Simulation-based Virtual Prototyping of Customized Catheterization Devices
YY Cai1, C-K Chui2, 3, X Ye4, JH Anderson5, K-M Liew1 and I Sakuma2 1
Nanyang Centre for Supercomputing & Visualization, Nanyang Technological University, Singapore 2
Biomedical Precision Engineering Lab, University of Tokyo, Japan
3
Biomedical Imaging Lab, Institiue for Infocomm Research, Singapore
4
College of Computer Science & State Key Lab of CAD/CG, Zhejiang University (China) and SolidWorks Corp. (USA) 5
School of Medicine, Johns Hopkins University, USA
Corresponding Person: Dr YY Cai, ASME Membership: N/A Mailing address: Nanyang Center for Supercomputing & Visualization, School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore-639798,
Republic of Singapore Email:
[email protected], Telephone: 65-67905777.
Abstract Human vascular systems have considerable anatomic variations. In diseased situation, significant pathological changes will be developed with the systems. However, vascular catheterization devices commercially available are essentially designed on normal or average anatomy. Their inadequacies in representing major deviations in human vascular anatomy may present problems during diagnostic or therapeutic interventions. A virtual reality (VR) based simulation method is described in this paper for prototyping of customized patient-specific catheterization devices. Techniques are developed to model patient-specific vascular network, to design catheterization devices, and to simulate physical-based interactions between blood vessels and the devices. Emphasis is made on the integration of normal and variant vascular models, the integration of modeling, visualization and interaction, and the integration of real-time simulation and virtual prototyping. Keywords: Customized device prototyping, normal and variant vasculature, VR, simulation-based design.
1. Introduction Interventional radiologists and cardiologists gain access to the site of internal lesions and pathology using catheters that are inserted into a blood vessel through a puncture in the skin. Real-time X-ray fluoroscopy is used to visualize the passage of the catheter navigation. The catheters can be used as conduits to pass therapeutic devices to treat diseased conditions. The principal advantage of this approach is to minimize the invasive nature of open surgery. Many of interventional procedures are performed on an outpatient basis reducing the cost and discomfort to the patient, as well as the time of convalescence [1-3].
Figure 1. A list of catheters Catheterization device development started in the 1960s and has evolved into one of the lucrative manufacturing businesses [4-6]. In the early years, pioneer physicians or surgeons prototyped their conceptual design of the catheter device using simplistic tools available in their homes. The prototype was then validated by inserting and navigating inside the vascular network of animals or even their own. Intensive testing was conducted in order to come up with an ideal design to access a particular region within the vascular network. Typically, the design was good to handle an average case with average anatomy or pathology. Today, many catheterization devices are developed after the names of those pioneers, e.g. Judkins, Mani, etc. Figure 1 illustrates a variety of catheters routinely used in hospitals. Presently, the variation in the size/length and shape of the tip of commercial catheters are only related to races, ages and diseased lesion (e. g. coronary or neurology). Standardized catheterization devices are easy for mass production that helps to reduce the production cost. However, they do not meet the needs of all patients and this can cause problems. For instance, during interventional procedures, often several catheters (cost to patient ranging from a few dollars to near hundred dollars each piece) will be used through a trial-and-error with non-reusable catheters to reach the target site. With increasing demands for improvement in the quality of heath-care delivery and reduction of the medical expense, there is a need for more patient-specific design and production of medical devices to treat individual people. Researchers have conceived the concept of mass customization in recent years [7-8]. The "one size fits all" model is probably out-of-date. This is particularly true when quality personal medical treatment is concerned. Mass customization of medical devices is, however, far more than making efficiency improvements through automated production processes, integrated supply and delivery chains and the like. R&D on new medical devices plays a vital role in this mass customization or personalization and catheterization devices are ideal examples for the study of mass customization. The rapid growing of computer-aided design [9], visualization [10], and simulation [11] technologies has provided a new platform for possible development of customized catheterization devices. As an enabling technology, VR [12] has found many applications in medical field from arthroscopic knee surgery [13] to anaesthesiology [14] to endoscopic surgery [15] to minimally invasive therapy [16]. Cardiovascular surgical training using VR technology is one of the hot areas [17-22]. In this work, we will discuss the development of patient-specific catheterization devices using the VR simulation technology. Emphasis is made on the integration of normal and variant vascular models, the integration of real-time simulation and virtual prototyping, and the integration of fidelity visualization and interaction. Although the intention of this work is to design devices targeted for specific patients, it is possible that a group of patients or similar pathologies also may be targeted if the degree of similarities between patients/pathologies is high and acceptable to the medical community. In addition, the concept of patient-specific device development can also be extended to other less invasive image guided vascular and non-vascular interventional
procedures. We use simulation-based design (SBD) for virtual prototyping of customized catheterization devices. SBD is rapidly emerging as an indispensable time and cost saving tool that has been widely applied in various industries including automobile, aircraft, and space [23-27]. SBD offers significant savings in resources over life testing, and overcomes a number of safety and environmental constraints. The underlying concept for using simulation-based design, analysis and visualization in an integrated way is that of the "virtual prototype". In Section 2, we present an integrated view of our VR simulation-based design for the development of patientspecific catheterization devices. Section 3 presents our vascular modeling with particular focus on various aspects of anatomy variants and shape construction from angio-grams that serve as inputs of patient-specific data. Section 4 discusses the modeling of catheterization devices. Section 5 describes our simulation system for designing of patient-specific cardiovascular catheterization devices. The paper is concluded in Section 6.
