High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

A General Approach to Model Biomedical Data from 3D Unorganised Point Clouds with Medial Scaffolds

We present the latest developments in modeling 3D biomedical data via the Medial Scaffold (MS), a 3D acyclic oriented graph representation of the Medial Axis (MA) [LK07, SP08]. The MS (and associated 3DMA) can be computed as the result of the singularities of a geometric wave propagation simulation. We consider here some of the potential applications of this shape model in the realm of biomedical imaging. We can reconstruct complex object surfaces and make explicit the coarse-scale structures, which are ready-to-use in a number of practical applications, including: morphological measurement for cortex or bone thickness, centerline extraction (curve skeleton) for tracheotomy or colonoscopy, surface partitioning for cortical or anatomical surface classification, as well as registration and matching of shapes of tumors or carpal bones. The MS permits to automatically and efficiently map an unorganised point cloud, i.e., simple 3D coordinates of point samples, to a coherent surface set and associated approximate MA. The derived MS is used to further recover significant medium and large scale features, such as surface ridges and main axial symmetries. The radius field of the MS provides an intuitive definition for morphological measurements, while the graph structure made explicit by the MS is useful for shape registration and matching applications