Autor Markéta Popelová Název práce Software tool for modelling coding and processing of information in auditory cortex of mice Abstrakt Porozumění zpracovávání a kódování informací ve sluchové k·ře (AC) je stále ne- dostatečné. Z několika r·zných d·vod· by bylo užitečné mít výpočetní model AC, například z d·vodu vysvětlení, či ujasnění procesu kódování informací v AC. Prv- ním cílem této práce bylo vytvořit softwarový nástroj (simulátor SUSNOMAC), zaměřený na modelování AC. Druhým cílem bylo navrhnout výpočetní model AC s následujícími vlastnostmi: Izhikevich·v model neuronu, dlouhodobá plasticita ve formě Spike-timing-dependent plasticity (STDP), šestivrstvá architektura, pa- rametrizované typy neuron·, hustota neuron· a pravděpodobnost vzniku synapsí. Navržený model byl testován v desítkách experiment·, s r·znými sadami para- metr· a v r·zných velikostech (až 100 000 neuron· s takřka 21 milióny synapsí). Experimenty byly analyzovány a jejich výsledky srovnány s pozorováním skutečné AC. V práci popisujeme a analyzujeme několik zajímavých pozorování o aktivitě modelované sítě a vzniku tonotopického uspořádání AC. 1

This thesis focuses on an adaptive quadratic spiking model of a motoneuron that is both versatile in its ability to represent a range of experimentally observed neuronal firing patterns as well as computationally efficient for large network simulation. The objective of research is to fit membrane voltage data to the model using a parameter estimation approach involving simulated annealing. By manipulating the system dynamics of the model, a realizable model with linear parameterization (LP) can be obtained to simplify the estimation process. With a persistently excited current input applied to the model, simulated annealing is used to efficiently determine the best model parameters that minimize the square error function between the membrane voltage reference data and data generated by the LP model. Results obtained through simulation of this approach show feasibility to predict a range of different neuron firing patterns.

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Este trabalho trata sobre a transferência de frequência em neurônios de disparo, especificamente neurônios integra-e-dispara com escoamento e neurônios de Izhikevich. Através de análises matemáticas analíticas e sistemáticas simulações numéricas é obtida a função de ganho, a transferência de frequência estacionária e dinâmica dos neurônios utilizados, para diversos valores dos parâmetros do modelo. Desse modo, são realizados múltiplos ajustes às curvas obtidas, e os coeficientes estimados são apresentados. Com base em todos esses dados, são obtidas diversas características dessas relações de transferência de frequência, e como suas propriedades variam com relação aos principais parâmetros do modelo de neurônio e sinapse utilizados. Diversos resultados interessantes foram apresentados, incluindo evidências de que a função ganho do neurônio integra-e-dispara pode se comportar de modo bastante semelhante à função de ganho e transferência estacionária do neurônio de Izhikevich, dependendo dos parâmetros adotados; a divisão do plano de parâmetros do modelo integra-e-dispara de acordo com a linearidade da transferência de frequência dinâmica; o limiar da intensidade de corrente contínua e de frequência de spikes pré-sinápticos de um neurônio de Izhikevich é determinado apenas pelo parâmetro b, no intervalo de parâmetros usual; modelos de sinapses distintos tendem a não alterar a forma da transferência de frequência estacionária de um neurônio de Izhikevich. / This work is about the frequency transfer of spiking neurons, specifically integrate-and-fire neurons and Izhikevich neurons. Through analytical and systematic numerical simulations the gain function, the stationary and dynamic frequency transfer of the adopted neuron models, are obtained for several values of the model parameters. Thus, multiple fits are made to the curves obtained, and the estimated coefficients are presented. Based on all these data, several characteristics of the frequency transfer relations are obtained, and information is obtained about how their properties vary with respect the parameters of the adopted neuron and synapse model. Several interesting results have been presented, including evidences that the integrate-and-fire neuron\'s gain function can behave quite similarly to the Izhikevich neuron\'s stationary transfer and gain function, depending of the adopted parameters. We also obtained the division of the parameters plane of integrate-and-fire model according to the linearity of the dynamic frequency transfer. It was also verified that the thresholds of the presynaptic spikes\' current intensity and frequency of an Izhikevich neuron are determined only by the parameter b, in the usual parameter range. In addition, it was observed that the considered distinct synapses models tend not to depart from the stationary frequency transfer of an Izhikevich neuron.

