Cite this article: Haoyu WANG, Jianhuang WU. A virtual reality based surgical skills training simulator for catheter ablation with real-time and robust interaction. Virtual Reality & Intelligent Hardware, 2021, 3(4): 302-314 DOI:10.1016/j.vrih.2021.08.004

A virtual reality based surgical skills training simulator for catheter ablation with real-time and robust interaction

Haoyu WANG ^1,² , Jianhuang WU ²

1. University of Chinese Academy of Sciences, Beijing 100049, China

2. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China

Abstract

Background

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia that can cause severe heart problems. Catheter ablation is one of the most ideal procedures for the treatment of AF. Physicians qualified to perform this procedure need to be highly skilled in manipulating the relevant surgical devices. This study proposes an interactive surgical simulator with high fidelity to facilitate efficient training and low-cost medical education.

Methods

We used a shared centerline model to simulate the interaction between multiple surgical devices. An improved adaptive deviation-feedback approach is proposed to accelerate the convergence of each iteration. The periodical beating of the human heart was also simulated in real time using the position-based dynamics (PBD) framework to achieve higher fidelity. We then present a novel method for handling the interaction between the devices and the beating heart mesh model. Experiments were conducted in a homemade simulator prototype to evaluate the robustness, performance, and flexibility of the proposed method. Preliminary evaluation of the simulator was performed by medical students, residents, and surgeons.

Results

The interaction between surgical devices, static vascular meshes, and beating heart mesh was stably simulated in a frame rate suitable for interaction.

Conclusion

Our simulator is capable of simulating the procedure of catheter ablation with high fidelity and provides immersive visual experiences and haptic feedback.

Keywords： Virtual reality ; Interventional radiology ; Surgical skills training ; Surgery simulator ; Catheter ablation

Content

1 Introduction

Over the last few decades, endovascular procedures have gained increasing popularity for their advantages over traditional open surgery as they are minimally invasive, and result in short hospital stays and fewer complications. However, this procedure requires physicians to be highly skilled at manipulating the surgical devices under the guidance of two-dimensional X-ray imaging. In addition to developing a complex understanding of three-dimensional anatomy from two-dimensional displays, physicians need years of practice to acquire good hand-eye coordination. Traditional training methods (e.g., apprenticeship with patients, using human cadavers or live animals, employing phantoms, etc.) are risky, expensive, and restricted to limited morphological models^[1]. Moreover, exposure to radiation during these training processes is harmful to the health of trainees. Interactive virtual reality-based simulators provide a promising solution to overcome all the above-mentioned difficulties as it offers a non-error-sensitive and radiation-free environment for physicians to practice surgical skills repeatedly^[2]. Studies have shown that training with a virtual reality-based simulator can improve a resident's endovascular surgical skills^[3,4].

VR-based simulators for training surgical skills have been developed since the 1990s and have gained increasing popularity in the last two decades^[5]. Simulators for training various types of surgical procedures have been built, and evaluation of their face and construct validity shows promising results^[6-9]. Weidenbach et al. developed an augmented reality simulator for training a two-dimensional echocardiographic examination^[10]. Preliminary evaluation of the system in student courses showed a training benefit, even for a short training period. Wijewickrema et al. presented a cochlear implant surgery simulator that was designed based on the concepts of surgical curriculum development and was assessed with a user study evaluation^[11]. Gupta et al. designed a cyber human system-based simulator framework for orthopedic surgical training by adopting the engineering principles of information-centric systems^[12]. Qualitative feedback surveys were conducted to evaluate the user-friendliness and effectiveness of the simulator.

