Anatomical shape reconstruction and manufacturing: solving topological changes of lumen vessel trough geometric approach

Over the last years there has been an increasing growth of interest in Rapid Prototyping (RP) techniques applied to various fields of medicine. RP makes it possible, in vascular surgery, to produce accurate anatomic replicas of patient vessels. These replicas can help the customization of surgical invasive interventions such as in situ stent-graft insertion in carotid region. The main goal of this work is to obtain high quality in lumen reconstruction and manufacturing replicas by RP technique. This goal is achieved through the complete control of each phase of the generating process. We present a semi-automatic method for carotid lumen reconstruction based on Boundary Representation (BRep). All parameters influencing the quality of the shape reconstruction are presented and discussed: shape acquisition, shape reconstruction and shape manufacturing. The shape acquisition starts by extracting the points belonging to the boundary of the lumen vessel, from Computer Tomography (CT) images. These points, parameterised in a vector, are the input data of the shape reconstruction algorithm based on B-Spline interpolation. The B-Spline type for representing curves and surfaces were chosen because of their properties of continuity and local control. In the shape reconstruction stage we had to face problems due to the topological change on the vessel structure. For vessel regions where there are not changes of topology, we use the closed B-Spline curves (belonging to adjacent acquisition planes) as generating curves to build a B-Spline surface. For vessel regions with at least a change of topology (ex. bifurcation region) our algorithm split automatically the involved curves to obtain three rectangular B-Spline patches. Such patches are joined together to obtain the bifurcation vessel lumen. The set of lumen surfaces is then inserted in a Boundary Representation in order to get a valid solid. To analyse the quality of the reconstructed shapes, the final object is compared with the acquisition image. This solid is correctly tessellated in triangles to produce the data format used by the RP devices (STL)