# 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  
A global 3D navigation map is presented which integrates 2D US images with a high-quality 3D context from MR images through 2D US-3D MR image registration. We apply a preoperative 3D US image to simplify the 2D US-3D MR image registration into two easily achieved steps: 2D US-3D US intra-modal registration and 3D US-3D MR intra-dimensional registration. The rigid registration transformation \(\rm T_{2 DUS}^{3 DMR}\) between 2D US and 3D MR images is calculated by \(\rm T_{2 DUS}^{3 DMR}=T_{2 DUS}^{3 DUS}\cdot T_{3 DUS}^{3 DMR}\), where \(\rm T_{2 DUS}^{3 DUS}\) is the transformation between intra-modal 2D and 3D US images, and \(\rm T_{3 DUS}^{3 DMR}\) is the transformation between intra-dimension 3D US and MR images. Figure 2 shows the workflow of 2D US-3D MR image registration. In the intraoperative preparatory stage, we employ a calibrated 3D US probe to collect a 3D US image of the heart. The 3D US-3D MR intra-dimension registration transformation \(\rm T_{3 DUS}^{3 DMR}\) is acquired manually by using an open source platform (3D slicer) ([[http://www.slicer.org](http://www.slicer.org)]([http://www.slicer.org](http://www.slicer.org))). Next, crucial 2D US-3D US intra-modal registration \(\rm T_{2 DUS}^{3 DUS}\) is achieved automatically by the following steps. Firstly, an N-wire calibration phantom is realized for calibration of the 2D US probe and to acquire the transformation \(\rm T_{2 DUS}^{TS}\) between 2D US image coordinate and tracking system (TS) coordinate. Similarly, an IXI-wire calibration phantom is utilized for calibration of the 3D US probe and to solve the transformation \(\rm T_{3 DUS}^{TS}\) between the 3D US image coordinate and the TS coordinate. The near-optimal initial transformation \(\rm\widetilde{T}_{2 DUS}^{3 DUS}\) can be calculated by  
\[\rm\widetilde{T}_{2 DUS}^{3 DUS}=T_{2 DUS}^{TS}\cdot\left(T_{3 DUS}^{TS}\right)^ {-1} \tag{1}\]  
Secondly, with the acquired near-optimal initial transformation \(\rm\widetilde{T}_{2 DUS}^{3 DUS}\), fast automatic intensity-based local adjustment is employed for accurate registration. In the local adjustment, mutual information (MI) is utilized as a similarity metric. Gradient ascent optimizer is used to find optimum value of the MI metric and final rigid transformation \(\rm T_{2 DUS}^{3 DUS}\). More detailed descriptions about calibrations of probes and image registration can be found in our previous work [19]. Figure 1: Configuration of an ultrasound (US) navigation system using global and local information. MR: magnetic resonance; IVUS: intravascular ultrasound. The calibrated 2D US probe collects a series of 2D US images and these 2D US images contain not only the intraoperative structure of heart but also the information of the catheter. On the one hand, these 2D US images are registered with 3D MR to finish a global 3D navigation map. On the other hand, we locate the tip of the catheter in these 2D US images and acquire the trajectory of catheter (for details, see Section 2.2.1). The IVUS probe is embedded in the interventional catheter and collects IVUS images with almost constant velocity (0.5 mm/s). The IVUS images contain the information of complex lesions, such as plaque, aneurysms, etc. By using IVUS images segmentation (for details, see Section 2.2.2), vascular borders (media-adventitia (MA) and lumen borders) and location information of the lesion are extracted. Finally, the segmented IVUS images are re-aligned to acquire a high-resolution aortic model for endovascular intervention guidance. To re-align segmented IVUS images, we use the pose determination method of IVUS images proposed by [PERSON] et al. [20]. As for the locations of IVUS images, due to constant velocity of image collection, the centers of segmented IVUS images are distributed at equidistant intervals on the acquired 3D catheter trajectory. In addition, as for the distribution angles of IVUS images, image planes are positioned perpendicular to the catheter trajectory.