Lec4 - IE521 Advanced Optimization Lecture 4 Dr Zeliha Akca October 2011 1 23 Reading Bertsimas 2.3 2.7 2 23 Problem of the Week RADIATION

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IE521 Advanced Optimization Lecture 4 Dr. Zeliha Akc ¸a October 2011 1 / 23
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Reading I Bertsimas 2.3 - 2.7 2 / 23
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Problem of the Week RADIATION TREATMENT I Radiation therapy is a technique used in the treatment of most cancer. I Radiation is depositted to the part of the body with tumor. Doctors decide the amount radiation required in the treatment. I Objective is to give the prescribed amount of radiation to the cancerous regions (tumors) and minimum amount of radiation to non-cancerous tissues. I Radiation affects the DNA’s of cells and reduces their ability to multiply. I Cancerous cells are more susceptible to radiation. I Radiation is given via beams with different angles and intensity. I Beams affect the entry regions the most. While the distance to entry increases the affect of radiation reduces. I The design of radiation therapy is very delicate. I Aim is to select the best set of beams with right intensity in order to give the best possible way of prescribed amount of radiation to tumor. 3 / 23
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Radiation Treatment I The radiation machine deliver beams with different angles to the patients body. I Exposure time of the beam is determined and is called as the intensity. I 2 main techniques are used: conformal therapy (in the shape of tumor), intensity-modulated radiation therapy (region divided into small rectangles). I Region is divided into small rectangles that are called voxel. I Construct intensity matrix for each voxel. A ij of A : Weight of beam j to be applied to voxel i 4 / 23
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Optimization in Radiation Therapy I Constructing dose matrix is to plan the theatment in backwards. I 3 different voxels: Target T , critical C , normal N . I For each voxel, objective function coefficients are determined: c T , c N , c C . I Big penalties may be set for normal voxels. 5 / 23
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Radyo Terapi LP Modeli Decision Variables: w = weight of beam vector x T = dose for target voxels x N = dose for normal voxels x C = dose for critical voxels Parameters: x U T = dose upper bnd for target voxels x L T = dose lower bnd for target voxels x U N = dose upper bnd for normal voxels x U C = dose upper bnd for critical voxels A T , A N , A C = Dose matrices min w , x T , x N , x C C T N x N s.t. x T = A T w x N = A N w x C = A Cw x N x U N x C x U C x L T x T x U T w 0 6 / 23
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Optimization in Radiation Therapy I To kill cancerous cells in a tumor radiation therapy is used. I Radiation is applied to 3 regions. I
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This note was uploaded on 01/09/2012 for the course IE 521 taught by Professor Zelihaakça during the Fall '11 term at Fatih Üniversitesi.

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Lec4 - IE521 Advanced Optimization Lecture 4 Dr Zeliha Akca October 2011 1 23 Reading Bertsimas 2.3 2.7 2 23 Problem of the Week RADIATION

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