Die diffusionsgewichtete Magnetresonanztomographie (DW-MRT) ist ein fester Bestandteil der radiologischen Diagnostik des Zentralnervensystems (ZNS), und zwar nicht nur bei Schlaganfällen sondern zunehmend auch bei Hirntumoren, Schädelhirntraumata, demyelinisierenden, degenerativen sowie entzündlichen Erkrankungen. Diese Pathologien gehen in der Regel mit einer Veränderung der lokalen Diffusionsbedingungen einher, die eine reguläre Diffusionsbildgebung beeinträchtigen. Durch die Bestimmung der Diffusionsparameter lassen sich mit Hilfe verschiedener mathematischer Verfahren Faserverbindungen visualisieren. Wie sich diese unterschiedlichen Methoden in Regionen mit aversiven Diffusionsbedingungen verhalten, konnte mit der Arbeit erstmals systematisch gezeigt werden. Hierzu wurden 29 Patientenuntersuchungen ausgewertet. Als Einschlusskriterium galt eine unilaterale, diffusionsrelevante Läsion mit Bezug zur Pyramidenbahn. Ausschlusskriterium war eine vollständige Hemiparese als Zeichen einer vollständigen Zerstörung der relevanten Leitungsbahn. Im Einzelnen handelte es sich bei den untersuchten Läsionen um drei höhergradige Astrozytome (WHO Grad III-IV), drei niedriggradige Astrozytome, acht Glioblastome, zwei Karzinommetastasen, zwei arteriovenöse Malformationen und je eine entzündliche Parasitose, ein Oligodendrogliom, eine Gliomatose und ein Kavernom. Untersucht wurden zwei deterministische (einfaches und interpoliertes streamlining) und drei probabilistische Methoden (ohne crossing fibers; mit Berechnung von zwei Fasern pro Voxel und constrained/bayesian). Läsionen jeglicher Art verursachten signifikant mehr Fehlschläge bei deterministischer als bei probabilistischer Traktographie. In neun Untersuchungen bei einfacher und in acht Untersuchungen bei interpolierter Traktographie zeigten sich fasch negative Ergebnisse. Probabilistisches Traktographieren eliminiert nicht falsch negative Ergebnisse, reduziert sie jedoch unter den oben genannten aversiven Difussivitätsbedingungen mit denen intraaxiale Läsionen einhergehen. Klinisches Wissen über die verbliebene Traktintegrität ermöglicht die Umwandlung der Traktographieergebnisse in Wahrscheinlichkeitswerte innerhalb eines Bayschen Modells. Außerdem ist nur unter Miteinbeziehung klinischer Informationen eine Traktographie nach dem constrained Modell möglich. Obwohl die probabilistische Traktographie weniger anfällig für falsch negative Ergebnisse ist als die deterministische, geht die erhöhte Sensitivität der Algorithmen auf Kosten der Spezifität. Dies zeigt sich in signifikant erhöhten bilateralen Traktvolumina und einem übermäßigen Unterschied der Traktvolumina von Läsionsseite zu kontralateraler Seite. Die probabilistisch, unconstrained durchgeführte Traktographie der Pyramidenbahn zeigte eine signifikant, durch die Läsion verursachte Volumenminderung des Traktes, während dies im constrained modellierten Fall durch die Daten nicht gezeigt werden konnte. Dies zeigt die Robustheit des Constrained Modells unter den aversiven klinischen Bedingungen einer intraaxialen Läsion ohne den Nachteil von erhöhten Fehltraktographien. Es kann konstatiert werden, dass sich die deterministischen Traktographieverfahren zur präoperativen Orientierung vor neurochirurgischen Eingriffen eignen. Jedoch ist eine nicht zu unterschätzende Anzahl von falsch negativen Ergebnissen zu berücksichtigen. In zweifelhaften Fällen sollte zusätzlich eine Darstellung mittels probabilistischen Algorithmen, am besten mittels Constrained Modell durchgeführt werden. / Diffusion weighted magnetic resonance imaging (DW-MRI) is a common part of radiologic diagnostics of the central nervous system (CNS). Not only for the diagnosis of strokes but also in tumors, trauma, degenerative, demyelinising and inflammatory diseases. These pathologies normally include an affection of local diffusion parameters, witch impede a regular diffusion imaging. Through estimating diffusion parameters it is possible to visualize fibre connections with different mathematical methods (diffusion tensor imaging, DTI). For the first time in this thesis it could be shown how these different methods are affected by aversive diffusion conditions. 29 examinations were evaluated. Including criteria in the study were unilateral diffusion relevant lesions with reference to the pyramidal tract. Exclusion criteria were a complete paresis or plegia as sign for a complete destruction of the relevant tract. In special 3 high grade astrocytomas (WHO III-IV) 3 low grade astrozytomas, 8 glioblastomas, 2 metastasis, 2 artero-venous-malformations and each one parasitosis, oligodendroglioma, gliomatosis and cavernoma. Two deterministic (one with a fixed step length and one with probabilistic sampling)) and three probabilistic methods (with /without crossing fibres and within a constrained Bayesian framework) were performed on the same data. Lesions of all kinds caused significantly more false negative results in deterministic tracking. 