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A Stable and Real-Time Nonlinear Elastic Approach to Simulating Guidewire and Catheter Insertions Based on Cosserat Rod Wen Tang∗ , Tao Ruan Wan, Derek A. Gould, Thien How, and Nigel W. John
Abstract—Interventional Radiology procedures (e.g., angioplasty, embolization, stent graft placement) provide minimally invasive therapy to treat a wide range of conditions. These procedures involve the use of flexible tipped guidewires to advance diagnostic or therapeutic catheters into a patient’s vascular or visceral anatomy. This paper presents a real-time physically based hybrid modeling approach to simulating guidewire insertions. The long, slender body of the guidewire shaft is simulated using nonlinear elastic Cosserat rods, and the shorter flexible tip composed of a straight, curved, or angled design is modeled using a more efficient generalized bending model. Therefore, the proposed approach efficiently computes intrinsic dynamic behaviors of guidewire interactions within vascular structures. The efficacy of the proposed method is demonstrated using detailed numerical simulations inside 3-D blood vessel structures derived from preprocedural volumetric data. A validation study compares positions of four physical guidewires deployed within a vascular phantom, with the coordinates of the corresponding simulated guidewires within a virtual model of the phantom. An optimization algorithm is also implemented to further improve the accuracy of the simulation. The presented simulation model is suitable for interactive virtual reality-based training and for treatment planning. Index Terms—Cosserat theory of elastic rod, guidewire insertion, minimally invasive interventions, physically based simulation.
I. INTRODUCTION NTERVENTIONAL radiology (IR) procedures use medical imaging techniques to guide needles, guidewires and catheters, inserted through minute skin incisions, to perform a wide range of minimally invasive therapeutic treatments. There has been considerable interest in simulating guidewire insertions for interactive virtual reality-based IR training and treatment
I
Manuscript received July 14, 2011; revised December 29, 2011 and April 30, 2012; accepted May 4, 2012. Date of publication May 15, 2012; date of current version July 18, 2012. Asterisk indicates corresponding author. ∗ W. Tang is with the School of Computing, the University of Teesside, Middlesbrough, TS1 3BA, U.K. (e-mail:
[email protected]). T. R. Wan is with the Bradford University, Bradford, BD7 1DP, U.K. (e-mail:
[email protected]). D. A. Gould is with the Royal Liverpool University Hospital, Liverpool, U.K. (e-mail:
[email protected]). T. How is with the Liverpool University, Liverpool, L69 3BX, U.K. (e-mail:
[email protected]). N. John is with the Bangor University, Bangor, LL57 2DG, U.K. (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2012.2199319
planning. However, realistic simulation of intrinsic physical behaviors of guidewires during insertion remains challenging. This paper presents a new hybrid modeling approach to realtime guidewire insertion simulation. The long slender body of guidewires (approximately 170 cm in length) and the corresponding flexible tips are computed using two different physically based models. Based upon the nonlinear elasticity of the Cosserat rod [1], the continuous configuration of a guidewire inside 3-D vascular structures is represented by the Cosserat centerline curve, which models both bending and twisting of the instrument. The shorter flexible tip (approximately 3 cm) of the instrument is modeled by a generalized bending model that is more computational efficient and reflects the different mechanical properties of the guidewire tips to that of the main instrument body. In this paper, we also describe our simulation algorithms with the use of a minimum coordinates formulation [2] to achieve stable and real-time computation. The paper also presents detailed results of a phantom validation. Previously, a mass-spring model [3] has been proposed to simulate guidewires’ bending using particles connected by springs. Alderliesten et al. proposed a non-real-time solution in [4] to take into account friction and contact during insertions using a quasi-static update. In order to guarantee the simulation accuracy with this approach, it is assumed that a guidewire must be inserted slowly without any acceleration. However, both the mass spring and friction contact models solely bending deformations of guidewires. In [5], the geometric nonlinearity of the large bending