approach is then proposed which provides a generic routine to extract polynomial models directly from observed data for binary CA., The identification of a CA model of an excitable media system directly from observed data is demonstrated for the first time. A multi-model realization is introduced to represent the excitable media system and the identification of the system model is achieved by transforming the identification problem from excitable media to binary CA. To further evaluate the effectiveness of the methods on real data, the new algorithms are then applied to data imaged from a Belousov-Zhabotinsky (BZ) chemical reaction. To extend the application of the proposed methods, the identification of hybrid CA which can represent complex behaviours and which has never been studied before, is investigated. Based on the difference in the evolution characteristics in different regions, segmentation methods are employed before estimating the CA models. The final representation of hybrid CA can then be obtained by combining the mathematical models of each region. Numerous examples using simulation and real data are used to demonstrate the effectiveness and applicability of the new methods.
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Mantel, Rolf-Martin. "Periodic forcing and symmetry breaking of waves in excitable media." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263610.
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Bordyugov, Grigory. "Dynamics and stability of pulses and pulse trains in excitable media." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981984177.
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McGowan, Robert. "Eikonal analysis of excitable reaction-diffusion equations in anisotropic and inhomogeneous media." Thesis, Glasgow Caledonian University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309345.
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Schmid, Gerhard. "Channel noise in excitable membranes /." Aachen : Shaker, 2005. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=013064715&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Liceaga, Daniel Olmos. "Pseudospectral solutions of reaction-diffusion equations that model excitable media : convergence of solutions and applications." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/31453.
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In this thesis, I develop accurate and efficient pseudospectral methods to solve Fisher's, the Fitzhugh-Nagumo and the Beeler-Reuter equations. Based on these methods, I present a study of spiral waves and their interaction with a boundary. The solutions of Fisher's equation are characterized by propagating fronts with a, shock-like wave behavior when large values of the reaction rate coefficient is taken. The pseudospectral method employed for its solution is based on Chebyshev-Gauss-Lobatto quadrature points. I compare results for a single domain as well as for a subdivision of the main domain into subintervals. Instabilities that occur in the numerical solution for a single domain, analogous to those found by others, are attributed to round-off errors arising from numerical features of the discrete second derivative matrix operator. However, accurate stable solutions of Fisher's equation are obtained with a multidomain pseudospectral method. A detailed comparison of the present approach with the use of the sinc interpolation is also carried out. Also, I present a study of the convergence of different numerical schemes in the solution of the Fitzhugh-Nagumo equations. These equations, have spatial and temporal dynamics in two different scales and the solutions exhibit shock-like waves. The numerical schemes employed are Chebyshev multidomain, Fourier pseudospectral, finite difference methods and in particular a method developed by Barkley. I consider two different models of the local dynamics. I present results for plane wave propagation in one dimension and spiral waves for two dimensions. I use an operator splitting method with the Chebyshev multidomain approach in order to reduce the computational time. I conclude this thesis by presenting a study of the interaction of a meandering spiral wave with a boundary, where the Beeler-Reuter model is considered. The phenomenon of annihilation or reflection of a spiral at the boundaries of the domain is studied, when the trajectory of the tip of a spiral wave is essentially linear. This phenomenon is analyzed in terms of the variable j, which controls the reactivation of the sodium channel in the Beeler-Reuter model.Science, Faculty of
Mathematics, Department of
Graduate
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Stevens, Roger P., and n/a. "A Computer Model of the Cellular Slime Mould Dictyostelium Discoideum." Griffith University. School of Computing and Information Technology, 2002. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20050906.112225.
