## 2 Materials and Methods
### Data Analysis  
For the purpose of treatment response monitoring, the quantitative assessment of PET studies before and after treatment can become the standard. In general, however, the uptake of PET radiotracers is not homogeneously distributed across the tumor due to necrosis, cell proliferation, blood flow, microvessel density, and hypoxia [22]. For this reason, it is interesting to quantify heterogeneity in tumor uptake to provide useful information for planning radiation therapy treatment. The area under the CSH can be a quantitative parameter capable of providing additional information on the tumor response and its heterogeneity. Lower values correspond to greater heterogeneity.  
To evaluate this innovative PET parameter in the evaluation of the treatment response, we analyzed PET images using a semiautomatic MATLAB tool [36] to reduce intra- and interoperator result variability. As a matter of fact, semiautomatic algorithms provide greater accuracy and consistency in defining PET volumes and they are important to quantify the response to therapy. In our tool, the operator dependence is minimal because it is limited to the change in the size of the bounding area containing the cancer region--no parameter setup is required.  
In the following, a brief explanation of the processing steps is presented. The user draws a line on the coronal PET image along the lesion, and the axial slice with SUV\({}_{\text{max}}\) is automatically identified and showed to the user. To manage ambiguous situations, physicians can make corrections to the volume of interest (VOI), including the tumor region, obtained as described in [36]. After a square bounding region enclosing the tumor is shown, the user can reduce the region size to discard any external area with high uptake to target. This approach allows the proper inclusion of cancer, excluding false positives. Furthermore, the number of PET slices containing the tumor in basal examinations is recorded to process the same slice volume in post-GK treatment examinations. In this way, the proposed tool is designed ad hoc to appropriately compare cumulative histograms between follow-up scans. According to the literature [19], the SUV threshold was set at 50% of SUV\({}_{\text{max}}\) and the area under the CSH curve was considered as a quantitative index  
Figure 1: An example of Cumulative standardized uptake value (SUV) Histogram (CSH) and Area Under the Curve (AUC). CSH shows the percentage of the tumor volume with a certain SUV. For example, the 60% of the tumor has a SUV \(>\) 1.  
of the MET uptake heterogeneity within the lesion volume. Figure 2 outlines the overall flow diagram of the proposed approach.  
In order to evaluate the ablation effect, the percentage change of AUC between pre- and post-treatment periods was obtained as follows:  
\[\Delta\text{AUC}=\frac{\text{AUC}_{\text{post}}-\text{AUC}_{\text{pre}}}{\text {AUC}_{\text{pre}}} \tag{3}\]  
AUC variation was analyzed and its correlation with the patients' outcomes was studied. Three outcome classes, based on variation of AUC and on shifting of CSH curve, were identified: positive response, stable response, and negative response. Figure 3 shows the workflow of the proposed study used to compare PET studies before and after GK treatment.  
Figure 3: The workflow of the proposed study.  
Figure 2: Flow diagram of the proposed semiautomatic approach to calculate CSH and AUC parameters. Adopted graphical and color notations are explained in the legend box.