Dynamic Models and Coupling in Medical 4D Imaging

In this work we present dierent approaches to improve parameter estimation from voxel-wise medical 4D data using one-dimensional dynamic models. Whereas these models have been used successfully to describe generic regions of interest as e.g. renal parenchyma or the human brain, the transition to voxel-wise data can be challenging. Reasons for this include noise or patient motion during the image acquisition. In this work we describe methods to improve parameter estimation in such a setting. Results are demonstrated on phantom and on real data for three example problems (estimation of relaxation time T1 in MRI, estimation of regional cerebral blood ow and estimation of renal function). We especially focus on the role of spatial coupling. To improve parameter estimation in the presence of noise, we extend parameter estimation by a class of spatial coupling terms, which is based on Schatten-p-norms of the Jacobian and was originally designed for RGB denoising. It is demonstrated that the novel methods can improve errors in T1 estimation up to 8% as compared to established methods.We further present results which indicate that this coupling can also improve parameter estimation in a joint setting, where not only dynamic parameters but also motion or control parameters of the model are recovered. We conclude by demonstrating limits of established models for blood ow estimation in the case of highly developed capillary tissue and extend generic existing knowledge on limits of perfusion. Specically, we simulate blood-ow through such a tissue patch and show that the estimated perfusion scales with the inverse voxel volume and thus leads to systematic overestimation.