In the domain of developing VR-based interventional simulators, many studies have been conducted since Anderson et al. first proposed an interventional simulator in 1996^[13]. Wang et al. proposed a simulator for percutaneous coronary revascularization procedures^[14]. They represented the vascular model with a centerline hierarchy model and simulated the behavior of surgical devices using the finite element method (FEM). Dawson et al. also proposed an interventional cardiology training simulator (ICTS)^[15]. In this simulator, a multi-body system was used to represent the catheter and the guidewire. Customized haptic devices have been developed to replicate the operation of a real surgical device. In the simulator proposed by Duriez et al., an incremental FEM method was proposed to simulate the interaction between the devices and the vascular model^[16]. Furthermore, Cai et al. proposed an interventional radiology simulator based on the FEM^[17]. They proposed a central topology-based continuous potential field to handle FEM-based numerical calculations. Wang et al. used a triangle mesh with a lower resolution to perform collision detection for optimization^[18]. They also used RGB-encoded depth techniques to approximate the X-ray imaging effect. In previous work, the perforation of vasculature was simulated by allowing violation of the constraints^[19]. In the simulator proposed by Luboz et al., linked rigid bodies were used to model the guidewire^[20]. In our previous work, a dynamic discretization strategy was proposed to adapt the surgical device model to vascular meshes with various geometrical features^[21,22]. In the percutaneous coronary intervention surgery simulator developed by Wang et al., a guidewire modeling method based on heterogeneous and integrated chainmail was proposed^[23]. Recently, the authors proposed a cardiovascular interventional system for personalized intervention planning and technique rehearsal^[24].

Many other approaches and simulation systems have been proposed for training surgical skills in interventional radiology, which will not be elaborated in this paper^[25-31]. Most of these methods and systems were not optimized for catheter ablation. Nevertheless, the interventional procedures are simulated using static vascular models, either by hierarchical center lines or triangular meshes, leading to a lack of realism. Additionally, preprocessing of the vascular models need to be performed to obtain additional information necessary for collision responses. This complicates the simulation and limits the source of the anatomical data.

In this study, we present a virtual reality-based interventional simulator for training surgical skills during catheter ablation. In our simulator, we used triangular meshes to represent the vascular system of virtual patients. The vascular mesh model was reconstructed from the segmented CT images of the patients. After an automatic process, including remeshing and smoothing, the mesh model was imported into our simulator for skills training or pre-surgery planning. As the cornerstone of our simulator, we proposed a realistic, stable, and fast method to simulate the interactive behavior of surgical devices. This method was optimized for the simulation of procedures involving more than one device by introducing a shared centerline model and using a deviation-feedback optimization technique. Additionally, a track-based motion control strategy was proposed to predict the behavior of the devices for optimization purposes. To achieve high fidelity, we proposed a method to simulate the heartbeat within a position-based dynamic framework. An offset vector field was created, and a synchronization mechanism was built to handle the interaction between the beating heart and the surgical devices. To provide an immersive training experience, we customized a series of hardware devices to capture the trainee's input and provided realistic haptic feedback. A preliminary evaluation of our simulator was made by a group of subjects, including medical students, residents, and surgeons.

2 Methods

The proposed training system can be decomposed into three key components: surgical device behavior simulation, heart beating simulation, and simulation of the interaction between devices and dynamic meshes.

2.1 Surgical device behavior simulation

Simulation of the interactive behavior of surgical devices is the core of our surgery simulator. The main surgical devices used in catheter ablation are catheters, which can be categorized into two types: sheath catheters and ablation catheters. In our method, either type of catheter can be used as linked rigid rods that are neither bendable nor stretchable. The centerline of the devices was discretized as a sequence of three-dimensional points carrying the discretized spatial and material properties of the device.

In this study, we propose a shared centerline model to represent interventional devices that are nested in one another. As shown in Figure 1, if a point on the centerline is shared by more than one device, its material property is weighted based on the stiffness of the individual device sharing this point.

We iteratively calculated the stable position of each point along the shared centerline by minimizing the total elastic energy of the system formed by the device and the vascular model. The total elastic energy included the bending and torque energy of the device and the elastic energy of the deformed vessel wall. In previous methods, collision detection was conducted frequently to update the elastic forces exerted on the centerline point by calculating its offset. However, this was extremely time-consuming and made successive iterations of the simulation very difficult. Instead, we used the calculated offset to update a point's external forces by incorporating a proposed feedback coefficient. This coefficient was based on the historical movements of this point in the previous iterations before convergence was reached. With this method, collision detection was avoided and the convergence was accelerated. Moreover, it caused the simulated device to behave more robustly when navigating in vascular meshes with variable geometrical features^[32].

To further relieve the computational burden of the simulation, we proposed a track-based motion control strategy to predict the shape of the virtual device once the user input signal is received. We assumed that the device tends to remain in its previous stable shape and slide forwards or backwards against the vessel wall^[33]. Based on this assumption, we shifted the points on the device centerline to predict the initial positions when the user input was captured. The predicted device centerline was very close to its next stable position. As a result, the convergence of iterations could be further accelerated.

