Radiation Oncology/Radiobiology/Equations
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Radiobiology Equations
Tumor Growth
[edit | edit source]- 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):
- Progressively slowing:
Definitions
[edit | edit source]- =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 curves
[edit | edit source]- Plating efficiency:
- Surviving fraction:
Do not distinguish mode of death (mitotic vs apoptotic)
Target theory
[edit | edit source]- Surviving fraction (single target-single hit):[3]
- Surviving fraction (multiple target-single hit):
- Quasi-threshold dose:[4]
Definitions
[edit | edit source]- =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 model
[edit | edit source]- 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:
Definitions
[edit | edit source]- =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-response
[edit | edit source]- Tumor control probability (TCP)
Definitions
[edit | edit source]- =number of fractions
Linear Energy Transfer
[edit | edit source]- 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
Definitions
[edit | edit source]- =average energy locally imparted to medium
- =track length
Relative Biological Effectiveness
[edit | edit source]- Relative Biological Effectiveness (RBE):[9]:115
Definitions
[edit | edit source]- =dose of 250 kVp x-rays
- =dose of test radiation required to produce equal biological effect to
Hypoxia
[edit | edit source]- Oxygen enhancement ratio:[1]:237
- OER Values:
- photon 3
- proton 3
- neutron 1.6
- energized ion 1
- alpha 1
References
[edit | edit source]- ↑ 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.
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: CS1 maint: uses authors parameter (link) - ↑ H. Awwad (2013). Radiation Oncology: Radiobiological and Physiological Perspectives. Springer. ISBN 9789401578653.
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: CS1 maint: uses authors parameter (link) - ↑ Beyzadeoglu, Murat, Ozyigit, Gokhan, Ebruli, Cüneyt (2010). Basic Radiation Oncology. Springer. ISBN 978-3-642-11665-0.
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: CS1 maint: uses authors parameter (link) - ↑ a b Roger G. Dale, Bleddyn Jones (2007). Radiobiological Modelling in Radiation Oncology. British Institute of Radiology. ISBN 9780905749600.
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: CS1 maint: uses authors parameter (link) - ↑ a b Lemoigne, Yves; Caner, Alessandra (2011). Radiation Protection in Medical Physics. Dordrecht: Springer. ISBN 9789400702479.
- ↑ 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.
- ↑ 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.
- ↑ Brahme, Anders (2014). Comprehensive Biomedical Physics. Newnes. p. 137. ISBN 9780444536334.
- ↑ a b Hall, Eric J.; Giaccia, Amato J. (2006). Radiobiology for the radiologist (6th ed.). Philadelphia: Lippincott Williams & Wilkins. ISBN 9780781741514.