# Automatic Needle Route Proposal in Preoperative Neck CT for Injection Laryngoplasty
## 2 Methodology
### Critical Region Segmentation  
In the usual TIL method, the needle is inserted through the cricothyroid membrane. The needle route takes a sub-mucosal way to reach the vocal folds while strictly avoiding the airway. If the needle pierces through the paraglotic membrane and enters the airway, it can cause bleeding and coughing during the procedure. Therefore, we first segment the airway in the preoperative neck CT. Figure 2 illustrates the segmentation process. **Initial segmentation:** The airway in neck CT can easily be obtained by intensity-based thresholding. Note that intensity in CT is encoded in the Hounsfield unit (HU) and air has an intensity of \(-1000\) HU [14]. The nearest material in the HU spectrum (i.e., fat) lies in \(-70\) to \(-30\) HU. Therefore, considering the HU tolerance for scanning air and fat-like material, we can safely segment the air by marking the voxels where the intensity is less than \(-200\) HU. However, such segmentation would also include the air outside the body or neck. **Airway segmentation:** To separate the desired airway from the outer air region, we perform a geodesic distance-based segmentation [8]. In such approach, the geodesic distance of the voxels with respect to a foreground seed is thresholded to determine the foreground voxels. Such segmentation is useful when the target region has even and continuous intensity. The intensity of the air in neck CT is also usually evenly distributed. However, there are two major challenges to incorporating this method for segmenting the airway, which are as follows:  
* Automatic localization of the foreground seed is difficult in our task because the airway location is inconsistent across patients due to anatomic and scan environment variation. * Optimal geodesic distance threshold for airway segmentation can vary because of the patient-specific anatomic variation. To overcome the seed localization challenge, we suggest segmenting the outer air first and then subtracting it from the initial segmentation result to obtain the airway. By doing so, we can ensure an accurate and automatic seed localization because outer air consistently resides in the anterior region of the CT volume, especially taking a large portion of the inferior-anterior area. To be specific, we identify the outer air seed \(\mathbf{q}_{s}\) at \((10,10,10)\) voxels from the right anterior-inferior corner of the CT volume. To overcome the optimal threshold variation problem, we propose a reformulation of the standard geodesic distance for segmentation. The proposed reformulation allows for segmentation with a fixed distance threshold across different subjects. **Reformulation of geodesic distance:** Standard geodesic distance \(D(\mathbf{q})\) combines the spatial distance with the intensity difference along the path \(\mathcal{P}\) from seed \(\mathbf{q}_{s}\) to the point \(\mathbf{q}\)[8]. At each point of the path, the combined difference is computed as a weighted L2-norm of the spatial and intensity gradients in the path direction at that point. Thus, the distance of a path refers to the summation of the combined differences at all the points in the path. The final geodesic distance \(D(\mathbf{q})\) is defined as the minimum distance of all the possible paths from seed \(\mathbf{q}_{s}\) to \(\mathbf{q}\). Formally, this can be expressed as follows:  
\[D(\mathbf{q})=\min_{\mathcal{P}\in\Pi_{\mathbf{q}_{s}}}\sum_{\mathbf{p}\in\mathcal{P}} \sqrt{||\
abla_{\mathcal{P}}\mathbf{p}||^{2}+\gamma^{2}|\
abla_{\mathcal{P}}I( \mathbf{p})|^{2}} \tag{1}\]  
Figure 2: Critical region segmentation. Initial air mask is obtained by HU thresholding. Outer air is then segmented based on the geodesic distance with respect to the outer air seed. The airway mask is obtained by subtracting the outer air from the initial air mask. where \(\Pi_{\mathbf{q}_{s}}\) includes all possible paths from seed \(\mathbf{q}_{s}\) to \(\mathbf{q}\) and \(\
abla_{\mathcal{P}}\) indicates the gradient along a path \(\mathcal{P}\).