2.2 Heart beating simulation

The simulation of periodic heart pumping is of great importance in building a realistic environment for training surgical skills. Our approach for simulating heart beating is based on the PBD framework. The position of the heart mesh vertices is directly controlled by adding constraints, which significantly improved the stability of the simulation.

The workflow of the proposed algorithm is shown in Figure 2. Before entering the simulation loop, the properties (position, velocity, and mass) and constraints for each particle needed to be initialized. Then, the simulation loop was started. For each vertex composing the heart mesh, all forces were calculated, and its position was predicted based on Newton's second law. We then traversed all constraint functions for this vertex and corrected its position to satisfy the constraints. At the end of the loop, the velocity and position were updated.

Within the PBD framework, constraint functions are defined to project the predicted positions of the vertices to the correct positions. Most of the forces exerted on the vertex can be represented by a constraint function. There are two types of constraints in our method: stretching and volume conservation.

Stretching constraint. In our heartbeat model, there were two types of stretching constraints. One constraint was the distance between adjacent particles, and the other was the distance between the current positions of a particle and its initial input position. The purpose of the former constraint was to maintain the shape of the heart unchanged morphologically and to achieve a smooth surface during deformation. The latter constraint ensured that the particles restore their initial state and maintain the shape of the heart.

Volume conservation constraint. The volume of the heart does not change significantly during the cycle of the heartbeat. Therefore, we conserved the volume of the heart mesh to constrain its behavior. The conservation constraint function is defined as follows:

C_{v o l u m e} (p_{1}, p_{2}, p_{3}, p_{4}) = \frac{1}{6} [(p_{1} - p_{2}) \times (p_{1} - p_{3})] ∙ (p_{1} - p_{3}) - V_{0}

where {

p_{1}

p_{2}

p_{3}

p_{4}

} denote the four corners of a tetrahedron and represent its initial volume. The above volume conservation constraint-solving method can be used directly in a tetrahedral mesh. However, the type of mesh used in this study was a triangular surface mesh. Instead of converting the triangular mesh to a tetrahedral mesh, we calculate the volume of the heart mesh more efficiently: 1) randomly generate a point in 3D space (e.g., the origin O). 2) construct tetrahedrons by connecting the generated point to the three vertices of each triangle in the mesh, and 3) sum the volume of each constructed tetrahedron.

A simple example of this is shown in Figure 3. The volume of the surface mesh composed of four triangles can be calculated as:

V_{(p_{1}, p_{2}, p_{3}, p_{4})} = V_{(p_{1}, p_{2}, p_{3}, O)} + V_{(p_{1}, p_{2}, O, p_{4})} + V_{(p_{1}, O, p_{3}, p_{4})} + V_{(O, p_{2}, p_{3}, p_{4})}

2.3 Interaction simulation between devices and meshes

In a real-life catheter ablation procedure, surgical devices move inside a beating heart. Therefore, it is of great importance for our interventional simulator to simulate the interactive behavior of surgical devices within a beating heart mesh model.

Collision detection involving meshes with shapes that vary over time frequently suffer from low efficiency and instability. To solve these problems, we divided the simulation into two stages: the offline preprocess stage and the online simulation stage.

Offline preprocess stage. In this stage, we first simulated heart beating for the target heart mesh using the algorithm proposed in Section 2.2. For any random cycle, we sampled N times and saved the instant position of every vertex for the heart mesh as a sequence of files. We denoted the saved sequential file as frame files,

F_{1}, F_{2} \dots F_{N}

. Note that a larger N indicates a more realistic and smoother heart-beating animation and larger hard disk and GPU memory consumption.

