Appendix A.

Pseudo code for mapping the dose from CTp to CT50 with the DDM algorithm:

1. create treatment plan with CT50;

2. copy the plan to CTp, which is DICOM-based registered with CT50, and recalculate the dose;

3. interpolate the dose from dose grid to image grid of CTp;

4. register CT p to CT50 with DIR and generate DVF (function of the DVF: for each image voxel in CT50, the corresponding transfer vector maps the voxel to CTp);

5. for each image voxel centered at r⃗ in CT50

{

// find corresponding point r⃗′ in CTp using the DVF.

$${\overrightarrow{r}}^{\prime }=\mathrm{T}(\overrightarrow{r})=\overrightarrow{r}+\mathrm{\Delta }\overrightarrow{r};$$

// determine the dose at r⃗′ in CTp by interpolation and assign it to CT50.

$$D_{\text{CT}p\to \text{CT}50}(\overrightarrow{r})=D_{\text{CT}p}(\overrightarrow{r}+\mathrm{\Delta }\overrightarrow{r});$$

}

6. interpolate the dose in CT50 image grid to dose grid