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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…
In this paper, we investigate protection strategies of sensitive body anatomy against the irradiation to the cancerous moving tumors in intensity modulated radiation therapy. Inspired by optimization techniques developed in statistical…
Traditionally, optimization of radiation therapy (RT) treatment plans has been done before the initiation of RT course, using population-wide estimates for patients' response to therapy. However, recent technological advancements have…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Auxiliary variables are often used to model a convex piecewise linear function in the framework of linear optimization. This work shows that such variables yield a block diagonal plus low rank structure in the reduced KKT system of the dual…
The primary objective of Phase I oncology trials is to assess the safety and tolerability of novel therapeutics. Conventional dose escalation methods identify the maximum tolerated dose (MTD) based on dose-limiting toxicity (DLT). However,…
Radiation therapy outcomes are decided by two key parameters, dose and timing, whose best values vary substantially across patients. This variability is especially critical in the treatment of brain cancer, where fractionated or staged…
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…
Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…
In this paper, a tractable methodology is proposed to approximate stochastic optimal feedback treatment in the context of mixed immuno-chemo therapy of cancer. The method uses a fixed-point value iteration that approximately solves a…
We developed a novel method of creating intensity modulated proton arc therapy (IMPAT) plans that uses computing resources efficiently and may offer a dosimetric benefit for patients with ependymoma or similar tumor geometries. Our IMPAT…
We consider a class of optimization problems with Cartesian variational inequality (CVI) constraints, where the objective function is convex and the CVI is associated with a monotone mapping and a convex Cartesian product set. This…
Beam angle optimization (BAO) largely determines the performance of fixed-field intensity modulated radiation therapy (IMRT), and it is usually considered as non-convex optimization and an NP hard problem. In this work, BAO is reformulated…
The purpose of this study is to evaluate the clinical usefulness of modulated arc (mARC) treatment techniques. The mARC treatment plans of the non-small cell lung cancer (NSCLC) patients were performed in order to verify the clinical…
Model predictive control (MPC) is an optimization-based control strategy with broad industrial adoption. Unfortunately, the required computation time to solve the receding-horizon MPC optimization problem can become prohibitively large for…
In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR)…
Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel computationally efficient approach…
Health policy decisions regarding patient treatment strategies require consideration of both treatment effectiveness and cost. Optimizing treatment rules with respect to effectiveness may result in prohibitively expensive strategies; on the…
Cancer therapy for deep-seated tumors requires precise irradiation of a small target deep within the patient while minimizing radiation exposure to surrounding tissues. This can be accomplished with a round beam sharply converging towards a…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…