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Chemotherapy is a class of cancer treatment that uses drugs to kill cancer cells. A typical chemotherapeutic protocol consists of several drugs delivered in cycles of three weeks. We present mathematical analyses demonstrating the existence…
Temporally modulated pulsed radiotherapy (TMPRT) delivers conventional fraction doses of radiation using temporally separated pulses of low doses (<30 cGy) yielding fraction-effective dose rates of around 6.7 cGy/min with the goal to…
We highlight emerging uses of artificial intelligence (AI) in the field of theranostics, focusing on its significant potential to enable routine and reliable personalization of radiopharmaceutical therapies (RPTs). Personalized RPTs require…
The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored…
The goal of radiation therapy for cancer is to deliver prescribed radiation dose to the tumor while minimizing dose to the surrounding healthy tissues. To evaluate treatment plans, the dose distribution to healthy organs is commonly…
In the precision medicine era, there is a growing need for precision radiotherapy where the planned radiation dose needs to be optimally determined by considering a myriad of patient-specific information in order to ensure treatment…
While spatial dose conformity delivered to a target volume has been pushed to its practical limits with advanced treatment planning and delivery, investigations in novel temporal dose delivery are unfolding new mechanisms. Recent advances…
Particle physics simulations are the cornerstone of nuclear engineering applications. Among them radiotherapy (RT) is crucial for society, with 50% of cancer patients receiving radiation treatments. For the most precise targeting of tumors,…
We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the…
Contours are used in radiotherapy treatment planning to identify regions to be irradiated with high dose and regions to be spared. Therefore, any contouring uncertainty influences the whole treatment. Even though this is the biggest…
Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be…
Radiation treatment planning involves optimization over a large number of voxels, many of which carry limited information about the clinical problem. We propose an approach to reduce the large optimization problem by only using a…
Noncoplanar radiation therapy treatment planning has the potential to improve dosimetric quality as compared to traditional coplanar techniques. Likewise, automated treatment planning algorithms can reduce a planner's active treatment…
Thanks to advancements in diagnosis and treatment, prostate cancer patients have high long-term survival rates. Currently, an important goal is to preserve quality-of-life during and after treatment. The relationship between the radiation a…
Background and Purpose: Increasing the number of arcs in volumetric modulated arc therapy (VMAT) allows for better intensity modulation and may improve plan quality. However, this leads to longer delivery times, which may cause patient…
This work presents a preliminary evaluation of the use of the convolutional neural network nnU-NET to automatically contour the volume of Glioblastoma Multiforme in medical images of patients. The goal is to assist the preparation of the…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that…
A general scheme of the excluded-volume approximation as applied to multicomponent systems with an arbitrary degree of degeneracy has been developed. This scheme also admits an allowance for additional interactions between the components of…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…