# Investigation of Guidewire Deformation in Blood Vessels Based on an SQP Algorithm
## 1 Introduction  
Today, minimally invasive interventional surgery is widely used in the treatment of cardiovascular diseases. Guidewire is one of the most important surgical instruments in minimally invasive interventional surgery. In interventional surgery, the operators manipulate and move the guidewire along the blood vessel to the lesion site, and take appropriate treatment for the disease. So, the operation of the guidewire has become an essential skill for surgeons. However, surgeons must undergo a significant amount of training to master the operating skills of interventional surgery, and the risk factor in interventional surgery is very high. In addition, the consequences of incorrect operations are serious and there are few opportunities for surgeons to accumulate experience in practice. With the development of computer technology and minimally invasive surgery, virtual surgery has played an increasingly important role in the medical field [1]. In the 1980s, computer-assisted surgery emerged in Europe and North America and received extensive attention and research. Key to the development of interventional simulation training systems was the first interventional simulation system, the Dawson-Kaufman simulator developed by HT Medical (a medical company) [2]. Subsequently, Simbionix and Mentice developed the Angio Mentor system and the VIST system, respectively [3,4]. [PERSON] and [PERSON] also developed their own interventional simulation training prototype systems [5,6]. Organizations such as the North American Society of Radiology and the European Society for Cardiovascular Interventional Radiology jointly developed tasks and strategies for simulation training [7]. These training systems provided doctors with a virtual surgical training environment to overcome many of the problems in a doctor's traditional learning process. The simulation of the movement of the guidewire within the blood vessel is a key technique for interventional surgery simulation. Most research has focused on the modeling of the interventional guidewire [8], and proposed a variety of instrument modeling methods based on physics [9], finite elements, and particle systems, etc. At the same time, some scholars studied the kinematics, working spaces, and singularity of surgical instruments, as well as interactive modeling methods for surgical instruments and ventricles [10,11]. A guidewire for interventional surgery and a guidewire used in a virtual training system for interventional surgery are shown in Figure 1.  
At present, various simulation methods for the deformation of guidewires in virtual interventional surgery have been proposed. [PERSON] defined the guidewire as a series of arcs that are smoothly connected to each other, which is based on finite element calculations, dynamically merging, splitting, adding, and removing arcs to simulate the deformation of guidewires [12]. To obtain more realistic simulation results, [PERSON] modeled the guidewire into a series of deformable light beams and applied incomplete constraints to calculate the deformation of the light beam by an incremental finite element method to obtain the deformation of the entire guidewire [13]. [PERSON] modeled the guidewire into a composite spring particle model and introduced additional bending forces to confine the guidewire to the interior of the blood vessel [14]. [PERSON] proposed a discrete geometric model consisting of a series of arbitrary cross-sections and non-deformable thin rods [15], which was applied by [PERSON] to simulate the deformation of guidewires [16]. Although there have been many deformation simulation studies on guidewires in interventional procedures, there are still few studies that can achieve high simulation accuracy in a certain calculation time. This paper proposes a scheme to simulate the deformation of a guidewire in the blood vessel, which can meet high simulation precision under a certain computational cost of algorithm.