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Excitable media are an important class of systems, examples of which include epidemics, predator-prey interactions, nervous systems, and heart muscle. Aggregating cellular slime moulds are an example of an excitable medium. The species of cellular slime mould Dictyostelium discoideum is an important model organism that many science laboratories use. Studying the aggregation of slime moulds increases knowledge about excitable media generally. One method of studying the aggregation of slime mould is to simulate theft behaviour on a computer model. This thesis presents the author's computer model of cellular slime mould Dictyostelium discoideum and the results of experiments carried out using the computer model. The experiments investigate the relation between the aggregation patterns and the various parameters of the model. These parameters are the density of artificial slime moulds, the acrasin threshold, the acrasin degradation rate, and the rate of acrasin secretion. Randomness has an effect on the aggregation patterns produced. Results of experiments are presented that examine the effect of randomness. Two forms of randomness are investigated: random secretion of acrasin by the artificial slime moulds; random initial reactivity of the artificial slime moulds. The computer model describes an artificial environment in which artificial slime mould amoebae interact with each other and their environment. Out of these individual interactions the global patterns that characterize slime mould aggregations emerge. The model facilitates the study of these individual interactions and hence the global patterns that emerge. The model and the experimental results described in this thesis contribute to the study of the aggregation phase of the life cycle of Dictyosteliuni discoideum. The author proposes mechanism that could underlie certain classes of aggregation patterns. These patterns include net-like aggregations and loop aggregations. The computer model presented in this thesis is successful in emulating the behaviour of the cellular slime mould Dictyostelium discoideum. In its present form the model is a useful tool to biologists. The results of experiments conducted with the model suggest mechanisms that may underlie certain pattern produced by living slime moulds. A result of particular interest is the initiation of the spiral wave pattern from a loop wave, which produces a loop aggregation.
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Stevens, Roger P. "A Computer Model of the Cellular Slime Mould Dictyostelium Discoideum." Thesis, Griffith University, 2002. http://hdl.handle.net/10072/365409.
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Excitable media are an important class of systems, examples of which include epidemics, predator-prey interactions, nervous systems, and heart muscle. Aggregating cellular slime moulds are an example of an excitable medium. The species of cellular slime mould Dictyostelium discoideum is an important model organism that many science laboratories use. Studying the aggregation of slime moulds increases knowledge about excitable media generally. One method of studying the aggregation of slime mould is to simulate theft behaviour on a computer model. This thesis presents the author's computer model of cellular slime mould Dictyostelium discoideum and the results of experiments carried out using the computer model. The experiments investigate the relation between the aggregation patterns and the various parameters of the model. These parameters are the density of artificial slime moulds, the acrasin threshold, the acrasin degradation rate, and the rate of acrasin secretion. Randomness has an effect on the aggregation patterns produced. Results of experiments are presented that examine the effect of randomness. Two forms of randomness are investigated: random secretion of acrasin by the artificial slime moulds; random initial reactivity of the artificial slime moulds. The computer model describes an artificial environment in which artificial slime mould amoebae interact with each other and their environment. Out of these individual interactions the global patterns that characterize slime mould aggregations emerge. The model facilitates the study of these individual interactions and hence the global patterns that emerge. The model and the experimental results described in this thesis contribute to the study of the aggregation phase of the life cycle of Dictyosteliuni discoideum. The author proposes mechanism that could underlie certain classes of aggregation patterns. These patterns include net-like aggregations and loop aggregations. The computer model presented in this thesis is successful in emulating the behaviour of the cellular slime mould Dictyostelium discoideum. In its present form the model is a useful tool to biologists. The results of experiments conducted with the model suggest mechanisms that may underlie certain pattern produced by living slime moulds. A result of particular interest is the initiation of the spiral wave pattern from a loop wave, which produces a loop aggregation.Thesis (Masters)
Master of Philosophy (MPhil)
School of Computing and Information Technology
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Goodfellow, Marc. "Spatio-temporal modelling and analysis of epileptiform EEG." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/spatiotemporal-modelling-and-analysis-of-epileptiform-eeg(0f76259a-1a58-44a9-b08b-1402c9b49896).html.