2. An Overview of Integrated Virtual Prototyping of Catheterization Devices A VR-based simulation method can be applied to prototype customized patient-specific medical devices particularly those used in image-guided interventional medical procedures. Input to the simulation-based design process is patient data acquired from various medical imaging modalities such as Computerized Tomography (CT), Rotational Angiography and Magnetic Resonance Angiography (MRA). A customized device is then designed using a desktop VR-based computer simulator. Figure 2 shows an overview of our method as an iterative optimization process.
Figure 2. Overview of virtual prototyping of patient-specific catheterization devices SBD in this application is an iterative optimization process starting from patient-specific images. A geometric 3-D model of the patient-specific vasculature is obtained through a reconstruction process integrating both normal and variant vasculatures. Based on the information we collected from both experiment and literature [28-30], physical properties of the vessel such as elasticity, Young’s modulus and shears modulus etc., are used as material parameters for the modeling of the interaction of the vessels with the catheterization devices. The material properties of the devices are assigned initially with those of popular and standard materials used in industry. The iterative VR simulation is then conducted with our simulator to obtain an optimized solution by changing various material parameters and testing on different navigation procedures with the aid of the integrated function of visualization and interaction. Typically, the optimized design is able to identify the suitable materials that will lead to a stable geometry of the catheterization devices. In the case of catheter and guide-wire devices, we concentrate on only the shape and material of the tip parts of the devices following most of the people [1-4]. A detailed design will then be developed using the CAD technology. This integrated
process of simulation and prototype design can take into account the patient-specific information of anatomy and pathology through an optimized and interactive simulation of maneuvering and passing of a virtual device in the blood vessels.
3. Human Vascular Modeling and Variant Representation Human vascular anatomy is highly individualized with normal vasculature explaining only as an average or idealized representation. Individual variation of vascular anatomy is very common and individual patient’s angiographic appearance can be very different from that seen in anatomy textbook or atlases. Therefore it is of clinical interest to understand both normal and common variations in vascular anatomy [31]. When pathological factors change from time to time, variations in vascular anatomy become even more significant. Their differences in both quantity and quality add difficulty in understanding the variability of the vascular network [32-33]. Modeling of vascular variation is therefore an important yet challenging task. Based on the work by H Lippert and R Pabst [34], our current study concentrates only on the ascending aorta, aortic arch and coronary arteries. To begin, we describe our general technique for geometric modeling of human vasculature (either normal or variant).
Figure 3. Vascular geometric modeling Geometric_Modeling_of_Human_Vasculature We have developed a novel geometric modeling approach to constructing the vascular network. Sweeping and blending operations are used to create initial vascular segments and bifurcations. In particular, piecewise Bézier patches are generated to represent the vascular segments. As for the bifurcation, three semi-tubular Bézier patches are generated using the same sweeping operation. Two 3-sided holes are formed surrounded by three semi-tubular patches. Each hole is filled with three Bézier patches. Constructive methods for modifying vascular joints are used to form visual smooth or GC1 vascular networks. First, the boundaries and the row next to the boundaries of semi-tubular patches are modified to allow cross-boundary tangential continuity, twist compatibility and unique existence of tangential plane. The new boundaries and derivatives of the holes are then used to generate new filling triangles. Our vascular network modeling procedures can be found in [35-36]. The current implementation took advantage of rectangular Bézier patch representation to display the vascular scenesfor real-time interactive simulation. Figure 3 shows a vascular network model created using the geometric modeling approach developed. This generic modeling approach can be used to model any patientspecific vasculature.
