Regularized estimation and model selection in compartment models

Dynamic imaging series acquired in medical and biological research are often analyzed with the help of compartment models. Compartment models provide a parametric, nonlinear function of interpretable, kinetic parameters describing how some concentration of interest evolves over time. Aiming to estimate the kinetic parameters, this leads to a nonlinear regression problem. In many applications, the number of compartments needed in the model is not known from biological considerations but should be inferred from the data along with the kinetic parameters. As data from medical and biological experiments are often available in the form of images, the spatial data structure of the images has to be taken into account. This thesis addresses the problem of parameter estimation and model selection in compartment models. Besides a penalized maximum likelihood based approach, several Bayesian approaches-including a hierarchical model with Gaussian Markov random field priors and a model state approach with flexible model dimension-are proposed and evaluated to accomplish this task. Existing methods are extended for parameter estimation and model selection in more complex compartment models. However, in nonlinear regression and, in particular, for more complex compartment models, redundancy issues may arise. This thesis analyzes difficulties arising due to redundancy issues and proposes several approaches to alleviate those redundancy issues by regularizing the parameter space. The potential of the proposed estimation and model selection approaches is evaluated in simulation studies as well as for two in vivo imaging applications: a dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) study on breast cancer and a study on the binding behavior of molecules in living cell nuclei observed in a fluorescence recovery after photobleaching (FRAP) experiment.