近年来，血管类疾病已经成为人类健康的第一杀手。每年有成百上千万人死于血管疾病。血管介入术是一种非常有前景的血管类疾病的治疗手段。血管介入术是一种微创手术，它已经被广泛的用于治疗中风，血管狭窄，血管瘤等疾病。相对于传统的开放式手术，它具有风险低，恢复快，住院时间短等优点。该疗法通常在透视影像的引导下由导管和导线在血管内协同完成手术过程。因为介入术的复杂性和特殊性，作为介入手术医生的必要技能，掌握手术中手眼协同，各种手术器具的使用和复杂细致的手术流程无疑是一个巨大的挑战。因此，迫切地需要一种高效、安全的训练系统。相对于传统的训练方法，基于虚拟现实技术的训练系统是一种非常好的训练手段。 / 为了建立一套高仿真的介入手术训练模拟器，首先，我们要为病人的血管网重建三维模型。我们提出了一种自动的提取中心线的方法，用来从分割好的CTA/MRA体数据中获取病人血管网的中心线。基于改进的平行传递算法，沿着这些中心线，生成了一系列连续的标架。根据这些标架，我们构造了血管的横截面，并在此基础上生成了光滑连续的三维血管模型。 / 其次，作为血管介入术中最基础和最重要的手术器械，我们为导管和导线建立了物理模型。我们提出了一种基于最小势能原理的可变形的模型用于模拟导管和导线对于受力的反应。我们还提出了一个快速并且稳定的多网格算法来保证模拟的真实性和严格的实时交互要求。另外，我们做了几组实验。通过这些实验，验证了多网格算法在稳定性、实时性、模拟的真实性等方面满足了我们对于训练用模拟系统的要求。 / 再次，为了模拟血管栓塞术的手术过程，我们提出了一种模拟线圈填充血管瘤的过程的新方法。通过加总线圈弯曲变形的弹性势能、血管瘤变形的弹性势能以及外力做的功，我们建立了在血管栓塞术的环境下的总势能模型。为了求解这个模型，我们提出了一个基于有限元方法的求解器。从而模拟了线圈在介入医生的操作下慢慢的进入血管瘤，并缠绕起来的过程。 / 另外，我们提出了一个分层圆柱网格模型（LCGM）用于模拟在血管网中血流的运动。这一模型在几何上和拓扑结构上都非常适合我们的应用。我们将血液在血管中的流动近似为一维的层流，并用一组线性等式描述了血管网中流速与血压的关系。通过求解这一线性系统，得到了在分层圆柱网格模型下血流的速度场。依据这个血流的速度场，我们采用平流-扩散模型来模拟造影剂在血管中的传播的过程。 / Vascular diseases have been becoming the number one cause of death worldwide in recent years. Millions of people were killed by vascular diseases each year. An increasingly promising therapy for treating vascular diseases is Vascular Interventional Radiology (VIR). VIR is a minimally invasive surgery (MIS) procedure, which has been widely used to cure stroke, angiostenosis, aneurysm and etc. A low risk, an accelerated recovery and a shorter stay in hospital are important advantages over the traditional vascular surgery. This therapy is performed by a guidewire-catheter combination inside the blood vessels under the guidance of the fluoroscopic imaging. Because of the complexity and particularity of these procedures, it is a great challenge to master hand-eye coordination, instrument manipulation and procedure protocols for each radiologist mandatory. An efficient and safe training system is needed urgently. In contrast to these traditional training methods, virtual reality (VR) based simulation systems is a pretty good surrogate. / In order to build a high fidelity interventional simulator for physician training, firstly, we reconstructed the three dimensional (3D) model for the vascular network of the patients. An method of automatic skeleton extraction was proposed to acquire the centerline of the vascular network from the segmented volume data from CTA/MRA. A series of continuing frames were generated along with the centerline based on improved parallel transporting method. According to these frames we built the crossections of the vessels and further the 3D vascular model with the smooth meshes. / Secondly, as the most basic and important instruments in the VIR procedure, the catheter and guidewire were modeled and simulated physically. We developed a deformable model to simulate complicated behaviors of guidewires and catheters based on the principle of minimum total potential energy. A fast and stable multigrid solver was proposed to ensure both realistic simulation and real time interaction. A series of experiments were conducted to evaluate our multigrid solver in terms of stability, time performance, the capability of simulating catheter behaviors and the realism of catheter deformation. / Thirdly, to simulate the procedure of embolization, we proposed a novel method to simulate the motion of coil and their interactions with the aneurysm. We formulated the total potential energy in the embolization circumstance by summing up the elastic energy deriving from the bending of coils, the potential energy due to the deformation of the aneurysm and the work by the external forces. A novel FEM-based approach was proposed to simulate the deformation of coils. And the motion of coils and their responses to every input from the interventional radiologist can be calculated globally. / Fourthly, we