# Tip Estimation Method in Phantoms for Curved Needle Using 2D Transverse Ultrasound Images
## 4 Discussion and Conclusions  
Needle insertion guided by ultrasound images is widely used for percutaneous interventions. However, the needle detection due to its deflection by the inevitable factors is challenging during the needle insertion. Such factors include needle-tissue interaction, improper insertion force, physiological motions, and so on. Automatic needle detection with needle tracking in 2D transverse US images could overcome these limitations and estimate needle tip through the curve-fitting method. The target of this study is to develop a robust needle detection and tracking method with the help of ultrasound images to estimate the needle tip precisely and accurately. We used a histogram method to detect the needle in transverse US images to decrease the effects of comet tail and poor reflection. In subsequent post-processing, the needle was tracked by the Kalman filter tracking method in consecutive US images with the help of the displacement of the probe. A third-order curve fitting method has been used to estimate the needle tip. When the probe is moved by the robot arm, the scanning time is different. We assume that the time when the probe stops to collect the data is the same. The less scan interval we choose, the more collection points we can obtain and the more scanning time it takes. Therefore, the scanning time \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Accuracy**} \\ \hline
**Intervals** & **Water** & **Phantom** & **Pork** & **Chicken** \\ \hline
1 mm & 0.32 \(\pm\) 0.10 & 0.33 \(\pm\) 0.15 & 0.37 \(\pm\) 0.07 & 0.29 \(\pm\) 0.09 \\
2 mm & 0.36 \(\pm\) 0.21 & 0.41 \(\pm\) 0.16 & 0.31 \(\pm\) 0.05 & 0.31 \(\pm\) 0.12 \\
3 mm & 0.45 \(\pm\) 0.16 & 0.46 \(\pm\) 0.18 & 0.56 \(\pm\) 0.08 & 0.33 \(\pm\) 0.09 \\
4 mm & 0.55 \(\pm\) 0.16 & 0.59 \(\pm\) 0.31 & 0.68 \(\pm\) 0.14 & 0.38 \(\pm\) 0.21 \\
5 mm & 0.60 \(\pm\) 0.13 & 0.59 \(\pm\) 0.29 & 0.90 \(\pm\) 0.20 & 0.40 \(\pm\) 0.14 \\
6 mm & 0.69 \(\pm\) 0.13 & 0.48 \(\pm\) 0.09 & 0.99 \(\pm\) 0.13 & 0.55 \(\pm\) 0.11 \\
7 mm & 0.83 \(\pm\) 0.17 & 0.62 \(\pm\) 0.14 & 0.84 \(\pm\) 0.30 & 0.52 \(\pm\) 0.17 \\
8 mm & 0.95 \(\pm\) 0.11 & 0.73 \(\pm\) 0.26 & 1.06 \(\pm\) 0.18 & 0.81 \(\pm\) 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The results of tip estimation (mm). Figure 10: The experiment with different scan intervals on the four platforms. mainly depends on the number of scanning points while the accuracy lies in how short the scan interval is. In other words, the accuracy of the tip estimation can be improved by reducing the scan interval to collect more needle positions. However, this will consume more scanning time and reduce the efficiency of tracking. Inversely, fewer collecting positions would cost less time but may lead to a more possibility of the failure of shape construction and a more possibility of large error of the tip estimation. As a result, how to balance precision and scanning time is very important to make the proposed method more efficient. In our experiment, it is found that a 4 mm scan interval has an error less than 1 mm, which is a better choice to satisfy both requirements. In the proposed method, needle shape tracking has a great contribution to the accurate localization, since the needle can be tracked precisely by Kalman filter through its prediction and update. However, needle shape tracking is heavily dependent on the scan interval, especially for a large curved needle, since Kalman filter is generally well functioned in the lineal system. As a result, if the needle is deflected during insertion, the Kalman filter would make mistakes and wrongly predict the needle position when the scan interval is large. In this study, it is found that Kalman filter would fail if the scan interval is more than 8 mm. This may due to the impact on the prediction of KF with a large deviation. Moreover, the deviation will not be eliminated even with the change of the ROI size.