Physics-Based Models for Catheter, Guidewire and Stent ... - CiteSeerX

Book Title Book Editors IOS Press, 2003

1

Physics-Based Models for Catheter, Guidewire and Stent Simulation Julien Lenoir a , Stephane Cotin a,b , Christian Duriez a and Paul Neumann a,b a b The Sim Group, CIMIT/MGH Harvard Medical School Abstract. For over 20 years, interventional methods have improved the outcomes of patients with cardiovascular disease or stroke. However, these procedures require an intricate combination of visual and tactile feedback and extensive training periods. An essential part of this training relates to the manipulation of diagnostic and therapeutic devices such as catheters, guidewires, or stents. In this paper, we propose a physics-based model of wire-like structures that can be used as a core representation for the real-time simulation of various devices. Our approach is computationally efficient, and physically realistic. A catheter/guidewire is simulated using a composite model, which can dynamically adapt its material properties to locally describe a combination of both devices. We also show that other devices, such as stents, can be modeled from the same core representation. Keywords. Simulation, Interventional Radiology, Real-Time, Physics-based

1. Introduction Over the last twenty years, interventional methods such as angioplasty, stenting, and catheter-based drug delivery have substantially improved the outcomes for patients with cardiovascular or neurovascular disease. However, these techniques require an intricate combination of tactile and visual feedback, and extensive training periods to attain competency. Traditionally, the best training environments on which to learn the anatomicpathologic and therapeutic techniques have been animals or actual patients. Yet, the development of computer-based simulation can provide an excellent alternative to traditional training. To reach this goal, aspects of the real procedure need to be simulated, including catheter1 and guidewire2 manipulation is the most important, but also therapeutical devices usage, like stents. In a real procedure, after puncturing the femoral artery, a guidewire-catheter combination is advanced under fluoroscopic guidance through the arterial network to the target location (brain, heart, abdomen). There, various therapeutic devices (stent, balloon,...) can be deployed and treatment can be delivered. A few computer-based training systems focusing on interventional radiology have been developed or commercialized as of today [12,7,4]. These systems include interactive models of catheters but do not deal with the complex interactions between a device and the vessels or between catheter and guidewire. We propose a composite model of catheter/guidewire that handles these two problems. A physics-based device model is used to create a realistic and accurate behavior, while a specific visualization technique is proposed to render 1A 2A

hollow, flexible tube inserted into a vessel to allow the passage of fluids or other devices flexible wire positioned in a vessel for the purpose of directing the passage of a catheter.

2

J. Lenoir, S. Cotin, C. Duriez, P. Neumann / Models for Catheter, Guidewire and Stent Simulation

both objects from one unified model. Also, an update of the model’s material properties is performed dynamically to describe a combination of both devices using a unique model. In addition, the core representation is derived to model stent devices. This paper is organized as follows: previous work is discussed in section 2, then the physical core model is outlined in section 3, the composite model of catheter/guidewire is exposed in section 4, a stent model example is described in section 5 and preliminary results are presented in section 6. 2. Previous work Previous work in the field of interventional radiology simulation has focused on the development of complete systems [4,12], visualization [11] and anatomical modeling [10]. In [12] the authors simulate the catheter using a linear elasticity FEM-based representation. In [4] the catheter simulation is based on a multi-body system composed of a set of rigid bodies and joints. This discrete model permits a good approximation of a catheter but requires many small links to represent a high degree of flexibility, thus leading to increased computation cost. Other work outside of the area of interventional radiology has focused on one-dimensional deformable models. For instance, Lenoir et al [9] proposed to simulate a surgical thread in real-time using a dynamic spline. Another way to model one-dimensional deformable objects is to use the Cosserat theory, as proposed by Pai [13]. This model is static and takes into account all possible deformations of a one-dimensional object. But contact handling with such a model is difficult and for catheter navigation, where collisions occur continuously along the length of the device, this remains an issue, and computation times for a large number of points can lead to non-interactive simulation times. Finally, some recent work directly related to the simulation of a catheter or guidewire has been proposed by Cotin et al [3]. This physics-based model consists of a set of connected beam elements that can model bending, twist and other deformations in realtime. The simulation is based on a static finite element representation. Different aspects of this model are presented in section 3 while our contribution begins in section 4 by presenting its application on simulating a catheter/guidewire and a stent in section 5. 3. The core model As previously mentioned, our approach is based on a physics-based model (described in details in [3]). The physical model is defined as a set of beam elements. Each element has 6 degrees of freedom, 3 in translation and 3 in rotation. The model is continuous and the equations are solved using a finite element approach. Since each element can bend, a lower number of elements is required to represent the catheter than with a rigid body approach [4]. The choice of a static over a dynamic model was made since the catheter or guidewire navigate inside blood vessels where the blood induces a damping factor. Under this assumption, the equations of the mechanical system can be written as: [K]U = F, where U represents the degrees of freedom, F the forces and torques applied on each nodes and [K] the stiffness matrix of the system. Yet, the significant flexibility of a catheter or guidewire can generate geometric non-linearities when navigating inside twisted parts of the vascular system. Since this cannot be handled by a linear model, we overcome this problem by defining [K] as a function of the degrees of freedom U: [K(U)]U = F.

