Basics of linear quadratic model
Download as PPTX, PDF5 likes2,181 views
1) The linear-quadratic (LQ) model is commonly used in clinical practice to model cell survival patterns after radiation exposure and calculate biologically equivalent doses. 2) While the LQ model reasonably predicts cell survival up to doses of around 10 Gy per fraction, it may overestimate biological effect at higher doses used in stereotactic radiotherapy. 3) Several modifications have been proposed to the LQ model to address its limitations at high doses, such as accounting for non-DNA targets and cell repopulation, but there is currently no clear alternative model.
![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]](https://image.slidesharecdn.com/linearquadraticmodelajeet-200510120457/85/Basics-of-linear-quadratic-model-5-320.jpg)
![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]](https://image.slidesharecdn.com/linearquadraticmodelajeet-200510120457/85/Basics-of-linear-quadratic-model-6-320.jpg)
Basics of linear quadratic model
- 1. α/β:Where does it stand today??
- 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. Targets
- 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. 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. 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. Linear cell survival and Quadratic cell survival
- 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. 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. 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. 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. So What`s the problem??
- 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. What happens when LQ Equation is used to calculate dose equivalence at high dose per fraction
- 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. 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. 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. Survival curve with LQ-L Model
- 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. 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. 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. 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. Thanks Do we have an alternative to LQ Model :No So we have to stay with it??