Planning Image-Guided Endovascular Interventions: Guidewire Simulation using Shortest Path Algorithms

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1 Planning Image-Guided Endovascular Interventions: Guidewire Simulation using Shortest Path Algorithms Sebastian Schafer 1,2, Vikas Singh 2,3, Kenneth R. Hoffmann 1,2, Peter B. Noël 2,3, Jinhui Xu 3 1 Department of Mechanical and Aerospace Engineering, SUNY at Buffalo 2 Department of Neurosurgery, Toshiba Stroke Research Center, SUNY at Buffalo 3 Department of Computer Science and Engineering, SUNY at Buffalo ABSTRACT Endovascular interventional procedures are being used more frequently in cardiovascular surgery. Unfortunately, procedural failure, e.g., vessel dissection, may occur and is often related to improper guidewire and/or device selection. To support the surgeon s decision process and because of the importance of the guidewire in positioning devices, we propose a method to determine the guidewire path prior to insertion using a model of its elastic potential energy coupled with a representative graph construction. The 3D vessel centerline and sizes are determined for a specified vessel. Points in planes perpendicular to the vessel centerline are generated. For each pair of consecutive planes, a vector set is generated which joins all points in these planes. We construct a graph representing these vector sets as nodes. The nodes representing adjacent vector sets are joined by edges with weights calculated as a function of the angle between the corresponding vectors (nodes). The optimal path through this weighted directed graph is then determined using shortest path algorithms, such as topological sort based shortest path algorithm or Dijkstra's algorithm. Volumetric data of an internal carotid artery phantom (Ø 3.5mm) were acquired. Several independent guidewire (Ø 0.4mm) placements were performed, and the 3D paths were determined using rotational angiography. The average RMS distance between the actual and the average simulated guidewire path was 0.7mm; the computation time to determine the path was 3 seconds. The ability to predict the guidewire path inside vessels may facilitate calculation of vessel-branch access and force estimation on devices and the vessel wall. Medical Imaging 2007: Visualization and Image-Guided Procedures, edited by Kevin R. Cleary, Michael I. Miga, Proc. of SPIE Vol. 6509, 65092C, (2007) /07/$18 doi: / Proc. of SPIE Vol C-1