J. Lenoir, S. Cotin, C. Duriez, P. Neumann / Models for Catheter, Guidewire and Stent Simulation

3

The system is then solved using an incremental approach [3] which permits faster computation times compared to other techniques. Additionally, the system of equations can be re-written by decomposing the model as a set of substructures [3], which improves even further the computation times. To control the deformation and navigation of the device, we use a combination of external forces and boundary conditions. Since the device (catheter, guidewire or stent) is manipulated by the interventional radiologist using only a combination of translations and rotations about the main axis of the device, this is taken into account in the model via a set of boundary conditions. Those constraints are transmitted along the all entire model via its deformations, according to the material properties. This physics-based representation will serve as the core of the two models we will introduce in the following sections. 4. Composite catheter-guidewire representation In this section we describe how catheter/guidewire combination (i.e. a configuration where the guidewire is partially or totally inserted inside a catheter) can be modeled as a composite model, involving the physics-based component introduced above and an animation component. By simulating only one model, we avoid the problems of handling numerous contact between the catheter and the guidewire, since both devices are co-axial. This proposition is detailed in [8] and is exposed briefly in this section as one example of a model that can be based on this generic core representation. 4.1. Animation component The animation part is based on the visual appearance of the catheter and the guidewire, which is needed to distinguish between them. A parameter limit represents the curvilinear position of the guidewire tip relatively to the catheter tip. Typically, the value of this parameter is zero when both device tips are at the same location, negative when the guidewire tip is inside the catheter and positive when it is outside. A change in the value of limit happens only when either the catheter or the guidewire is pushed or pulled. This modification is shown during the rendering of the model, by using the limit value to define two different objects. Both objects are rendered as generalized cylinders [1,2]

(a) Basic elements

(b) Surface construction

Figure 1. Generalized cylinder construction.

(cf. figure 4). This technique permits to define a smooth surface (figure 1(b)) based on a path (the nodes position of the core model) and a cross section (circle) (figure 1(a)). In addition, new rendering techniques [5] permit to take advantage of the graphics hardware to optimize the rendering speed. Yet, realistic visualization is not enough to simulate the combination of two nested devices. To be able to exhibit realistic behaviors for both objects, special attention has to be placed on the mechanical interaction between the catheter and the guidewire, as illustrated in the following section.

