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1 A Simulator with Elastic Guidewire and Vascular for Minimally Invasive Vascular Surgery Xiaoran CHENG, Xiaoliang XIE, Guibin BIAN, Zengguang HOU, Shiqi LIU, and Zhanjie GAO The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences November 9, 2017

2 Outlines Introduction Guidewire model Vascular model PCI simulation

3 Outlines Introduction Guidewire model Vascular model PCI simulation

4 1. Introduction facts 1/23 Cardiovascular diseases (CVDs) are the NO. 1 cause of death globally. An estimated 17.3 million people died from CVDs in 2013, representing 31% of all global deaths. Of these deaths, an estimated 7.4 million were due to coronary heart disease. Coronary artery disease is the main cause of death among CVDs. Main causes: Smoking Lack of exercise Unhealthy diet 8&oe=utf 8&in=&cl=2&lm= 1&st= 1&cs= %2C &os= %2C &adpicid=0&ln=1000&fr=&fmq= _R&ic=0&s=undefined&se=&sme=&tab=0&width=&height=&face=undefined&ist=&jit=&cg=&bdtype=0&objurl=http%3A%2F%2Fimg3.qianzhan123.c om%2fnews%2f201503%2f25%2f f5a32d6d735b05f 600x5000.jpg&fromurl=ippr z2c%24qazdh3fazdh3f3h z%26e3bqtwgziwg z%26e3bv54azdh3f1jpwtsazdh3f8candc cmaddju1 z%26e3bip4s&gsm=0

5 2/23 Sc n io fo Use coronary catheterization to rm at V S ie n ce s 1. Introduction main treatments Percutaneous coronary intervention (PCI) In visualize the blood vessels on X ray imaging. Coronary artery bypass graft surgery (CABG) Perform a coronary angioplasty, use a balloon catheter in which a deflated balloon is advanced nc ec hi na PCI is a non surgical procedure used to treat (stenosis) ofinflated the coronary intonarrowing the obstructed artery and to relieve arteries of the heart found in coronary artery disease. the narrowing; certain devices such as stents can Access blood stream through the femoral ornormal blood flow to an obstructed coronary CABGthe a surgical procedure to restore be deployed to keep the blood vessel open. radial artery. artery. Sc ie

6 1. Introduction main treatments 3/23 Percutaneous coronary intervention (PCI) V Advantages Less pain, smaller physical trauma Shorter hospital stay Challenges Urgent need for qualified PCI surgeons S Coronary artery bypass graft surgery (CABG) PCI is a non surgical procedure used to treat narrowing (stenosis) of the coronary arteries of the heart found in coronary artery disease. CABG a surgical procedure to restore normal blood flow to an obstructed coronary artery.

7 1. Introduction motivation 4/23 Traditional training paradigm Virtual training paradigm See one, do one, teach one Train in the operating room : suffer from radiation damage Use animals: costly Lack of objective judgment Interact with the virtual devices without Is there a new way to overcome supervision these disadvantages? Without radiation damage Easy to repeat and cost less Have objective judgment

8 1. Introduction prototype 5/23 C-arm KEY ISSUES Human machine interface Modelling of the vascular and surgical Human Force feedback device instruments, suchphantom as guide wire, catheter, Realistic force feedback of human machine interface Collision detection Assessment Hemodynamics The PCI procedure simulation system

9 Outlines Introduction Guidewire model Vascular model PCI simulation

10 2. Guidewire model 6/23 Catheters The key problem of simulation system is how to build a realistic and real time catheter/guidewire with complex and realistic 3D vascular model. The mass spring model (Luboz et al) The energy model (Alderliesten et al) Guidewires Guidewires and catheters are long, thin, flexible and inextensible devices. A guidewire model based on Lagrange multipliers, which is used to maintain the inextensibility of the virtual guidewire, is proposed here.

11 2. Guidewire model description 7/23 The centerline of the guidewire is described as a chain of spatial nodes and directors. The guidewire is discretized into N spatial nodes. N 1 directors which are right hand orthonormal bases are used to describe the center line elements. is a unit vector and parallel to. The unit quaternions are used to denote the directors. Step1: Calculate the involved energies. Step2: Get the force and torque of each node. Step3: Integrate and get the new position of each node.

12 2. Guidewire model main steps 8/23 Step1: Calculate the energies: bending energy (BE), internal friction dissipation energy (FDE), visco elastic dissipation energy (VDE) and constraint energy (CE). CE BE Bending energy measures how much energy is required to bring the two shapes into alignment The bending and torsional strains 2 VDE FDE The intrinsic bending and torsion are used to change the initial shape of the guidewire.

13 2. Guidewire model main steps 9/23 Step1: Calculate the energies: bending energy (BE), internal friction dissipation energy (FDE), visco elastic dissipation energy (VDE) and constraint energy (CE). BE Internal friction dissipation energy is used to model the energy loss due to internal friction. CE 1 2 VDE FDE The relative velocity

14 2. Guidewire model main steps 10/23 Step1: Calculate the energies: bending energy (BE), internal friction dissipation energy (FDE), visco elastic dissipation energy (VDE) and constraint energy (CE). CE BE Visco elastic dissipation energy is used to model the energy loss due to internal friction during rotation. VDE The relative angular velocity FDE 1 2

15 2. Guidewire model main steps 11/23 Step1: Calculate the energies: bending energy (BE), internal friction dissipation energy (FDE), visco elastic dissipation energy (VDE) and constraint energy (CE). CE BE Constraint energy is used to maintain the parallel constraint. 1 2 VDE FDE