Στην παρούσα εργασία μελετάμε τη μοντελοποίηση του υποθαλαμικού πυρήνα των βασικών γαγγλίων με χρήση του μαθηματικού νευρωνικού μοντέλου Izhikevich. Βάση της μελέτης μας αποτελούν μικροηλεκτροδιακές καταγραφές, που έχουν ληφθεί κατά τη διάρκεια νευροχειρουργικών επεμβάσεων εν τω βάθει εγκεφαλικής διέγερσης, για τη συμπτωματική θεραπεία της νόσου Πάρκινσον. Θα ξεκινήσουμε με μια εισαγωγή στην φυσιολογία του νευρικού κυττάρου και στην ανατομία των βασικών γαγγλίων. Θα αναλύσουμε τα βασικά ποιοτικά μοντέλα που ερμηνεύουν τη συμμετοχή των τελευταίων σε κινητικές διεργασίες, αλλά και την εμπλοκή τους στη νόσο Πάρκινσον. Μετά από μια σύντομη αναφορά στη μέθοδο της εν τω βάθει διέγερσης και στις μικροηλεκτροδιακές καταγραφές, θα εστιάσουμε στα δυναμικά τοπικού πεδίου και στη νευροφυσιολογική σημασία τους. Συνεχίζοντας, θα κάνουμε μια περιεκτική ανασκόπηση των βασικότερων μαθηματικών μοντέλων νευρώνων και ύστερα θα επικεντρωθούμε στον υποθαλαμικό πυρήνα, περιγράφοντας δύο πρόσφατα μοντέλα που έχουν κατασκευαστεί για την προσομοίωση των νευρώνων αυτού. Έπειτα, θα περάσουμε στην περιγραφή του μοντέλου Izhikevich και στην τροποποίησή του για την αναπαραγωγή των χαρακτηριστικών του νευρώνα του υποθαλαμικού πυρήνα. Κατόπιν, θα αναλύσουμε τη μεθοδολογία που ακολουθήσαμε στην παρούσα υλοποίηση και τις βασικές θεωρήσεις της μοντελοποίησης μας. Θα ολοκληρώσουμε με την παρουσίαση των αποτελεσμάτων, το σχολιασμό αυτών και τις ιδέες για μελλοντική επέκταση της μεθόδου μας. / The main objective of this MSc thesis is the study of subthalamic nucleus, by using the Izhikevich neuron model. Microelectrode recordings, taken during deep brain stimulation operations for Parkinson’s disease, have been used for that purpose. In chapters 1-2, there is an introduction to the physiology of the neuron and the basal ganglia anatomy. In the two following chapters, we are analyzing the basic qualitative models that describe the involvement of the basal ganglia in movements and the pathophysiology of Parkinson’s disease. We are briefly discussing the method of deep brain stimulation, microelectrode recordings processing and the extraction of local field potentials. In chapter 5, the basic mathematical neuron models are discussed. We are focusing on the subthalamic nucleus and we are describing two recently developed mathematical models of the subthalamic neuron. In chapter 6, we are outlining Izhikevich neuron model and its modification in order to describe the subthalamic neuron. In addition, we are analyzing the methodology developed for the implementation of the modeling process and our basic considerations. In chapter 7, the results of the simulation are presented and discussed, so that our conclusions provide ideas for further research.

