Censor Yair, Bortfeld Thomas, Martin Benjamin, Trofimov Alexei
Department of Mathematics, University of Haifa, Mt Carmel, Haifa 31905, Israel.
Phys Med Biol. 2006 May 21;51(10):2353-65. doi: 10.1088/0031-9155/51/10/001. Epub 2006 Apr 26.
We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.
我们提出并研究了一个统一模型，该模型基于分裂可行性问题，在单一数学框架中处理剂量约束（物理剂量、等效均匀剂量（EUD）等）和辐射源约束。该模型不对约束施加外部目标（优点）函数。优化算法使一个加权接近度函数最小化，该函数测量到约束集的距离平方和。如果分裂可行性问题是一致的（即有解），这保证收敛到一个可行解点，否则，收敛到一个最小违反物理剂量约束和EUD约束的解。我们给出的计算结果证明了该模型的有效性和所提出算法方案的能力。