Online simulation stage. In this stage, we imported the sequential frame files that contained positional information for all heart mesh vertices at different instances during a complete heartbeat cycle. For the

i^{t h}

vertex

v_{i j}

of the heart mesh in the

j^{t h}

frame file

F_{j}

, we calculated its position offset

∆ v_{i j}

from vertex

v_{i 1}

, which represented the

i^{t h}

vertex in the first frame file

F_{1}

. After the simulation loop started, we displayed the beating heart using morphing animation techniques. Once the surgical devices entered the beating heart area, instead of computing the device center's intersection with the instance of heart mesh, we computed its intersection with the heart mesh

M_{1}

imported from the first frame file

F_{1}

. Note that the heart mesh

M_{1}

stays invariant, therefore we could perform a fast and stable collision query between the device centerline and the static triangular mesh. We then used the collision result as the input to calculate the behavior of the surgical device using the algorithm explained in Section 2.1. For every vertex

p

in the device centerline, we determined its nearest vertex in the heart mesh

M_{1}

and denoted the index of this vertex as

s

. Then, we obtained the morphing frames' index pair

< u, v >

, and calculated the visual offset

∆ p

for vertex

p

as follows:

∆ p = ∆ v_{s u} * t + ∆ v_{s v} * (1 - t)

where

t \in (0, 1)

is the morphing parameter between

F_{u}

and

F_{v}

. We added

∆ p

to vertex p to obtain the new visual position and uploaded it to the GPU for rendering. With this method, we can perform collision detection with a static heart mesh instead of meshes with time-varying shapes. This implies that stable device behavior simulation results and realistic interactions between the beating heart models can be obtained.

2.4 Hardware

In addition to the simulation algorithms explained above, we designed and built a mobile hardware platform as the interface for trainees. We used translation and rotation sensors to capture the corresponding movement of a real surgical device manipulated by a physician. We also assembled devices to provide essential force feedback such as realistic haptic experiences.

The hardware platform was equipped with a PC (Intel i7-6920HQ CPU @3.5 GHz, NVIDIA GTX 1080 8G RAM) with Windows 10 OS and a 24-inch monitor, as shown in Figure 4. Our training system was developed in C++ with Visual Studio 2015 community, and the graphic API used was OpenGL.

3 Results

Parameter Setting

The parameters used in our algorithm are listed in Table 1. Note that the parameter settings may vary between the different scales of the vascular model. In our case, one unit of virtual space represents 1mm in the real world. The initial scales of the different models may be different. Nevertheless, we can rescale the models to match our coordinate measurements. Thus, our parameter setting works well for vascular models with geometrical features and complexity. Note that all the experiments conducted in this section run in real time (frames per second greater than 30).

Parameter setting for the simulation system

Parameters	Value	Remarks
$s_{m}$	1.0	Scale for the vascular model used in the simulation
$ε$	1.0E-10	Once the calculated displacement for a surgical vertex is less than $ε$ , we consider the equilibrium for this device to have been reached
$\bar{t}$	7.5	Average length of the rods of the simulated devices
$k_{p}$	1.5	Proportional parameter of the feedback coefficient
$k_{i}$	0.03	Integral parameter of the feedback coefficient
$r_{b}$	4.0	Radius of the bounding sphere attached to the device centerline point

Experiment 1: Multiple device simulation

To evaluate the proposed algorithm for simulating the interactive behavior of multiple devices, we translated and rotated a virtual guidewire and a pigtail catheter, which are two commonly used devices for interventional procedures, to observe their behavior.

As demonstrated in Figure 5, initially the guidewire was completely inside the catheter, and the catheter retained its relaxed shape, which looks like a pigtail. The tip of the catheter became less curved as we translated the guidewire forward. This is because the tip of the guidewire is very soft and has little resistance to bending, which is a design feature to protect the vein from being penetrated by incorrect manipulation. However, the guidewire becomes stiffer from its tip to its distal end. When the stiff part of the guidewire passes through the pigtail part of the catheter, the guidewire straightens the highly curved part of the catheter. When we translate the guidewire backward to its initial position, the shape of the catheter's tip recovers slowly. Our results show that the weighted material properties used in our algorithm can realistically simulate such interactions between nested interventional devices in real time.

When torque is applied at the distal end of the guidewire, only the outside part of the guidewire rotates around its axis, while the shape of the catheter remains the same. This is because the diameter of the guidewire is negligible compared to its length. In our algorithm, we assume that the torque propagates instantly from the distal end to the tip. Additionally, the shape of the inside part of the guidewire is constrained by the catheter because of its nested spatial relationship. However, when torque is applied at the distal end of the catheter, the catheter and guidewire rotate around the catheter's axis at the same time. This is because the catheter is the outermost device and its shape changes freely. Meanwhile, the outside part of the guidewire is still constrained by the catheter, so it rotates along with the catheter. The results demonstrate that our algorithm can realistically simulate the rotational manipulation of surgical devices.

