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Simulations of synthetic diffusion MRI data based on Brownian motion
Valla, Radek ; Mikl, Michal (referee) ; Labounek, René (advisor)
This master thesis focuses on dMRI (diffusion magnetic resonance imaging) and its dependance on diffusion in human brain tissue. It is described how to retrieve an image from gained data and its properties, advantages and disadvantages. It mentions problem in detecting kissing fibres due to its similarity with crossing fibres. Design of mathematical models of axons is decribed and suggested measurement to detect difference in signals for kissing and crossing fibres. It describes new simulator of diffusion-weighted MRI (dMRI) data which is able to generate it based on random walk algorithm with geometrical constraints not only for crossing fiber geometry, but also as o novelty for bending and kissing fiber geometries. This study contains results of simulations and disscusion about their usefulness with suggestions for simulator improvement. Simulated dMRI data shows significant difference in certain gradients. Data reconstruction shows, that these reults cannot be reconstructed into the same geometry as it was simulated for.
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The influence of stochastic behaviour of ion channels on the signal and information transfer at excitable neuronal membranes
Šejnová, Gabriela ; Kuriščák, Eduard (advisor) ; Maršálek, Petr (referee)
The stochastic behavior of voltage-gated ion channels causes fluctuations of conductances and voltages across neuronal membranes, contributing to the neuronal noise which is ubiquitous in the nervous system. While this phenomenon can be observed also on other parts of the neuron, here we concentrated on the axon and the way the channel noise influences axonal input-output characteristics. This was analysed by working with our newly created computational compartmental model, programmed in Matlab environment, built up using the Hodgkin-Huxley mathematical formalism and channel noise implemented via extended Markov Chain Monte Carlo method. The model was thoroughly verified to simulate plausibly a mammalian axon of CA3 neuron. Based on our simulations, we confirmed quantitatively the findings that the channel noise is the most prominent on membranes with smaller number of Na+ and K+ channels and that it majorly increases the variability of travel times of action potentials (APs) along axons, decreasing thereby the temporal precision of APs. The simulations analysing the effect of axonal demyelination and axonal diameter correlated well with other finding referred in Literature. We further focused on spike pattern and how is its propagation influenced by inter-spike intervals (ISI). We found, that APs fired...
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Analysis of dynamical interactions of axon shafts and their biopysical modelling.
Šmít, Daniel ; Zápotocký, Martin (advisor) ; Reingruber, Jūrgen (referee) ; Maršálek, Petr (referee)
in English While axon fasciculation plays a key role in the development of neural networks, very lit- tle is known about its dynamics and the underlying biophysical mechanisms. In a model system composed of neurons grown ex vivo from explants of embryonic mouse olfactory epithelia, we observed that axons dynamically interact with each other through their shafts, leading to zippering and unzippering behaviour that regulates their fasciculation. Taking advantage of this new preparation suitable for studying such interactions, we carried out a detailed biophysical analysis of zippering, occurring either spontaneously or induced by micromanipulations and pharmacological treatments. We show that zippering arises from the competition of axon-axon adhesion and me- chanical tension in the axons. This is upheld on quantitative level by conforming change of network global structure in response to various pharmacological treatments, without active involvement of growth cones. The calibrated manipulations of interacting shafts provide qualitative support for the hypothesis, and also allow us to quantify the mechan- ical tension of axons in our system. Furthermore, we introduce a biophysical model of the zippering dynamics, which efficiently serves the purpose of estimating the magnitude of remaining involved...
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Simulations of synthetic diffusion MRI data based on Brownian motion
Valla, Radek ; Mikl, Michal (referee) ; Labounek, René (advisor)
This master thesis focuses on dMRI (diffusion magnetic resonance imaging) and its dependance on diffusion in human brain tissue. It is described how to retrieve an image from gained data and its properties, advantages and disadvantages. It mentions problem in detecting kissing fibres due to its similarity with crossing fibres. Design of mathematical models of axons is decribed and suggested measurement to detect difference in signals for kissing and crossing fibres. It describes new simulator of diffusion-weighted MRI (dMRI) data which is able to generate it based on random walk algorithm with geometrical constraints not only for crossing fiber geometry, but also as o novelty for bending and kissing fiber geometries. This study contains results of simulations and disscusion about their usefulness with suggestions for simulator improvement. Simulated dMRI data shows significant difference in certain gradients. Data reconstruction shows, that these reults cannot be reconstructed into the same geometry as it was simulated for.
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The Theoretical Background of Neuronal Networks
ROKŮSEK, Zdeněk
In focus of this dissertation is the theoretical background of the neural networks with a description of basic models of these neural networks and their application in practice. Furthermore, this work provides a concise historical overview of the exploration on field of the neural calculations. It also clarifies neuro-physiological motivation that conducts to the mathematical model of the neuron just like the neural networks. The number of options of neural networks and ways how to apply them is high. The neural networks can be used to define figures or to compress data, and so on. Among the most familiar models of a neural network is the multilayer neural network, the model of MADALINE, the associative network or the Hopfield´s network.
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