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Basics of linear quadratic model

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Basics of linear quadratic model

  1. 1. α/β:Where does it stand today??
  2. 2. Cell Kill • Radiation causes damage to the “target” • Target can be single or multiple • A lethal event for the cell can occur by the following ways – Single or multiple hits of single or multiple targets • A target in a cell could be the nucleus or the cytoplasm
  3. 3. Targets
  4. 4. Mathematical Models • These depict the survival patterns of studied cells exposed to a range of radiation doses. • Two basic models – Target model – Repair model • Most widely used in clinical practice – Linear-Quadratic model
  5. 5. Target models • Single hit - single target • Single hit – multi target • Two hit – single target [Quadratic ] • Two component model Single hit-single target + two hit-single target [Linear- Quadratic] Single hit-single target + single hit-multiple target [Multi- Target]
  6. 6. Single hit on a target S = e-D/D0 = e-αD Single hit and multiple hits on targets S = e-αD-βD2 Multiple hits on a target S = e-βD2 Single hit/target + Single hit on multiple targets S=e-D/1D0[1-(1-e-D/D0)n]
  7. 7. Linear cell survival and Quadratic cell survival
  8. 8. Concept of α & β • α : Component of killing which is proportional to the dose • β : Component of killing which is proportional to square of the dose. • S = e -αD- βd 2 and α/β ratio is the dose at which linear and quadratic components of killing are equal • E/α = BED = (1 + d / (α/β)) * D = RE * D Relative Effectiveness (RE)
  9. 9. LQ MODEL IS APPROPRIATE • Assumptions: – Cell killing is primarily a result of DNA damage (DSBs) – For multifractionated treatment, the fractions are well separated in time – Irradiation time for EBRT is short and with a constant dose rate – α/β for tumour is 10 Gy, and for late complications is 3 Gy – No tumour repopulation occurs within 2 weeks, and – LQ modelling is valid up to 23 Gy per fraction
  10. 10. LQ MODEL: Hypo fractionated Treatments  In vitro studies: LQ Model fits well between 0-16 Gy *Garcia LM et al Phys Med Biol 2006;51:2813–2823  In Vivo studies :Also shows that LQ model reliably predicts dose response between 2-20 Gy Barendsen GW et al. Int J Radiat Oncol Biol Phys 1982;8:1981–1997 Van der Kogel AJ. Radiat Res Suppl 1985;8:S208–S216 Peck JW, Gibbs FA. Radiat Res 1994;138:272–281
  11. 11. α/β values: fixed or changing?? • Traditional concept: – α/β for rapidly proliferating tissues and tumor – α/β for slowly proliferating tissues and late responding tissues • Recent concept: – α/β values depend on the end points chosen and also proliferating capacity of tumors – α/β =3.5 Gy for AV malformations and for <3 cm 4.6-6.4 Gy* – α/β =1.5-2 Gy $ for for biochemical failure in prostate cancers and another study reported as α/β >30 Gy # – α/β =8.5 for well oxygenated and 15.5 for hypoxic colonogens of prostate cancer@ *Kocher M et al. Radiotherapy and oncology 2004;71:109-114 # Richard Shaffer et al. Int. J. Radiation Oncology Biol.Phy. 2011;79;4:1029-36 $ Bentzen M Soren et al. Radiotherapy and oncology. 2005;76:1-3 @ Nahum A E et al. Int. J. Radiation Oncology Biol.Phy. 2003;57;2:391-401
  12. 12. So What`s the problem??
  13. 13. LQ Model: Application in SRT and SBRT  Leith JT et al*. calculated the radiation doses required to control metastatic brain lesions using data from in vitro survival curves. – Found that the calculated dose required to obtain a high tumour control probability was at least 25 to 35 Gy Vs 15-20 Gy (clinical doses)  Karlson et al**. Found in the treatment of Arterio-venous malformations that 42 Gy/12# was more effective than the equivalent dose of 15 Gy/1# by LQ model *Acta Neurochir Suppl 62:1827,1994. **Neurosurg 57:42-49, 2005
  14. 14. What happens when LQ Equation is used to calculate dose equivalence at high dose per fraction
  15. 15.  Radiation Effect on Vasculature and supporting cells:  Ionizing radiation can damage supporting tissue such as microvasculature, mainly at high doses  Vascular endothelial damage is triggered above 10 Gy per fraction secondary to the activation of acid sphingomyelinase*,# *Garcia-Barros M et al. Science 300:1155-1159, 2003 # Fuks Z et al. Cancer Cell 8:89-91, 2005  Radiation Effects on tumor stem cells:  Relatively radio resistant Stem cell play a role in malignant gliomas and other tumors  Stem cells have a radiation threshold after which they die (Usually >17-18 Gy)** **Chang HJ, et al. Nat Med 11:484-490,2005
  16. 16. Modifications of LQ Model  LQ-L Model: Accounts for high dose per fraction # # Guerrero M et al. Phys Med Biol 49;4825-4835;2004  Biophysical Models: To take in to account the dynamic interaction of radiation and tissues* – Γ-LQ Model (Kinetic model), *Scheidegger S, et al. Z Med Phys .2011 Sep;21(3):164-73. 2011  LQ-R Model: Accounts Redistributions and Re-oxygenation** ** Brenner D J et al,Int. J. Radiation Oncology Biol. Phys.1995;32;2:379-390
  17. 17. Modifications of LQ Model (Cont..)  Modified LQ Model : Accounts for increased overall treatment time E = - ln S = n * d (α + βd) - γT Including T ("kick off time") which allows for a time lag before the tumor switches to the fastest repopulation time:  LQ Model for Low dose rate brachytherapy: Where g represents how much less effective the repairable component has become
  18. 18. Survival curve with LQ-L Model
  19. 19. • Adds up the LQ and the Multi target model. • Gives Equivalent functions: SFED (Single fraction equivalent dose),BED and SED (standard effective dose) for comparison of various SBRT regimens
  20. 20. LQ Model: High LET vs. Low LET Radiation • Assumes high LET radiation affects α co-efficient of damage more than β co-efficient. • Introduced a new parameter RBEM αH=αLRBEM
  21. 21. LQ Model: Conclusion I  It is a mechanistic, biologically-based model.  It has sufficiently few parameters to be practical  It is reasonably well validated, experimentally and theoretically, up to about 10 Gy /fraction, and would be reasonable for use up to about 18 Gy per fraction  To date, there is no evidence of problems when LQ has been applied in the clinic within above constraints.
  22. 22. LQ Model: Conclusion II  It does not take in to account the non-DNA targets of radiation.  It overestimates the BED at doses used in SBRT and SRT treatments.  It can not be used to equate doses between high LET and low LET radiations  It does not take in to account the cell kinetics and interaction of radiation with other factors.
  23. 23. Thanks Do we have an alternative to LQ Model :No So we have to stay with it??

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