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The problem of chemotherapy treatment optimization can be defined in order to minimize the size of the tumor without endangering the patient's health; therefore, chemotherapy requires to achieve a number of objectives, simultaneously. For…
Purpose: To make the planning of volumetric modulated arc therapy (VMAT) faster and to explore the tradeoffs between planning objectives and delivery efficiency. Methods: A convex multicriteria dose optimization problem is solved for an…
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
Radiation therapy is considered to be one of important treatment protocols for cancers. Radiation therapy employs several beams of ionizing radiation to kill cancer tumors, but such irradiation also causes damage to normal tissues.…
Background: Beam angle optimization (BAO) is a critical component of radiation therapy (RT) treatment planning, where small changes in beam configuration can significantly impact treatment quality, especially for proton RT. Mathematically,…
We present a method of directly optimizing on deviations in clinical goal values in radiation therapy treatment planning. Using a new mathematical framework in which metrics derived from the dose-volume histogram are regarded as functionals…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
In this article, we apply a new methodology for precision tuning to the N-body problem. Our technique, implemented in a tool named POP, makes it possible to optimize the numerical data types of a program performing floating-point…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensity-modulated particle therapy (IMPT) treatment planning. Proton therapy…
The authors propose robust adaptive strategies based on stochastic minimax optimization for a series of simulated treatments on a one-dimensional patient phantom. The plan applied during the first fractions should be able to handle…
Radiation therapy with carbon ions is a novel technique of cancer radiotherapy, applicable in particular to treating radioresistant tumours at difficult localisations. Therapy planning, where the medical physicist, following the medical…
We show that (i) any constrained polynomial optimization problem (POP) has an equivalent formulation on a variety contained in an Euclidean sphere and (ii) the resulting semidefinite relaxations in the moment-SOS hierarchy have the constant…
For the cascaded planning and control modules implemented for robot navigation, the frequency gap between the planner and controller has received limited attention. In this study, we introduce a novel B-spline parameterized…
Purpose: To demonstrate the feasibility of fast Monte Carlo (MC) based inverse biological planning for the treatment of head and neck tumors in spot-scanning proton therapy. Methods: Recently, a fast and accurate Graphics Processor Unit…
Resource allocation problems in many computer systems can be formulated as mathematical optimization problems. However, finding exact solutions to these problems using off-the-shelf solvers is often intractable for large problem sizes with…
Inverse treatment planning in radiation therapy is formulated as optimization problems. The objective function and constraints consist of multiple terms designed for different clinical and practical considerations. Weighting factors of…
Background: Intensity-modulated proton therapy (IMPT) using pencil beam technique scans tumor in a layer by layer, then spot by spot manner. It can provide highly conformal dose to tumor targets and spare nearby organs-at-risk (OAR). Fast…
Intensity modulated proton therapy (IMPT) provides highly conformal dose distributions through the application of multiple, angularly spaced fields, each applying an ad-hoc pattern of spatially varying particle fluences. In particular,…
Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…