A computational solution of the inverse problem in radiation-therapy treatment planning☆
References (24)
- et al.
Program IRREG—calculation of dose from irregularly shaped radiation beams
Comput. Prog. Biomed.
(1972) - et al.
Optimized radiotherapy treatment planning using the complication probability factor (CPF)
Rad. Onc. Biol. Phys.
(1980) - et al.
Optimization of external beam radiation therapy
Internat. J. Rad. Onc. Biol. Phys.
(1977) Computation of optimal radiation treatment plans
J. Comput. Appl. Math.
(1977)Computational methods in beam therapy planning
Comput. Prog. Biomed.
(1972)- et al.
The equivalent tissue-air ratio method for making absorbed dose calculations in a heterogeneous medium
Radiology
(1978) - et al.
Computer generated isodose curves for high energy x-ray machines
Amer. J. Roentgen. Rad. Therapy and Nucl. Med.
(1974) Scatter-air ratios
Phys. in Med. and Biol.
(1972)Limitations of two-dimensional treatment planning programs
Med. Phys.
(1982)The relaxation method for linear inequalities
Canad. J. Math.
(1954)
The relaxation method for linear inequalities
Canad. J. Math.
Row-action methods for huge and sparse systems and their applications
SIAM Rev.
Cited by (92)
Optimization model applied to radiotherapy planning problem with dose intensity and beam choice
2020, Applied Mathematics and ComputationCitation Excerpt :Nonlinear methods can be solved by classic Newton’s methods [19] or even using fuzzy logic systems [20,21]. However, based on [7-18] we employ matheuristics methods to solve the new model, in which the metaheuristics Variable Neighbourhood Search (VNS) and Tabu Search (TS) solve the beam choice problem and convert the model into a mixed integer linear. From then on, one uses exact methods Primal Simplex (PS), Dual Simplex (DS) and Interior Point Method (IPM) for the dose intensity problem and final solution.
Iterative methods for solving consistent or inconsistent matrix inequality AXB≥C with linear constraints
2015, Applied Mathematical ModellingFundamentals of Physically and Biologically Based Radiation Therapy Optimization
2014, Comprehensive Biomedical PhysicsIntensity-Modulated Radiation Therapy Planning
2014, Comprehensive Biomedical PhysicsThe physical and mathematical aspects of inverse problems in radiation detection and applications
2012, Applied Radiation and IsotopesFrom analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective
2012, Physica MedicaCitation Excerpt :On the other hand, the main ingredients of the algebraic inverse planning approach were, separately, known when this approach was proposed. Full discretization was known and used in other fields and iterative projection methods such as the sequential projection method of Agmon et al. that we used in [16] (also used later by Lee et al. [37] under a different name) or the Cimmino simultaneous projections method [22] that we used in [17] were known. See, e.g., Bauschke and Borwein [6] or Censor and Zenios [20, Chapter 5] for general presentations of iterative projection methods for the convex feasibility problem and Censor et al. [18] for a very recent work.
- ☆
A preliminary report on this research was presented at the Eighth International Conference on the Use of Computers in Radiation Therapy, 9-12 July 1984, Toronto, Canada [24].