Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Non-coplanar beam orientation optimization for total marrow irradiation using IMRT c † Dionne M. Aleman † Michael B. Sharpe ‡ Velibor V. Miˇ si´ † Department of Mechanical and Industrial Engineering, University of Toronto ‡ Princess Margaret Hospital; Department of Radiation Oncology, University of Toronto June 17, 2009 CORS-INFORMS International Meeting 2009, Toronto Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Bone Marrow Transplants (BMTs) ◮ Method of treatment for blood and bone marrow cancers (leukemia and lymphoma); also for aplastic anemia and sickle cell disease ◮ To transplant bone marrow, existing bone marrow must be eradicated – current method is total body irradiation (TBI) ◮ More effective methods of bone marrow elimination – total marrow irradiation (TMI) Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Intensity Modulated Radiation Therapy (IMRT) ◮ Conventional radiotherapy: beam is of homogeneous intensity ◮ IMRT: beam is broken into numerous beamlets; each beamlet’s intensity is controllable ◮ Used successfully for other types of cancer (head-and-neck) Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Has IMRT been applied to TMI before? Yes, but ◮ Not within a mathematical framework ◮ Previous work studies irradiation from a greater distance Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References ... So what are the problems? ◮ For a set of beam directions, which beamlet intensities are optimal? And... ◮ Which beam directions do we use in the first place? Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References ... So what are the problems? ◮ For a set of beam directions, which beamlet intensities are optimal? And... ◮ Which beam directions do we use in the first place? Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References ... So what are the problems? ◮ For a set of beam directions, which beamlet intensities are optimal? And... ◮ Which beam directions do we use in the first place? Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Beam Orientation Optimization (BOO) ◮ Beams are obtained by ◮ Rotating the gantry – 10 ◦ increments ◮ Translating the couch along patient’s vertical axis – 10 cm increments ◮ Beams are non-coplanar Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Coplanar vs. non-coplanar Coplanar Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Coplanar vs. non-coplanar Non-coplanar Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References BOO Model Overview ◮ Set of beam orientations is denoted by Θ ◮ Quality of set is denoted by function F (Θ) ◮ Goal is to optimize F (Θ) over all possible sets of beams Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References The function F ◮ Beam set quality can be formulated in many ways ◮ We use fluence map optimization (FMO) value from Romeijn et al. [2006] Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References FMO Model Overview (1) ◮ For a set of beam directions, which beamlet intensities are optimal? ◮ x i is intensity of beamlet i , i ∈ B Θ ◮ z js is dose in voxel j in structure s , j ∈ { 1 , . . . v s } , s ∈ S ◮ z js = � i ∈ B Θ D ijs x i Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References FMO Model Overview (2) ◮ The dose in each voxel can be penalized: � p s � + + w s ( z js − T s ) p s F js ( z js ) = w s ( T s − z js ) (1) + ◮ w s , w s are weights for underdosing and overdosing; p s , p s are powers for underdosing and overdosing � � 1 � v s ◮ Total penalty is � j =1 F js ( z js ) s ∈ S v s Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References FMO Model Overview (2) ◮ The dose in each voxel can be penalized: � p s � + + w s ( z js − T s ) p s F js ( z js ) = w s ( T s − z js ) (1) + ◮ w s , w s are weights for underdosing and overdosing; p s , p s are powers for underdosing and overdosing � � 1 � v s ◮ Total penalty is � j =1 F js ( z js ) s ∈ S v s Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References FMO Model Overview (2) ◮ The dose in each voxel can be penalized: � p s � + + w s ( z js − T s ) p s F js ( z js ) = w s ( T s − z js ) (1) + ◮ w s , w s are weights for underdosing and overdosing; p s , p s are powers for underdosing and overdosing � � 1 � v s ◮ Total penalty is � j =1 F js ( z js ) s ∈ S v s Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References FMO Model Overview (3) Model is � � � v s 1 � min j =1 F js ( z js ) s ∈ S v s (2) z js = � subject to i ∈ B Θ D ijs x i , ∀ j ∈ { 1 , . . . , v s } , s ∈ S x i ≥ 0 , ∀ i ∈ B Θ FMO model is convex, solvable using projected gradient method Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References Add/Drop (A/D) Algorithm ◮ Neighborhood search algorithm ◮ Previously used in Kumar [2005] and Aleman et al. [2008] Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D 1. Select a beam and a component (gantry angle/z trans.) 2. Enumerate all the Θ in the beam-component neighborhood of current Θ (Θ ( i ) ) 3. Calculate F for all of these solutions 4. Set Θ ( i +1) to the most improving new Θ (if any) Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Current solution – Θ ( i ) , F (Θ ( i ) ) = 700 Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Select a beam and a component Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Enumerate solutions in the neighborhood of Θ ( i ) Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Θ 1 , F (Θ 1 ) = 490 Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Θ 2 , F (Θ 2 ) = 520 Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Θ 3 , F (Θ 3 ) = 780 Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
Introduction Beam Orientation Optimization Add/Drop Algorithm Results References One iteration of A/D - graphical example Θ 4 , F (Θ 4 ) = 770 Non-coplanar beam orientation optimization for TMI Medical Operations Research Laboratory (morLAB)
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