A Generic Framework for Vessel Tree Segmentation. Introducing High-Level Physiological Knowledge into the Segmentation Process (Een algemeen raamwerk voor de segmentatie van bloedvatenbomen. De introductie van hoog-niveau fysiologische kennis in het segmentatieproces)

IntroductionMultiple organs in the human body feature vascular trees; by the aid of imaging techniques such as CT and MR, they can be visualised in 3D. The segmentation of these structures can benefit many applications ultimately leading to better diagnosis and treatment, such as navigation within the organ, which allows to retrieve a certain pathology on another image or during surgery, or the careful removal of a part of the organ that is perfused by a single vessel tree. The statistical analysis of the segmented tree might also lead towards an automated analysis and novel insights. However, manual segmentation of these structures is tedious and time-consuming, hence there is a need for automated segmentation.A variety of methods to segment vascular structures has been proposed. However, none of these methods explicitly look for a plausible vessel tree structure.This work is the first to present a framework for the segmentation of tree-like structures that includes high-level knowledge, such as Murray's physiological model, which is presented below, into the segmentation process. ModelIn homogeneous organs, such as the liver and the lungs, the vasculature shows certain regularities, e.g. it constitutes a fractal-like tree shape and features certain relations between the radii and angles in a bifurcation. In 1926 Murray was able to explain these characteristics by applying the principle of minimum work, which postulates that biological systems have evolved to be the most efficient, onto the flow of blood vessels. Using the principles of fluid dynamics, he deduced a set of mathematical equations describing the properties of the vasculature: the cube of the radius of a vessel segment is proportional to the flow, and the total blood volume is minimal while still perfusing the entire organ.The combination of these principles with a homogeneous organ in which the tree structure can develop freely, yields the mentioned fractal-like tree structure.The physiological model is complemented by an intensity model. The intensity model assumes a constant intensity distribution for the vasculature and for the surrounding tissue. Additionally it approximates the intensities in a CT scan by including partial volume effects, a point spread function, and spatially correlated noise. MethodThe proposed framework for vessel tree segmentation uses a bottom-up approach while incorporating high level knowledge, i.e. the vessel tree model that was described in the previous section. The method looks for a vascular tree structure that fits the image while (virtually) perfusing the organ with minimal work. It consists of three consecutive steps. First, a large set of candidate bifurcation locations is determined. Subsequently, individual vessel segments of varying diameter are constructed between each two candidate bifurcation locations. This way, a graph is constructed consisting of the candidate bifurcation location as nodes and the candidate vessel segments as edges. Finally,an overall vessel tree is found by selecting the subset of these segments and nodes that perfuses the whole organ, while trying to minimise an objective function containing a data term, and physiology-based volume and flow terms. The data term, based upon the intensity model, measures how well the detected vessel tree fits to the image, the volume term measures the total amount of blood in the vasculature, and the flow term measures the compliance of the segments' radii with their estimated flow. The selection of the optimal subset of vessel segments into a single vessel tree is an NP-hard combinatorial optimization problem, which is approximated with an approach inspired by ant colony optimisation. ValidationThe algorithm has been validated on artificial 2D images mimicking liver CT scans, and clinical 3D liver CT scans. For the artificial images there was a significant p