# Ultrasound Navigation for Transcatheter Aortic Stent Deployment Using Global and Local Information
## 2 Materials and Methods
### A Global 3D Navigation Map Based on 2D US-3D MR Image Registration
#### 2.2.1 Multi-Feature Particle Filter Tracking Method for the 3D Trajectory of the Catheter
(c) Particle weight decision:  1: Calculate particle weight \(w_{t,m}\) by comparing differences in features between template region \(\mathbf{R}_{t}\) and region of the particles \(\,\mathbf{{}^{s}}\mathbf{R}_{t,m}\), \((w_{t,m}=\mathbf{\hat{H}}\left\{\mathbf{R}_{t},\,\mathbf{R}_{t,m}\right\})\); (\(\mathbf{\hat{H}}\left\{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{bm



images is useful in guiding stent deployment and assessing the efficacy of catheter interventions [23]. We develop an improved level set method to detect MA and lumen borders in IVUS images [24]. Level set function evolves from initialization \(\varphi_{0}\) to final borders under the influence of curve force and image force [25]. Appropriate initialization will obtain accurate segmentation. Therefore, we propose an appropriate initialization \(\varphi_{0}\) determination method through features classification. Firstly, [PERSON] texture energy measure [26] is applied to represent the features of the pixels in IVUS images. Secondly, support vector machine (SVM)-based feature classification [27] is applied to regionalize IVUS images and provides a rough target area \(M\) for the following appropriate initialization \(\varphi_{0}\). For MA border detection, pixels in the first IVUS image of the sequence are the training data. For lumen border detection, pixels inside vessel region of the first image are the training data. SVM classification models are acquired through the training data. By testing other IVUS images, image regionalization results are calculated during MA border detection (Figure 4b). Similarly, regionalization results are also acquired during lumen border detection (Figure 4c). Thirdly, searching-eliminating-interpolating technology is applied to process the rough target area \(M\) and acquire appropriate initialization \(\varphi_{0}\). Image regionalization results of \(M_{\text{ADR}}\) (adventitia region) and \(L_{\text{LR}}\cup L_{\text{AR}}\) (the union of lumen region and artifact region) are rough target areas for MA and lumen border initializations, respectively. The searching step is implemented to search for the contour point of interest \(P_{1}\) and the eliminating step can remove improper points of \(P_{1}\) in the process. The final interpolating step is used to acquire smooth initialization \(\varphi_{0}\). More detailed descriptions about IVUS segmentation can be found in paper [24]. ### US Navigation System for Transcatheter Aortic Stent Deployment Using Global and Local Information

The surgical workflow of proposed the US navigation system for transcatheter aortic stent deployment contains three stages: preoperative preparatory, intraoperative preparatory and intraoperative navigation. \(\bullet\)**Preoperative preparatory**

1. Collecting preoperative MR images of patient's heart. 2. Segmenting the heart and aorta from preoperative MR images via open source platform. 3. Finishing path planning in segmented phantoms of heart and aorta. \(\bullet\)**Intraoperative preparatory**

1. Using a calibrated 3D US probe to collect a 3D US image only once. 2. Preparing catheter and stent for aortic stent deployment. Figure 4: Support vector machine (SVM) classification of image. (**a**) an IVUS image; (**b**) image regionalization results during MA border detection; (**c**) image regionalization results during lumen border detection. \(\bullet\) **Intraoperative navigation**

1. During insertion of the stent and IVUS probe into aorta through a catheter, a calibrated 2D US probe is implemented to collect the real-time 2D intraoperative US images, and an IVUS probe is used to collect IVUS images. 2. US navigation system displays a 3D global navigation map to users. In this map there are 3D cardiac MR images of the patient, along with an US image plane providing an updated interior view of the aorta. Position information of inserted catheter is overlaid on this 3D image. 3.