Space-Varying Coefficient Models for Diffusion Tensor Imaging using 3d Wavelets

In this paper, the space-varying coefficients model on the basis of B-splines (Heim et al., (2006)) is adapted to wavelet basis functions and re-examined using artificial and real data. For an introduction to diffusion tensor imaging refer to Heim et al. (2005, Chap. 2). First, wavelet theory is introduced and explained by means of 1d and 2d examples (Sections 1.1 { 1.3). Section 1.4 is dedicated to the most common thresholding techniques that serve as regularization concepts for wavelet based models. Prior to application of the 3d wavelet decomposition to the space-varying coe cient elds, the SVCM needs to be rewritten. The necessary steps are outlined in Section 2 together with the incorporation of the positive de niteness constraint using log-Cholesky parametrization. Section 3 provides a simulation study as well as a comparison with the results obtained through B-splines and standard kernel application. Finally, a real data example is presented and discussed. The theoretical parts are based on books of Gen cay et al. (2002, Chap. 1, 4-6), Härdle et al. (1998), Ogden (1997) and Jansen (2001) if not stated otherwise

Diffusion Tensor Imaging: on the assessment of data quality - a preliminary bootstrap analysis

In the field of nuclear magnetic resonance imaging, diffusion tensor imaging (DTI) has proven an important method for the characterisation of ultrastructural tissue properties. Yet various technical and biological sources of signal uncertainty may prolong into variables derived from diffusion weighted images and thus compromise data validity and reliability. To gain an objective quality rating of real raw data we aimed at implementing the previously described bootstrap methodology (Efron, 1979) and investigating its sensitivity to a selection of extraneous influencing factors. We applied the bootstrap method on real DTI data volumes of six volunteers which were varied by different acquisition conditions, smoothing and artificial noising. In addition a clinical sample group of 46 Multiple Sclerosis patients and 24 healthy controls were investigated. The response variables (RV) extracted from the histogram of the confidence intervals of fractional anisotropy were mean width, peak position and height. The addition of noising showed a significant effect when exceeding about 130% of the original background noise. The application of an edge-preserving smoothing algorithm resulted in an inverse alteration of the RV. Subject motion was also clearly depicted whereas its prevention by use of a vacuum device only resulted in a marginal improvement. We also observed a marked gender-specific effect in a sample of 24 healthy control subjects the causes of which remained unclear. In contrary to this the mere effect of a different signal intensity distribution due to illness (MS) did not alter the response variables

Varying Coefficient Tensor Models for Brain Imaging

We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani. The motivating example is 3-dimensional, involving a special type of nuclear magnetic resonance measurement technique that is being used to estimate the diffusion tensor at each point in the human brain. We aim to improve the current state of the art, which is to apply a multiple regression model for each voxel separately using information from six or more volume images. We present a model, based on P-spline tensor products, to introduce spatial smoothness of the estimated diffusion tensor. Since the regression design matrix is space-invariant, a 4-dimensional tensor product model results, allowing more efficient computation with penalized array regression

Space-Varying Coefficient Models for Brain Imaging

The methodological development and the application in this paper originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique enabling diagnosis and monitoring of several diseases as well as reconstruction of neural pathways. We reformulate the current analysis framework of separate voxelwise regressions as a 3d space-varying coefficient model (VCM) for the entire set of DTI images recorded on a 3d grid of voxels. Hence by allowing to borrow strength from spatially adjacent voxels, to smooth noisy observations, and to estimate diffusion tensors at any location within the brain, the three-step cascade of standard data processing is overcome simultaneously. We conceptualize two VCM variants based on B-spline basis functions: a full tensor product approach and a sequential approximation, rendering the VCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regressions with subsequent regularization. Due to major efficacy, we apply the sequential method to a clinical DTI data set and demonstrate the inherent ability of increasing the rigid grid resolution by evaluating the incorporated basis functions at intermediate points. In conclusion, the suggested fitting methods clearly improve the current state-of-the-art, but ameloriation of local adaptivity remains desirable