16 2. Guidewire model main steps 12/23 Step2: Calculate the force and torques. The inner force: The inner torque: Newton s second law of motion Inextensible constraint The principal of virtual work 0 Jacobian of the constraint

17 2. Guidewire model main steps 13/23 Step3: Update the new position and the unit quaternion. Numerical integration the position of each node. Explicit way The sum of inner and external torques The sum of inner and external forces Time step h Numerical integration of the rotational state

18 2. Guidewire model experiments 14/23 The guidewire is described by 21 spatial control points and it is initialized as a horizontal line. When the simulation begins, the guidewire will swing under the influence of gravity. Thus we can measure the maximum error of the guidewire model without manual operation. The model error is defined as. This experiment is used to simulate the behavior of guidewire under the gravity force and the first two points of the guidewire are fixed. Time step 10ms 1ms 0.1ms Lagrange multipliers[2] Penalty method[1] Comparison of the two methods mm mm mm mm 1. Fast and Stable Guidewire Simulator for Mnimally Invasive Vascular Surgery mm mm 2. A Fast and Stable Guidewire Model for the Minimally Invasive Surgery based on the Lagarange Multipliers.

19 Outlines Introduction Guidewire model Vascular model PCI simulation

20 3. Vascular model mass spring model 15/23 The vascular model based on the mass-spring theory 0 pi Based on the OpenGL and Bullet,we aim to design a virtual training system, including the elastic guidewire model and the elastic vascular model. Regular mass spring model Select the MSMs model considering the effectiveness of the surgery simulation the virtual body spring is added to model the force pressed by the surrounding tissues denotes the original position, pi denotes the real time position, the virtual spring force can be calculated as follows: f vir i k Structure Spring Shear Spring Stretch Spring Figure 3.1 MSMs model vir i Irregular mass spring vascular model 0 vir 0 ( pi pi ) di ( pi pi ) ' p i 0 p i

21 3. Vascular model mass spring model 16/23 The vascular model based on the mass-spring theory Based on the OpenGL and Bullet,we aim to design a virtual training system, including the elastic guidewire model and the elastic vascular model. Experiments Figure 3.2 The simulation of mass spring model

22 3. Vascular model main steps 17/23 In order to overcome the drawbacks in Figure 3.2, we introduce the length invariance constraint, the angle invariance constraint, into our mass spring model, aiming to find a proper modifier. T subject to: Then, we always keep consistent with Finally, we eliminate the middle variable The constraints: The length constraint: The angle constraint: The volume constraint:

23 3. Vascular model main steps 18/23 Step1: Calculate the inner forces and the external forces: Step2: Use the Newton s second law to calculate the acceleration, update the velocity and the position of point : Calculate the inner force added on point : Then, the force added on the point can be calculated as: Here, denotes the collision force. The Newton s second law: Here, is the mass matrix, and is the position matrix. Update the velocity of point : Update the position of point :

24 3. Vascular model main steps 19/23 Step3: Introduce the length and angle invariance constraints into our mass spring model and calculate the modifier : Figure 3.4 The length constraint For any spring,, there exists, subject to:, Then, we can obtain: Figure 3.5 The dihedral angle constraint For any line segment, we add the angle invariance constraint :, =0 is the external force added on the model, and is the original angle,which can be calculated as: Figure 3.6 The new constraint Here,,

25 3. Vascular model main steps 20/23 Step4: Update the position : For any point, there is For any point, Modify the point position:, 1 For any point, we initialize,,. 2 Update the velocity of point : / 3 Update the position of point : 4 For any point, add the constraints, 5 For any point, there is. For any point, 6 Modify the point position: The algorithm:

26 3. Vascular model experiments 21/23 Experiment I and Experiment II Experiment I in Figure 3.7 is performed to demonstrate the efficiency of our new constraint which replaces the dihedral angle constraint. Experiment II in Figure 3.8 is performed to show the smoothly deformation after using the constraints to modify the point position. The comparison between old constraint and new constraint Constraint Type Iteration Constraint Numbers Responding Time(s) Old constraint New constraint Figure 3.7 The comparison of the old constraint Figure 3.8 The simulation before and after and the new constraint introducing the constraints

27 Outlines Introduction Guidewire model Vascular model PCI simulation

28 4. PCI simulation 22/23 Reconstructed from real patient CT data A subbranch artery Vascular model

29 4. PCI simulation 23/23 ie n ce s Experiments Sc The experiment in Figure 4.1 is performed based on the elastic guidewire model and the elastic n vascular model, to simulate the intervention process of the guidewire. rm at In this paper, we modeled an elastic guidedwire model based on the Cosserat fo 1. io Conclusions Based on the mass spring model, we model the elastic vascular model, and na 2. In rod theory. 3. We simulate the collision process between the virtual guidewire and the ie virtual vascular. In the future, the physical parameters of our virtual vascular model will be Sc 4. nc ec hi we introduce the length constraint and the angle constraint into the model. adjusted according to thefigure real 4.1 vascular parameters. The simulation process 5. We will optimize our model based on GPU.

30 Institute of Automation Chinese Academy of Sciences A Simulator with Elastic Guidewire and Vascular for Minimally Invasive Vascular Surgery Xiaoran CHENG, Xiaoliang XIE, Guibin BIAN, Zengguang HOU, Shiqi LIU, and Zhanjie GAO