proposed our Layered Cylindrical Gird Model (LCGM) for simulating blood flow in vascular network, which is pretty suitable for sampling the vascular network geometrically and topologically. The blood flow in vessels was regarded as 1D laminar flow and formulated into a set of linear equations based on the Poiseuille law to describe the relationship between the speed of flow and the pressure. Solving those equations, we got the velocity fields in the blood flow. In terms of the velocity fields, an advection-diffusion model was adopted to simulate the propagation of contrast agent with the blood flow. / Finally, all above techniques and procedures were implemented and integrated into a simulation system for training the medical students to acquire the endovascular skill, and an empirical study was also designed based on a typical selective catheteriza- tion procedure to assess the feasibility and effectiveness of the proposed system. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / 最后，我们将所有以上提到的技术和方法集成到模拟系统中用于训练医学院的学生，并使他们获得血管介入术的技能。并且，我们基于一个典型的导管插入术过程，使用经验分析的方法对模拟系统的可用性和效率进行了评估。 / Li, Shun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 105-116). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in also Chinese. / Abstract --- p.i / Acknowledgement --- p.vi / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Vascular Modeling --- p.14 / Chapter 2.1 --- Introduction and Related Work --- p.14 / Chapter 2.2 --- Vascular Skeleton Graph Construction --- p.15 / Chapter 2.2.1 --- Chamfer distance transform and Dijkstra's shortest-path algorithm --- p.17 / Chapter 2.2.2 --- End vertices retrieval --- p.19 / Chapter 2.2.3 --- The algorithm of vascular skeleton extraction --- p.21 / Chapter 2.3 --- Vascular Modeling --- p.21 / Chapter 2.3.1 --- Tubular Model --- p.21 / Chapter 2.3.2 --- Bifurcation Model --- p.23 / Chapter 3 --- Catheter Simulation --- p.28 / Chapter 3.1 --- Introduction and Related Works --- p.28 / Chapter 3.2 --- Catheter Simulation --- p.31 / Chapter 3.2.1 --- Kirchhoff Theory of Elastic Rod --- p.32 / Chapter 3.2.2 --- Problem Formulation --- p.34 / Chapter 3.2.3 --- The Multigrid Iterative Solver --- p.38 / Chapter 3.3 --- Collision detection --- p.45 / Chapter 3.4 --- Validation of the Catheter Simulation Method --- p.47 / Chapter 3.4.1 --- Stability --- p.49 / Chapter 3.4.2 --- Time Performance --- p.50 / Chapter 3.4.3 --- Preservation of Curved Tip --- p.51 / Chapter 3.4.4 --- The realism of catheter deformation --- p.53 / Chapter 4 --- Coil Embolization Simulation --- p.59 / Chapter 4.1 --- Introduction and Related Work --- p.59 / Chapter 4.2 --- Methodology --- p.61 / Chapter 4.2.1 --- Total potential energy of a coil --- p.61 / Chapter 4.2.2 --- The FEM-based numeric solver for interactive coil simulation --- p.61 / Chapter 5 --- Angiography Simulation --- p.70 / Chapter 5.1 --- Introduction and related works --- p.70 / Chapter 5.2 --- The Equations of Fluid --- p.72 / Chapter 5.3 --- Layered Cylindrical Gird Model --- p.73 / Chapter 5.4 --- Numerical Method --- p.76 / Chapter 5.4.1 --- Evaluation of the velocity field of blood flow --- p.76 / Chapter 5.4.2 --- Evaluation of the density field --- p.78 / Chapter 5.5 --- Results --- p.81 / Chapter 6 --- System Implementation and Evaluation --- p.84 / Chapter 6.1 --- Introduction and Related Work --- p.84 / Chapter 6.2 --- System Construction --- p.85 / Chapter 6.3 --- Empirical Study of the Training System --- p.89 / Chapter 7 --- Conclusion and Discussion --- p.98 / Chapter 7.1 --- Geometric Modeling of Vasculature --- p.99 / Chapter 7.2 --- Catheterization Simulation --- p.99 / Chapter 7.3 --- Embolization Simulation --- p.100 / Chapter 7.4 --- Angiography Simulation --- p.101 / Chapter 7.5 --- System and Evaluation --- p.102 / Publication List --- p.103 / Bibliography --- p.105