GROUP_4 PRESENTATION

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GROUP_4PRESENTATION

• A NEW LINEAR PROGRAMMING APPROACH TO RADIATION
  THERAPY TREATMENT PLANNING PROBLEMS

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INTRODUCTION

• 1.3 million U.S. citizens are newly diagnosed
  with cancer (American Cancer Society 2004)
• 300,000 patients per year

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• Radiation Therapy
• Can reduce the quality of life
• Too little radiation dose to the targets
• Patients life must be balanced
• To design optimal radiation therapy treatment
  plans

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Beams of radiation
Clinical targets
Critical structures
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• Why is not a single beam usen at radiation??
• Kill the targets
• Risk to damage normal cells in critical
  structures located along the along path of the
  beam

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• Deliver beams
• Intersections are the targets
• Intersection gt The highest radiation dose
• Low radiation dose gt The critical structures

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Types of Radiation Therapy

• Conformal radiation therapy
• Conventional conformal radiation therapy
• External beam radiation delivery technique gt
  intensity-modulated radiation therapy
  ( IMRT )

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IMRT

• Complex nonuniform dose distributions
• High radiation doses to targets
• Limiting the radiation dose for healty cells
• These dose distributions are obtained by
  dynamically blocking different parts of the beam
• Optimization techniques

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FMO Type of Optimization Problems

• Fluence Map Optimization (FMO) Problems
• Design an optimal radiation density profile in
  the patient
• Deliver prescription dose to cancerous cells
• Not exceed tolerance dose to normal cells

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OR Approaches To The IMRT Radiation Therapy

• Quadratic Programming
• Not allows sufficient flexibility for
  high-quality treatment
• Global and Mix-integer Pragramming
• Allows flexibility but
• not feasible to employ in real-life while
  ensuring the global optimal solution

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Expected Programming Model

• Expected Prog. Model should ensure
• Add flexibility as compared with quadratic
  programming models
• Prevent difficulties such as multiple local
  optima that occur in mixed-integer and/or
  non-convex global optimization models

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Goal Of The Paper

• New approach to the FMO problem
• Based on employing linear programming
  approximations to convex programming formulations
  
• Model ables to incorporate several measures
  (additional aspects) while retaining linearity
• Duality theory

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Terminology and Notation

• Targets are cancerous cells (s1,....,T)
• Critical Structures are normal cells
  (sT1,....,S)
• Both cells are called generally as structures
• (s1,....,S)
• Each beam is decomposed into small beamlets
  (i1,......,N)
• Each structure is decomposed into several number
  of voxels (j1,.....,Vs)

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Notation
Decision Variables
The weight (intensity) of beamlet i ,
i1,.....,N
Parameters
The dose received by voxel j in structure s
from beamlet i at unit intensity
(weight) j1,.....,Vs s1,....,S i1,.....,N
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Notation

• Beamlet intensity ?

Dose received by voxels
Linear relationship
Represent dose received by each voxel as a
function of the beamlet intensities as follows
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Model Formulation of The Paper

• Basic Constraints are called full-volume
  constraints
• F1? Deliver minimum prescription dose L to all
  voxels in the targets
• F2? Do not deliver more than a maximum tolerance
  dose U to all voxels in both targets and
  critical structures

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Full-Volume Constraints
Lower Bound on the dose received by all voxels
in structure s
Upper Bound on the dose received by all voxels
in structure s
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Penalty Function and Objective Function

• Define for each structure, a penalty function of
  the dose received by the voxels in that structure
• Denote the penalty function for structure s by

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The Objective Function to Minimize
Scaling term ?
Ensuring penalty functions are insensitive to the
relative sizes in different problems
Is described as a function of z
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Variable Transformation

• This transformation simplifies the model
  formulation

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Model Formulation of the Paper
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Model Formulation of the Paper
Objective Function
Transformation
Lower Bound (F1)
Upper Bound (F2)
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Penalty Function
Only voxels that are overdosed are penalized
Underdose penalty function
Overdose penalty function
0 for critical structures
0 for critical structures
Lower doses are always preferred to higher doses
in critical structures
For targets, the overdose and underdose
thresholds will often be chosen to be equal
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Approximate penalty functions by piecewise-linear
functions

• By this approximation,
• They can reformulate their FMO model in a linear
  form as linear programming problem

Penalty functions for a target and a critical
structure
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Approximation of penalty function by
piecewise-linear convex functions
Each of these variables has zero lower bound and
an upper bound given by the size of the segment
The dose to a voxelgtsum of all segment variables
for that voxel
Decision variablegt
kth linear segment in the piecewise linear
convex penalty function for each voxel (j,s).
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Our Model Formulation
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Our Model Formulation
Our model is perfectly linear with several
assumptions
Closed form
We remove both the convexity and the maximum
function
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Required Values
Following table represents
Values, we use approximate values according to
the paper
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Required values
is equal to 85 for all voxels in the targets ,
s1,2 (only for targets)
is equal to 100 for all voxels in both targets
and critical structures
is equal to 100 for all targets
is equal to 0 for critical structures and 100 for
targets
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Required values
is equal to 50 for all voxels in the targets ,
s1,2 (only for targets) and 0 for critical
structures
is equal to 60 for all voxels in the targets ,
s1,2 and 70 for critical structures, s1,2
LETS SOLVE THE MODEL
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Dose-Volume Histogram (DVH)

• The fraction of the structures volume ?
• receives at least a certain amount of dose
• The value of DVH at dose d ? the fraction of
  voxels in the structure who receives a dose of at
  least d units

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Partial Volume Constraints

• Traditional Partial-Volume Constraints
• Incorporate constraints on the shape and location
  of the DVH of a structure
• New Class of Partial-Volume Constraints
• Formulate risk management constraints in terms of
  tail averages

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New Class of Partial-Volume Constraints
Constrain the average dose in a tail of a given
size as opposed to the max and min dose in that
tail
Linear and has computational advantage
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Results of The Paper

• Validate the model,
• Tuned the parameters of the model by manual
  adjustment,
• Test robustness

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• THANK YOU FOR YOUR LISTENING...