## 2 Materials and Methods
### Workflow  
The method used to validate the DIR applied to the CT-CBCT image pairs was based on a known transformation for each voxel [6]. This method requires an independent 'third-party' image registration software system to generate the reference DVF. We will refer to the third-party software as the'reference DIR software', as it will be used to generate a reference DVF. The only requirement for the reference and the clinical DIR software systems should be the independence of each other in the DIR procedure to avoid biasing the results. As a guarantee of the correctness of the procedure, it is not essential that the reference software should be any more accurate in the DIR process than the clinical one.  
The set of selected clinical patient images (CT and CBCT) that must be tested are registered using the reference software (see Figure 1a, spatial analysis workflow). This registration is considered as the reference for the patient CT-CBCT data sets (refDVF). As a second step, the HN phantom CT images are artificially deformed into 'warped' phantom CT (wCT) images by applying the refDVF transformation. Using the clinical DIR software, the phantom CBCT image is registered with the wCT phantom image, generating a test DVF to be evaluated (testDVF). Note that the term refDVF relates to the patient image registration throughout, whereas the term testDVF always refers to the warped phantom CT and phantom CBCT DIR.  
Figure 1: Schematic workflow of CT-CBCT DIR validation method for spatial and dosimetric analysis. (**a**) Spatial Analysis. The HN patient CBCT-CT DIR was considered as reference DVF (refDVF). The refDVF was generating using third-party reference software. Post-processed phantom CT images were digitally warped using the reference DVF resulting in warped phantom CT scans. The phantom CBCT and warped CT images were then registered in the clinically used DIR software, generating an evaluated DVF (testDVF). The testDVF was compared with the refDVF by using a TRE metric and an operative tolerance level (OTL) analysis performed to quantify the accuracy of the DIR. (**b**) Dosimetric Analysis. Treatment plans were calculated in the TPS on each patient’s adapted-CT image (patient CT image warped into CBCT image) resulting in a delivered dose. The delivered dose was transferred back to the patient’s planning CT image via both the refDVF (reference dose) and the testDVF (test dose). The dose difference between the two was calculated with a clinical assessment, involving a radiation oncologist, required for a final DIR validation.  
The quality of the registration was assessed as the ability of the clinical software to replicate the refDVF, artificially introduced into the phantom wCT images. The target registration error (TRE) was computed as a metric to evaluate the difference between the refDVF and the testDVF (Section 2.5). As recommended by the TG132, the percentage of voxels with a TRE within 2 mm was compared with a designated Operative Tolerance Level (OTL) value (Section 2.6). If the testDVF does not overcome the OTL analysis, the evaluated registration process should be re-started, adjusting certain registration parameters, such as the volume of interest.  
The propagation of dosimetric errors due to differences in the DIR maps is schematized in Figure 1b, labelled as the dosimetric analysis workflow. The VMAT clinical treatment plans were recomputed in the clinical TPS for each patient's CBCT adapted-CT images to avoid bias in the dose calculation (see Section 2.4), and back-projected to the corresponding patient's CT images, via both the refDVF and testDVF, generating reference dose (refDose) and evalutated dose (testDose) arrays, respectively. The dosimetric differences between the refDose and testDose should be evaluated in conjunction with clinical radiation oncologists.