Experiment 2: Heartbeat simulation.

To evaluate the efficiency and robustness of our method for simulating a heart beating, we first simulated the complete cycle of a heartbeat using two heart mesh models. Then, a comparative experiment was conducted to demonstrate the robustness of our algorithm.

Figure 6 shows screenshots of four moments in a complete cycle of a heartbeat for both meshes. The ventricle and atrium contract and relax periodically, while the volume of the heart remains unchanged the entire time. In addition, both heart mesh models remain geometrically stable after thousands of beating periods have passed. Due to the PBD framework, the vertices composing the heart model are strictly constrained and their final positions are corrected at the end of each simulation loop to ensure the stability of the simulation results.

In contrast, we use a spring-mass model to represent the heart mesh and perform integration using the explicit Euler method and the fourth-order of the Runge-Kutta method. As shown in Figure 7, the simulation results exhibit a hyperplastic phenomenon when the time step is large. The same phenomenon also appears as the simulation progresses, and the situation worsens over time.

Experiment 3: Ablation simulation

In this experiment, we manipulated the virtual surgical devices to perform the key operation in the catheter ablation procedure. First, a sheath catheter was inserted into the atrium. A steerable ablation catheter was then inserted through the sheath catheter. The purpose of this procedure is to navigate the metal tip of the catheter to any desired position on the atrium wall for further treatment. As shown in Figure 8a, the gray area represents the sheath catheter and light blue represents the ablation catheter. The white object at the tip of the ablation catheter represents the metal part that can generate extreme heat for use in various treatments. The steerable feature of the ablation catheter is simulated by dynamically changing the intrinsic curve angle of the steerable part of the ablation catheter. Through suitable manipulation of the sheath and ablation catheter, the metal tip can be navigated anywhere on the atrium wall. As shown in Figure 8b, we can access the back wall of the atrium by bending the ablation catheter. By rotating the sheath catheter and unbending the ablation catheter, we can access the front wall of the atrium, as shown in Figure 8c. By cooperatively manipulating both catheters, we can obtain access to the pulmonary vein area, as shown in Figure 8d and e.

Experiment 4: Interaction between devices and beating heart

To evaluate the robustness and fidelity of our methods for simulating the interactive behavior between the surgical devices and the beating heart mesh, we navigated the virtual catheter and guidewire to obtain access to the coronary artery and observed their behavior under the X-ray imaging effect.

As shown in Figure 9, once the catheter passed the artery arch and entered the beating heart area, the part of the heart mesh that collided with the catheter started to move along with the beating heart mesh. The synchronization between the surgical device and the beating mesh was ensured by calculating and adding the visual offset for each surgical centerline vertex before rendering the entire simulated surgery scene. In addition, by using smoothing and leaping offset vectors among adjacent device centerline vertices, the zigzag phenomenon can be avoided. The middle and right panels in Figure 9 show that the simulated surgical devices were stable and operated well even when the guidewire was inside the very low-level branch of the coronary artery.

User Evaluation

To evaluate the effectiveness of our simulator, a group of 34 subjects, including 15 medical students, 10 residents, 5 attending cardiologists, and 4 interventional radiologists, were recruited to perform a complete catheter ablation procedure using our simulator. Subsequently, each participant completed a questionnaire in which they could rate various aspects of the simulator on a 5-point Likert scale. The questionnaire was designed to collect the participants' opinions on three subjects: realism, real-time usage, and usefulness. The results listed in Table 2 show that most of the participants gave high ratings for the realism of our simulator, especially with respect to the simulation of heartbeats and instrument behaviors. However, the ranking of the haptic feedback realism was relatively low because our force feedback device is currently only capable of exerting a manually configured, invariant force on the instruments. The average rankings for the real-time usage of our simulator were equal to or higher than 4.7, demonstrating that our methods are efficient in providing an interactive training environment with little latency. From the perspective of usefulness, our simulator obtained a mean score of 3.9 on skill assessment, which is likely due to the lack of automatic and numerical skill assessments throughout the procedure. Nevertheless, most of the participants agreed that our simulator was better than the traditional training methods in most ways and was quite suitable for training catheter ablation skills.

