# Tip Estimation Method in Phantoms for Curved Needle Using 2D Transverse Ultrasound Images
## 1 Introduction  
With the help of the beveled-tip needle, percutaneous interventions and therapies have been widely involved in current clinical procedures, such as brachytherapy [1; 2], tissue biopsy [3; 4], and drug delivery [5; 6]. In intervention procedures, less needle misplacement will lead to a more reliable treatment and a more accurate medical practice. According to the clinical studies [7; 8], the needle is easy to be deflected, which will cause needle tip misplacement and may lead to unsafe procedures. Due to the needle-tissue interaction, improper insertion force or physiological motions, such as breathing may cause targets or obstacles to be unstable, which will lead to an unexpected error. To address the challenge, real-time feedback is highly required. Usually, medical imaging devices are used, such as ultrasound (US) [9], computerized tomography (CT) [10; 11], or magnetic resonance imaging (MRI) [2; 12]. Generally, the image-guided percutaneous interventions are conducted with the use of CT or MRI. However, ultrasound-guided procedures are more attractive due to their advantages such as none ionizing radiations and real-time detection. Many studies for the guidance of the needle during the insertion operation have been conducted with the help of ultrasound devices, and 2D ultrasound images are quite general to use, especially for the sagittal one (shown in Figure 1). [PERSON] et al. proposed to use circular Hough transform to locate the needle tip accurately, even when the imaging is out-of-plane [13]. [PERSON] et al. localized the needle axis and estimated the needle tip by using a Gabor Filter in sagittal US images [14]. To execute in real-time, they improved the processing time by applying the bin packing method [15]. Recently, a template-based tracking method with the efficient second-order minimization optimization method has been used to track the needle [16]. In recent studies, more and more novel ideas have been used to locate the needle and evaluate its tip to sagittal US images, such as the use of signal attenuation maps [17], convolution neural networks (CNN) [18], and maximum likelihood estimation sample consensus (MLESAC) method [19]. However, a demerit of using sagittal US images is that out-of-plane bending of the needle cannot be detected. Therefore, the methods applied on sagittal US images are not suitable for the needle which may be deflected by the inevitable factors, especially for long needles. An alternate solution for this problem is to use a 3D US image, which has been widely studied in recent researches. [PERSON] et al. used a RANSAC method to detect the needle in a 3D US situation and Kalman filter has been used to reduce the error [20]. [PERSON] et al. used the particle filtering to track a robot-guided flexible needle by using 3D US [21]. In addition, a convolutional neural network with conventional image processing techniques has also been used to track and detect the needle [22] and a naive Bayesian classifier was used to localize the needle among 3D US volume voxels [23]. However, the large 3D US volumetric dataset would make it difficult to obtain and process the online data. Due to the above disadvantages, sagittal US images and 3D US volume are not suitable for a long flexible needle. To locate the needle accurately, methods that use transverse US images (shown in Figure 1) have been used successfully in some studies. For example, [PERSON] et al. [24] present a method to track the flexible needle during the insertion into a gelatin tissue by using 2D US images perpendicular to its needle tip. However, the background is pure without noise, which makes it impractical. [PERSON] et al. [25; 26; 27] focus on the research about the needle insertion, in permanent prostate brachytherapy (PPB), where needles are typically 200 mm and easily to be deflected, indicating the fact that the rectum limits the movement of US probe. As a result, it is hard to acquire the sagittal images of the curved needle to observe the deflection during needle insertion.