# Investigation of Guidewire Deformation in Blood Vessels Based on an SQP Algorithm
## 4 Discussion  
This study aimed to provide a solution for the deformation of a guidewire within the blood vessel in an interventional surgical training system. In this paper, based on the principle of minimum energy, the guidewire was regarded as a rigid light rod articulated model. An SQP algorithm was used to nonlinearly plan the relative deflection angles of all the light rods between the contact points, in order to obtain the deformation state of the guidewire. We verified the feasibility of this solution from two perspectives. Firstly, by comparing the results of an ABAQUS software simulation and the algorithm calculation, which yielded a calculation accuracy of about 5%. Secondly, the calculation accuracy was proven to be about 11% through design experiments. This accuracy can fully meet the requirements of a virtual training system for authentic simulation. Moreover, we proposed a method for expressing the relative magnitude of the stress at each point on the guidewire. By comparing the color map on the guidewire in Figures 4 and 7, it was shown that this representation is effective and feasible.  
As long as information on the location of contact is provided, the solution presented herein can more realistically simulate the deformation of a guidewire in any type of contact with any shape of blood vessel. Moreover, we believe that in order not to increase the computational cost of the algorithm, it is possible to treat a multi-point contact on a straight line or a line contact with little curvature change as a point contact. As for line contacts with large curvature changes, we can replace all other contact points with several points with large curvature changes. This processing not only can greatly reduce the number of constraints and computational costs of the algorithm, but also has an effect on the simulation accuracy of the deformation within an acceptable range.  
In addition, we discussed the effect of the discrete density of the guidewire model on computational cost and simulation accuracy of the algorithm. Under the premise of higher algorithm simulation accuracy, the discrete density corresponding to the shorter algorithm time was selected. We have proven that the discrete density was more suitable around a value of 1, and the algorithm takes less than 0.2 s.  
Of course, we believe that there is a more reasonable way to deal with discrete density. The discrete density used in the algorithm is constant. If the curvature of a portion of a guidewire is very small, it can also achieve high simulation accuracy at a small discrete density. Therefore, if the discrete density of each part of the guidewire is determined by the curvature, the number of design vectors of the algorithm will be reduced, and the calculation amount and calculation time of the algorithm will be lower, correspondingly. Therefore, we will explore the relationship between the discrete density and curvature of the guidewire in future work.  
Conceptualization, Q.T.; Formal analysis, L.L.; Funding acquisition, Y.T.; Project administration, L.L.; Resources, W.W.; Software, Q.T.; Supervision, Y.T.; Validation, W.C.; Visualization, F.X.; Writing - review & editing, Q.T.  
This research received no external funding.  
Research was supported by the Special Plan of Major Scientific Instruments and Equipment of the State (Grant No.2018 YFF01013101), the National Natural Science Foundation of China (51775322, 91748122, 61603237), the IIOT Innovation and Development Special Foundation of Shanghai (2017-GYHLW01037) and a project named \"Key technology research and demonstration line construction of advanced laser intelligent manufacturing equipment\" from the Shanghai Lingang Area Development Administration.  
The authors declare no conflicts of interest.