Figure 4. Normal and variant aortic arteries Classifiation_of_Normal_and_Variant_Aortic_and_Coronary_Arteries Many people have variant aortic and/or coronary arteries though the variants are not dominant. There are typical 9 classes of aortic arteries and 3 classes of coronary arteries in both normal and variant systems (Figs. 4 and 5). Each of the artery class could have one or more different types each with a certain rate of occurance. The classification is mainly based on the topology of the relevant arteries’ branching order and connectivity. In the “normal”cases of aortic arteries (about 70% of population), the innominate artery of the right brachiocephalic trunk (RBT) arises first, followed by the left common carotid (LCC) and left subclavian (LS) arteries. Similarly, in majority of human population (around 60% of population), the right coronary artery (RCA) will originate in the ascending aorta from the right sinus. Figures 4 and 5 show the details (class, type, occurring rate and topology) of the variant aortic and coronary arteries.
Figure 5. Normal and variant coronary arteries Human vascular system is highly complex. Note that having variant coronary arteries does not necessary indicate any health problem.
Figure 6. Construction of coronary arteries from angiograms 3D_Vascular_Reconstruction_from_Patient-specific_Images The reconstruction algorithm involves extraction of the central line of the arteries of interest. Each image provides the vascular central line from a specific angle. All those central lines are then combined to form the 3D vascular segments. The diameters of the arterial segments can also be extracted from images [37-38]. The scanned images and extracted arteries provide topological information of the patient vascular network which
may help identifying vascular variation. Figure 6 shows the construction of the 3D coronary arteries from a pair of angiogram images.
4. Virtual Catheter Modeling and Manipulation Catheters can be characterized by the type of materials, the number of lumens, the internal and external diameters, the working length and the tip shape. In terms of device function, catheters can be mainly classified as angiographic or balloon catheters. The diameters and tip shapes are the most prominent parameters. A catheter has the distal end and the proximal end. The distal end is the tip where surgeons have to pay attention in order to suit the device with the anatomical configurations of the blood vessels. The external diameter of catheters ranges from 3 to 34 frenchs (1 mm=3 frenchs). Catheters are often made of polyvinyl chloride (PVC), silastic or polyurethane. PVC catheter is very rigid thus may cause vessel perforation. To avoid complication linked to fibrin sheath and venous thrombus, soft silastic catheter can provide better patient comfort and better biocompatibility, eliciting little fibrotic reaction. However, to have the same tensile strength as polyurethane, silastic needs to have a thicker wall. Therefore, the outer diameter of a silastic catheter for a comparable flow is usually larger. Polyurethane is less biocompatible as compared to silicone. It is stiffer with smaller friction coefficient. Having higher burst pressures and greater tensile strengths, polyurethane catheters cause significantly less thrombophlebitis than silastic catheters. Other types of materials used to make catheters include nylon, polypropylene, polyester, custom thermoplastics, polyamide nylon and elastomeric hydrogels.
Figure 7. Definition of the virtual catheter segments Geometrically_Based_Modeling_of_a_Virtual_Catheter Our virtual catheter model is defined using combination of one or more segments of arcs defined by three parameters in its local coordinate system. The parameters are the length (L), the radius of arc (ra) and the radius of the cylinder around which the arc is twisted (rc) as shown in Fig. 7. The origin of the coordinate system is the point where the curve joins the next segment. The coordinates of each point on the curve can be parameterized to C(s) = (x(s), y(s), z(s)) where 0 ≤ s ≤L. The computation of these coordinates is done in following steps: • Step 1: Determine L, the length of the straight-line segment. • Step 2: Set ra set by users via bending the arc in the x-y plane. Suppose that the center of this arc is (0, ra, 0). The parameterized coordinates of the arc can be expressed as follows: (u(s), v(s), w(s)) = (ra sin(s/ra), ra (1 - cos(s/ra)), 0) •
Step 3: Define radius rc by twisting the arc to make the curve wrap round a cylinder. The points on the curve can then be expressed as: (x(s), y(s), z(s)) = (rc sin(u(s)/rc), v(s), rc (1 – cos(u(s)/rc)))
The virtual catheter shape is represented in a tree structure with the segment nodes. Only the leaf nodes contain pointers to each element shape. Physical-based parameters such as stiffness are kept with each element shape. Inserting a sub-shape is possible at any level of the shape tree. A new node is declared to store an element shape chosen for insertion. The parent of this node is assigned to be the parent of the current active segment. This new node is then inserted as the next node of the current active segment. Any node can be removed from the tree.
