Related papers: Optimal radiotherapy treatment planning using mini…
In this paper we study a problem in radiotherapy treatment planning, where the evolution of the radiation field is governed by a deterministic Boltzmann transport equation. We show existence, uniqueness and regularity of solutions to an…
The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
Radiotherapy is used to treat cancer patients by damaging DNA of tumor cells using ionizing radiation. Photons are the most widely used radiation type for therapy, having been put into use soon after the first discovery of X-rays in 1895.…
Radiotherapy treatment planning is a challenging large-scale optimization problem plagued by uncertainty. Following the robust optimization methodology, we propose a novel, spatially based uncertainty set for robust modeling of radiotherapy…
The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…
We present a novel application of Tensor Network methods in cancer treatment as a potential tool to solve the dose optimization problem in radiotherapy. In particular, the Intensity-Modulated Radiation Therapy (IMRT) technique - that allows…
In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors with radiotherapy influence. Under certain assumptions on the given data in the model, we prove existence and uniqueness of a weak…
In this paper we consider an optimal control problem arising from a chemotherapeutic drug treatment for tumor cells in a living tissue. The mathematical model for the interaction of chemotherapeutic drug and the normal, tumor and immune…
In many applied optimization settings, parameters that define the constraints may not guarantee the best possible solution, and superior solutions might exist that are infeasible for the given parameter values. Removing such constraints,…
In this paper, we develop a computationally-efficient approach to minimum-time trajectory optimization using input-output data-based models, to produce an end-to-end data-to-control solution to time-optimal planning/control of dynamic…
In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize…
Radiation therapy is a critical component of cancer treatment. However, the delivery of radiation poses inherent challenges, particularly in minimizing radiation exposure to healthy organs surrounding the tumor site. One significant…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health…
In the past decades mathematical optimization has found its way into radiation therapy and has made profound practice changing impact. Today, virtually all advanced treatment delivery methods, such as IMRT, VMAT, tomotherapy, LDR/HDR…
We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variations in OAR and tumor sensitivities to…
We present an optimization-based approach to radiation treatment planning over time. Our approach formulates treatment planning as an optimal control problem with nonlinear patient health dynamics derived from the standard linear-quadratic…
This paper deals with the classic radiotherapy dose fractionation problem for cancer tumors concerning the following goals: a) To maximize the effect of radiation on the tumor, restricting the effect produced to the organs at risk (healing…
Stereotactic body radiotherapy (SBRT) is characterized by delivering a high amount of dose in a short period of time. In SBRT the dose is delivered using open fields (e.g., beam's-eye-view) known as "apertures". Mathematical methods can be…