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In this thesis we investigate the mechanisms underlying the generation of abnormal EEG rhythms in epilepsy, which is a crucial step towards better treatment of this disorder in the future. To this end, macroscopic scale mathematical models of the interactions between neuronal populations are examined. In particular, the role of interactions between neural masses that are spatially distributed in cortical networks are explored. In addition, two other important aspects of the modelling process are addressed, namely the conversion of macroscopic model variables into EEG output and the comparison of multivariate, spatio-temporal data. For the latter, we adopt a vectorisation of the correlation matrix of windowed data and subsequent comparison of data by vector distance measures. Our modelling studies indicate that excitatory connectivity between neural masses facilitates self-organised dynamics. In particular, we report for the first time the production of complex rhythmic transients and the generation of intermittent periods of 'abnormal' rhythmic activity in two different models of epileptogenic tissue. These models therefore provide novel accounts of the spontaneous, intermittent transition between normal and pathological rhythms in primarily generalised epilepsies and the evocation of complex, self-terminating, spatio-temporal dynamics by brief stimulation in focal epilepsies. Two key properties of these models are excitability at the macroscopic level and the presence of spatial heterogeneities. The identification of neural mass excitability as an important processes in spatially extended brain networks is a step towards uncovering the multi-scale nature of the pathological mechanisms of epilepsy. A direct consequence of this work is therefore that novel experimental investigations are proposed, which in itself is a validation of our modelling approach. In addition, new considerations regarding the nature of dynamical systems as applied to problems of transitions between rhythmic states are proposed and will prompt future investigations of complex transients in spatio-temporal excitable systems.
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Yu, Han Baek. "Combinatorial and probabilistic aspects of coupled oscillators." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524195989591036.
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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." Thesis, The University of Sydney, 2008. http://hdl.handle.net/2123/3685.
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A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.
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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." University of Sydney, 2008. http://hdl.handle.net/2123/3685.
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Doctor of PhilosophyA detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.
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Lenk, Claudia [Verfasser], Michael [Akademischer Betreuer] Köhler, Philipp [Gutachter] Maaß, and Oliver [Gutachter] Steinbock. "Role of coupling conditions for pattern formation in excitable media : study of atrial fibrillation mechanisms and oscillator arrays in the Belousov-Zhabotinsky reaction / Claudia Lenk ; Gutachter: Philipp Maaß, Oliver Steinbock ; Betreuer: J. Michael Köhler." Ilmenau : TU Ilmenau, 2017. http://d-nb.info/1178142566/34.
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Silva, Pedro André Arroyo. "Modelo matemático com parâmetros que dependem da discretização: aplicação ao estudo de fenômenos de propagação discreta em meios excitáveis." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7194.
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A formação de padrões espaço-temporais são observados em processos químicos e bio-lógicos. Apesar dos sistemas bioquímicos serem altamente heterogêneos, aproximações homogenizadas contínuas formadas por equações diferenciais parciais são utilizadas fre-quentemente. Estas aproximações são usualmente justificadas pela diferença de escalas entre as heterogeneidades e o tamanho da característica espacial dos padrões. Em certas condições do meio, por exemplo, quando há um acoplamento fraco entre as células car-díacas, os modelos homogenizados discretos são mais adequados. Entretanto, os modelos discretos são menos manejáveis, por exemplo, na geração de malha para 2D e 3D, se comparado com os modelos contínuos. Aqui estudamos um modelo matemático homoge-nizado contínuo que se aproxima do modelo homogenizado. Este modelo é dado a partir de equações diferencias parciais com um parâmetro que depende da discretização da ma-lha. Dessa maneira nos referimos a este por um modelo matemático com parâmetros que dependem da discretização. Validamos nossa aproximação em um meio excitável genérico que simula três fenômenos em 1D: a propagação do potencial de ação transmembrânico no tecido cardíaco, a propagação do potencial de ação em filamentos de axônios cobertos por bainhas de mielina e a propagação do ativador e inibidor em microemulsões químicas. Para o caso 2D desenvolvemos uma versão da nossa aproximação que reproduz ondas espirais em um meio com acoplamento fraco.