The selected segment is deleted along with its children. There are 3 default elements: straight, arc and bend. Two nodes can be merged at any time to form a new node and the parent of this node is set to be the parent of the current active segment. The active segment and its next node are inserted as the children of this node. Splitting can only be done on previously merged node. For simulation and analysis purpose, the catheter node design is in line with Finite Element Method (FEM) described below. FEM_Modeling_of_A_Virtual_Catheter Using the same node definition, the virtual catheter is actually represented in a discretized form of 3D finite beam elements. Before FE analysis can be carried out, users are required to assign physical properties to the elements of the virtual catheter. Young’s Modulus E and Shear Modulus G of polyurethane are used as the default material values for a virtual catheter. Other properties include the cross-sectional area, the second moment of area about the principal plane x-y and the second moment of area about the principal plane x-z. In [37], we reported the detailed FEM modeling of a virtual catheter for the purpose of catheterization simulation mainly focusing on the interaction between catheter device and vascular network. When a surgeon navigating a virtual catheter inside a patient’s vascular vessels, he/she can only push, pull or twist the proximal end of the virtual catheter. The force applied to the end will cause the catheter nodes to deform. However, the nodes are constrained with the patient vasculature. The vessels will react to the external stimuli originated from the surgeon’s hand. As a result, a series of contact forces will be generated between the catheter nodes and the vascular wall. A stiffness matrix for each element is calculated for the numerical analysis via integration and summation. All the element stiffness matrices are then assembled to form the global stiffness matrix. Thereafter, FE analysis can be performed to examine the effect of each variation of material properties and forces assigned at various points. Most remarkably, the proximal stimuli will cause the change of the distal end. Figure 8 shows an incremental deformation at the distal end of the virtual catheter in response to the external proximal force and the contact forces using FEM (only one contact force is visualized at the distal end).
5. VR-based Simulation System and New Catheter Design We have been developing VR technology for training of minimally invasive vascular interventional procedures [21-22]. There are three major components with our VR simulator: • a computational engine to serve various numerical computing tasks from vascular modeling to catheter navigation; • a visualization environment to include all interactive graphics and VR operations; and • an interactive haptic apparatus to provide provisions for manipulating of catheterization devices. Figure 9 illustrates our simulator that won us an INFORAD Merit Award at the 2002 Annual Meeting of Radiology Society of North America [39]. The simulator also has a patented technology for tactile and haptic manipulating of catheterization devices [40]. The next subsections details the visualization environment in our system. Volumetric_Anatomic_Visualization_with_Aligned_Patient-specific_Vascular_Model We use the Visible Human Data (VHD®) to provide a global model of the human anatomy. This is because for safety reason diagnosis imaging is limited to local region with relative lower resolution. VHD®, however, offers great detail of a complete human anatomy with scan resolution of 1mm. The vascular system from the VHD® is reconstructed and superimposed to the volume rendered VHD® global anatomy. The patient-specific vascular segments can be added to the global vascular model. However, an alignment process is required in order that the integrated vascular model is able to provide (1) accurate patient vascular information including variant information; (2) the complete global vascular model to allow a simulation process for the purpose of virtual device prototyping. It should be pointed out that the VHD® and patient-specific data are two different entities. To fuse them for producing a complete vascular model, the VHD® model needs a transformation including scaling, rotations or even non-linear deformation. However, since our device prototyping is concentrating only on a local region of the coronary and aortic arteries, the transformation is a local approximation. Figure 10 illustrates the VHD® volumetric images with aligned patient-specific vascular model.
Figure 8. FEM modeling of a virtual catheter
Figure 9. A user is navigating a virtual catheter into the left coronary artery from the aorta arch with the VR interventional simulator. A fluoroscopic view with only X-ray sensitive catherterization device is displayed in the left monitor, and corresponding 3D view of the catheterization device and the patient-specific vascular model is shown in the right monitor.