deformation of guidewires are approximated by using an incremental linear finite element model. In addition, a substructure analysis was used for improving the computational speed. The use of dynamic splines for surgical threads and knot tying was also demonstrated in [6] and [7], which also effectively simulated realistic bending effects of surgical threads without twisting being presented. Recent approaches have been proposed to handle the nonlinear elasticity of surgical threads. Pai [8] simulated the static configuration of a thread based on the theory of the Cosserat elastic rod using computationally expensive Newton iterations. The effect of material torsion of threads was considered by Spillmann [9] using a quaternion representation. Other nonCosserat rod approaches include modeling a guidewire as a series of finite-element beams [5] and a nonphysically based forward kinematics approach to predict the catheter’s tip position but assume that the catheter bends with zero torsion and with constant curvature [13]. Our approach solves dynamic deformations of guirewires using a discrete differential geometry
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formulation. Furthermore, we use a parallel transport approach [2] to compute elastic forces without stiff constraints, resulting in a stable and fast simulation for very long elastic medical instruments in contact with complex vascular anatomy. Our previous works [14], [15] only modeled the slender body of guidewires without taking into account the different configurations and mechanical properties of the flexible tips. The geometric configurations and mechanical properties of the tip of a guidewire differs from that of the main slender body. Therefore, its design and simulation are of vital importance in ensuring a smooth guidewire insertion to reduce the likelihood of vessel trauma. Although algorithms presented in [5] and Alderliesten et al. [4] are also capable of modeling guidewire tips by assigning different geometric configurations and mechanical properties, the same simulation models were applied throughout the whole device, which is computationally inefficient especially since these methods already suffered from realtime performance issues. By explicitly modeling flexible tips using a less expensive physically based model than the elasticrod model for the slender body, our approach is computationally efficient and effective. Furthermore, we present detailed numerical analysis and validations regarding the tip configurations and mechanical properties in terms of the bending stiffness and frictional characteristics. The hybrid modeling approach presented in this paper provides an efficient framework for the guidewire tip modeling in conjunction with the Cosserat rod model for the main body to achieve physical accuracy. To further improve the simulation accuracy, an optimization scheme is also applied to decrease the insertion error. Detailed results of the experimental validation is presented comparing displacements of the tip and the slender body against the physical guidewire insertions of different stiffness and tip configurations in a vascular phantom. We present experimental results of incorporating physical properties of real guidewires and different friction coefficients to evaluate simulation accuracy. II. METHOD AND ALGORITHM A. Proposed Guidewire Model Let Γ(r) be the long slender body of a guidewire of length L with its centerline curve r(s, t), the material coordinate s ∈ [0, L] along the centerline, and time t. The tip of the guidewire Γ(h) is constructed using a generalized bending model (see Fig. 2). The dynamic centerline r(s, t) is the curve passing through the center of mass of every cross section at a time instance t. The material frame [d1 , d2 , d3 ] is a right-hand orthonormal basis attached to each mass point along the centerline, representing the twist around the centerline of the guidewire’s material at that point. A reference frame [u, v, d3 ] adapts to the centerline’s evolution at each mass point. Theorem 1: The material frame of the Kirchhoff model to a Cosserat curve is defined to be inextensible and no shearing can occur [1] d3 (s, t) =
r (s, t) . |r (s, t)|
(1)
Fig. 1. (Top image) Guidewire configuration as an elastic rod is defined by its centerline r(s). Further, the orientation of each mass point of the wire is represented by an orthonormal basis [d 1 (s, t), d 2 (s, t), d 3 (s, t)] such that d 3 is constrained to align tangentially to the centerline curve. (Bottom image) Guidewire inserted into a blood vessel.
