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Tracking of axonal bundles in diffusion MRI brain images
Piskořová, Zuzana ; Vojtíšek, Lubomír (referee) ; Labounek, René (advisor)
The aim of this thesis is to design tracking algorithm which will be able to track white matter bundles in diffusion MRI data, this problem is called tractography. Tractography is feasible because specific profile of diffusion appears in white matter. The introduction to the topic includes summary of methods for estimation of diffusion profile and basic tracking algorithms. In this work diffusion tensor model (DTI) was used for estimation of diffusion profile. Based on the DTI, vector field characterizing direction of diffusion for every voxel was created. Combining vector field with seedpoint, we achieved task solvable by Euler or Runge-Kutta method. Termination criteria were established for maximum curvature of trajectory and minimum value of fractional anisotropy (FA). Algorithm was tested on mathematical and tractographical phantom before it was used on real biological data. The results of tracking on phantoms proved the funcionality of the algorithm. Expected error appeared in areas of crossing fibers, it is related to DTI model limitations. To solve problematic fibers characterized by seedpoint near the border of the fiber, FA-weighted trilinear interpolation was designed. Implementation of this algorithm, however, did not cause better results. The results of tracking on the real data were controversial. Tracking was performed on 5 healthy subjects and 4 anatomicaly specific tracts. The results were compared with tractographic atlas.
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Absoption in mathematics and orientation towards mathematics
Kmínková, Eliška ; Rendl, Miroslav (referee) ; Pavelková, Isabella (advisor)
In the beginning of my dissertation me and my supervisor set out several objectives. We concerned ourselves on incentives factores acting prejudice in favour of mathematics and incite orientations for mathematics as well. Various kinds of interests (individual, situational, actual, special-interest), achievement motivation, flow experience and perceived capability for mathematics. We prepared two various lessons of mathematics for the students in graduation class of gymnasium - the first one conventional, the second one experimental, alternative method. We concerned ourselves in students' preferences - which classwork is convenient to successful 1 sudents in mathematics and which one to students which go badly in maths. Next objectiv was observing the group of students "orientated on mathematis", preparing themselves for leaving examination in mathematics and preparing themselves for study in faculties where is this subject is one of the major. What influences the love for mathematics? Situation interest - we took of both from lessons comparison by the students and of their flow experience during lessons. Students' flow experience was almost similar in both lessons, though a little bit better flow experience had students in conventional lesson. The students has been enquired which kind of lesson was better...
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Stochastic models for genetic analysis
Selementová, Martina ; Zichová, Jitka (referee) ; Kulich, Michal (advisor)
Nazev prace: Slochasticke niodcly pro geneliekou analyzu Autor: MartinaSelementova Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalafske prace: Mgr. Michal Kulich, PhD, e-mail vedouciho: kuliclX^karlin.mff.cuni.cz Abstrakt: V pfedlozene praci studujerne elementarni stochasticke melody pro modelovani genetickych populaci. Nejprve uvadime zakladni pojmy obecne gcnetiky pro snadnejsi oricntaci v textu. V naslcdujicich kapitolach se zabyvame dynamikou vyvoje populace a zakladnimi problemy vyberu v populaci. lllavnim tcmatem je nahodne kfizeni v populaci, ktcre dale aplikujeme na pohlavne va/ane geny, letraploidy. autosterilizacni geny a na pfi'pad dvou lokusu. Ve druhe casti se xabyvame problemy vybcru: zamC'fili jsme se pf-edevsim na vyber xalozeny na gcnolypu aplikovany na pohlavi a pohlavne vazane geny a dale na lamiliarni vyber a konkretnf pn'klad Rh faktoru. Klicova slova: nahodne kfizeni, vyber Title: Stochastic Models for Genetic Analysis Author: Martina Selementova Department: Department oi'Probability and Mathematical Statistics Supervisor: Mgr. Michal Kulich, PhD. Supervisor's e-mail adress: kulich(«)karlin.mff.cuni.cz Abstract: In the presented work we study elementary stochastic methods for modeling genetic populations. First we show some basic notion of general genetics for...
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Rezonanční frekvence generátorů syntetizovaných proudů
Kordík, Jozef ; Trávníček, Zdeněk ; Šafařík, P.
This contribution focuses on axisymmetric synthetic jet actuators from the theoretical point of view. In order to evaluate their resonance frequencies, four mathematical models were derived. The results were compared with experimental data, and analyzed. With respect to the theoretical and experimental results, the applicability and limits of the models were discussed. The results illustratively prove correctness of the previous derivation based on transformation of mechanical energy.
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Cardiovascular involvement in patients with Fabry disease
Jirák, Daniel ; Hájek, Milan (advisor) ; Vymazal, Josef (referee) ; Žižka, Jan (referee)
The evaluation of clinical magnetic resonance (MR) images is influenced by errors (subjective evaluation, noise, etc.). It is possible to eliminate these errors by using certain mathematical and statistical methods. One of these methods is texture analysis (TA), which can describe images quantitatively by computed texture parameters. The aim of this thesis was to analyze MR images of various subjects (phantoms, apples, calf muscles, livers) by TA and to evaluate its possible use in clinical practice. The main tasks of the thesis were: 1) to develop a new phantom suitable for TA and MR imaging that is biochemically and mechanically stable 2) to optimize an algorithm for TA parameter selection and classification 3) to apply TA in evaluating MR images. The first methodical part of the thesis deals with the optimization of texture parameter selection and texture classification. For this purpose a new type of phantom was developed. This PSAG phantom, with a nodular structure from polystyrene spheres (PS) placed into agar (AG), is suitable for MR imaging and for TA because it produces a strong MR signal and because its T1 and T2 relaxation times are in the range of biological tissue and can be easily modified by employing various densities of PS spheres or by the addition of a contrast agent. Measurements of PSAG...
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