Figure 10. Patient-specific vascular model aligned with the VHD data Virtual_Catheterization_Simulation_for_Design_of_Catheterization_Device The original concept of our simulation system was to train the junior surgeons or students for less invasive vascular surgical procedures. As a training simulator, it is valuable to allow manipulation of a number of different catheters or guide-wires using a haptic apparatus. When a specific catheter is selected, it can be pushed, pulled, and rotated via the apparatus to navigate the distal end to a desired location. Due to thecomplexity of the vascular anatomy and blood vessel structure, real catheterization procedures are performed with the aid of X-ray fluoroscopic images to confirm the position of the catheter tip relative to the vascular anatomy. Users rely on hand-eye coordinated experience in deciding further movement of the catheterization devices. For instance, users can feel resistance forces from the contacts between the device and the inner vessel walls. Variations in resistant forces can indicate whether the catheter tip is stuck in a cavity or narrow regions if the feedback force is too large. Accordingly, users can change the catheter position by proper manipulation of the device. For catheterization device development, the corresponding virtual catheter can be further refined during the interactive catheterization simulation by re-configuring of various properties such as stiffness, twistability, etc. Various materials are collected and kept in a database for selection or changes. This virtual catheterization simulation allows iteratively testing of materials to identify an optimized selection. The distal tip region of the catheter is important for proper manipulations within specific vascular regions and considerable efforts have been made in its design. Today, many different catheter tip shapes have been designed serving a specific navigation function to enter a particular vascular region such as the origin of the right or left coronary artery from the aorta. Our virtual catheterization design offers a novel method in identifying catheter and device tip to enter a specific region. Figure 11 shows a virtual catheter displayed in the relational 3D view for the virtual device and the patient-specific vascular model. The system simulates a path representing a portion of the body cavity and determines the best fit between the geometry of the device and the geometry of the vascular path. Often this simulation process is an iterative job and a good design can be obtained after many rounds of trials. This iterative testing can be considered as a validation process as well. When the catheter tip is experimentally determined, a detail design can be performed.
Figure 11. A virtual catheter is being navigated into the coronary artery from the aorta arch with the patientspecific vascular model Detail_Design_with_ SolidWorks_CAD_System Generally, a real catheter is composed of several segments and its distal end is the core component for navigating to a target artery. The shaft of the catheter is usually straight over most of its length. To achieve additional stiffness and torque control of the catheter shaft, stainless steel or nylon braiding are often used as a middle layer between extruded plastic layers. The catheter tip is its most distal segment that may have single or multiple side holes. The presence of side holes allows for increased volume of contrast delivery with lesser tendency for catheter recoil. Some catheter tip designs may incorporate a soft tip. The hub at the catheter proximal end is bonded to the shaft and must have a strong, airtight seal. Catheter specifications may also be imprinted on the sleeve of the hub. Naturally, a feature-based modeling approach is most suitable for catheter building.
Figure 12. A customized catheter designed with the details of selected components
The SolidWorks CAD tool is integrated with the simulation-based catheterization device development. Thedetail design starts from the design recommendation obtained from the VR simulation in the form of a three-dimensional representation. Feature based technology is adopted here allowing parametrically modeling of the catheter device according to their material, shape, contrast medium flow rate limitations, length, size, and functions. Figure 12 shows three major parts of a catheter device: (1) a distal tip is iteratively generated by the VR simulation-based design. In the detail CAD design, we use sweeping technique to create the catheter tube with circular cross-section (not necessary uniformed) moving along the central curve. The injection holes at the distal tip are designed for contrast media injection; (2) a catheter usually has one lumen for other therapeutic devices to move in and out. A novel braiding method is developed for the design of the intermediate layer with braided wires; (3) a hub is the proximal part with a catheter serving various functions such as device exchanges, etc. This detail design process aims to equip the device with the specified or desired properties such as pliability, torque-ability, stiffness/softness, stability, strength, and shape memory; (4) a mandrel is shaped according to the geometry of the distal tip obtained through the VR-based simulation and the shaped mandrel can then be used to form the catheter tip of the prototype. 6. Conclusion We reported our work on designing customized, patient-specific catheterization devices used in image-guided less invasive vascular procedures. Essentially, we have extended, for medical device prototyping, the use of various medical imaging modalities commonly available in the hospitals. The SBD concept is applied here for prototyping of catheterization devices. VR technology enables this innovative design process and can help the development of customized patient-specific catheterization device with potential improvement of healthcare quality. Note that the system is not yet FDA approved although initial clinical validation study has been developed [41].