Thus, the director d3 is constrained to align at a tangent to the centerline curve. The reference directors u and v span the cross-sectional plane normal to the centerline tangent d3 . The directors of the material frame d1 and d2 are on the same plane to u and v separated by a twisting angle θ. Theorem 2: From differential geometry, it is known that there exists a Darboux vector Ω(s, t) such that dk = Ω(s, t)×dk ,
k = 1, 2, 3
Ω(s, t) = Ω1 (s, t)d1 + Ω2 (s, t)d2 + Ω3 (s, t)d3
(2) (3)
where the prime indicates differentiation with respect to the s coordinate. The Darboux vector measures the strain rates for the bending and torsion of the Cosserat curve for the spatial evolution of the material frame. Values of Ω1 (s, t) and Ω2 (s, t) measure the strain in the two bending directions of the material frame, while Ω3 (s, t) measures the torsional strain. A 2-D vector called the curvature binormal κb is introduced to represent bending in the two directions d1 and d2 , such that κb = Ω1 (s, t)d1 + Ω2 (s, t)d2 . The twist about the centerline is expressed as m = Ω3 (s, t). Thus, the Darboux vector Ω(s, t) consists of an adapted material frame along the centerline traversal and a twist about the tangent by an angle θ (see Fig. 1). By substituting (3) into (2) and because dk · dk = 1 and dk × dj = 0, k = j, we derive the material curvature vector κ as κ = [κ1 , κ2 ]T = [κb · d2 , −κb · d1 ]T .
(4)
Thus, the potential energy from these strain rates can be derived. B. Energy Formulation The elastic bending and twisting potential energies are constructed in terms of the material curvatures κb and the material twist m respectively 1 1 E(Γ(r)) = B([κb · d2 , −κb · d1 ]T )2 ds + βm2 ds 2 2 (5)
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The slender body of the device is simulated as a naturally straight isotropic rod. This assumption leads to a simplified expression for twists mi = Δθi . The guidewire’s tip is shorter in length and has different mechanical properties to the shaft. A small set of vertices xk (n + 1 ≤ k ≤ n + m), m n, is employed for modeling the tip. The bending and stretching deformations of the tip are modeled according to the dihedral angle, αk (see Fig. 1), and ek − ek , respectively, the stretch of the edge length Δk = ¯ k where e = xk +1 − xk is the deformed edge and the e¯k is the undeformed edge. Therefore, the potential bending energy for a curved guidewire tip is approximately proportional to the integral of the mean curvature squared by looking at the dihedral angles between adjacent edges (see Fig. 1) E(Γ(h)) = kb
n +m −1 k =n
Fig. 2. (Top image) Centerline of the guidewire is discretized into xi and the orientation of each edge element [d i1 , d i2 , d i3 ]. (Bottom image) Tip of the guidewire is defined by particles xn + k and the dihedral angle α k . The orientation of the tip is defined by [d n1 , d n2 , d n3 ] at the edge en of the slender body.
where B ∈ R2×2 is the stiffness tensor measuring the anisotropic bending response along the material axes d1 and d2 . A guidewire is assumed to have a uniform cross section. 2 Thus, only the diagonal terms B11 = B22 = E π 4r are considered, where E denotes the flexural modulus governing the bending resistance and r is the radius of the device. In (5), β = 12 Gπr2 is the twisting stiffness constant with G denoting the shear modulus governing the torsional resistance. A spatially discrete centerline representation to the aforementioned continuous model is to divide s ∈ [0, L] into n segments (see Fig. 2). Thus, the discrete centerline is given by a set of n + 1 vertices xi (0 ≤ i ≤ n + 1) and a set of n + 1 material frames [dj1 , dj2 , dj3 ] attached to each edge ej = xj +1 − xj , j(0 ≤ j ≤ n) (see Fig. 1). We rewrite (5) in terms of discrete material curvatures κi and twist mi as 1 Bκ2i 1 βm2i + 2 i=1 l¯i 2 i=1 l¯i N
E(Γ(r)) =
N
(6)
where barred quantities denote the evaluation on the undeformed configuration l¯i = 12 (|¯ ei−1 | + |¯ ei |). Following [2], in (6), the discrete material curvature at a vertex i, 1 ≤ i ≤ n is κi =
(κb)i =
i 1 ((κb)i · dj2 , −(κb)i · dj1 ) 2 j =i−1
× di3 2di−1 3 . i−1 1 + d3 · di3
(7)
|ek −1 × ek | 2 α |ek −1 | + |ek | k
(8)