2 1. INTRODUCTION Cerebrovascular disease ranks third in cause of death, resulting in more than 160,000 deaths 1 in the United States. Initially, the standard approach to cerebrovascular interventions was invasive surgery, carotid endarterectomy. However, with the introduction of the Seldinger technique 2, by which the site of disease can be accessed by using the vasculature itself as a pathway, x-ray angiography and the introduction of computer-tomographic angiography (CTA) provide substantial assistance in the diagnosis and treatment of vascular disease. In vascular diagnosis and intervention, a remote artery, e.g., the femoral artery is punctured, and a guidewire is placed in the artery and brought to the region of interest under fluoroscopic guidance. The catheter and the interventional device(s) such as stents, balloons or coils, are brought to the site of intervention by moving them along the guidewire, i.e., the guidewire functions as a monorail for these devices. Recent studies have shown that periprocedural failure during carotid artery stenting still occurs in 5% of interventions 3,4. This remains above the acceptable risk of 3% needed for carotid stenting to reach its full potential. Vessel tortuousity, one of the identified risk factors in periprocedural failure, is of particular interest as it can be accessed using x-ray angiographic or CTA data. Modeling the path of a guidewire inside the tortuous vessel area may give much useful information about device bending and force interaction between the vessel wall and the device traversing over the guidewire, leading to feasible tortuousity estimation. Thus, knowledge of the guidewire path forms the basis and is critical to proceeding with interactions of other devices with the vessel. The guidewire is initially shaped as a straight, but flexible, beam with a very flexible tip, which is typically prebent, or will be bent by the surgeon prior to insertion into the patients vasculature. As the guidewire is advanced through the patient s vasculature, it can achieve any arbitrary shape and path inside the vessel lumen due to its relatively high flexibility and the surgeon s interaction. After the guidewire has been moved to and beyond the region of interest (ROI), the surgeon relaxes his/her force on the guidewire. If the guidewire has not been bent into the plastic deformation area of the material during insertion, it will return to its initial relaxed shape according to its elasticity. The only constraint that prevents the guidewire from returning to this relaxed shape (i.e., the shape of its minimal energy) is the geometry of the vessel. Guidewire modeling has been approached through different methods. Several groups have used modifications of the finite element method (FEM), e.g. linear elastic 5 and static 6,7 finite element representations incorporating connected beam elements to model bending, twists and other deformations. The primary objective of these efforts was to incorporate the proposed algorithms into neuroradiological surgical simulators. Therefore, the algorithms and the algorithm evaluations emphasized mainly realistic behavior of the simulated device inside the vessel lumen while undergoing forced translation, rather than quantitative evaluations. Konings, et al. 8 approached the problem by expressing the path of the guidewire as an energy function. The guidewire was divided into connected beam elements, and the energy function model was minimized in an iterative fashion. Evaluations of a 2D model showed an error of 10% of the lumen diameter for corresponding points, subsequent 3D model evaluations showed a variation between 10% and 43% of the vessel lumen diameter to the actual guidewire path. Parts of the proposed algorithms, both finite element and analytical, have been included in surgical simulators An interesting contribution of Konings, et al. was, we believe, demonstrating the feasibility of using an analytical model to realistically predict the guidewire path in the vessel lumen. However, the minimum to their analytical model was obtained by iterative minimization of the associated energy functional. In this study, we present a graph-based modeling which preserves the analytical modeling ideas proposed; in addition, it allows determination of the minimal energy state, i.e., the relaxed state given the vessel geometry, very efficiently, using a relatively simple objective function for the energy. We show that this approach can be applied quite naturally to a 3D problem with relatively high resolution without significant deterioration in computation time. In addition, it is extremely flexible, i.e., because of the approach used to map the spatial representation to the graph representation, additional mechanical and physical properties of the guidewire, which may be affect the final path, could be included in the objective function without any changes to the underlying graph model Proc. of SPIE Vol C-2

3 2. METHODS The method is based on a development of the spatial representation that allows use of graph-theoretic algorithm. The spatial representation employs segmenting the vessels and specifying spatial locations through which the guidewire passes. This spatial representation is then transformed into a graph-theoretic representation which allows the calculation of the minimum energy path. The approach is then evaluated in a phantom study. 2.1 GRAPH CONSTRUCTION As a first step to graph construction, the spatial representation of the possible guidewire paths is developed. The vessel is imaged and 3D vessel centerline and lumen is determined. The 3D centerline points, CP, are input as an ordered set (proximal to distal ordering, see Figure 1 a). Here, cp i CP refers to the i-th centerline point. Let the vessel direction from cp i to cp j be denoted by a vector u ij ; u ij defines a supporting plane P i for each cp i where P i is perpendicular to u ij. The radius of the vessel at cp i is denoted by r(cp i ). The region of the vessel at cp i (and in P i ) is represented by a 2D mesh with m points (Note: the sampling selected should be sufficiently dense to provide a large selection of paths and to reflect the desired path resolution, we chose a sampling of 0.4mm, which is comparable to the voxel size). M denotes the mesh where M i refers to the one at supporting plane P i and m ij refers to the j-th point in M i !4k.. (a) (b) FIGURE 1. (a) Input set of ordered centerline points, cp i. (b) Meshes, M i, generated at each centerline point; each mesh contains mesh points, m ij. We then impose a geometric ordering on the elements of M so that two supporting planes P i and P j do not cross. To do this, we calculate the angle α between the plane normals for P i and P j where j = i+1. The product of sine(α) and the vessel radius r(cp i ) yields a. If a /d(i,j) > 1, the supporting planes are determined as crossing, where d(i,j) refers to the Euclidian distance between cp i and cp j. If such a crossing occurs P j and the corresponding M j are discarded. The mesh points in consecutive Ps (M i and M j, where j=i+1) are then connected; these vectors v pqrs connects mesh points m pq M q and m rs M s. All such vectors constitute VS, where VS qs VS denotes vectors between M q and M s. (Figure 2). Proc. of SPIE Vol C-3

