# Investigation of Guidewire Deformation in Blood Vessels Based on an SQP Algorithm
## 3 Results
### Experiments  
The experimental platform is shown in Figure 11. A simple blood vessel model is made in SolidWorks and printed with a 3D printer. The orange objects in the picture, with width of 1.5 mm and thickness of 0.8 mm, correspond to our sample vessel wall. The vessel wall is affixed to the surface of a transparent acrylic sheet with scale paper, and another acrylic sheet is affixed over the vessel wall. When the guidewire advances inside the blood vessel, the position of the contact point of the guidewire with the blood vessel wall and the deflection angle can be obtained from the scale paper. In order to obtain the length of the guidewire from the contact point to the entrance of the blood vessel (O), the position of the contact point can be marked on the guidewire with a highlighter, and after the guidewire is taken out, the corresponding length is measured with a scale. If the guidewire enters the blood vessel from the entrance at the origin, Figure 12a,b show two positions during the advancement of the guidewire, known as position I and position II, respectively. If the contact between the guidewire and the vessel wall is in line contact, it is not necessary to constrain each point on the contact line, but only a few special points with large differences in curvature are needed, which can reduce the computational cost of the algorithm, while also ensuring the accuracy of the simulation. Figure 11: The experimental platform. For position I and position II, three contact points are taken as constraints of the algorithm. Tables 4 and 5 present the contact information of the guidewire at the contact points in position I and position II, respectively, including the coordinates of the contact point, the deflection angle of the guidewire, the length (L) between different contact points, and the length (\(\text{l}_{\text{in}}\)) of the guidewire that has been put into the blood vessel. We can get the deformation simulation results of guidewire with the SQP algorithm according to the contact information, as shown in Figure 13a,b. \begin{table}
\begin{tabular}{c c c c c} \hline
**Contact Points** & **Coordinate (mm)** & **Deflection Angle (Rad)** & **L (mm)** & \(\text{l}_{\text{in}}\) (mm)** \\ \hline O & (0,0) & 1.187 & - & \\ P\({}_{1}\) & (9.5,14.5) & 0.820 & \(\text{L}_{\text{OP}_{1}}\)\(=18\) & 87 \\ P\({}_{2}\) & (59, 28.3) & 0.061 & \(\text{L}_{\text{OP}_{2}}\)\(=\)\(71\) & \\ \hline \end{tabular}
\end{table} 
Table 4: Contact information about position I. \begin{table}
\begin{tabular}{c c c c} \hline
**Contact Points** & **Coordinate (mm)** & **Deflection Angle (Rad)** & **L (mm)** & \(\text{l}_{\text{in}}\) (mm)** \\ \hline O & (0,0) & 1.518 & - & \\ P\({}_{3}\) & (80,28.5) & 0.244 & \(\text{L}_{\text{OP}_{3}}\)\(=91.5\) & 112.5 \\ P\({}_{4}\) & (98,42.5) & 0.644 & \(\text{L}_{\text{OP}_{4}}\)\(=112.5\) & \\ \hline \end{tabular}
\end{table} 
Table 5: Contact information about position II. Figure 12: Two positions during the advancement of the guidewire: (**a**) Position I; (**b**) Position II. In the experiment, the guidewire inside the blood vessel was marked with a highlighter every 5 mm, and the coordinates on the scale paper were recorded, then compared twith the coordinates of the corresponding points obtained by the algorithm. As is shown in Figure 14, we use z to represent the distance between the two coordinates of the same point, which is the error between the algorithm simulation and the real experiment. Equation (27) shows the average value of the algorithm error corresponding to position I and position II, respectively. \[ \begin{array}{l}\mathrm{z}_{arg\_1}\approx 0.513\;\mathrm{mm},\\ \mathrm{z}_{avg\_11}\approx 0.578\;\mathrm{mm}.\end{array}  \tag{27}\]  
Therefore, the deformation simulation accuracy of the guidewires in these two positions is:  
\[