Radiation Oncology/Radiobiology/Equations



Radiobiology Equations


Tumor GrowthEdit

  • Mitotic Index:[1]:252
  • Labeling Index:
  • Growth fraction:
  • Tumor volume doubling time:
  • Potential doubling time:
  • Cell loss factor:
  • Gompertzian Growth[2]:475
    • Progressively slowing:
    • Small t (early):
    • Large t (late):

DefinitionsEdit

  • =M phase duration
  • =cell cycle duration (total duration of all phases)
  • =correction factor for uneven distribution of cells
  • =S phase duration
  • = tumor volume
  • = original tumor volume
  • = time
  • ,= constants

Cell survival curvesEdit

  • Plating efficiency:
  • Surviving fraction:

Do not distinguish mode of death (mitotic vs apoptotic)

Target theoryEdit

  • Surviving fraction (single target-single hit):[3]
  • Surviving fraction (multiple target-single hit):
  • Quasi-threshold dose:[4]

DefinitionsEdit

  • =dose
  • =dose that decreases surviving fraction to 37%
  • =extrapolation number, doses required to kill all cells
  • =dose that decreases SF to 10%
  • =number of fractions

Linear Quadratic modelEdit

  • Fraction of cells surviving single dose :[1]:228[5]:31
  • Fraction of cells surviving fractions :[5]:31
  • Biologically Effective Dose (same RBE):[1]:230
  • BED for high LET radiation (RBE adjusted):[4]:268
  • BED (time adjusted):[6]
  • Isoeffective dose:[7][8]

  • Equivalent Dose in 2 Gy Fractions:

DefinitionsEdit

  • =number of fractions
  • =dose
  • =linear coefficient, reflects cell radiosensitivity
  • =quadratic coefficient, reflects cell repair mechanisms
  • =kick-off or onset time
  • =average cell-number doubling time
  • =total absorbed dose
  • =weighting factor

Dose-responseEdit

  • Tumor control probability (TCP)



DefinitionsEdit

  • =number of fractions

Linear Energy TransferEdit

  • Linear Energy Transfer (LET):[9]:106
Radiation type LET (keV/μm)
Co-60 photon 0.2
250 kVp photon 2.0
150 MeV proton 0.5
10 MeV proton 4.7
14 MeV neutron 100
18 MeV carbon 108
2.5 MeV alpha 166
75 MeV argon 250
2 GeV iron 1000

Optimal RBE as a function of LET at 100 keV/μm

DefinitionsEdit

  • =average energy locally imparted to medium
  • =track length

Relative Biological EffectivenessEdit

  • Relative Biological Effectiveness (RBE):[9]:115

DefinitionsEdit

  • =dose of 250 kVp x-rays
  • =dose of test radiation required to produce equal biological effect to

HypoxiaEdit

  • Oxygen enhancement ratio:[1]:237
  • OER Values:
    • photon 3
    • proton 3
    • neutron 1.6
    • energized ion 1
    • alpha 1

ReferencesEdit

  1. a b c d David S. Chang, Foster D. Lasley, Indra J. Das, Marc S. Mendonca, Joseph R. Dynlacht (2014). Basic Radiotherapy Physics and Biology. Springer. ISBN 9783319068411. 
  2. H. Awwad (2013). Radiation Oncology: Radiobiological and Physiological Perspectives. Springer. ISBN 9789401578653. 
  3. Beyzadeoglu, Murat, Ozyigit, Gokhan, Ebruli, Cüneyt (2010). Basic Radiation Oncology. Springer. ISBN 978-3-642-11665-0. 
  4. a b Roger G. Dale, Bleddyn Jones (2007). Radiobiological Modelling in Radiation Oncology. British Institute of Radiology. ISBN 9780905749600. 
  5. a b Lemoigne, Yves; Caner, Alessandra (2011). Radiation Protection in Medical Physics. Dordrecht: Springer. ISBN 9789400702479. 
  6. Levitt, S.H. (2006). Technical basis of radiation therapy : practical clinical applications ; with 146 tables (4th ed.). Berlin: Springer. p. 8. ISBN 978-3-540-21338-3. 
  7. Wambersie, A.; Menzel, H. G.; Andreo, P.; DeLuca, P. M.; Gahbauer, R.; Hendry, J. H.; Jones, D. T. L. (7 December 2010). "Isoeffective dose: a concept for biological weighting of absorbed dose in proton and heavier-ion therapies". Radiation Protection Dosimetry 143 (2-4): 481–486. doi:10.1093/rpd/ncq410. 
  8. Brahme, Anders (2014) (in en). Comprehensive Biomedical Physics. Newnes. p. 137. ISBN 9780444536334. https://books.google.co.uk/books?id=9RR0AwAAQBAJ&dq=isoeffective+dose+d1+d2&source=gbs_navlinks_s. 
  9. a b Hall, Eric J.; Giaccia, Amato J. (2006). Radiobiology for the radiologist (6th ed.). Philadelphia: Lippincott Williams & Wilkins. ISBN 9780781741514.