Results of the questionnaire for our simulator showing the mean and the standard deviation (SD) of the scores.

Subject	Factor	Mean (SD)
Realism	X-ray imaging	4.1 (0.135)
	Heartbeat	4.5 (0.372)
	Haptic feedback	3.8 (0.781)
	Instrument behavior	4.4 (0.596)
	Instrument manipulation	4.2 (0.574)
	Multiple instruments interaction	4.6 (0.635)
Real-time	No latency when manipulating a single instrument	4.8 (0.231)
	No latency when interacting with beating heart	4.7 (0.338)
	No latency when manipulating multiple instruments	4.7 (0.275)
Usefulness	Compared with traditional training methods	4.5 (0.733)
	Useful for skill training	4.6 (0.831)
	Useful for skill assessing	3.9 (0.681)

4 Discussion

In this study, we proposed several methods to build a realistic and robust simulation system for training surgical skills during catheter ablation. As the cornerstone of our simulator, we simulated the behavior of the surgical devices by modeling them as a discretized centerline with shared points and weighted material properties. A track-based motion control strategy was proposed to predict the initial shape of the device at the beginning of every simulator loop, leading to a significant decrease in the total amount of required calculations. In addition, an adaptive deviation-feedback approach was proposed to accelerate the convergence of the iteration for calculating the stable position of the device centerline. The adaptive feedback parameter can also increase the robustness of the simulation. To build a realistic training system for atrial fibrillation, it is necessary to simulate a heart beating in real time. Within the PBD framework, we formulated the periodic contraction and relaxation for the ventricle and atrium and added stretch and volume constraints to simulate the deformation of the triangular heart model. We then sampled a complete cycle of the heartbeat and saved them as sequential frame files. The offset vector for each heart mesh vertex and each frame file were calculated during the initialization stage. The beating heart was rendered using a morphing animation technique. Before rendering the simulated surgery scene, the corresponding offset vector was added to its neighbor device's centerline point to make the device move along with the beating heart mesh. In this way, collision detection with morphing meshes was avoided, allowing the simulation remains stable while a higher degree of realism was achieved. To provide a realistic haptic experience, we built a hardware platform to capture user input so that trainees could manipulate real interventional devices.

Experimental results show that our method can stably simulate the behavior of multiple surgical devices with high fidelity at interactive frame rates. The PBD-based heart beating algorithm demonstrated a significant advantage over other mass-spring models with respect to robustness and performance. When simulating the catheter ablation procedure, we were able to navigate the surgical devices to any desired position to perform further operations. When interacting with the beating heart mesh, the surgical devices moved periodically in perfect synchronization. Thus, the results of the preliminary evaluation show that our simulator is capable of providing a realistic, real-time, and immersive environment for training catheter ablation skills.

5 Future work

In the present work, we assumed that the vascular model is static and empty, however the human circulatory system is dynamic with periodically contracting vessels (i.e., pulses), especially near the heart. In addition, our track-based strategy assumed that the material of the devices is highly hydrophilic; thus, some frictions are considered. Our future work will focus mainly on finding solutions to the above-mentioned problems, including the integration of friction, hemodynamics-based blood simulation, and the incorporation of these into our interventional radiology simulator.

Reference

Mitchell E L, Sheahan M G, Schwiesow M. Simulation in vascular surgery. In: Comprehensive Healthcare Simulation: Surgery and Surgical Subspecialties. Cham: Springer International Publishing, 2019, 327–347. DOI:10.1007/978-3-319-98276-2_26

Gallagher A G, Cates C U. Virtual reality training for the operating room and cardiac catheterisation laboratory. The Lancet, 2004, 364(9444): 1538–1540 DOI:10.1016/s0140-6736(04)17278-4

Dawson D L, Meyer J, Lee E S, Pevec W C. Training with simulation improves residents' endovascular procedure skills. Journal of Vascular Surgery, 2007, 45(1): 149–154 DOI:10.1016/j.jvs.2006.09.003

Bagai A, O'Brien S, Al Lawati H, Goyal P, Ball W, Grantcharov T, Fam N. Mentored simulation training improves procedural skills in cardiac catheterization. Circulation: Cardiovascular Interventions, 2012, 5(5): 672–679 DOI:10.1161/circinterventions.112.970772