where kb is the elastic bending stiffness of the tip. The flexible tip of a guidewire has a strong resistance to stretching, but easily bends. Thus, a large stretching stiffness and a small bending stiffness are chosen for modeling the tip. There is no material twisting about the tangent at each tip node. A rigid body transformation is applied to obtain the final position of the tip at each of the simulation time step by rotating the flexible tip according to the turning angle θn of the guidewire based manipulation. C. Numerical Solution and Parameter Optimization The dynamics of the shaft and its tip are solved by the Lagrangian equations of motion. The total internal force on each node on the shaft is obtained by differentiating the potential energy E(Γ(r)) with respect to the coordinates xi and θi . The internal force at each node of the tip is computed by differentiating the potential energy E(Γ(h)) with respect to the coordinates of the tip-node position xk . Euler integration is applied to the equations of motion and a data structure of axis-aligned bounding boxes is used to achieve real-time collision detections. In addition to impulse forces derived from the friction and the collision, motions of a guidewire are controlled by the insertion force and the turning angle at its base. As it is inserted, the wire travels along a curved path due to contact forces exerted by the vessel wall to the tip and the shaft. The clinician will turn the base to control the arc direction [19], while simultaneously inserting at the base with a constant pushing force [17], [20]. Therefore, the pushing force and the turning angle are input parameters for the guidewire base manipulation. An optimization algorithm applied as an additional preprocessing step is used to improve the simulation accuracy. Although real-time simulations are achieved without this additional step, optimal input parameters can be obtained through optimization. At each iteration during this stage, the pushing force f and the turning angle θ of the base manipulation are evaluated as variables to be optimized for displacements of the guidewire tip and the shaft. Other parameters such as the tip and the shaft elasticity parameters and friction coefficients are assumed to be known constants. The objective function to minimize is the difference between the displacement of the physical
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TABLE I FLEXURAL MODULUS AND TYPES OF GUIDEWIRES USED IN EXPERIMENTS
guidewire and the displacement of the simulated guidewire in the phantom experiment, by minimizing the squared sum of distances between the displacements as the following objective function: N −1 minxreference − xsimulated 2 (9) (f j , θj ) = arg min i i i=0
where f j , θj denotes desired input parameters, j is the iteration step, and N is the total number of nodes. A randomized optimization algorithm called the covariance matrix adaptation (CMA) [23] is used. The solution from the previous time step provides the initial guess for the current solution to speed up the optimization. III. RESULTS AND VALIDATION A. Material and Datasets Two 3-D vascular structures of an abdominal aortic aneurysm and the major aortic branches are derived from DICOM datasets obtained from CT medical scans. The raw datasets are optimized to support precise contact computations in our simulation program using a similar approach to [5]. A physical silicone phantom of a life-size arterial using rapid prototyping from CT imaging data (Elastrat, Zurich, Switzerland) of the normal abdominal aorta and pelvic arteries down to the common femoral artery bifurcations is used. The actual position of a guidewire as it is inserted into the phantom is obtained and subsequently compared with the position of a corresponding simulated guidewire. Four commonly used guidewires of different stiffness and tip configurations are selected, representing their uses at different stages of an interventional procedure. Of these selected guidewire types: Bentson straight tip (Boston Scientific, USA), Cook fixed core straight tip and Cook fixed core safe TJ curved tip (Cook Medical Inc., USA) are as representative of access guidewires, Terumo stiff angled tip (Terumo Corp., Japan) is an example of a selection guidewire. We measured the material flexural modulus Eb of the physical 3 guidewires as Eb = 2 πPdl2 h , where P is the normal force, l is the tested guidewire length, d is the diameter of the guidewire, and h is the deflection of a local point. Table I lists the flexural modulus and types of the four selected guidewires.
