{'fraction_non_alphanumeric': 0.01714898177920686, 'fraction_numerical': 0.0010718113612004287, 'mean_word_length': 5.482638888888889, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Estimation of curvature and torsion of discrete mammalian cell paths through porous media. (Estimation des courbures et torsions des trajectoires discrètes de cellules mammaliennes à travers des milieux poreux)

The extraction of cancerous cells from body uids is an important procedure in clinical diagnostics and therapy. Notably, when the separation technique is based on cell chromatography, it is important to have precise knowledge about binding capacities of target cells in porous media. Therefore, experiments using time-resolved micro-computed tomography were designed and carried out at the European Synchrotron Radiation Facility. The curvature and torsion distributions of cell paths in a two-phase ow through a porous medium are valuable information to characterize the efficiency of chromatographic processes. However, the computation of torsion is very challenging, since it is based on higher order derivatives which are very sensitive towards discretization noise. In this thesis, two new curvature and torsion estimation methods of particle paths are presented. The first method is based on a Fourier approximation. Case studies showed a decrease of the torsion estimation error of at least 65% compared to the commonly used spline approximation. Moreover, the smoothing parameter of the Fourier approximation can remain unchanged for both a wide range of lateral resolutions and curvatures and torsion values. Since this Fourier approximation approach cannot be applied at non-equidistant points, a second method based on the discretization of the differential-geometric formulas (DDGF) was developed. The spline approximation and the DDGF led to similar mean torsion errors. However, the filter mask remains unchanged for the DDGF, whereas the smoothing parameter of the spline approximation must be adapted to the curve shape and discretization