## 2 Materials and Methods
### Demonstration of Clinical Application  
The extracted pairs of CBCT and planning CT images for the 10 clinical patients selected were imported into MICE Toolkit v.1.1.0 (NONPI Medical AB, Stockholm, Sweden), which was used in this study as the reference software. The MICE Toolkit was used to produce the refDVF, being the only independent DIR software available in our institute for comparison with our clinical system (Velocity AI, described below). Within the MICE, the open-source Elastix software module [26] was employed. The registration method used in this case is of the same type as the one in the clinical platform but implemented independently. It consists of a B-spline method with an adaptive stochastic gradient descent optimiser, with the number of resolutions equal to 3, the maximum number of iterations of 1000 and an interpolator order of 3, similar to those parameters reported in the literature [27]. The DVF from each DIR (in total, 20 DVFs) was subsequently exported in the MATLAB format, converted to the binary format, and used as the refDVF.  
The Velocity AI Oncology Imaging Informatics System v.4.0 (Varian Medical System, Palo Alto, CA, USA) was the DIR module used in our institute in clinical practice. The post-processed phantom scans were imported into the Velocity AI and linked to each of the 10 patients selected for the study. Both the phantom CT and CBCT images were rigidly registered to the CT image of the patient. This was done to align the phantom CT image with the clinical refDVF to produce a more clinically realistic warped phantom CT image.  
Following the workflow described in Figure 1, using the Velocity AI, the HN phantom CT images were artificially deformed into wCT images, using each of the imported refDVFs. Then, the phantom CBCT image was registered with the phantom wCT image, generating a testDVF obtained using the Velocity AI algorithm. The 'CBCT corrected multi-pass deformable' modality in the Velocity AI was used to generate the testDVF. This applies a 'fade correction' prior to the registration, which enhances the low signal regions in the CBCT image [28]. The Velocity AI's primary registration algorithm uses a multi-resolution approach based on mutual information. The transform is a cubic B-spline, the interpolator is a bi-linear interpolation function, and the optimiser is based on the steepest gradient descent method [28]. The testDVF was then exported from the Velocity AI in a binary format. This workflow was repeated for all 20 registrations for the 10 patients. To ensure that the simulated deformation could be used as a reference to validate the image registration algorithm, for each case the warped phantom CT images were carefully inspected to verify that the changes induced in the phantom scans produced by the refDVF were realistic. Each testDVF was compared to the refDVF using the MATLAB in-house scripts. The quality of the registration was assessed as the ability of the testDVF to replicate the artificially generated refDVF.  
For each patient and treatment fraction considered, an adapted-CT image of each refDVF was generated in the Velocity AI. The adapted-CT images used the HU values of the patient CT image, mapped onto the CBCT image, to avoid bias in the dose calculation [28]. The adapted-CT images were then imported into the Eclipse TPS, and the VMAT clinical treatment plans were recomputed on each patient's adapted-CT images and sent back to the Velocity AI. To assess the dose propagation errors due to the differences in the DIR maps, the dose on the adapted-CT was back-projected to the corresponding patient CT images via both the refDVF and testDVF.