On April 11th 2012, Peter Mondrup Rasmussen succesfully defended his PhD entitled Mathematical modeling and visualization of functional neuroimages. The work received much praise. Congratulations to Peter!

The work was performed in collaboration between DTU Informatics (Lyngby, DK), the Danish Research Centre for Magnetic Resonance (Hvidovre, DK), and the Center for Functionally Integrative Neuroscience (Aarhus, DK).

Supervisor: Lars Kai Hansen, Technical University of Denmark

Co-supervisors:

• Kristoffer H. Madsen, Danish Research Centre for Magnetic Resonace,Copenhagen University Hospital Hvidovre.
• Torben E. Lund, Center of Functionally Integrative Neuroscience, Aarhus University Hospital

Abstract: This dissertation presents research results regarding mathematicalmodeling in the context of the analysis of functional neuroimages.Specifically, the research focuses on pattern-based analysis methodsthat recently have become popular within the neuroimaging community.Such methods attempt to predict or decode experimentally definedcognitive states based on brain scans. The topics covered in thedissertation are divided into two broad parts: The first partinvestigates the relative importance of model selection on the brainpatterns extracted form analysis models. Typical neuroimaging datasets are characterized by relatively few data observations in a highdimensional space. The process of building models in such data setsoften requires strong regularization. Often, the degree of modelregularization is chosen in order to maximize prediction accuracy. Wefocus on the relative influence of model regularization parameterchoices on the model generalization, the reliability of the spatialbrain patterns extracted from the analysis model, and the ability ofthe resulting model to identify relevant brain networks defining theunderlying neural encoding of the experiment. We show that known partsof brain networks can be overlooked in pursuing maximization ofprediction accuracy. This supports the view that the quality ofspatial patterns extracted from models cannot be assessed purely byfocusing on prediction accuracy. Our results instead suggest thatmodel regularization parameters must be carefully selected, so thatthe model and its visualization enhance our ability to interpret thebrain.The second part concerns interpretation of nonlinear models andprocedures for extraction of 'brain maps' from nonlinear kernelmodels. We assess the performance of the sensitivity map as means forextracting a global summary map from a trained model. Such summarymaps provides the investigator with an overview of brain locations ofimportance to the model's predictions. The sensitivity map proves as aversatile technique for model visualization. Furthermore, we perform apreliminary investigation of the use of pre-image estimation forlocalized interpretation of nonlinear models. In the context of imagedenoising the pre-image analysis proves to enhance the reliability ofbrain patterns extracted from multivariate models of the neuroimaging data.