Virtual surgery simulation is indispensable for virtual vascular interventional training system, which provides the doctor with visual scene between catheter and vascular. Soft tissue deformation, as the most significant part, determines the success or failure of the virtual surgery simulation. However, most soft tissue deformation model cannot simultaneously meet the requirement of high deformation accuracy and real-time interaction. To solve the challenge mentioned above, this paper proposes a fast and accurate vascular tissue simulation model based on point primitive method. Firstly, the proposed model simulates a deformation of the internal structure of the vascular tissue by adopting a point primitive method. Besides, the stretching constraint and elastic potential energy constraint are introduced to control and correct node motion. Furthermore, a mapping function from the interior to the surface of the vascular tissue is constructed based on moving least squares algorithm to render the visual effect of deformation. Finally, a training system based on the proposed model is set up on the PHANTOM OMNI force-tactile feedback device to realize the deformation simulation of the virtual vascular tissue. Experimental results shows that the proposed model can enhance real-time performance of the training system under the premise of ensuring deformation accuracy, as well as simulate the elasticity of soft tissue.

Due to the development of the social economy and the improvement of people’s living standards, vascular diseases occur frequently in the middle-aged and elderly population in China. So far, minimally invasive vascular interventional surgery is the most direct and effective treatment method for vascular diseases [

Although the virtual vascular interventional training system has many advantages for the treatment of vascular diseases, there are still some challenges that need to be solved or balanced when it is set up. At present, the mass-spring model [

To address above challenges, this study proposes a fast and accurate vascular tissue simulation model based on a point primitive method. The proposed model can trade off the deformation accuracy against real-time performance during virtual surgery simulation. During the simulation, a deformation model is constructed based on a point primitive method to capture the motion of nodes modeled inside the vascular tissue. Moreover, stretching constraint and elastic potential energy constraint are employed to simulate the elasticity of vascular tissue by adjusting the node motion. And then a mapping function from interior to the surface of vascular tissue is built to render the deformation with the help of the moving least square algorithm.

The rest part of the paper is organized as follows. Section 2 elaborates on the vascular tissue simulation model based on point primitive method. Then, experimental results and analysis to verify the performance of the proposed vascular tissue simulation model are presented and discussed in Section 3. Finally, the conclusion is presented in Section 4.

The framework of our proposed model in the virtual vascular interventional training system is shown in

This study uses the point primitive method to construct a deformation model. The main idea of the method is to use a set of discrete nodes to calculate the stress and strain generated by the soft tissue deformation. Then, based on the obtained stress and strain values, displacement of each node is calculated in deformation, thereby capturing vascular tissue deformation.

Assuming that the internal structure of the vascular tissue can be discretized into

The properties of each node are obtained from a kernel function in the support domain. Generally, the smaller the distance between the neighbor nodes and the center node is, the larger effect they have. Therefore, in order to measure the effect of the center node

where

where

where

Similarly,

where

If the vascular tissue has an elastic deformation under external force, the strain energy will be generated in it. Therefore, we estimate the strain energy

The strain energy is a function of displacement vector

It turns out that the force

Finally, the deformation displacement vector

where

Since the earlier deformation model fails to simulate the biomechanical property of vascular tissue, we added stretching constraint and elastic potential energy constraint in this model using position-based dynamics method. As a result, we can realistically characterize the properties of real vascular tissue.

With the position-based dynamics method, the node positions determined by

where

where

As shown in

where

Hence, the correction factor

The internal structure of the vascular tissue is divided into a set of virtual tetrahedrons based on discrete nodes. Here, an elastic potential energy constraint is designed to describe the elasticity of objects using the spring potential of each tetrahedron with elastic coefficients. As shown in

where

Hence, the correction factor

The final deformation position of the node that satisfies the stretching constraint and the elastic potential energy constraint is determined by using

As illustrated in Section 2.1, the motion of vascular tissue is analyzed with the internal nodes. Thus, we need to establish a mapping function from the interior to the surface of vascular tissue to visualize the deformation process and render the deformation effect based on moving least square algorithm. A set of discrete particles is used to describe the surface structure of vascular tissue, and each surface particle can be represented by the internal nodes in its support domain. The support domain of surface particle

where

The approximation function of the field function

where

where

where

Finally, derived

where

It can be seen that the weight function plays an important role in constructing the approximate function. Therefore, the cubic spline function is adopted as the weight function, which is defined as

where

Therefore, the displacement of surface particle

where the shape function is described as

All the experiments are based on a desktop with NVIDA GeForce RTX 2080Ti, Intel(R) Core(TM) i9-9900K CPU (3.60 GHz, 8 cores) and 32G RAM, and run on the Windows 10 operating platform. We adopt VC++ 2019, 3Dmax 2019, and OpenGL 4.6 to program the proposed algorithm and model, and use PHANTOM OMNI hand controller to perform force-tactile interaction operation, which realizes the deformation simulation of the virtual aortic vessels as shown in

During the simulation, we firstly used 3Dmax software to reconstruct the 3D geometric model of vascular tissue according to the medical CT image. Besides, we employed OpenGL to visually render the vascular model and virtual surgical scene with illumination and texture mapping. Then the operator used the PHANTOM OMNI to interact with vascular tissue through a virtual surgical instrument, resulting in producing deformation under the action of an external force. Finally, the feedback force generated by the deformation is output to PHANTOM OMNI, making the operator feels the feedback force.

