Radiation Oncology/Radiobiology/Equations

Radiobiology Equations Tumor Growth Mitotic Index:Basic Radiotherapy Physics and Biology 9783319068411 David S. Chang, Foster D. Lasley, Indra J. Das, Marc S. Mendonca, Joseph R. Dynlacht Springer 2014252 Labeling Index: Growth fraction: Tumor volume doubling time: Potential doubling time: Cell loss factor: Gompertzian GrowthRadiation Oncology: Radiobiological and Physiological Perspectives 9789401578653 H. Awwad Springer 2013475 Progressively slowing: Small t (early): Large t (late): Definitions =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 Plating efficiency: Surviving fraction: Do not distinguish mode of death (mitotic vs apoptotic) Target theory Surviving fraction (single target-single hit):Basic Radiation Oncology Beyzadeoglu, Murat, Ozyigit, Gokhan, Ebruli, Cüneyt Springer 2010 978-3-642-11665-0 Surviving fraction (multiple target-single hit): Quasi-threshold dose:Radiobiological Modelling in Radiation Oncology Roger G. Dale, Bleddyn Jones British Institute of Radiology 2007 9780905749600 Definitions =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 Fraction of cells surviving single dose :228Lemoigne Yves Caner Alessandra Radiation Protection in Medical Physics 2011 Springer Dordrecht 978940070247931 Fraction of cells surviving fractions :31 Biologically Effective Dose (same RBE):230 BED for high LET radiation (RBE adjusted):268 BED (time adjusted):Levitt S.H. Technical basis of radiation therapy : practical clinical applications ; with 146 tables 2006 Springer Berlin 978-3-540-21338-3 8 4th Isoeffective dose:Wambersie A. Menzel H. G. Andreo P. DeLuca P. M. Gahbauer R. Hendry J. H. Jones D. T. L. Isoeffective dose: a concept for biological weighting of absorbed dose in proton and heavier-ion therapies Radiation Protection Dosimetry 7 December 2010 143 2-4 481–486 10.1093/rpd/ncq410Brahme Anders Comprehensive Biomedical Physics 2014 Newnes 9780444536334 137 https://books.google.co.uk/books?id=9RR0AwAAQBAJ&dq=isoeffective+dose+d1+d2&source=gbs_navlinks_s en Equivalent Dose in 2 Gy Fractions: Definitions =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 Tumor control probability (TCP) Definitions =number of fractions Linear Energy Transfer Linear Energy Transfer (LET):Hall Eric J. Giaccia Amato J. Radiobiology for the radiologist 2006 Lippincott Williams & Wilkins Philadelphia 9780781741514 6th106 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 =average energy locally imparted to medium =track length Relative Biological Effectiveness Relative Biological Effectiveness (RBE):115 Definitions =dose of 250 kVp x-rays =dose of test radiation required to produce equal biological effect to Hypoxia Oxygen enhancement ratio:237 OER Values: photon 3 proton 3 neutron 1.6 energized ion 1 alpha 1 References