Statistical Diffusion Tensor Imaging

Magnetic resonance diffusion tensor imaging (DTI) allows to infere the ultrastructure of living tissue. In brain mapping, neural fiber trajectories can be identified by exploiting the anisotropy of diffusion processes. Manifold statistical methods may be linked into the comprehensive processing chain that is spanned between DTI raw images and the reliable visualization of fibers. In this work, a space varying coefficients model (SVCM) using penalized B-splines was developed to integrate diffusion tensor estimation, regularization and interpolation into a unified framework. The implementation challenges originating in multiple 3d space varying coefficient surfaces and the large dimensions of realistic datasets were met by incorporating matrix sparsity and efficient model approximation. Superiority of B-spline based SVCM to the standard approach was demonstrable from simulation studies in terms of the precision and accuracy of the individual tensor elements. The integration with a probabilistic fiber tractography algorithm and application on real brain data revealed that the unified approach is at least equivalent to the serial application of voxelwise estimation, smoothing and interpolation. From the error analysis using boxplots and visual inspection the conclusion was drawn that both the standard approach and the B-spline based SVCM may suffer from low local adaptivity. Therefore, wavelet basis functions were employed for filtering diffusion tensor fields. While excellent local smoothing was indeed achieved by combining voxelwise tensor estimation with wavelet filtering, no immediate improvement was gained for fiber tracking. However, the thresholding strategy needs to be refined and the proposed model of an incorporation of wavelets into an SVCM needs to be implemented to finally assess their utility for DTI data processing. In summary, an SVCM with specific consideration of the demands of human brain DTI data was developed and implemented, eventually representing a unified postprocessing framework. This represents an experimental and statistical platform to further improve the reliability of tractography

Swiss Corporate Sustainability Survey 2012 : Nachhaltigkeit in Schweizer Unternehmen

StudieDas Thema Nachhaltigkeit ist viel diskutiert und immer wieder Gegenstand von Untersuchungen. Der Erkenntnisgewinn der bereits existierenden Studien liegt grösstenteils in der Bedeutung von Nachhaltigkeit für Konsumenten, deren Kaufverhalten oder deren Verständnis des Begriffs Nachhaltigkeit. Wo aber steht der Werkplatz Schweiz bezüglich Nachhaltigkeit? Welche Herausforderungen sehen Unternehmen und wie wird Nachhaltigkeit in der Praxis umgesetzt? Die Studie "Swiss Corporate Sustainability Survey 2012" gibt Antwort auf diese und andere Fragen

Wissen Macht Geschlecht: Ein ABC der transnationalen Zeitgeschichte

Im Zentrum der vorliegenden Festschrift stehen Begriffe, die mit Carola Sachses Arbeit und dem Themenfeld Wissen – Macht – Geschlecht. Zeitgeschichte in transnationalen Bezügen verbunden sind. Es konzentriert sich auf die transnational vergleichende Auseinandersetzung mit drei zentralen Phänomenen des langen 20. Jahrhunderts: dem beschleunigten Zuwachs wissenschaftlichen Wissens, dem hohen Ausmaß an Gewalt in Kriegen, Bürgerkriegen und Genoziden sowie dem Wandel der Geschlechterverhältnisse. Diese Themenstellung umfasste Carola Sachses in Hamburg und Berlin entstandenen Arbeiten, die einen Bogen schlagen von der Auseinandersetzung mit betrieblicher Sozial- und Geschlechterpolitik, über die Arbeitsmarktpolitik und den Forschungsschwerpunkt „Rationalisierung und Geschlecht“ bis hin zu den Herrschaftsmechanismen im Nationalsozialismus. Wissen, Macht und Geschlecht als zeithistorische Problemstellung gab außerdem den Rahmen vor für die Projekte und Forschungsschwerpunkte, die sich in Wien anschlossen. Die Bände der Serie Proceedings stellen die Ergebnisse wissenschaftlicher Arbeitstreffen zu aktuellen Themen vor und sollen zugleich die weitere Kooperation zu diesen Themen durch das Angebot einer elektronischen Plattform unterstützen