Acknowledgement The authors wish to thank Singapore’s Agency of Science, Technology and Research (A*STAR) for support of this research. Thanks should also go to the anonymous reviewers for their helpful comments on this report. The third author would like to thank the support from China NSF (602720601), and The Software Special Fund from China Ministry of Science and Technology (2003AA4Z1020). Reference [1]. [1]. Topol, E. J., 1994, Textbook of Interventional Cardiology, WS Saunders Company, Philadelphia, USA. [2]. Myler, R. K., Boucher, R. A., Cumberland, D. C., and Stertzer, S. H., 1990, “Guiding Catheter Selection for Right Coronary Artery Angioplasty”, Catheterization and Cardiovascular Diagnosis, 19, pp.58-67. [3]. Kim, D., and Orren, D. E., 1992, Peripheral Vascular Imaging and Intervention, Mosby-Year Book, St. Louis, USA. [4]. Kern, M., and Deligonul, U., 1996, The Interventional Cardiac Catheterization Handbook, Mosby, St. Louis, USA. [5]. Meier, B., and Mehan, V. K., 1995, Atlas of Coronary Balloon Angioplasty, Marcel Dekker, Inc, New York, USA. [6]. Vlietstra, R. E., and Holmes, D. R. Jr, 1994, Coronary Balloon Angioplasty, Blackwell Scientific Publications, USA. [7]. Stan, D., 1996, Future Perfect, 10th anniversary edition, Addison-Wesley Pub Co, England. [8]. Pine, B. J. II., and Gilmore, J. H., 2000, Markets of One - Creating Customer-Unique Value through Mass Customization, Harvard Business School Press, USA. [9]. McMahon, C., and Browne, J., 1998, CAD/CAM: Principles, Practice and Manufacturing Management, Addison-Wesley, Second Edition, England. [10]. Earnshaw, R. A., Vince, J., and Jones, H., 1997, Visualization and Modeling, Academic Press, USA. [11]. Law, A. M., and Kelton, D. W., 1999, Simulation Modeling and Analysis, McGraw Hill, Third Edition. [12]. Klein, L. W., 2000, “Computerized Patient Simulation to Train The Next Generation of Interventional Cardiologists: Can Virtual Reality Take The Place of Real Life?”, Catheterization and Cardiovascular Interventions, 51(4), pp.528-528. [13]. Gibson, S., Samoski, J., Mor, A., et al, 1997, “Simulating Arthroscopic Knee Surgery Using Volumetric Object Representations, Real-time Rendering and Haptic Feedback,” Proceedings of First Joint Conference CVRMed-MR-CAS’97, Grenoble, pp. 369-378.
[14]. Blezek, D., Robb, R., Camp, J., and Nauss, L., 1996, “Anesthesiology Training Using 3D Imaging and Virtual Reality,” Proceedings of SPIE 1996, 2707, pp. 402-410. [15]. Dumay, A., and Jense, G., 1995, “Endoscopic Surgery Simulation in a Virtual Environment.” Computer in Biology and Medicine, 25, pp. 139-148. [16]. Kuhn, C., Künapfel, U., Krumm, H. G., and Neisius, B., 1996, “A Virtual Reality Based Training System for Minimally Invasive Therapy.” Computer Assisted Radiology, Edited by Lemke, H., Vannier, M., Inamura, K., and Farman, A., Amsterdam: Elsevier Science, pp.764-769. [17]. Cotin, S., Dawson, S. L., Meglan, D. et al, 2000, “ICTS: An Interventional Cardiology Training System.” Studies in Health Technology and Informatics, 70, pp. 59-65. [18]. Dawson, S. L., and Kaufman, J. A., 1998, “The Imperative for Medical Simulation,” Proceedings of IEEE, 86(3), pp. 479-483. [19]. Higgeins, G. A., Meglan, D., Millman, A. S., Horst, R., and Merril, G. L., 1999, “Virtual Reality Surgery: Implementation of A Coronary Angioplasty Training Simulator,” Cardiovascular Surgery, Surgical Technology International, 4, pp.379-383. [20]. Dawson, S. L., Cotin, S., Meglan, D., et al, 2000, “Designing A Computer-based Simulator for Interventional Cardiology Training,” Catheterization and Cardiovascular Interventions, 51(4), pp.522527. [21]. Cai, Y. Y., Chui, C. K., Ye, X. Z., and Anderson, J. H., 2003, “VR Simulated