daVinci (VIsual Navigation of Catheter Insertion) [1] represents a new concept in providing physicians with a realtime interactive simulation of vascular catheterization procedures. It provides the interventional radiologist with a hands-on, user-friendly, image based environment to augment training enhance pretreatment planning and design interventional products and devices. daVinci is based on computational modeling of human anatomical images and provides the user with capabilities for realtime simulated navigation of catheters in both 2-D and 3-D modeled vessels.
Figure 1: User interface for daVinci. The left window provides a 2D fluoroscopic image view, the upper right window displays a 3D geometric view of vasculature; the lower right window gives the cross sectional image views relative to the catheter tip position.
With the goal of creating a realistic realtime interactive environment for daVinci, an incremental Finite Element Modeling (FEM) has been developed for the analysis of catheter navigation in the vascular structure. The catheter is discretized into a finite number of FEM nodes. This FEM analysis uses a potential field concept to speed up the determination of interaction between the walls of vessels and the catheter, which is normally the most time consuming portion in FEM calculation. DaVinci uses the primary arterial vasculature of VHDTM data and the secondary tertiary networks for other scanned human vasculature data to build the potential field for this FEM realtime computation.
The vascular anatomy is represented by the central lines and their corresponding radii of the vessels. These vessels are assumed in the existing version of daVinci as circular cylindrical structures with varied radii. The coordinates of points at the central lines are first segmented from image data. The corresponding radii of the vessels are then obtained from the area of their cross-sections with the assumption that they are in circular form. The potential field is defined as a sparse grid space which, with a given thickness embraces the vessels. The ratio of the grid size and the average radius of the vessels can be varied. The thickness of the potential field can also be adjusted according to the movement step of the catheter that is defined in the FEM computation. The distances at the grid points in the region of the potential field with respect the central lines of the vessels and the associated unit vectors pointing from the points to the central lines are computed and stored in an optimized format.
The distance and unit vector respectively at a grid point in the potential field, are used as references to determine the magnitude and direction of the contract force for FEM calculations. The contact force between the vessel wall and catheter can be defined as f=cdn at a FEM node of the catheter when the catheter is moved at this grid point. f denotes the contact force, d denotes the distance, n denotes the unit directional vector, and c is a coefficient reflecting the interaction of the material properties of the catheter and the vessel.
Figure 2: Potential field of vasculature. The red dots represent the vessels and the yellow dots show the region of the surrounding potential field.
The contact force at a FEM node, however, is determined in most cases by trilinear interpolation of the contact forces at the eight grid points surrounding the node. Furthermore, the distance at a grid point is normalized with respect to the corresponding radius of the vessel to facilitate checking whether a node is inside or outside the vessel during the navigation. By doing so, we can easily determine that a FEM node is outside of the vessel when its distance is larger than one. Within the precomputed potential field, the z-index of a grid point is used as the pointer for a x-y plane. Each grid point at this x-y plane can then be distinguished by its x- and y- indices. We can therefore, conduct inside/outside checking and compute contact force efficiently for FEM analysis using this potential field as a precomputed grid space.
Figure 3: A close look of the potential field of an example vessel. The arrows give the directions of the unit vectors at the grid points, and their magnitudes denote the respective distances. Blue color indicates the largest distance and red is meant for the shortest in this picture.
Figure 4: 2D fluoroscope view of catheter navigating along the aorta remodeled from VHDTM image data.
[1] Anderson, J., Brody, W., Kriz, C., Wang, Y., Chui, C.K., Cai, Y.Y., Viswanathan, R. and Raghavan, R., daVinci: a vascular catheterization and interventional radiology-based training and patient pretreatment planning simulator , Society of Cardiovascular and Interventional Radiology 21st Annual Meeting, March, 1996, Seattle, WA USA.