Clinical flexible needle puncture path planning based on particle swarm optimization
Introduction
Percutaneous puncture is an important means of interventional therapy for cancer. The flexible needle is gradually applied to clinical surgery, for it is minimally invasive and its path can bypass important organs. It is important to study the deformation law of flexible needles in tissues and plan the puncture path to guarantee accuracy.
In the current studies about the deformation of the flexible needle, what can accurately explain the bending behavior of the flexible needle in the tissue is the cantilever model [1]. In addition, some studies analyzed the bending deformation of flexible needles from different aspects and established different mechanical models [2], [3], [4], [5]. In view of the low rigidity of the flexible needle body, Webster III et al. [6] approximated the single-segment trajectory of the flexible needle in the tissue to circle arc. During the puncture process, the main factor that causes the needle to bend is the inclination of the needle tip. The orientation of needle bevel which can be changed by rotating the needle body determines the bending direction of the needle. Therefore, during the puncture process, the needle path can be controlled by rotating the needle body [7,8]. In the studies of the puncture path of the flexible needle, the main model is bicycle motion model, in which, the puncture trajectory of the flexible needle is regarded as a curve formed by the stitching of multiple arcs. The transformation between each arc is achieved by rotating the needle body [9]. Many studies made considerable progress based on this model [10], [11], [12], [13]. In addition to the arc model, Park W et al. [14] adapted the path-of-probability (POP) algorithm to path planning of flexible needles with bevel tips. They controlled the trajectory of the flexible needle by rotating the needle body. Their research solved the path planning problem for flexible needles in more general cases that included obstacles. Pedro et al. [15] presented a flexible needle steering system that combined an MR-compatible robot with a Fiber Bragg Grating (FBG)-based needle tip tracker, and improved puncture accuracy by closed-loop method. Zhang et al. [16] glued the strain gauges on the needle surface to achieve real-time detection of needle bending. In recent years, intelligent algorithms are applied to flexible needle path planning, such as rapidly-exploring random tree algorithm [17], [18] and Markov decision processes [19]. Compared with these algorithms, the particle swarm algorithm is simpler and more directional. In addition, parameters of PSO can be easily adjusted when the boundary conditions change. Because of its advantages, PSO has been widely used in industrial path planning [20], [21]. When PSO algorithm is applied to flexible needle path planning, the path can be obtained by changing the most basic elements of the path, such as the length of each arc and the angle between adjacent arcs. In this way, the path is simpler and more efficient. In view of these advantages of particle swarm optimization, it is chosen to plan the flexible needle path in this paper. Previous studies have proven that it is feasible to apply the PSO algorithm to flexible needle path planning [22].
In this paper, as the single-segment trajectory of a flexible needle is approximated into circular arc, the spatial transformation method of three-dimensional path planning is studied. A simpler PSO than existing research is used by controlling the central angle of a single arc and rotation angle of the needle body between adjacent arcs. Puncture experiments are carried out to probe puncture accuracy of the algorithm under certain conditions.
Section snippets
Calculation of path radius
The path of flexible needle is regarded as a three-dimensional curve of multi-section arc splicing due to its low rigidity. The value of the single arc radius cannot be directly measured in the experiment but can be obtained by measuring the bending deflection of the needle tip under certain puncture situation. The relationship between various parameters is shown in Fig. 1.
The following equations can be obtained from Fig. 1:
Where, R is the radius of the needle path, L is the
Path planning based on PSO
The basic idea of PSO is firstly obtaining a number of random particles (initial population) through the way of uniform distribution, secondly setting the objective function, and finally obtaining the optimal solution of the objective function.
As the PSO is used in three-dimensional path planning in this paper, two variables need to be defined as particles, which are the values of the center angle of each arc and the angle of rotation of the needle body between adjacent arcs. With the two
Comparative simulation
Rapidly-exploring random tree (RRT) is one of the mainstream algorithms. It was chosen by many researchers as flexible needle path planning algorithm because of its high speed and accuracy [17,23]. In order to prove that PSO has advantages in flexible needle path planning, RRT is selected as the comparison algorithm.
In this paper, the performance of the two algorithms is compared through simulation. The coordinates of the initial point is set to (0, 0, 0); the coordinates of the target point is
Experimental device and methods
In this paper, the puncture experiments are mainly divided into two parts. The purpose of Experiment 1 is to find the radius of flexible needle path under different puncture parameters and select the appropriate puncture parameters for path planning. The purpose of Experiment 2 is to explore the puncture error of PSO path planning method under certain conditions.
Relationship between experimental parameters and radius
In Experiment 1, the flexible needle diameter, the tip tilt angle, the puncture speed and the gelatin powder mass ratio were changed. The deflection of the flexible needle tip under different parameters was measured, and the radius under the corresponding parameters was calculated as shown in Fig. 8.
It can be seen from Fig. 8(a) that the increase of the diameter of the flexible needle makes the bending radius increase. When the needle diameter increases from 0.55 mm by 27% to 0.7 mm, the
Conclusion
In this paper, the radius of the flexible needle path under four parameters was studied through puncture experiment, and the influence of each parameter on the radius was briefly discussed. The experimental results show that the increase of the diameter of the flexible needle and the inclination angle of the needle tip makes the radius increase; the increase of the puncture speed will slightly decrease the radius; when the mass ratio of gelatin increases, the radius is greatly reduced. At the
Declaration of Competing Interest
The authors declare no conflict of interest.
Acknowledgments
This material was based upon the work supported by the National Natural Science Foundation of China (grant no. 51475274), the Natural Science Foundation of Shandong Province (ZR2019MEE017), the Key R&D Program of Shandong Province (2019GHZ002) and the National Key R&D Program of China (2019YFC0119200).
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