1. Radiation Therapy (RT)

2. What is cancer? Failure of the mechanisms that control growth and proliferation of the cells Uncontrolled (often rapid) growth of the tissue Formation of the tumor Metastasis; spread to distant locations

3. Tumor biology Tumors consist mainly from fully functional (mature) cells Clonogenic (stem) cells are capable of infinite proliferation and therefore responsible for tumor growth Dividing stem cells divides continuously and tumor is growing exponentially

4. Tumor biology Growth rate described by doubling time T d Potential doubling time (cell cycle period) Real doubling time (cell loses; up to 90%) Initial number of clonogen cells in individual volume element is N i =  i V i Number of clonogen cells after  T is

5. Cancer treatment Cancer usually treated by: Chemotherapy Surgery Radiation therapy Treated also by Hyperthermia Hormone therapy Molecular targeted therapy

6. Ionizing radiation effects Standard physical effects take place first Chemical reactions follows them Biological consequences Damage to the cell is mainly due to DNA damage Cell is considered to survive if unlimited reproductive potential is preserved

7. Dosimetry Dose (actually absorbed dose) is defined as energy absorbed per unit mass D=  E/  m Biological effects not due to increased temperature Lethal dose increases temperature by approximately 0.001 degree C

8. Radiobiology LQ survival curve Death from single hit Death from multiple sublethal hits

9. Number of clonogen cells Survival curve predict average number N of survived cells after irradiation of the cells One of the hypothesis says that All clonogen cells has to be eliminated to cure the tumor Cells follow Poisson statistics

10. Radiation therapy Use of ionizing radiation to kill cancer cells, while delivering as low dose as possible to normal tissue

11. How the systems look today…

12. How the systems work today… Conventional radiotherapy uses uniform beams that results uniform dose Technique that uses nonuniform beams can produce arbitrary dose distribution in tumor (IMRT)

13. How we plan today… Despite IMRT capabilities, uniform dose distribution is demanded

14. How we will plan in the future… Customized nonuniform dose distributions on a patient specific basis

15. Planning and imaging We may image Anatomy Functions or molecular processes Molecular imaging maybe gives us an answer how to shape the dose

16. Positron emission tomography Nuclear medicine medical imaging technique Produces a 3D image of molecular processes in the body

17. How PET works Production of radioisotope Bounding of radioisotope to some bioactive compound Injecting patient by that radiolabeled compound Imaging of spatial distribution of that compound

18. PET usage Delineation of the tumor volume and its stage (past and present use) In the future, probably very important tool for the assessment of: tumor clonogen cells density distribution oxygen status of the tumor tumor response to the radiation treatment

19. BCRT Planned dose distribution in target volume is not uniform, but tailored on patient specific basis Integral tumor dose is constrained Planned dose distribution should result highest probability to eliminate tumor Planned dose conforms to the spatial tumor biology distribution

20. Spatial biology distribution The only missing link in the BCRT chain Properties are phenomenologically characterized by: Clonogen density  Radiosensitivity  Redefined  =  ’[1+  ’/  ’ D];  ’,  ’ are LQ parameters Proliferation rate 

21. Local tumor kinetics Parameters for one volume element! S i is number of cells after something happens, relative to initial number Growth of the cells with time Killing the cells after irradiation

22. Local tumor control probability Taking into account growth and kill Initial number of clonogen cells in individual volume element is N i =  i V i Recalling equation for TCP from Poisson statistics

23. Local tumor control probability Probability to eliminate all cells in i-th volume element  T in interval between RT fractions

24. Global TCP maximization TCP for whole tumor is product of TCPs for each voxel Total dose to the tumor is constrained To maximize TCP, we construct Lagrangian

25. Solution of the optimization problem We assume that all volume elements are equal We choose reference radiobiological parameters  ref,  ref,  ref and reference dose D ref that would give sensible TCP

26. Special cases Constant radiobiology parameters implies uniform dose Not a surprise, just gives us confidence that method may be correct Variable clonogen density  Dose increases logarithmically with clonogen density.

27. Another two special cases Nonuniform radiosensitivity  Nonuniform proliferation rate  Dose increases linearly with proliferation rate. Dose is approximately inversely proportional to the radiosensitivity.

28. Conclusions The formalism proposed here is questionable because is based on an LQ model Not valid for high doses Presumes uniform dose distribution Formalism does not take into account Redistribution of the cells through cell cycle Reoxygenation of hypoxic cells It presumes that spatial distribution of biological parameters is known

29. Conclusions Formalism gives a rough overview how to optimally shape the dose distribution Simplistic (beginners) approach to the patient specific radiation therapy, which is believed to be future of RT by many renowned researchers.