B. Experiment Setup Two identical digital cameras are used to obtain orthogonal images in the anterior–posteria and lateral planes as each of the guidewires are introduced into the silicone model. Three anatomical locations namely the lowest left renal artery origin, the aortic bifurcation, and internal iliac artery bifurcation are chosen to steer the guidewire tip to reach these positions. All guidewires are inserted under the same conditions to the same sites multiple times to ensure the reproducibility of the guidewire configuration in the physical experiment setup. From the two sets of perpendicularly aligned images, the 3-D position of the physical guidewire is extracted using a 3 × 4 projection matrix [16]. Each insertion is repeated eight times, thus in total 96 experiments were performed, i.e., four guidewires for three target locations, carried out eight times. 1) Error Measures: The algorithm is evaluated by comparing simulation results with the position of the physical guidewires as the reference positions for each insertion experiment. The root-mean-square (RMS) distance between the node positions in the simulated guidewire and the corresponding reference guidewire is computed. The targeting error for the guidewire steering is measured via the displacement of the tip. For a guidewire with N vertices, the error measure is defined as follows: N −1 1 (xsi − xri 2 ) (10) (RMS) = N i=0 where xsi denotes the simulated vertex position and xri the corresponding reference point. 2) Simulation Parameters: To demonstrate the feasibility of the algorithm and assess simulation accuracy, extensive simulations are carried out using different modeling parameters. Parameters affecting the guidewire path and the displacement of its tip to a target location are: input values for the base manipulation, physics properties of the gudiewire shaft and the tip, and the friction at the tip and the shaft. The bending stiffness parameters for the shafts are based on the measured flexural modulus in Table I. The remaining parameters are difficult to obtain through measurements and so are set based on trial experiments, which are the twisting stiffness of the guidewire shafts, the bending and stretching stiffness of the tips, and the friction and restitution coefficients for the tip and the shaft. Coating the surface of a real guidewire reduces friction in order to facilitate the detection of blood vessel curvatures [22] and prevent blood platelet adhesion and thrombus formation to ensure smooth navigation through vessels and catheters. In particular, the tip of guidewires is specially designed to be flexible with either straight or curved or angled ends, thus, providing safe navigation throughout challenging anatomy and decreasing the likelihood of vessel trauma. In our model, Signorini’s and Coulomb’s friction laws are used to resolve friction contacts between the guidewire surface and the vessel inner surface. Although friction coefficients of different types of guidewires with various coating materials
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TABLE II SIMULATION PARAMETERS
TABLE III RMS DISTANCE ERRORS WITH RESPECT TO GUIDEWIRE SHAFTS AND TIPS: TIP: μ = 0.05, η = 0.01, α = 100.0, β = 0.8; SHAFT-μ = 0.2, η = 0.01; BASE OPERATION: f = 0.4, θ = 45 0
Fig. 3. Comparison of the simulated guidewire configuration (green) with the physical guidewire configuration (light gray) in the phantom experiment. (Top) Cook safe TJ tipped at the internal iliac artery bifurcation. (Middle) Terumo stiff angled tipped guidewire at the internal iliac artery bifurcation. (Bottom) Bentson straight tipped guidewire at the aortic bifurcation.