To verify the effectiveness of the proposed model and the stability of the virtual vascular interventional training system, we built a straight, bent, and twice bent deformation simulation process for a hand dorsal vein, aortic vessels, and retinal artery vessels, respectively, as shown in

This study added the same stress force to real and virtual hand dorsal vein, computed their displacement, and compared the force-displacement curves to verify the accuracy of the proposed model. The mass-spring model [

Real-time performance is a key factor in virtual surgery, because it directly affects the authenticity of a virtual vascular interventional training system. Frames per second (FPS) is an important indicator to measure real-time performance. Commonly, 30 frames can meet the demand for virtual surgery training. Also, the larger the FPS is, the higher the visual refresh rate is, and the better the real-time performance is [

The visual characteristic, operational characteristic, and tactile characteristic of the virtual vascular interventional training system directly influence its force-tactile perception performance and friendliness of human-computer interaction. Therefore, the analytic hierarchy process [

Analytic hierarchy process, which evaluates the force-tactile perception performance of the simulation system based on the proposed model, is mainly divided into the following three steps:

(1) Establish the hierarchical structure of the evaluation system

The force-tactile perception performance of the simulation system is taken as the evaluated object, and its characteristics are hierarchized to build a hierarchical structure, including the target layer, criterion layer, indicator layer, and scheme layer, which is constructed as shown in

(2) Determine the weight of evaluation indicator

Criterion layer |
Weight of criterion layer |
Indicator layer |
Weight of indicator layer |
Consistency check | Comprehensive weight of evaluation indicator ( |
---|---|---|---|---|---|

Visual characteristic |
0.106 | 0.567 | consistency | 0.060 | |

0.056 | 0.006 | ||||

0.104 | 0.011 | ||||

0.273 | 0.029 | ||||

Operational characteristic |
0.633 | 0.069 | consistency | 0.044 | |

0.155 | 0.098 | ||||

0.776 | 0.491 | ||||

Tactile characteristic |
0.261 | 0.125 | consistency | 0.033 | |

0.875 | 0.228 |

Eighteen doctors have been participating in the study from the first affiliated hospital of Nanjing Medical University, including 8 interns, 3 residents, 4 associate chief physicians, and 3 chief physicians. The doctors score each evaluation indicator based on the 1–9 ratio scale [

(3) Comprehensive evaluation result

Evaluation indicator | Evaluation standard | |||||
---|---|---|---|---|---|---|

≤60 | 60~70 | 70~80 | 80~90 | 90~100 | ||

not fluent | general | relative fluent | fluent | extremely fluent | ||

≤24Hz | 24~45Hz | 45~65Hz | 65~85Hz | ≥85Hz | ||

slow | relative slow | general | fast | extremely fast | ||

coarse | general | relative clear | clear | extremely |
||

not natural | general | relative natural | natural | extremely natural | ||

bad | relative |
general | good | excellent | ||

low | relative |
general | high | extremely |
||

≤300Hz | 300~320Hz | 320~340Hz | 340~360Hz | ≥360Hz | ||

bad | relative |
general | good | excellent |

Firstly, doctors are invited to interact with the virtual vascular tissue simulation system based on the six different models through PHANTOM OMNI. Secondly, please they observe the visual characteristics, operational characteristics, and tactile characteristics carefully and define the evaluation standard of the force-tactile perception performance according to the interaction results, shown in

where

The comprehensive evaluation results of the force-tactile perception performance of the simulation system is summarized in

Model | Proposed model | Mass-spring model [ |
Finite element model [ |
Tensor-mass method [ |
Filling model [ |
Position-based dynamics method [ |
---|---|---|---|---|---|---|

94.806 | 81.372 | 80.634 | 80.594 | 79.820 | 81.971 |

In this paper, we proposed a fast and accurate vascular tissue simulation model based on point primitive method in a virtual vascular interventional training system. The deformation simulation is built on PHANTOM OMNI force-tactile feedback device with 3Dmax 2019, VC++ 2019, and OpenGL 4.6. This method establishes a deformation model to control the motion of the nodes using the point primitive method inside the vascular tissue. Besides, in this deformation model, the stretching constraint and elastic potential energy constraint are added to characterize the elasticity of soft tissue. In addition, the mapping function from the interior to surface of the vascular tissue is constructed to render the deformation effect. Experimental results show that the proposed model not only provides high deformation accuracy, but also has a fast real-time performance.

To apply the proposed model to a virtual vascular interventional training system, the force feedback needs to provide high fidelity. Follow-up research will focus to more accurate calculation, high-efficiency data processing. Furthermore, this study only simulated the deformation of vascular tissue due to the limitation of CPU computational power, which did not consider further interactions and simulations after deformation, such as constructing the cutting and bleeding simulations. In the future, we will attempt to study the cutting simulation of the vascular tissue by accelerating the deformation computation with the aid of GPU.