A computational solution of the inverse problem in radiation-therapy treatment planning
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.
scientific article; zbMATH DE number 4039156