between catheters and guidewires are shown in [21], no data are available for friction between the guidewire’s surface and vascular anatomy. Coefficients of friction and restitution used in our experiments are guided by the information provided in [21]. A small friction coefficient is set for the tip and a slightly bigger friction coefficient is chosen for the shaft to reflect low friction in guidewire insertion. Table II illustrates parameter values and ranges used in simulation experiments. Table III shows the average RMS distance, the RMS distance range, the standard deviation (STDEV) over the three target locations. The simulation accuracy for the tip is separated from the measurement for the shaft. The error ranges for the less stiff wires are larger due to the fact that larger pushing forces are required to steer the guidewires to the target and the softer guidewires have more contacts with the vascular inner surface. However, the accuracy can be improved using the proposed optimization algorithm to find optimal simulation parameters. Figs. 3 and 4 show image comparisons of simulated guidewire and the corresponding physical guidewire in the vasculature phantom experiments. The simulation accuracy is shown from
the close distance between the simulated guidewire and the corresponding reference guidewire. 3) Parameter Optimization: The randomized optimization algorithm as a preprocessing step can be used to optimize the base manipulation inputs. The algorithm is based on an adaptive evolutionary algorithm for stochastic direct optimization using evolutionary computing, in particular genetic algorithms and evolution strategies [24]. The algorithm is run with a maximum of 200 objective function evaluations and a population size of 10. Iterations are terminated when the value of the objective function is less than a minimum threshold. Table IV shows the result of the optimization for the input parameters for the insertion at the lowest left renal artery origin. Less stiff guidewires require larger pushing forces than stiffer guidewires. C. Simulation Results 1) Accuracy with Respect to the Flexural Modulus: Guidewires of different stiffness behave differently when propagated inside the vasculature. To assess the simulation accuracy with the use of the flexural modulus obtained from the physical guidewires, experiments are carried out by comparing simulations using a 15% increase or decrease of the tested flexural modulus with the simulation using the tested flexural modulus. The left column of Fig. 4 summarizes the results. The use of physical properties of real guidewires generally decreases the RMS distance errors. However, the RMS distance error with
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Left column shows the results of the bending tests and right column shows the results of the friction tests.
TABLE IV OPTIMIZATION RESULTS
a Cook straight tipped guidewire is slightly higher than using the 15% decreased value. The anomaly seen in this case is acceptable given the result is highly dependent on the chosen parameters. Friction coefficients for the shaft and the tip are fixed for all simulations in this test. Also stiffer guidewires followed reference paths more closely than the less stiff ones. 2) Accuracy with Respect to Friction: The effect of friction contacts to the simulation accuracy is assessed by using the tested flexural modulus with different friction coefficients for the
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Fig. 6. Example of a guidewire insertion from the femoral artery through the aortic arch into the right coronary artery for accessing narrow complex vasculature anatomy.
TABLE V COMPUTATION TIME (MILLISECOND) Fig. 5. Simulation results based upon the second vasculature dataset. (Top) Guidewire insertion example is delivered from the insertion point at the lowest left renal artery origin to reach a subbranch artery. (Bottom-left) Guidewire sliding through a catheter. (Bottom-right) Example of large bending of a guidewire reaching a subbranch artery.
guidewire shaft. Friction coefficients for the tip μ = 0.01, η = 0.01 are set to allow low friction at the tip. The right column of Fig. 4 summarizes results of the friction tests. Low friction generally decreases the error. 3) Interaction between Catheter and Guidewire: The same simulation algorithm for the guidewire shaft is also used for the simulation of catheters. When dealing with friction between the surface of guidewires and the inner surface of the catheter, we choose a friction coefficient between 0.1 and 1.0 as in [21]. The contact between the catheter and the guidewire is detected through a spherical collision contact between two circles with diameters equal to the catheter and the guidewire, respectively. A guidewire sliding inside the catheter occurs at contact points and the same friction algorithms are applied. The bottom left image of Fig. 5 demonstrates a guidewire inserted through a catheter. 4) Collision Detection and Responses: At each simulation step, axis-aligned bounding boxes are used to facilitate collision detection between the guidewire and the vascular anatomy. This data structure offers efficient intersection and distance queries against a set of 3-D objects. Each simulated node of the guidewire is attached with an implicit bounding sphere that has the same radius as the guidewire. Signed distance functions are used as straightforward analytic expressions for collision detection. If a node is detected as penetrating the blood vessel wall, an impulse force is applied to the node. 5) Simulation Performance: The numerical stability is crucial for achieving robust simulations. An overall computation time under 5 ms is achieved for each simulation step, resulting in an overall performance of 400 frames per second (FPS) on
an Intel Core 2 Due Processor T9600 PC. Images in Figs. 5 and 6 show a guidewire insertion starting from the proximity end of the vasculature and moving toward a target allocated in a branch artery origin, resulting in large bending and twisting deformations yet the simulation is easily achieved in real-time at 400 FPS. Table V summarizes the computational time for collision detection, rendering, and the physics computation with different insertion lengths. The optimization is achieved by utilizing an optimization toolbox [25] with our C++ simulation programs.