4

J. Lenoir, S. Cotin, C. Duriez, P. Neumann / Models for Catheter, Guidewire and Stent Simulation

4.2. Catheter / guidewire interaction When the guidewire is inserted inside the catheter or the catheter moves along the guidewire, the overall shape of both the catheter and guidewire is modified due to a change in the bending stiffness and bending moment in the overlapped portion. The region where the catheter and guidewire are coaxial offers a stiffer resistance to transverse loading. We simulate this meaningful visual cue as a fiber reinforced composite material. The transversal stiffness of the overlapped region can be modeled with the wellestablished empirical expression, the Halpin-Tsai equations [6]: Etrans =

Ecath (1+ξηf ) , 1−ηf

η=

Eguide −Ecath Eguide +ξEcath

where f is the ratio, in the overlapped section, of the guidewire volume over the volume of the guidewire-catheter combination; ξ is a function of the material properties and geometry of the instruments. Lookup tables describing typical values of ξ under different composition configurations have been published in the literature [6]. The stiffness for the overlapped section can be updated in real-time and the composite physical model reflects this change, accordingly. 5. Stent representation We propose also to combine our real-time finite element model of wire-like structures with a generic representation of tubular shapes to provide an efficient and flexible way to describe a large range of devices, such as stents, but possibly angioplasty balloons too. The deformation scheme is based on the following idea: a set of beam elements is used to define the skeleton of the device, and is then mapped to a surface representation adapted to the particular device being modeled (see Figure 2). Since the main difference between such devices and wire-like structures is their ability to handle radial deformations, we mostly need to define the relationship between the skeleton and the surface representation. Skeleton made of beam elements Collidable point

Surface node

Figure 2. A stent modeled as a skeleton combined with a deformable surface representation.

The displacement Us of a surface point Ps is defined as a linear combination of two deformations, one due to the beam deformation (Usb ) and one local deformation (Usl ). The Usb vector is directly obtained from the beam model by interpolation of the displacement Ub of the n beam nodes, as describe by the following equation: Usb = Pn i=0 wi U bi = [H]Ub. The beam model gives the relation between forces Fb and displacements Ub of beam nodes: Ub = [Kb]−1 Fb. Then, the forces Fs applied on the surface point are distributed to the different beam nodes using the transpose matrix of [H]: Fb = [H]T Fs Then a local deformation model gives also the relation between local motion displacement Usl and forces applied to surface point: Usl = [Klocal ]−1 Fs, where [Klocal ] is the local stiffness matrix used to compute [K] (cf. section 3).

J. Lenoir, S. Cotin, C. Duriez, P. Neumann / Models for Catheter, Guidewire and Stent Simulation [Us] (l)

[Fs]

5

[Us] (l)

Ps [Ub]

Beam deformation

[Fs]

Local deformation

Figure 3. The deformation of a tubular structure is composed of a global deformation (left) included by the deformation of the skeleton and a local deformation of surface (right)).

Using compliance (flexibility) formulation we can combine the two contributions: Us = Usb + Usl = ([Klocal ]−1 + [H][Kb]−1 [H]T )Fs Finally, a list of points sampled is distributed on the surface of the device, which will be used for collision detection purpose. 6. Results The first result (illustrated in Figure 4(a)) show the effectiveness of the physics-based model. In this simulation, the catheter navigates through the vascular network and is simulated with 100 nodes in real-time (about 45 frames per second). The model exhibits a realistic behavior, sliding against the vessel walls and passing through bifurcations.

(a) Two step of a simulation in the vessel network.

(b) Stent deployment

Figure 4. Catheter simulation in artery and stent deployment.

The second result (illustrated in Figure 4(b)) shows a stent deployed in an artery. The bending properties as well as the radial stiffness of the stent can be controlled to model a large set of devices. Once released inside the vessel, the stent deploys automatically under the influence of internal forces. Then, the collision detection representation of the stent model is used to handle contact with the vessel wall thus stopping the expansion of the stent. The last result (illustrated in Figure 5) shows the interaction between two nested devices. In this animation, a straight guidewire is inserted into a curved catheter and, as it is moving toward the tip of the catheter, straightens it, This is a direct result of the use of our composite model, and illustrates both the changes in the visual and bending properties of the combined representation. 7. Conclusion and future work This paper proposes a unique representation to interactively model various devices required for simulating interventional radiology procedures. While the core model exhibits realistic behaviors typical of wire-like structures, we show how it can be enhanced to

