Analysis of the Pulmonary Vascular Tree Using Differential Geometry Based Vector Fields

摘要

We extract topological and local structural information from X-ray-computed tomography (CT) volume images of the vascular tree of the lung. We then produce an abstract model of the topology and geometry of the tree which is suitable for generating physical models. Physiologists model the vascular tree as a connected network of tubes and, to date, the only accurate data available to produce such models has come from dissection and measurement. Modeling the dynamic behavior of the tree in a living organism has been, until now, impossible. Building models from CT scans will increase the volume and quality of information available for both the study of physiology and diagnosis. We present an efficient, accurate analysis technique for volume images of tube networks. Using local operations that link techniques based on morphology to differential geometry, we transform the volume into a vector field which resembles idealized, axis-parallel fluid flow through the tube network. This field provides information to condense the salient features of the image into an augmented Euclidean minimum spanning tree (EMST). This augmented EMST proves to be a convenient and logical abstract representation of the vascular tree.