4 FIGURE 2. Creation of vector set VS qs incorporating the vectors v pqrs connecting all points in two subsequent meshes (M q, M s ). With the spatial representation complete, we proceed to the graph construction. First, an empty graph G=(V, E) is constructed. The vertex set V is initialized to the vector set VS. By construction, G is a k level graph, where each level corresponds to a vector set between two consecutive supporting planes. The edge set E is defined as the connection between two subsequent levels, or vertex sets VS. An edge e=(v pqrs, v rstu ) E exists if the vectors corresponding to the vertices share a common mesh point (Figure 3). We illustrate a corresponding graph in Figure 4. VrsW e = (Vpqrs, Vrsw) Vpqrs FIGURE 3. Two spatial vectors, v pqrs and v rstu, sharing a common mesh point (m rs ), are connected by the edge e. Proc. of SPIE Vol C-4

5 FIGURE 4. The completed graph structure. Nodes represent the vertices, V, at level k, and the arrows represent the connecting edges, e E. Notice that not all vertices are interconnected across levels because vertices must share a common mesh point to share an edge. We now encode the mechanical properties of the guidewire into G. We assume that the guidewire is made up of a number of beam elements represented by vectors Vpqrs. In a simple, discrete model, we can take the angle (theta) between the beam elements as corresponding to the local bending of the guidewire. We then use theta and Hooke s law 21 to calculate the weight of the edges connecting the respective vertices, i.e., Θ = 1 ( ( v ) cos (1) 2 () e = Θ pqrs v rstu w (2) where w(e) can be understood as representing the energy required to bend the guidewire locally by angle, Θ. A guidewire path GP i will therefore have a weight equal to the sum of the edges w(e k ) chosen to travel on between subsequent levels (3). k = i GP w( ) (3) j e i Notice that the path of minimum GP i (or energy) passing through all k levels of G could be considered as equivalent to the equilibrium path of the guidewire, one with the minimum elastic energy. Our minimum energy path problem defined on G can be solved optimally using single source shortest path algorithms, such as topological sort based shortest path algorithm or Dijkstra's algorithm, with defined source and sink nodes at levels 1 and k. Note, that with this weighting scheme for the edges, edges with large angles will be preferentially de-selected. This will bias the path to those paths which do not include these large-angle bends, i.e., to paths near the center of the vessel. The removal of the crossing planes removes this bias and allows consideration of all paths, in particular those near the vessel wall in regions of high curvature. 2.2 PHANTOM MODEL OF THE HUMAN CAROTID ARTERY Several groups have proposed methods to construct vessel phantoms Although they have been developed for different applications, there are basically three phantom designs: walled 13-15, non-walled 16 and real-vessel phantoms 17. In each design, the vessel structure is encased in a tissue-mimicking material, which usually has a low x-ray attenuation coefficient. In this study, a walled-phantom design was applied. The encasing material was Sylgard (Dow Corning, Midland, USA), a silicon-based compound. It has a low x-ray attenuation coefficient, is liquid prior to curing, and is transparent and rigid after curing. The vessel wall was constructed from a polyethylene tube. The tube provided low surface friction, was easily deformable, and had a low x-ray attenuation coefficient. The inner diameter of the tubing was chosen to be 3.65 mm following the results by Bharadvaj et al. 18 for the diameter of the internal carotid Proc. of SPIE Vol C-5

