Advances in Statistical Modeling of High Dimensional Data:
Variable selection, and Challenges in Image Analysis

Volker Schmid, LMU München

Bayesian Modelling for Perfusion Imaging

Perfusion imaging aims to investigate the kinetics in human tissue in vivo. This is of interest in particular in oncology, cardiology and neurology. Using a (magnetic) contrast agent, a series of (magnetic resonance) images is obtained, which show the distribution of contrast agent in the tissue over time. Such scans are typically analysed using kinetic models composed of a (maybe unknown) input function and and an (usually exponential) response function. In order to assess the tissue perfusion, one has to perform deconvolution or optimize the highly non-linear convolved model. The latter approach is typically prone to convergence problems, whereas deconvolution often is affected by numerical instability. We present a Bayesian approach to model perfusion images. Prior knowledge about kinetic parameters allows for a more robust estimation of these parameters and the computation of interval estimators. Contextual information can be used to make the models even more robust and/or to find connections between tissue voxels. Spatial priors (Gaussian Markov random fields) are used to account for spatial context and to reduce estimation errors. Temporal smoothing priors (penalty splines) are used to reduce observation noise. At last, we present a comprehensive model for the analysis of complete drug studies with perfusion imaging.

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