Training for Less Invasive Vascular Intervention,” Computers & Graphics, 27(2), Pergamon, pp. 215–221. [22]. Anderson, J. H., Chui, C. K., Cai, Y. Y., et al, 2002, “Virtual Reality Training In Interventional Radiology,” Seminars in Interventional Radiology, 19(2), Thieme Medical Publishing, New York, pp. 179-184. [23] Alexandrov, N. M., Alter, S. J., Atkins, H. L., et al, 2002, “Opportunities for Breakthroughs in Large-Scale Computational Simulation and Design,” NASA/TM-2002-211747. [24]. Alexandrov, N. M., and Lewis, R. M., 2003, “Outstanding Issues in Simulation-Based Design Optimization,” SIAM Conference on Computational Science and Engineering. [25]. Martin, J. L., 1999, “Geometric Modelling for Simulation Based Ship Design, Marconi Naval Systems,” Proceedings of 10th International Conference on Computer Applications in Shipbuilding, USA. [26]. Haug, E. J., Choi, K. K., Kuhl, J. G., and Wargo, J. D., 1995, “Virtual Prototyping Simulation for Design of Mechanical Systems,” ASME Journal of Mechanical Design, 117 (B), pp. 63-70. [27]. Tsai, C. S., Chang, K. H., and Wang, J., 1995, “Integration Infrastructure For a Simulation-Based Design Environment,” Proceedings of the Computers in Engineering Conference and the Engineering Data Symposium, 1995 ASME Design Theory and Methodology Conference, pp. 9-20, USA. [28]. Yamada, H., 1997, Strength of Biological Materials, edited by Evans F.G., Williams & Wilkins. [29]. Fung, Y. C., 1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag. [30]. Fung, Y. C., 1984, Biodynamics: Circulation, Springer-Verlag. [31]. Kadir, S., 1991, Atlas of Normal and Variant Angiographic Anatomy, WS Saunders Company, Philadelphia, USA. [32]. Bergman, R. A., Thompson, S. A., and Afifi, A. K., 1984, Catalog of Human Variation, Urban & Schwarzenberg Inc., Baltimore, USA. [33]. Freed, M., and Grines, C. L., 1992, Manual of Interventional Cardiology, Birmingham, Physicians Press, pp.50-66. [34]. Lippert, H., and Pabst, R., 1985, Arterial Variations in Man: Classification and Frequency, JF Bergman Verlag, Munich. [35]. Ye, X. Z., Cai, Y. Y., Chui, C. K., and Anderson, J. H., 2002, “Constructive Modeling of G1 Bifurcation,” International Journal of Computer Aided Geometric Design, 19, Elsevier, pp. 513-531. [36]. Cai, Y. Y., Ye, X. Z., Chui, C. K., and Anderson, J. H., 2003, “Constructive Algorithms for GC1 Generation of Vascular Network,” Advances in Engineering Software, 34(7), Elsevier, pp. 439–450. [37]. Wang, Y. P., Chui, C. K., Lim, H. L., Cai, Y. Y., and Mak, K. H., 1999, “Real-time Interactive Simulator for Percutaneous Coronary Revascularization Procedures,” Computer Aided Surgery, 3(5), Wiley-Liss. [38]. Hua, W., Chui, C. K., Wang, Y. P., et al, 2000, “A Semiautomatic Framework for Vasculature Cxtraction from Volume Image,” Proceedings of 10th International Conference on Biomedical Engineering, Singapore, pp. 515-516. [39]. Anderson, J. H., Chui, C. K., Cai, Y. Y., et al, 2001, “PC Based Simulator for Cardiovascular Catheterization and Image Guided Therapy,” Radiology (Supplement) Scientific Program, 87th Radiological Society of North America Annual Meeting RSNA, Chicago, USA. [40]. Chui, C. K., Chen, P., Wang, Y. P., Ang, M. H. Jr., Cai, Y. Y., and Mak, K. H., Tactile Controlling and Imaging Manipulating Apparatus for Computer Simulation of Image-guided Surgery, US Patent 6538634. [41]. Chui, C. K., Li, Z., Anderson, J. H., Murphy, K., Venbrux, A. C., Ma, X., Gailloud, P., Cai, Y. Y., Wang, Y. P., and Nowinski, W. L., 2002, “Training and Pretreatment Planning of Interventional Neuroradiology
Procedures - Initial Clinical Validation,” Proceedings of the 10th Annual Medicine Meets Virtual Reality Conference, California.