Badash I, Burtt K, Solorzano C A, Carey J N. Innovations in surgery simulation: a review of past, current and future techniques. Annals of Translational Medicine, 2016, 4(23): 453 DOI:10.21037/atm.2016.12.24

Iwata N, Fujiwara M, Kodera Y, Tanaka C, Ohashi N, Nakayama G, Koike M, Nakao A. Construct validity of the LapVR virtual-reality surgical simulator. Surgical Endoscopy, 2011, 25(2): 423–428 DOI:10.1007/s00464-010-1184-x

Fucentese S F, Rahm S, Wieser K, Spillmann J, Harders M, Koch P P. Evaluation of a virtual-reality-based simulator using passive haptic feedback for knee arthroscopy. Knee Surgery, Sports Traumatology, Arthroscopy, 2015, 23(4): 1077–1085 DOI:10.1007/s00167-014-2888-6

Yamaguchi S, Konishi K, Yasunaga T, Yoshida D, Kinjo N, Kobayashi K, Ieiri S, Okazaki K, Nakashima H, Tanoue K, Maehara Y, Hashizume M. Construct validity for eye-hand coordination skill on a virtual reality laparoscopic surgical simulator. Surgical Endoscopy, 2007, 21(12): 2253–2257 DOI:10.1007/s00464-007-9362-1

Rahm S, Germann M, Hingsammer A, Wieser K, Gerber C. Validation of a virtual reality-based simulator for shoulder arthroscopy. Knee Surgery, Sports Traumatology, Arthroscopy, 2016, 24(5): 1730–1737 DOI:10.1007/s00167-016-4022-4

10.

Weidenbach M, Wick C, Pieper S, Quast K J, Fox T, Grunst G, Redel D A. Augmented reality simulator for training in two-dimensional echocardiography. Computers and Biomedical Research, 2000, 33(1): 11–22 DOI:10.1006/cbmr.1999.1527

11.

Wijewickrema S, Copson B, Zhou Y, Ma X J, Briggs R, Bailey J, Kennedy G, O'Leary S. Design and evaluation of a virtual reality simulation module for training advanced temporal bone surgery. In: 2017 IEEE 30th International Symposium on Computer-Based Medical Systems (CBMS). Thessaloniki, Greece, IEEE, 2017, 7–12 DOI:10.1109/cbms.2017.10

12.

Gupta A, Cecil J, Pirela-Cruz M, Ramanathan P. A virtual reality enhanced cyber-human framework for orthopedic surgical training. IEEE Systems Journal, 2019, 13(3): 3501–3512 DOI:10.1109/jsyst.2019.2896061

13.

Anderson J H, Brody W, Kriz C J, Wang Y P, Raghavan R, Viswanathan R. Da vinci: a vascular catheterization and interventional radiology-based training and patient pretreatment planning simulator. Journal of Vascular and Interventional Radiology, 1996, 7(1): 373 DOI:10.1016/s1051-0443(96)70159-8

14.

Wang Y P, Chui C, Lim H, Cai Y Y, Mak K. Real-time interactive simulator for percutaneous coronary revascularization procedures. Computer Aided Surgery, 1998, 3(5): 211–227 DOI:10.3109/10929089809149843

15.

Dawson S L, Cotin S, Meglan D, Shaffer D W, Ferrell M A. Designing a computer-based simulator for interventional cardiology training. Catheterization and Cardiovascular Interventions, 2000, 51(4): 522–527 DOI:10.1002/1522-726x(200012)51

16.

Duriez C, Cotin S, Lenoir J, Neumann P. New approaches to catheter navigation for interventional radiology simulation. Computer Aided Surgery, 2006, 11(6): 300–308 DOI:10.3109/10929080601090623

17.

Cai Y Y, Chui C, Ye X Z, Wang Y P, Anderson J H. VR simulated training for less invasive vascular intervention. Computers & Graphics, 2003, 27(2): 215–221 DOI:10.1016/s0097-8493(02)00278-9

18.

Wang F, Duratti L, Samur E, Spaelter U, Bleuler H. A computer-based real-time simulation of interventional radiology. In: 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Lyon, France, IEEE, 2007, 1742–1745 DOI:10.1109/iembs.2007.4352647

19.

