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This article explores the role of Deformable Dose Accumulation (DDA) in Adaptive Radiotherapy (ART). DDA involves combining doses from different treatment sessions to ensure optimal dose delivery and respect dose constraints. Dr. Hualiang Zhong supports DDA, emphasizing its ability to improve cumulative dose calculations, while Dr. Jennifer Pursley raises concerns about the uncertainties and limitations of DDA. Both perspectives offer valuable insights for medical physicists and radiation oncologists. While DDA is considered important for ART, caution is advised due to challenges in accurately registering deformable images. The article also discusses alternative approaches to estimate delivered dose, such as using the original treatment plan or accumulating specific dose parameters across fractions. The rebuttal section presents differing opinions on the usefulness and accuracy of DDA, with one author suggesting that DDA can provide more informative dose distributions if errors are properly managed, while the other author proposes direct dose summation as a more practical and consistent approach for online ART. [Extracted from the article]

Purpose: We evaluate the performance of a deformable image registration (DIR) software package in registering abdominal magnetic resonance images (MRIs) and then develop a mechanical modeling method to mitigate detected DIR uncertainties. Materials and Methods: Three evaluation metrics, namely mean displacement to agreement (MDA), DICE similarity coefficient (DSC), and standard deviation of Jacobian determinants (STD‐JD), are used to assess the multi‐modality (MM), contour‐consistency (CC), and image‐intensity (II)‐based DIR algorithms in the MIM software package, as well as an in‐house developed, contour matching‐based finite element method (CM‐FEM). Furthermore, we develop a hybrid FEM registration technique to modify the displacement vector field of each MIM registration. The MIM and FEM registrations were evaluated on MRIs obtained from 10 abdominal cancer patients. One‐tailed Wilcoxon‐Mann‐Whitney (WMW) tests were conducted to compare the MIM registrations with their FEM modifications. Results: For the registrations performed with the MIM‐CC, MIM‐MM, MIM‐II, and CM‐FEM algorithms, their average MDAs are 0.62 ± 0.27, 2.39 ± 1.30, 3.07 ± 2.42, 1.04 ± 0.72 mm, and average DSCs are 0.94 ± 0.03, 0.80 ± 0.12, 0.77 ± 0.15, 0.90 ± 0.11, respectively. The p‐values of the WMW tests between the MIM registrations and their FEM modifications are less than 0.0084 for STD‐JDs and greater than 0.87 for MDA and DSC. Conclusions: Among the three MIM DIR algorithms, MIM‐CC shows the smallest errors in terms of MDA and DSC but exhibits significant Jacobian uncertainties in the interior regions of abdominal organs. The hybrid FEM technique effectively mitigates the Jacobian uncertainties in these regions. [ABSTRACT FROM AUTHOR]

We discuss the stability of complex exponential frames in , . Specifically, we improve the -theorem and obtain explicit upper and lower bounds for some complex exponential frames perturbed along the real and imaginary axes, respectively. Two examples are given to show that the bounds are best possible. In addition, the growth of the entire functions of exponential type on the integer sequence is estimated.