Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Beam selection in radiotherapy design
AU - Ehrgott, Matthias
AU - Holder, Allen
AU - Reese, Josh
PY - 2008/3/1
Y1 - 2008/3/1
N2 - The optimal design of a radiotherapy treatment depends on the collection of directions from which radiation is focused on the patient. These directions are manually selected and are based on the treatment planner’s experience. Once the angles are chosen, there are numerous optimization models that decide a fluency pattern (exposure times) that best treats a patient. So, while optimization techniques are often used to decide how long a patient will be exposed to a high-energy particle beam, the directions themselves are not optimized. The problem with optimally selecting directions is that the underlying mixed integer models are well beyond our current solution capability. We present a rigorous mathematical development of the beam selection problem that provides a unified framework for the problem of selecting beam directions. This presentation provides insights into the techniques suggested in the literature and highlights the difficulty of the problem. We also compare several techniques head-to-head on two-dimensional problems.
AB - The optimal design of a radiotherapy treatment depends on the collection of directions from which radiation is focused on the patient. These directions are manually selected and are based on the treatment planner’s experience. Once the angles are chosen, there are numerous optimization models that decide a fluency pattern (exposure times) that best treats a patient. So, while optimization techniques are often used to decide how long a patient will be exposed to a high-energy particle beam, the directions themselves are not optimized. The problem with optimally selecting directions is that the underlying mixed integer models are well beyond our current solution capability. We present a rigorous mathematical development of the beam selection problem that provides a unified framework for the problem of selecting beam directions. This presentation provides insights into the techniques suggested in the literature and highlights the difficulty of the problem. We also compare several techniques head-to-head on two-dimensional problems.
KW - Optimization
KW - Set covering
KW - Vector quantization
KW - Radiotherapy
KW - Radiosurgery
KW - Medical Physics
U2 - 10.1016/j.laa.2007.05.039
DO - 10.1016/j.laa.2007.05.039
M3 - Journal article
VL - 428
SP - 1272
EP - 1312
JO - Linear Algebra and its Applications
JF - Linear Algebra and its Applications
SN - 0024-3795
IS - 5-6
ER -