# 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
CR error is usually calculated by

\[E^{\mathrm{CR}}=\underset{i,j}{\text{mean}}\left\{\|\mathrm{T}^{\mathrm{PR}^{ i}}_{\mathrm{US}}*P^{\mathrm{US}}-\mathrm{T}^{\mathrm{PR}^{i}}_{\mathrm{US}}*P^{ \mathrm{US}}\|\right\} \tag{2}\]

During the evaluations of 2D and 3D US probe calibrations, we performed 8 calibration trials and used 10 images per trial, 80 datasets in total. The acquired CR error of the 2D US probe's calibration is 0.61 mm and the CR error of 3D US probe's calibration is 1.42 mm. #### 3.1.2 2D US-3D MR Images Registration

The registration results of 2D US-3D US images, 3D US-3D MR images and final 2D US-3D MR images are shown in Figure 6. The registration accuracy of 2D US-3D MR images was quantitatively evaluated by calculating the target registration error (TRE). Ten contour points of ventricle in 2D US and the corresponding contour points of ventricle in 3D MR model were manually delineated by a surgeon to calculate TRE. TRE is the average Euclidean distance of these corresponding contour points. A mean TRE of 2.70 mm (range 1.05-3.67 mm) is obtained during 2D US-3D MR image registration. Figure 6: Registration results of 2D US-3D US, 3D US-3D MR and final 2D US-3D MR images (red volume is the left ventricle model; blue volume is the right ventricle model). (**a**) Registration results of 3D US-3D MR images; (**b**) Registration results of 2D US-3D MR images; (**c**) Registration results of 2D US-3D US images. ### Evaluation of Local High-Resolution Navigation Information

Local high-resolution navigation information is achieved by combining the 3D trajectory of the catheter from US images tracking with segmented IVUS images. Therefore, the effectiveness of local navigation can be validated by verifying these two critical factors. #### 3.2.1 Evaluation of Multi-Feature Particle Filter Method for Catheter's 3D Trajectory

During the experiment, we inserted the catheter into the aortic phantom and scanned large areas with a calibrated 2D US probe. Multi-feature particle filter tracking method was used to track aortic cross-sections in the collected 2D US images. The corresponding parameters in particle filter tracking were set as \(a=0.5\), \(\delta=0.7\), and the number of particles was 40. Aortic cross-sections were tracked in 200 US images with the multi-feature particle filter tracking methods. The tracking error is determined by the Euclidean distance between aortic cross-section center from automatic tracking and manually delineative center. The average tracking error of multi-feature particle filter method is 0.87 mm (lateral error is 0.43 mm and longitudinal error is 0.76 mm). After tracking aortic cross-sections in US images, threshold technology is applied to obtain those pixels whose intensities are higher than 220 inside the aortic cross-section. The centroid of those pixels is the detected position of the cross-section of the catheter. In Figure 7, the red circle represents the tracked aortic cross-section and the green point is the located tip of catheter. Based on the positions of the catheter's tip, the 3D trajectory of the catheter is acquired. Figure 8 shows two trajectories of the catheter, including an automatic trajectory of the catheter from our multi-feature particle filter tracking method and a 3D trajectory from the manually delineative catheter's tip. The distance between the manual trajectory and automatic trajectory using multi-feature particle filter tracking method is 1.48 mm. Figure 7: Tracking result of aortic cross-section and catheter’s tip in US images, (**a**) the US image which contains the catheter’s tip; (**b**) the US image which does not contain the catheter’s tip. #### 3.2.2 Evaluation of the Improved Level Set Method for IVUS Images Segmentation

Accurate IVUS segmentation and borders detection can provide lesion location inside the vessel for local navigation. For clinical patients who need stent placements, the collected IVUS images contain information on the lesions but various artifacts exist. A segmentation method applicable for real patients is critical.