6

J. Lenoir, S. Cotin, C. Duriez, P. Neumann / Models for Catheter, Guidewire and Stent Simulation

Figure 5. Guidewire deforming a catheter.

represent a guidewire/catheter combination or a stent, for instance. The incremental FEM representation of the core model ensures accurate, real-time, physics-based simulations of devices such as catheters and guidewires. Each additional model based on this representation benefits from its realism (torsion and bending are taken into account) but adds specific levels of modeling or visualization. The composite model of catheter/guidewire combines an optimized visualization technique (that can render both objects from one unified model) with a method that dynamically updates the model’s material properties in real-time. Finally, a stent model can also be derived from the core representation, demonstrating its genericity. A surface layer attached to the core deals with the vascular surface interaction. We would like to enhance our stent model by managing the interaction between the stent surface and the physics core in a finer way. We also would like to generalized the usage of our physics core to other therapeutic devices like angioplasty balloons. References [1] T.O. Binford. Generalized cylinder representation. In Shapiro S.C., editor, Encyclopedia of Artificial Intelligence, pages 321–323. John Wiley & Sons, 1987. [2] J. Bloomenthal. Graphics Gems, volume 1, chapter Calculation of Reference Frames along a Space Curve, pages 567–571. Academic Press, 1990. [3] S. Cotin, C. Duriez, J. Lenoir, P. Neumann, and S. Dawson. New approaches to catheter navigation for interventional radiology simulation. In proceedings of Medical Image Computing and Computer Assisted Intervention (MICCAI), Palm Springs, California, USA, 2005. [4] S. Dawson, S. Cotin, D. Meglan, D. Shaffer, and M. Ferrell. Designing a computer-based simulator for interventional cardiology training. Catheterization and Cardiovascular Interventions, 51:522–527, december 2000. [5] Laurent Grisoni and Damien Marchal. High performance generalized cylinders visualization. In proceedings of Shape Modeling’03 (ACM Siggraph, Eurographics, and IEEE sponsored), pages 257–263, Aizu (Japan), july 2003. [6] J.C. Halpin and J.L. Kardos. The halpin-tsai equations: a review. Polymer Engineering Science, 16:344 – 52, 1976. [7] U. Hoefer, T. Langen, J. Nziki, F. Zeitler, J. Hesser, U. Mueller, W. Voelker, and R. Maenner. Cathi catheter instruction system. In Computer Assisted Radiology and Surgery (CARS), 16th International Congress and Exhibition, pages 101 – 06, Paris, France, 2002. [8] J. Lenoir, S. Cotin, C. Duriez, and P. Neumann. Interactive physically-based simulation of catheter and guidewire. In Second Workshop in Virtual Reality Interactions and Physical Simulations (VRIPHYS), Pisa, Italy, 7th november 2005. [9] J. Lenoir, P. Meseure, L. Grisoni, and C. Chaillou. Surgical thread simulation. Modelling and Simulation for Computer-aided Medecine and Surgery, November 2002. [10] V. Luboz, X. Wu, K. Krissian, C.-F. Westin, R. Kikinis, S. Cotin, and S. Dawson. A segmentation and reconstruction technique for 3d vascular structures. In proceedings of Medical Image Computing and Computer Assisted Intervention (MICCAI), 2005. [11] M. Manivannan, S. Cotin, M. Srinivasan, and S. Dawson. Real-time pc-based x-ray simulation for interventional radiology training. In Proceedings of 11th Annual Meeting, Medicine Meets Virtual Reality, pages 233–39, 2003. [12] W.L. Nowinski and C.-K. Chui. Simulation of interventional neuroradiology procedures. In proceedings of International Workshop on Medical Imaging and Augmented Reality (MIAR), pages 87–94, Hong Kong, june 2001. IEEE Computer Society, 2001. [13] D. Pai. Strands: Interactive simulation of thin solids using cosserat models. Eurographics, 2002.