Lenoir J, Cotin S, Duriez C, Neumann P. Interactive physically-based simulation of catheter and guidewire. Computers & Graphics, 2006, 30(3): 416–422 DOI:10.1016/j.cag.2006.02.013

20.

Luboz V, Zhang Y, Johnson S, Song Y, Kilkenny C, Hunt C, Woolnough H, Guediri S, Zhai J, Odetoyinbo T, Littler P, Fisher A, Hughes C, Chalmers N, Kessel D, Clough P J, Ward J, Phillips R, Gould D. ImaGiNe Seldinger: First simulator for Seldinger technique and angiography training. Computer Methods and Programs in Biomedicine, 2013, 111(2): 419–434 DOI:10.1016/j.cmpb.2013.05.014

21.

Wang H Y, Wu J H, Wei M Q, Ma X. A robust and fast approach to simulating the behavior of guidewire in vascular interventional radiology. Computerized Medical Imaging and Graphics, 2015, 40: 160–169 DOI:10.1016/j.compmedimag.2014.10.006

22.

Wang H Y, Wu J H, Cai Y Y. An adaptive deviation-feedback approach for simulating multiple devices interaction in virtual interventional radiology. Computer-Aided Design, 2019, 117: 102738 DOI:10.1016/j.cad.2019.102738

23.

Wang W W, Li S, Qin H, Hao A M. Novel, robust, and efficient guidewire modeling for PCI surgery simulator based on heterogeneous and integrated chain-mails. In: 2015 14th International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics). Xi'an, China, IEEE, 2015, 105–112 DOI:10.1109/cadgraphics.2015.22

24.

Hao A M, Cui J H, Li S, Zhao Q P. Personalized cardiovascular intervention simulation system. Virtual Reality & Intelligent Hardware, 2020, 2(2): 104–118 DOI:10.1016/j.vrih.2020.04.001

25.

Guo S X, Cai X J, Zhao Y, Gao B F. A novel VR-based simulator for the interventional surgical catheter and guidewire cooperation. In: 2018 13th World Congress on Intelligent Control and Automation (WCICA). Changsha, China, IEEE, 2018, 21–25 DOI:10.1109/wcica.2018.8630397

26.

Alderliesten T, Konings M K, Niessen W J. Modeling friction, intrinsic curvature, and rotation of guide wires for simulation of minimally invasive vascular interventions. IEEE Transactions on Biomedical Engineering, 2007, 54(1): 29–38 DOI:10.1109/tbme.2006.886659

27.

Mi S H, Hou Z G, Yang F, Xie X L, Bian G B. A collision response algorithm for 3D virtual reality minimally invasive surgery simulator. The 26th Chinese Control and Decision Conference (2014 CCDC), 2014, 4594–4599 DOI:10.1109/ccdc.2014.6852993

28.

Mao Y R, Hou F, Li S, Hao A M, Ai M J, Qin H. Robust and high-fidelity guidewire simulation with applications in percutaneous coronary intervention system. VRST '13: Proceedings of the 19th ACM Symposium on Virtual Reality Software and Technology. 2013, 27–30 DOI:10.1145/2503713.2503743

29.

Kerrien E, Yureidini A, Dequidt J, Duriez C, Anxionnat R, Cotin S. Blood vessel modeling for interactive simulation of interventional neuroradiology procedures. Medical Image Analysis, 2017, 35: 685–698 DOI:10.1016/j.media.2016.10.003

30.

Wang Y Z, Serracino-Inglott F, Yi X D, Yuan X F, Yang X J. Real-time simulation of catheterization in endovascular surgeries. Computer Animation and Virtual Worlds, 2016, 27(3/4): 185–194 DOI:10.1002/cav.1702

31.

Bergou M, Wardetzky M, Robinson S, Audoly B, Grinspun E. Discrete elastic rods. ACM Transactions on Graphics, 2008, 27(3): 63

32.

Sandgren T, Sonesson B, Ahlgren Å R, Länne T. The diameter of the common femoral artery in healthy human: Influence of sex, age, and body size. Journal of Vascular Surgery, 1999, 29(3): 503–510 DOI:10.1016/s0741-5214(99)70279-x

33.

Schröder J. The mechanical properties of guidewires. Part I: Stiffness and torsional strength. CardioVascular and Interventional Radiology, 1993, 16(1): 43–46 DOI:10.1007/bf02603036