6 artery. To achieve a shape similar to those of the internal carotid, we reconstructed the 3D centerlines of a number of carotids from angiograms 19 and inspected them. Combinations of wires were shaped to resemble the features seen in the renderings of these 3D centerlines. These wires were then passed through the polyethylene tube, which took on the geometry of the wires. The tube containing the wires was placed in a 4 cm diameter cylinder. The cylinders were filled with Sylgard and hard cured. After curing, the wires were removed from the polyethylene tubing, and the cylindrical casing was removed from the Sylgard. An image of the thereby constructed phantom is shown in Figure 5. FIGURE 5. Vessel phantom with a lumen length of 143mm and a lumen diameter of 3.65 mm. 2.3 EXPERIMENTAL SETUP AND DATA ACQUISITION The phantom was fixed on the patient bed of a Toshiba Infinix Angiography system (Toshiba Medical Systems Corporation, Tokyo, Japan) to prevent movement of the phantom during guidewire insertion. To allow simultaneous fluid flow through the phantom and guidewire insertion, a valve system was designed and attached to each phantom prior to image acquisition. A pulsatile flow pump was used to generate flow which approximated that inside a human carotid artery. Blood was simulated by a 30/70 glycerin/water mixture. A guidewire made of plastic with a diameter of 0.4 mm was used. Prior to guidewire insertion the phantom was filled with contrast agent and a rotational angiogram was acquired. Three users, experienced in the use of guidewires, were instructed to place the guidewire inside the phantom using the subjective easiest path. After each insertion of the guidewire, rotational angiographic sequences were obtained, and the phantom and guidewire were reconstructed D VESSEL AND GUIDEWIRE CENTERLINE EXTRACTION The reconstructed 3D data consisted of x8bit volume, with a mm voxel size. The 3D vessel lumen and guidewire were segmented from the volumes using thresholded region growing. The centerlines of both phantom vessel and guidewire were determined using region growing accompanied by a wavefront-based technique EVALUATIONS Initial evaluations focused on the dependence/independence of the simulated guidewire path from defined source and sink nodes at levels 1 and k in the constructed graph G. Recalling that each level k consists of n vertices, where n is equal to the number vectors v pqrs defined between subsequent meshes M p and M s, a total of n 2 start-/endpoint combinations are evaluated. At each level k, the returned guidewire postions p k (i) are averaged to create p k (4). Subsequently the variation around p k is calculated (5). p k 1 = pk () i (4) n i Proc. of SPIE Vol C-6

7 s = n ( pk () i p k ) i 2 (5) Prior to further evaluations, the simulated guidewires are fitted using cubic spline. One of the simulations Gw s is chosen to be compared to the real three guidewires Gw r. For each point i in Gw r, the closest point j in Gw s is determined (6). If in this procedure two points in Gw r are assigned to the same point in Gw s, the latter is discarded. The established point correspondences are used to determine the RMS distance between simulated and real guidewires (7). d rs () i ( G () i G ( j) ) = min (6) r s RMS 4. RESULTS rs = 1 r r ( drs () i ) i 2 (7) Thirty-four different starting points and 34 different end points, in total 1156 simulations, were evaluated to assess start and endpoint dependence/independence. The graph had in total 36 levels (k). Results showed that after an initial convergence period all simulations settled into the same path and only departed from the common path very close to the end (Figure 6). Processing time for one guidewire simulation in this evaluation was less than one second (our implementation was done in C++ using LEDA (Alogrithms Solution Software GmbH, Saarbruecken, Germany) and the GNU Scientific Library (GSL) 22 ) s [cm] Centerline Index FIGURE 6. RMS distance between 1156 simulations for all possible combinations of start and endpoints. Three independent user placements were compared with one guidewire simulation. The starting point and end point of the simulation has no impact on the guidewire path except near the extreme regions of the vessel as shown in Figure 6. The simulation path agrees very well with the actual path for the proximal portion of the vessel (to within approximately 1.0 mm and with an RMS difference of about 0.5 mm (Figure 7)), paths differ in the distal region by approximately 1.3 mm RMS. These deviations in the distal region may result from the lack of structural support for the guidewire near the end of the phantom so that the shape is more influenced by its free floating tip distal to the phantom than by the phantom geometry. Having a vessel diameter of 3.65 mm, we have on average only a divergence of 15% of the vessel lumen. In the most distal region, divergences of up to 40% of the vessel lumen did occur. In Figure 8, we present three renderings of the simulation and actual paths in the carotid phantom. Proc. of SPIE Vol C-7

