Discussion.

We have established a threshold limit of 13mm maximum 1D and 6.8mm 3D

deformation beyond which dose warp accuracy fails for both uniform homogeneous dose and dose painting geometries. The linear response observed in this study between applied force and deformation is typical of the biomechanical properties of human bladder in contrast to other pelvic organs like rectum, vaginal tissue and liver which show increased resistance to deformation with applied force [208, 209] .

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 10 20 30 40 50 60 70 80 90 100 3D G am m a Pas s rate Force (N) No Dose Warping MIM VELMD VELSD

Comparison of 3D gamma pass rate between true doses in deformed geometry and the warped dose map in reference geometry

Although 3D gamma (γ3%3mm) pass rates ( in the deformed geometry) are excellent up to

30N for the dose painting geometries studied, the conformity index(average dose volume 30 cc or greater) differs by 20% or larger even for the lowest deformation studied. This is in contrast to a uniform 10 x 10 cm2 field where the γ3%3mm pass rates and conformity

index studied at 5 Gy dose level agree with one another. This is also consistent with Dice similarity coefficient comparison (DSC) between high dose volumes from dose painting. Even at the lowest 10N applied force, the DSC between 5Gy dose volumes is only 0.82 for dose painting at the edges of the organ. Thus, although a uniform homogeneous dose may yield acceptable results in terms of both 3D gamma pass rates and volume of dose received by the organ, this does not apply for dose painting. As a result, while employing dose warping for dose painting scenarios like those encountered in Stereotactic Body Radiation Therapy (SBRT) and other hypofractionated treatments with adaptive radiotherapy potential, the volume of dose received by the target from dose warping needs to be evaluated because dose painting is done under the assumption that high dose gradients are localized to the target.

Further when the warped dose in reference geometry was compared to the true dose received by the organ in deformed geometry (Section 5.13), all the DIR algorithms performed poorly. There was no significant improvement over the baseline disagreement except at greater than 40N induced deformation, for dose painting at the edges of organ. In many instances it was found that dose warping induced more errors than the baseline disagreement.

It should be noted that although boundary matching appears perfect even at 70 N (34mm deformation) between images from all the DIR algorithms, this does not guarantee the

accuracy of dose warping. Dose warp accuracy is a function of registration accuracy and dose gradient at a particular voxel. As a result, a small registration error at a high dose gradient will likely have a greater impact on the overall dose warp accuracy as compared to a larger registration error at a low dose gradient[127]. This effect is shown in the gamma wash color map at 40 N (18 mm deformation) for dose painting at the edges of organ. The maximum disagreement as indicated by the red color wash (γ3%3mm >1) occurs

in the area of high dose gradient and large deformation for all the DIR algorithms studied (Fig.5.14 a-c). Although beyond the scope of this study, the high dose islands described at the edges of the bladder phantom are routinely encountered in clinical practice in intensity modulated treatment of prostate cancer. Fig. 5.13d shows a typical patient anatomy with overlap of prostate with bladder and rectal volumes along with the

prescribed target dose (75.6 Gy) at the edges of bladder. The deformation of organs and the resultant dose warp accuracy for dose painting as described in this study will have a significant impact on the partial dose volumes received by the organs at risk.

Figs. 5.14 a, b, c showing sagittal view (y-z plane) of gamma volume at 40N deformation for dose painting at the superior and inferior edges of the organ for MIM, VELMD and VELSD DIR algorithms respectively.

Fig 5.14 d Sagittal view of a typical patient anatomy with prostate, bladder and rectal volumes showing high dose islands at the edges of the organs at risk as studied in the deformable bladder phantom

It is known that the smoothing parameters used in DIR algorithms have a significant impact on dose warp accuracy[104]. MIM uses an intensity based algorithm which seeks to minimize the intensity differences between two images while the intensity based B- spline algorithm used by VelocityAI tries to balance both the intensity information regularized by the inherent cost function and the spatial information regularized by the smoothness criteria[174]. The presence of uniform low contrast regions throughout the deformable bladder phantom makes this scenario particularly challenging for both the commercial algorithms studied because of the lack of intensity differences in the internal anatomy of the phantom. In the absence of user ability to edit the deformation parameters in the commercial DIR platforms, both the algorithms interpolated the deformation incorrectly in low contrast regions as the deformation was increased beyond 30N causing the resultant errors in dose warping. It is likely that the registration accuracy and

consequently the dose warping accuracy would have been improved in the presence of high contrast features like implanted fiducial markers inside the phantom as found in the study using deformable gel[102] . A similar approach with implanted aluminum fiducial markers will be done in future studies using the deformable bladder phantom.

The deformable phantom used in this study has a uniform CT number (±10 HU) and density similar to bladder, prostate, pancreas, stomach, kidney, liver, breast, diaphragm etc., in human anatomy[102, 171] and, as such, the results in this study would apply to those organs. The results do not apply to dose warp accuracy in density changing anatomy like the lung or where the mass is not conserved (full vs. empty bladder, organ atrophy, tumor inflammation etc). Although symmetric bilateral compression was studied, future study will include asymmetric compression, changes in the direction of

applied force, and 3D compression. The viscoelastic polymer used can be molded to any organ shape and has the potential to adjust the tensile properties to match other organs in human anatomy which will be subject of future work.