IV. DISCUSSION AND CONCLUSION The hybrid solution for guidewire insertions presented in this paper allows real-time simulation of large nonlinear elastic deformations of guidewires with varied shaft stiffness and tip configurations. The phantom validation results show submillimeter RMS errors for four guidewires placed at three repeatable anatomical locations, indicating the attainment of high levels of mechanical fidelity for guidewire performance. Our simulation system will benefit from further validation to improve translation into the clinical environment. Given these promising results, we aim to specifically validate guidewire simulation within clinical settings before incorporating local and global vessel deformations, which require an extension to our current collision detection algorithm. The optimization algorithm needs to be investigated further to improve the accuracy of the tip targeting displacements for motion planning. Finally, haptic interactions [26] can also be incorporated into the current model for interactive virtual reality training and assessment.
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Wen Tang received the B.Sc. degree in engineering from Xian University of Engineering Science and Technology, Xian, China, and the Ph.D. degree from the University of Leeds, Leeds, England, U.K. She is a Reader in Computer Graphics and Visualization in the School of Computing, Teesside University, Middlesbrough, U.K. Her research is focused on the design of computational algorithms for physically based simulation and modelling of computational biomechanics, virtual surgery, computational solid, and real-time computer graphics and animation.
Tao Ruan Wan received the B.Sc. and M.Sc. degrees from Xi’an University of Engineering Science and Technology, Xi’an, China, and the Ph.D. degree from the University of Leeds, Leeds, U.K. He is a Senior Lecturer in the School of Computing, Informatics, and Media, University of Bradford, Bradford, U.K. His research interests include computational models for 3-D visualization and simulation, and real-time physically based modeling and simulations, including soft-tissue modeling and computerbased surgical simulation. Dr. Wan received the Woolmen’s Company Best Doctoral Dissertation Award at London in 1996.
Derek A. Gould is a Professor and Consultant Clinical Interventional Radiologist (IR) in the Royal Liverpool University Hospital, Liverpool, U.K. for 27 years. His current research interests include the development of novel interventional techniques and interventional skills training. In 2002, he formed a multidisciplinary group Collaborators in Radiological Interventional Virtual Environments to develop simulator models with appropriate fidelity, to remove the risks of skills training from patients. Prof. Gould has been the Chair (currently a coopted member) of the British Society of Interventional Radiologists Education Committee, during which time he completed an interventional radiology training syllabus in 2006.
Thien How is a Senior Lecturer in the Department of Clinical Engineering, University of Liverpool, Liverpool, U.K. His current research interests include vascular haemodynamics, design, and evaluation of vascular prostheses for the bypass of peripheral arteries and clinical aspects of arterial reconstruction, etc.
Nigel W. John is the Chair in computing at Bangor University, Bangor, U.K., and is the Director of the Wales Research Institute of Visual Computing, Wales, U.K. He leads research activities at Bangor University in visualization and medical graphics. He was formerly the Head of the Manchester Visualization Centre, University of Manchester, Manchester, U.K. He has been responsible for a variety of projects funded by the Research Councils and European Commission involving visualization and virtual environments. His current research interests include medical visualization, simulation, and training systems.
