Biological Optimization of Hadrontherapy. Uwe Oelfke
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1 4/2/2012 page 1 Biological Optimization of Hadrontherapy Uwe Oelfke DKFZ Heidelberg (E040) Im Neuenheimer Feld Heidelberg, Germany u.oelfke@dkfz.de
2 4/2/2012 page 2 Contents Introduction and General Framework Objective function and physical/biological input Dose Delivery and Biological Optimization Oxygen Effect
3 4/2/2012 page 3 The HIT facility
4 Depth dose curves
5 Conformal Avoidance: Photons Protons C12 Photons Protons C12
6 Prostate Ca: Different Modalities
7 4/2/2012 page 7 The framework of biological optimization Physical optimization hadron therapy Dose constraints DVH constraints. Biological Optimization Biological effect: E Two main components Macroscopic model for the dose dependence of E Microscopic model describing the dependence of E on intrinisic radiation quality only E αd 2 βd
8 4/2/2012 page 8 Inverse Planing: Optimization Loop Treatment Parameters - DOF RBE Data Physical Dose, LET RBE Model Optimization Alg. Update of TP Objective Function Physical Photon Dose Biological Effect Clinical Experience
9 4/2/2012 page 9 Photons vs. DET protons Reduction of integral dose and lower dose levels
10 4/2/2012 page 10 Prostate Ca: DET Protonen vs. DET C12 DET Protons DET C12 C12 : + Steeper Gradient at Target Edge - Higher Integral Dose (Distal Tail)
11 4/2/2012 page 11 Physical Optimization with different types of radiation high Conformality IMPT IMHIT 3D PT IMXT 3D XRT low Integral dose high
12 high Differential RBE = RBE T /RBE HT IMPT IMHIT Conformality 3D PT IMXT?? 3D XRT Integral dose
13 4/2/2012 page 13 RBE and LET 9 kev/mm 25 kev/mm F = 25/A F = 9/A
14 4/2/2012 page 14 Spread-out Bragg Peak (SOBP)
15 4/2/2012 page 15 RBE-measurment
16 4/2/2012 page 16 RBE-results : LET dependency
17 4/2/2012 page 17 RBE-results: dose dependency
18 4/2/2012 page 18 Objective function Effect based objective function (LQ model): F 2 E (w) (E i(w) Epres ) i T Prescribed effect: E pres = a x D pres +b x D 2 pres Extend OF to OARs
19 4/2/2012 page 19 Superposition of many beamspots in voxel i: dose D i j w j D ij effect E (w) 2 i α i(w)d i(w) β i(w)d i(w) (a i and b i depend on radiation quality (energy (depth) of primary particles and tissue type)
20 4/2/2012 page 20 Mixed radiation averaging αij α i j w D j D i ij α ij derived from microscopic model or directly from experimental data energy (depth) dependend radiation quality from bixel j at voxel i Analogue for ij
21 4/2/2012 page 21 LET calculations dose-averaged LET 20 Monte Carlo simulations analytical LET model cf. Wilkens and Oelfke, Med. Phys. 30(5) 2003 LET [kev/µm] dose [a.u.] dose av. LET depth in water [cm] LET dose approximation: laterally constant LET LET(d, r) LET(d,0)
22 4/2/2012 page 22 Biological Optimization: Carbon Ions What microscopic model for a ij? What clinical endpoints? University Clinic/GSI/DKFZ approach Tumor (Chordoma, radioresistent) a x = 0.1 (1/Gy); (a/b) x = 2 Gy Healthy brain (late effects) same parameters Continous biological dose at tumor boundaries Microscopic model for a, b TRiP98 (LEM) GSI
23 4/2/2012 page 23 Dose and a as a function of depth Input for optimization: D ij and a ij a(depth, cell type) from measurements or biological models, e.g., LEM/TRiP98* dose (Gy) alpha (1/Gy) * Krämer and Scholz (2000) PMB 45, MeV/u carbon chordoma cells CHO cells depth (mm)
24 Alpha vs Distance to peak for different energies chordoma cells: a =0.1 Gy, b=0.05 (photons) 1,4 1,2 1 0,8 0,6 Alpha [ 1/ Gy] MeV MeV MeV MeV 0,4 0, Distance to Peak [mm]
25 4/2/2012 page 25 Biological Optimization : Dose Delivery SOBPS Multifield Optimization DET or 3D Scanning
26 4/2/2012 page 26 Results: biologically optimized SOBP dose (Gy), RBE x dose (GyE) present study TRiP / GSI dose depth (mm) RBE x dose carbon ions on chordoma cells
27 4/2/2012 page 27 Biologically optimized SOBP p eff. dose (GyE) p dose (Gy) p (RBE=1.1) C p (RBE=1.1) C depth (mm) depth (mm) Constant RBE: Carbon Protons?
