Radiation Therapy (RT)

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Radiation Therapy (RT)
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What is cancer?

• Failure of the mechanisms that control growth and
  proliferation of the cells
• Uncontrolled (often rapid) growth of the tissue
• Formation of the tumor
• Metastasis spread to distant locations

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Tumor biology

• Tumors consist mainly from fully functional
  (mature) cells
• Clonogenic (stem) cells are capable of infinite
  proliferation and therefore responsible for tumor
  growth
• Dividing stem cells divides continuously and
  tumor is growing exponentially

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Tumor biology

• Growth rate described by doubling time Td
• Potential doubling time (cell cycle period)
• Real doubling time (cell loses up to 90)
• Initial number of clonogen cells in individual
  volume element is NiriVi
• Number of clonogen cells after DT is

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Cancer treatment

• Cancer usually treated by
• Chemotherapy
• Surgery
• Radiation therapy
• Treated also by
• Hyperthermia
• Hormone therapy
• Molecular targeted therapy

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Ionizing radiation effects

• Standard physical effects take place first
• Chemical reactions follows them
• Biological consequences
• Damage to the cell is mainly due to DNA damage

• Cell is considered to survive if unlimited
  reproductive potential is preserved

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Dosimetry

• Dose (actually absorbed dose) is defined as
  energy absorbed per unit mass
• DDE/Dm
• Biological effects not due to increased
  temperature
• Lethal dose increases temperature by
  approximately 0.001 degree C

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Radiobiology

• LQ survival curve
• Death from single hit
• Death from multiple sublethal hits

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Number of clonogen cells

• Survival curve predict average number N of
  survived cells after irradiation of the cells
• One of the hypothesis says that
• All clonogen cells has to be eliminated to cure
  the tumor
• Cells follow Poisson statistics

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Radiation therapy

• Use of ionizing radiation to kill cancer cells,
  while delivering as low dose as possible to
  normal tissue

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How the systems look today
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How the systems work today

• Conventional radiotherapy uses uniform beams that
  results uniform dose
• Technique that uses
• nonuniform beams
• can produce arbitrary
• dose distribution in
• tumor (IMRT)

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How we plan today

• Despite IMRT capabilities, uniform dose
  distribution is demanded

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How we will plan in the future

• Customized nonuniform dose distributions on a
  patient specific basis

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Planning and imaging

• We may image
• Anatomy
• Functions or molecular processes
• Molecular imaging maybe gives us an answer how to
  shape the dose

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Positron emission tomography

• Nuclear medicine medical imaging technique
• Produces a 3D image of molecular processes in the
  body

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How PET works

• Production of radioisotope
• Bounding of radioisotope to some bioactive
  compound
• Injecting patient by that radiolabeled compound
• Imaging of spatial distribution of that compound

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PET usage

• Delineation of the tumor volume and its stage
  (past and present use)
• In the future, probably very important tool for
  the assessment of
• tumor clonogen cells density distribution
• oxygen status of the tumor
• tumor response to the radiation treatment

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BCRT

• Planned dose distribution in target volume is not
  uniform, but tailored on patient specific basis
• Integral tumor dose is constrained
• Planned dose distribution should result highest
  probability to eliminate tumor
• Planned dose conforms to the spatial tumor
  biology distribution

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Spatial biology distribution

• The only missing link in the BCRT chain
• Properties are phenomenologically characterized
  by
• Clonogen density r
• Radiosensitivity a
• Redefined aa1b/a D a, b are LQ
  parameters
• Proliferation rate g

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Local tumor kinetics

• Parameters for one volume element!
• Si is number of cells after something happens,
  relative to initial number
• Growth of the cells with time
• Killing the cells after irradiation

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Local tumor control probability

• Taking into account growth and kill
• Initial number of clonogen cells in individual
  volume element is
• NiriVi
• Recalling equation for TCP from Poisson statistics

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Local tumor control probability

• Probability to eliminate all cells in i-th volume
  element
• DT in interval between RT fractions

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Global TCP maximization

• TCP for whole tumor is product of TCPs for each
  voxel
• Total dose to the tumor is constrained
• To maximize TCP, we construct Lagrangian

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Solution of the optimization problem

• We assume that all volume elements are equal
• We choose reference radiobiological parameters
  rref, aref, gref and reference dose Dref that
  would give sensible TCP

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Special cases

• Constant radiobiology parameters implies uniform
  dose
• Not a surprise, just gives us confidence that
  method may be correct ?
• Variable clonogen density r

Dose increases logarithmically with clonogen
density.
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Another two special cases

• Nonuniform radiosensitivity a
• Nonuniform proliferation rate g

Dose is approximately inversely proportional to
the radiosensitivity.
Dose increases linearly with proliferation rate.
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Conclusions

• The formalism proposed here is questionable
  because is based on an LQ model
• Not valid for high doses
• Presumes uniform dose distribution
• Formalism does not take into account
• Redistribution of the cells through cell cycle
• Reoxygenation of hypoxic cells
• It presumes that spatial distribution of
  biological parameters is known

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Conclusions

• Formalism gives a rough overview how to optimally
  shape the dose distribution
• Simplistic (beginners) approach to the patient
  specific radiation therapy, which is believed to
  be future of RT by many renowned researchers.