We present a multi-layer multi-column computational model of neocortex that is built based on the activity and connections of known neuronal cell types and includes activity-dependent short term plasticity. This model, a network of spiking neurons, is validated by showing that it exhibits activity close to biology in terms of several characteristics: (1) proper laminar flow of activity; (2) columnar organization with focality of inputs; (3) low-threshold-spiking (LTS) and fast-spiking (FS) neurons function as observed in normal cortical circuits; and (4) different stages of epileptiform activity can be obtained with either increasing the level of inhibitory blockade, or simulation of NMDA receptor enhancement. The aim of this research is to provide insight into the fundamental properties of vertical and horizontal inhibition in neocortex and their influence on epileptiform activity. The developed model was used to test novel ideas about modulation of inhibitory neuronal types in a developmentally malformed cortex. The novelty of the proposed research includes: (1) design and implementation of a multi-layer multi-column model of the cortex with multiple neuronal types and short-time plasticity, (2) modification of the Izhikevich neuron model in order to model biological maximum firing rate property, (3) generating local field potential (LFP) and EEG signals without modeling multiple neuronal compartments, (4) modeling several known conditions to validate that the cortex model matches the biology in several aspects,(5) modeling different abnormalities in malformed cortex to test existing and to generate novel hypotheses.

Artificial neural networks have shown great potential and have attracted much research interest. One problem faced when simulating such networks is speed. As the number of neurons increases, the time to simulate and train a network increases dramatically. This makes it difficult to simulate and train a large-scale network system without the support of a high-performance computer system. The solution we present is a "real" parallel system - using a parallel machine to simulate neural networks which are intrinsically parallel applications. SpiNNaker is a scalable massively-parallel computing system under development with the aim of building a general-purpose platform for the parallel simulation of large-scale neural systems. This research investigates how to model large-scale neural networks efficiently on such a parallel machine. While providing increased overall computational power, a parallel architecture introduces a new problem - the increased communication reduces the speedup gains. Modeling schemes, which take into account communication, processing, and storage requirements, are investigated to solve this problem. Since modeling schemes are application-dependent, two different types of neural network are examined - spiking neural networks with spike-time dependent plasticity, and the parallel distributed processing model with the backpropagation learning rule. Different modeling schemes are developed and evaluated for the two types of neural network. The research shows the feasibility of the approach as well as the performance of SpiNNaker as a general-purpose platform for the simulation of neural networks. The linear scalability shown in this architecture provides a path to the further development of parallel solutions for the simulation of extremely large-scale neural networks.

In 2007, Modolo and colleagues derived a population density equation for a population of Izhekevich neurons. This population density equation can describe oscillations in the brain that occur in Parkinson’s disease. Numerical simulations of the population density equation showed bursting behaviour even though the individual neurons had parameters that put them in the tonic firing regime. The bursting comes from neuron interactions but the mechanism producing this behaviour was not clear. In this thesis we study numerical behaviour of the population density equation and then use a combination of analysis and numerical simulation to analyze the basic qualitative behaviour of the population model by means of a simplifying assumption: that the initial density is a Dirac function and all neurons are identical, including the number of inputs they receive, so they remain as a point mass over time. This leads to a new ODE model for the population. For the new ODE system, we define a Poincaré map and then to describe and analyze it under conditions on model parameters that are met by the typical values adopted by Modolo and colleagues. We show that there is a unique fixed point for this map and that under changes in a bifurcation parameter, the system transitions from fast tonic firing, through an interval where bursting occurs, the number of spikes decreasing as the bifurcation parameter increases, and finally to slow tonic firing. / Graduate

The aim of the research is to provide a computationally efficient neural network model for the study of deep brain stimulation efficacy in the treatment of Parkinson's disease. An Izhikevich neuron model was used to accomplish this task and four classes of neurons were modeled. The parameters of each class were estimated using a genetic algorithm with a fitness function based on spike frequency as a function of input current. After computing the optimal parameters the neurons were interconnected to form the network model. The estimated parameters were capable of replicating the normal firing characteristics for each type of neuron, but failed to replicate richer spiking characteristics such as post-inhibitory bursting and tonic firing. Without these characteristics, the network was unable to produce biologically feasible results. Findings indicate the Izhikevich model relies heavily on manual tuning and must be trained under an extensive set of conditions to allow for the majority of spiking characteristics to be learned. The use of the Izhikevich model in a network simulation will always be limited to the characteristics trained on a single neuron. When connected to the network the neuron may be exposed to a variety of unlearned conditions and therefore may not be capable of replicating biologically realistic behavior. / Electrical and Computer Engineering

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