The spatio-temporal patterns formations are observed in chemical and biological pro-cesses. Although biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. These approaches are usually justified by the difference scales between the characteristic spatial size of the patterns. Under some conditions of the medium, for instance, under weak coupling between cardiac cells, discrete models are more adequate. On the other hand discrete models may be less manageable, for instance, in terms of mesh generation, com-pared to the continuum models. Here we study a mathematical model to approach the discreteness which permits the computer implementation on non-uniform meshes. The model is cast as a partial differential equation but with a parameter that depends on the discretization mesh. Therefore we refer to it as a mathematical model with parameters dependent of discretization. We validate the approach in a generic excitable media that simulates three different phenomena in 1D: the propagation of action potential in car-diac tissue, the propation of the action potentialin filaments of axons wrapped by myelin sheaths, and the propagation of the activator/inhibitor in chemical microemulsions. For the 2D case we develop a version to this approach in microemulsions where it was possible to reproduce spiral waves with weak coupling of the medium.
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Yermakov, Leonid M. "Type 2 Diabetes Leads to Impairment of Cognitive Flexibility and Disruption of Excitable Axonal Domains in the Brain." Wright State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright1559401756413422.
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Gravner, Janko. "Mathematical aspects of excitable media." 1991. http://catalog.hathitrust.org/api/volumes/oclc/24563504.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1991.Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 120-123).
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Sailer, Franz-Xaver [Verfasser]. "Controlling excitable media with noise / von Franz-Xaver Sailer." 2006. http://d-nb.info/980114284/34.
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Beato, Valentina [Verfasser]. "Noise-induced pattern formation in excitable media / vorgelegt von Valentina Beato." 2006. http://d-nb.info/983001995/34.
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Uang, Ting Fang, and 汪庭芳. "The emergency of transition layer and the front propagation equations in excitable media." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/56116389105588795388.
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Bordyugov, Grigory [Verfasser]. "Dynamics and stability of pulses and pulse trains in excitable media / vorgelegt von Grigory Bordyugov." 2006. http://d-nb.info/981984177/34.
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Wang, Guanqun. "Investigation and Construction of Self-oscillating Systems." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-7997.
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Self-oscillating reactions have been widely observed and studied since the last century because they exhibit unique behaviors different from the traditional chemical reactions. Self-oscillating systems, such as the Belousov-Zhabotinsky (BZ) reaction, oxidation reaction of CO on single crystal Pt, and calcium waves in the heart tissue, are of great interest in a variety of scientific areas. This thesis contributes to the understanding of wave transition in BZ reaction, and to possible applications of non-equilibrium behaviors of polymer systems. In BZ reaction, two types of wave patterns, target and spiral, are frequently observed. The transition from one to another is not fully understood. Hence, a systematic investigation has been performed here to investigate the mechanism by which heterogeneity affects the formation of wave patterns. A BZ reaction catalyst was immobilized in ion exchange polystyrene beads to form active beads. Then active and inactive beads with no catalyst loading were mixed together with various ratios to achieve various levels of heterogeneity. In the same reaction environment, different wave patterns were displayed for the bead mixtures. We observed a transition from target patterns to spiral patterns as the percentage of the active beads in the beads mixture decreased. The increase of the heterogeneity led to wave pattern transition. Heterogeneity hindered the propagation of target waves and broke them into wavelets that generated spiral waves. In an effort to develop practical applications based on non-equilibrium phenomena, we have established a novel drug delivery system. A proton generator Zirconium Phosphate (ZrP) was imbedded inside a pH sensitive polymer matrix, poly acrylic acid (PAA). Through the ion exchange with sodium cation (Na+), ZrP generates protons to control the swelling/shrinking behaviors of PAA. The drug encapsulated in the matrix can be released in a controlled manner by adjusting the supply of Na+. This system might be developed into vehicles to deliver drugs to specific targets and release at a proper time. This new delivery technique will be convenient and significantly increase the efficiency of medicines.
