Computational models for deformable image registration and kinematic functional analysis: Grow from the flow

This thesis explores the development of novel image registration techniques for different applications in image-guided radiotherapy. Despite the existence of a variety of different metrics, multi-modal registration still presents a challenging setup with only a small number of algorithms able to handle demanding multi-modal tasks such as MR/CT registration. To this end, Chapter 2 introduces SOLID, a multi-modal metric that relies on the notion of curvature to identify corresponding structures in multi-modal datasets. Although, gradient-based features have been used in the past, this is the first work that introduces higher-order features. We further implement a registration algorithm that uses the proposed SOLID metric together with a smoothness regularization and a Discrete Cosine Transform (DCT) based optimization scheme. The proposed algorithm is tested on a variety of datasets with different contrasts and from different anatomical regions. Although the smoothness regularization is a practical choice that presents a decent one-fits-all solution, dedicated and physically motivated regularization models are required when we need to heavily rely on the registration estimate for clinical applications. To this end, Chapter 3 discusses the development of a novel generalized div-curl (GDC) registration framework that allows the user to choose from a variety of physical models for the regularization. The GDC framework incorporates a large spectrum of physical models including control over the incompressibility, irrotationality and volume expansion smoothness of the estimated deformations. The resulting framework enables the incorporation of a wide spectrum of physical models, thereby catalyzing the development of registration methods tailored for kinematic functional analysis. In Chapter 4 we employ the physically informed GDC registration framework for CT ventilation imaging (CTVI). This is achieved by selecting a physical regularization model that captures critical physiological characteristics of respiratory motion. Specifically, our model accounts for the regional character of expansions and contractions forcing them to be spatially smooth. This is the first example of a dedicated registration method for kinematic functional analysis of lung ventilation. The volume change based CTVI approach is coupled to a density-based CTVI component. The resulting Hybrid Estimation of Computed Tomography Obtained Respiratory function (HECTOR) method is therefore able to generate ventilation maps from 4DCT data, combining information from both the deformation field (volume change profile) and the CT scans (HU-derived density measures). The capacity to generate ventilation maps by simply post-processing 4DCT scans opens up the way for further analyzing the longitudinal evolution of regional ventilation over time. One obstacle is however the inherent noise and imaging artifacts that are intrinsic to CTVI maps. To overcome this, in Chapter 5 we discuss the development of a Bayesian model that incorporates physiological prior assumptions on how local ventilation changes establish and evolve. More specifically, our proposed framework places higher confidence in temporally monotonic changes. Doing this, the model is able to differentiate between noise/artifacts and genuine functional changes. Finally, the central ideas and findings of the present work are discussed in Chapter 6 together with some limitations that we hope to address in future work.