9 examinations in simple and 8 in interpolated traktographies showed false negative results. Probabilistic tracking did not eliminate false negative results, but reduced them under the aversive diffusion parameters. Clinical knowledge on remaining tract integrity allows the conversion of the tracing results into probabilities within a Bayesian model. The lowered false negative rate of the probabilistic methods compared to the deterministic methods is the raised sensitivity at expenses on a lowered specificity. This can be seen in significantly raised bilateral tract lumina and an overestimated difference between tract volumes on lesion and non affected side. The probabilistic unconstrained tractographie showed a significant lowered tract volume due to the lesion; however this could not be shown for the constrained modelling. This shows the robustness of the constrained model under the aversive clinical conditions of intraaxial lesions without the disadvantage of more false tractrographies. It can be stated, that preoperative tractographies are a useful instrument of pre interventional orientation before neurosurgical operations. However a not quite low number of false negative results have to be accounted. In problematic cases an additional visualisation with probabilistic algorithms should be performed, preferably in a constrained model.

A new method, probability distribution of diffusivities (time scaled square displacements between succeeding video frames), was developed to analyze single molecule tracking (SMT) experiments. This method was then applied to SMT experiments on ultrathin liquid tetrakis(2-ethylhexoxy)silane (TEHOS) films on Si wafer with 100 nm thermally grown oxide, and on thin semectic liquid crystal films. Spatial maps of diffusivities from SMT experiments on 220 nm thick semectic liquid crystal films reveal structure related dynamics. The SMT experiments on ultrathin TEHOS films were complemented by fluorescence correlation spectroscopy (FCS). The observed strongly heterogeneous single molecule dynamics within those films can be explained by a three-layer model consisting of (i) dye molecules adsorbed to the substrate, (ii) slowly diffusing molecules in the laterally heterogeneous near-surface region of 1 - 2 molecular diameters, and (iii) freely diffusing dye molecules in the upper region of the film. FCS and SMT experiments reveal a strong influence of substrate heterogeneity on SM dynamics. Thereby chemisorption to substrate surface silanols plays an important role. Vertical mean first passage times (mfpt) in those films are below 1 µs. This appears as fast component in FCS autocorrelation curves, which further contain a contribution from lateral diffusion and from adsorption events. Therefore, the FCS curves are approximated by a tri-component function, which contains an exponential term related to the mfpt, the correlation function for translational diffusion and a stretched exponential term for the broad distribution of adsorption events. Lateral diffusion coefficients obtained by FCS on 10 nm thick TEHOS films, thereby, are effective diffusion coefficients from dye transients in the focal area. They strongly depend on the substrate heterogeneity. Variation of the frame times for the acquisition of SMT experiments in steps of 20 ms from 20 ms to 200 ms revealed a strong dependence of the corresponding probability distributions of diffusivities on time, in particular in the range between 20 ms and 100 ms. This points to average dwell times of the dye molecules in at least one type of the heterogeneous regions (e.g. on and above silanol clusters) in the range of few tens of milliseconds. Furthermore, time series of SM spectra from Nile Red in 25 nm thick poly-n-alkyl-methacrylate (PnAMA) films were studied. In analogy to translational diffusion, spectral diffusion (shifts in energetic positions of SM spectra) can be studied by probability distributions of spectral diffusivities, i.e. time scaled square energetic displacements. Simulations were run and analyzed to study contributions from noise and fitting uncertainty to spectral diffusion. Furthermore the effect of spectral jumps during acquisition of a SM spectrum was investigated. Probability distributions of spectral diffusivites of Nile Red probing vitreous PnAMA films reveal a two-level system. In contrast, such probability distributions obtained from Nile Red within a 25 nm thick poly-n-butylmethacrylate film around glass transition and in the melt state, display larger spectral jumps. Moreover, for longer alkyl side chains a solvent shift to higher energies is observed, which supports the idea of nanophase separation within those polymers.