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(8039297), Xiaoling Zhai. "SIGNAL PROPAGATION WITHIN A HETEROGENEOUS BACTERIAL COMMUNITY." Thesis, 2019.
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Reliable signal transmission among cells is important for long-range coordination. While higher organisms have designated structures for signal transmission, such as axons, it remains unclear how simpler communities of cells are organized to relay signals. Furthermore, many biological systems exhibit spatial heterogeneity, which can interrupt signal propagation. In this thesis, we investigate this problem by modeling the spatial organization and dynamics of electrochemical signaling, and we compare our results to experiments from our collaborators on Bacillus subtilis bacterial biofilms. The experiments show that only a fraction of cells participates in signal propagation and that these cells are spatially clustered with a size distribution that follows a power-law decay. These observations suggest that the fraction of participating cells is just at the tipping point between a disconnected and a fully connected conduit for signal transmission. We utilize percolation theory and a minimal FitzHugh-Nagumo-type excitable dynamics model to test this hypothesis, and genetically modified biofilms with altered structure and dynamics to validate our modeling. Our results suggest that the biofilm is organized near the critical percolation point in order to negotiate the benefit and cost of long-range signal transmission. Then, more detailed experiments show that the participation probability is correlated from cell to cell and varies in space. We use these observations to develop an enhanced percolation model, and show using simulations and a renormalization argument that the main conclusions are unaffected by these features. Finally, we use our dynamic model to investigate the effects of heterogeneity beyond the radial wave regime and into the spiral wave regime. We find that spatial correlations in the heterogeneity promote or suppress spiraling depending on the parameters, a surprising feature that we explain by demonstrating that these spirals form by distinct mechanisms. We characterize the dependence of the spiral period on the heterogeneity using techniques from percolation theory. Taken together, our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.
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Christoph, Jan. "Intramural Visualization of Scroll Waves in the Heart." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0023-9642-D.
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Berg, Sebastian Stephan. "Characterization and Control of Wave Propagation in the Heart." Doctoral thesis, 2018. http://hdl.handle.net/11858/00-1735-0000-002E-E607-5.
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Bittihn, Philip. "Complex Structure and Dynamics of the Heart." Doctoral thesis, 2013. http://hdl.handle.net/11858/00-1735-0000-0001-BBB6-B.
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Lilienkamp, Thomas. "A State Space Odyssey — The Multiplex Dynamics of Cardiac Arrhythmias." Doctoral thesis, 2018. http://hdl.handle.net/11858/00-1735-0000-002E-E4D8-0.
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Dormann, Sabine. "Pattern Formation in Cellular Automaton Models - Characterisation, Examples and Analysis." Doctoral thesis, 2000. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2000102612.
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Cellular automata (CA) are fully discrete dynamical systems. Space is represented by a regular lattice while time proceeds in finite steps. Each cell of the lattice is assigned a state, chosen from a finite set of "values". The states of the cells are updated synchronously according to a local interaction rule, whereby each cell obeys the same rule. Formal definitions of deterministic, probabilistic and lattice-gas CA are presented. With the so-called mean-field approximation any CA model can be transformed into a deterministic model with continuous state space. CA rules, which characterise movement, single-component growth and many-component interactions are designed and explored. It is demonstrated that lattice-gas CA offer a suitable tool for modelling such processes and for analysing them by means of the corresponding mean-field approximation. In particular two types of many-component interactions in lattice-gas CA models are introduced and studied. The first CA captures in abstract form the essential ideas of activator-inhibitor interactions of biological systems. Despite of the automaton´s simplicity, self-organised formation of stationary spatial patterns emerging from a randomly perturbed uniform state is observed (Turing pattern). In the second CA, rules are designed to mimick the dynamics of excitable systems. Spatial patterns produced by this automaton are the self-organised formation of spiral waves and target patterns. Properties of both pattern formation processes can be well captured by a linear stability analysis of the corresponding nonlinear mean-field (Boltzmann) equations.