A computational solution of the inverse problem in radiation-therapy treatment planning
type: Item
instance of: scholarly article
title: A computational solution of the inverse problem in radiation-therapy treatment planning
zbMATH Open document ID: 0637.65060
DOI: 10.1016/0096-3003(88)90064-1
author: Yair Censor
author: Martin D. Altschuler
author: William D. Powlis
published in: Applied Mathematics and Computation
publication date: 1988-01-01T00:00:00Z
review text: Discretizing both, the patient section and the radiation field, the inverse problem of radiation-therapy treatment planning is reduced to the linear feasibility problem of finding a vector \(x=(x_ 1,x_ 2,...,x_ n)\) satisfying relations of the form \(\sum^{n}_{i=1}D_{ij}x_ i\leq b_ k\) (\(\forall)\) \(j\in B_ k\), \(k=1,2,...,K\); \(t_ q\leq \sum^{n}_{i=1}D_{ij}x_ i\) (\(\forall)\) \(j\in T_ q\), \(q=1,2,...,Q\); \(\sum^{n}_{i-1}D_{ij}x_ i\leq c\) (\(\forall)\) \(j\in C\); \(x_ i\geq 0\) (\(\forall)\) \(i=1,2,...,n\), where \(b_ k\), \(t_ q\), c, \(B_ k\), K, \(T_ q\), Q, C are given and the numbers \(D_{ij}\) are derived from the calculated doses, \(D_ s(j)\), per unit beam weight delivered to each pixel (portion of the patient section) from each source. The linear feasibility problem is solved using a relaxation method and some experimental results are presented. Consequences and limitations of this methodology, some open problems and comparison with other methodologies are also discussed.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4039156
zbMATH Keywords: inverse problem
zbMATH Keywords: radiation-therapy treatment planning
zbMATH Keywords: linear feasibility problem
zbMATH Keywords: relaxation method
zbMATH Keywords: comparison
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
full work available at URL: 0096-3003(88)90064-1
OpenAlex ID: W2076432449
cites work: The Relaxation Method for Linear Inequalities
cites work: Row-Action Methods for Huge and Sparse Systems and Their Applications
cites work: Q3325518
cites work: Q4170564
cites work: Computation of optimal radiation treatment plans
Wikidata QID: Q128054421
description: scientific article; zbMATH DE number 4039156