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Feilke, Martina (2015): Estimation and model selection for dynamic biomedical images. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik



Compartment models are a frequently used tool for imaging data gained with medical and biological imaging techniques. The solutions of the differential equations derived from a compartment model provide nonlinear parametric functions, based on which the behavior of a concentration of interest over time can be described. Often, the number of compartments in a compartment model is unknown. As the model complexity itself, which is, the number of compartments, is certainly an important information, it is desirable to estimate it from the observed data. Additionally, the unknown parameters have to be estimated. Therefore, methods dealing with both the parameter estimation and model selection in compartment models are needed. The methods proposed in this thesis are motivated by two applications from the field of medical and biological imaging. In the first application, the quantitative analysis of Fluorescence recovery after photobleaching (FRAP) data, compartment models are used in order to gain insight into the binding behavior of molecules in living cells. As a first approach, we developed a Bayesian nonlinear mixed-effects model for the analysis of a series of FRAP images. Mixed-effect priors are defined on the parameters of the nonlinear model, which is a novel approach. With the proposed model, we get parameter estimates and additionally gain information about the variability between nuclei, which has not been studied so far. The proposed method was evaluated on half-nucleus FRAP data, also in comparison with different kinds of fixed-effects models. As a second approach, a pixelwise analysis of FRAP data is proposed, where information from the neighboring pixels is included into the nonlinear model for each pixel. This is innovative as the existing models are suitable for the analysis of FRAP data for some regions of interest only. For the second application, the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast, we use a compartment model which describes the exchange of blood between different, well-mixed compartments. In the analysis of such data, the number of compartments allows conclusions about the heterogeneity of cancerous tissue. Therefore, an estimation and model selection approach based on boosting, with which the number of compartments and the unknown parameters can be estimated at the voxel level, is proposed. In contrast to boosting for additive regression, where smoothing approaches are used, boosting in nonlinear parametric regression as described in this thesis is a novel approach. In an extension of this approach, the spatial structure of an image is taken into account by penalizing the differences in the parameter estimates of neighboring voxels. The evaluation of the method was done in simulation studies, as well as in the application to data from a breast cancer study. The majority of the program code used in the three approaches was newly developed in the programming languages R and C. Based on that code, two R packages were built.