8 deviation [cm] simulation-original 1 simulation-original 2 simulation-original simulated guidewire centelrine index FIGURE 7. Deviation of the simulation from the three independent guidewire placements. (a) (b) (c) FIGURE 8. Different projection views of the simulated (light) and original (dark) guidewire in the carotid artery phantom. 5. CONCLUSION We have proposed a new graph-representation-based technique to calculate guidewire paths inside the carotid artery. A few salient advantages of a graph-theory-based guidewire path simulation include the fast modeling of the vasculature from minimal data input (vessel centerline and corresponding diameter), real time modeling due to the nature of the used shortest path algorithms, and easy incorporation of different mechanical aspects into the modeling function. This approach, yields a unique solution for specific vessel geometries, is supported by the experimental reproducibility Proc. of SPIE Vol C-8

9 of the guidewire path inside different vessel models [12]. Simulation results indicate that the proposed algorithm provides accurate paths of guidewires in a vessel phantom, yielding good agreement with the actual guidewire paths. The designed algorithm appears to be independent of guidewire entrance and exit point of the given 3D vessel segment. This technique may facilitate calculation of vessel-branch access and force estimation on devices and the vessel wall thereby improving treatment planning and decisions made in the course of the intervention. It may prove to be useful prior to and during endovascular interventions, either incorporated into a 3D visualization toolkit used during endovascular procedures, or to give the surgeon a projected guidewire path by displaying the 2D projections on the viewing stations of an angiographic biplane system. 6. ACKNOWLEDGEMENTS This work was supported by NIH Grant EB002916, NIH Grant HL52567, NSF CAREER Award CCF , and the Toshiba Medical Systems Corporation. REFERENCES [1] Kochanek K, Murphy SL, Anderson RN, Scott C. Deaths: Final Data for 2002 National Vital Statistics Report, Volume 53, No.5, 2004 [2] S Seldinger. Catheter replacement of the needle in percutaneous arteriography; a new technique Acta Radiol. 39(5):368-76, 1953 [3] Roubin S, Iyer S, Halkin A, Vitek J, Brennan C. Realizing the potential of Carotid Artery Stenting: Proposed Paradigms for Patient Selection and Procedural Technique Circulation, 113: , 2006 [4] Wholey MH, Al-Mubarek M, Wholey MH. Updated Review of the Global Carotid Artery Stent Registry Catheterization and Cardiovascular Intervention, 60: , 2003 [5] Nowinski WL, Chui CK. Simulation of Interventional Neuroradiology Procedures Proc. Medical Imaging and Augmented Reality , 2001 [6]Cotin S, Duriez C, Lenoir J, Neumann P, Dawson S. New Approaches to Catheter Navigation for Interventional Neuroradiology Simulation Proc. MICCAI 05, 8(2): [7] Wang YP, Chui CK, CAI YY, Mak KH. Topology Sorted Finite Element Method Analysis of Catheter/Guidewire Navigation in Reconstructed Coronary Arteries Computers in Cardiology, 24: : 1997 [8] Konings MK, van de Kraats EB, Alderliesten T, Niessen WJ. Analytical gudeiwire motion algorithm for simulation of endovascular interventions Med. Biol. Eng. Comp., 41: [9] Dawson, S. L., S. Cotin, Meglan D, Shaffer DW, Ferrell MA. Designing a computer-based simulator for interventional cardiology training Catheter Cardiovasc Interv., 51(4): , 2000 [10] Cai Y, Chui CK, Ye X, Wang Y, Anderson JH. VR simulated training for less invasive vascular intervention Computers & Graphics. 27: [11] Alderliesten T, Konings MK, Niessen WJ. Simulation of minimally invasive vascular interventions for training purposes Computer Aided Surg., 9(1-2):3-15, 2004 [12] Schafer S, Hoffmann KR, Walczak A, Ionita C, Noël PB. Reproducibility of Guidewire and Stent Path for Endovascular Interventions Medical Physics, 32: 1918, 2005 Proc. of SPIE Vol C-9

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