A new method, probability distribution of diffusivities (time scaled square displacements between succeeding video frames), was developed to analyze single molecule tracking (SMT) experiments. This method was then applied to SMT experiments on ultrathin liquid tetrakis(2-ethylhexoxy)silane (TEHOS) films on Si wafer with 100 nm thermally grown oxide, and on thin semectic liquid crystal films. Spatial maps of diffusivities from SMT experiments on 220 nm thick semectic liquid crystal films reveal structure related dynamics. The SMT experiments on ultrathin TEHOS films were complemented by fluorescence correlation spectroscopy (FCS). The observed strongly heterogeneous single molecule dynamics within those films can be explained by a three-layer model consisting of (i) dye molecules adsorbed to the substrate, (ii) slowly diffusing molecules in the laterally heterogeneous near-surface region of 1 - 2 molecular diameters, and (iii) freely diffusing dye molecules in the upper region of the film. FCS and SMT experiments reveal a strong influence of substrate heterogeneity on SM dynamics. Thereby chemisorption to substrate surface silanols plays an important role. Vertical mean first passage times (mfpt) in those films are below 1 µs. This appears as fast component in FCS autocorrelation curves, which further contain a contribution from lateral diffusion and from adsorption events. Therefore, the FCS curves are approximated by a tri-component function, which contains an exponential term related to the mfpt, the correlation function for translational diffusion and a stretched exponential term for the broad distribution of adsorption events. Lateral diffusion coefficients obtained by FCS on 10 nm thick TEHOS films, thereby, are effective diffusion coefficients from dye transients in the focal area. They strongly depend on the substrate heterogeneity. Variation of the frame times for the acquisition of SMT experiments in steps of 20 ms from 20 ms to 200 ms revealed a strong dependence of the corresponding probability distributions of diffusivities on time, in particular in the range between 20 ms and 100 ms. This points to average dwell times of the dye molecules in at least one type of the heterogeneous regions (e.g. on and above silanol clusters) in the range of few tens of milliseconds. Furthermore, time series of SM spectra from Nile Red in 25 nm thick poly-n-alkyl-methacrylate (PnAMA) films were studied. In analogy to translational diffusion, spectral diffusion (shifts in energetic positions of SM spectra) can be studied by probability distributions of spectral diffusivities, i.e. time scaled square energetic displacements. Simulations were run and analyzed to study contributions from noise and fitting uncertainty to spectral diffusion. Furthermore the effect of spectral jumps during acquisition of a SM spectrum was investigated. Probability distributions of spectral diffusivites of Nile Red probing vitreous PnAMA films reveal a two-level system. In contrast, such probability distributions obtained from Nile Red within a 25 nm thick poly-n-butylmethacrylate film around glass transition and in the melt state, display larger spectral jumps. Moreover, for longer alkyl side chains a solvent shift to higher energies is observed, which supports the idea of nanophase separation within those polymers.