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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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Implementation of a Language Interpreter for Mathematical Calculations
Kobelka, Martin ; Šátek, Václav (referee) ; Veigend, Petr (advisor)
The main goal of this bachelor thesis is to design and implement the new programing language, which can be used for mathematical computations, implement the demonstration interpret of this language and design a graphical user interface for it. The user interface makes it easy to write the calculation, enables effective and clear visualization of calculation results and basic debugging of calculation. The properties of the resulting language are described in the thesis with the several experiments with the interpret, which implements a~subset of the language. Differences between designed solution and other platforms are also described in the thesis.
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Algebraic Equations Calculations
Kuchařová, Eva ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work investigates the solution of linear algebraic equations by a conversion to the system of differential equations. Moreover, several more frequently used methods are described in addition. The theoretical part of work describes the mathematical. Next, the examples of using the Matlab a TKSL programs are presented to show and compare the results of calculations. The source codes used are included. The work proves that the solution of algebraic equations by the conversion to the system of differential equations is applicable and further solved by the Euler's method. The parallel solution is also described. As the output of this work, the lin2dif program was developed. It realizes the conversion among the systems of equations. Finally, the description of the work progress, design, implementation and usage of the program are summarized.
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Implementation of a Language Interpreter for Mathematical Calculations
Kobelka, Martin ; Šátek, Václav (referee) ; Veigend, Petr (advisor)
The main goal of this bachelor thesis is to design and implement the new programing language, which can be used for mathematical computations, implement the demonstration interpret of this language and design a graphical user interface for it. The user interface makes it easy to write the calculation, enables effective and clear visualization of calculation results and basic debugging of calculation. The properties of the resulting language are described in the thesis with the several experiments with the interpret, which implements a~subset of the language. Differences between designed solution and other platforms are also described in the thesis.
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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.
|
|
|
Algebraic Equations Calculations
Kuchařová, Eva ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work investigates the solution of linear algebraic equations by a conversion to the system of differential equations. Moreover, several more frequently used methods are described in addition. The theoretical part of work describes the mathematical. Next, the examples of using the Matlab a TKSL programs are presented to show and compare the results of calculations. The source codes used are included. The work proves that the solution of algebraic equations by the conversion to the system of differential equations is applicable and further solved by the Euler's method. The parallel solution is also described. As the output of this work, the lin2dif program was developed. It realizes the conversion among the systems of equations. Finally, the description of the work progress, design, implementation and usage of the program are summarized.
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