28 4/2/2012 page 28 3D treatment planning for carbon ions RBE x dose (100% = 3 GyE) dose (100% = 1Gy) Single field plan 9314 spots Optimization time: ~10 min
29 4/2/2012 page 29 Multifield Optimization
30 4/2/2012 page 30 Multifield optimization: two opposing fields single field optimization multifield optimization carbon ions on chordoma cells dose (Gy), RBE x dose (GyE) RBE x dose dose RBE x dose dose depth (mm) both fields together depth (mm) one field only
31 4/2/2012 page 31 DET with normal (dose) optimization dose KonRad patient with clivus chordoma 5 beams, DET LET RBE dose
32 4/2/2012 page 32 DET with biological optimization dose RBE dose LET
33 4/2/2012 page 33 3D treatment planning for carbon ions RBE x dose (100% = 3 GyE) dose (100% = 1Gy) Single field plan 9314 spots Five fields (IM) DET* (3 layers) spots * Deasy ICCR 1997
34 4/2/2012 page 34 Differential RBE RBE increases with increasing LET Enhanced RBE within the tumor RBE increases with decreasing dose Enhanced RBE within normal tissue and OARs
35 4/2/2012 page 35 Example: Protons vs. Carbons ions eff. dose (GyE) RBE p (RBE=1.1) C depth (mm) C12 C12 (D=1Gy) depth (mm)
36 4/2/2012 page 36 The Oxygen Effect: TPS module for the optimization of Hypoxic Tumors
37 4/2/2012 page 37 Aim Create a TPS routine for carbon ions that optimizes the biological effect under consideration of the influence of the partial oxygen pressure (po 2 ) on radiosensitivity. Major Assumption: Volumetric images are available that represent tumor hypoxia and that large changes in hypoxia occur on a timescale shorter than the imaging to treatment end time.
38 4/2/2012 page 38 Radiosensitivity changes with po 2 Carlson et al.
39 4/2/2012 page 39 Change of HRF a with LET, data from Furusawa et al. (2000)
40 4/2/2012 page 40 Dose and LET of a primary carbon ion spread out Bragg peak (SOBP).
41 4/2/2012 page 41 Proposed Routine
42 4/2/2012 page Analytic LET model Carbon ion beam splits up into fragments inside the patient Fragments have a different mass and charge than original carbon ions i.e. stopping power changes Contribution of fragments to dose and LET cannot be neglected Proposing a simple model based on the power law for the range of protons. Based on: Bortfeld (1997) and Wilkens and Oelfke (2003)
43 4/2/2012 page 43 Depth dose and LET of a carbon ion beam Results of analytic calculations compared to Monte Carlo results.
44 4/2/2012 page 44 Maximum Hypoxia Reduction Factor (HRF) of carbon ions
45 4/2/2012 page 45 Simulate subvoxel oxygen distributions PET information on mm scale po 2 changes on µm scale: a) Assume that PET information can be converted to the mean po 2 of a voxel b) Simulate subvoxel oxygen distributions on a 2D grid by randomly placing capillaries and solving the partial differential equation for the oxygen diffusion and consumption. c) For each mean voxel po 2 we obtain an average subvoxel distribution (histogram) Petit et al. (2009)
46 4/2/2012 page 46 Subvoxel oxygen distributions Result of our own simulations displayed as in Petit et al. (2009)
47 4/2/2012 page 47 Calculate the HRF for a given po 2 and LET HRF K ( p, LET ) 1 r exp( s LET p K )
48 4/2/2012 page 48 Calculate LQ parameters a H and H for a given po 2 distribution and LET Total cell survival in a given subvoxel oxygen distribution for dose D: S ( D) i x i exp( ) HRF a a A 2 p, LET HRF p, LET i D A i D 2 Calculate total cell survival for doses from 0 Gy to 20 Gy Fit LQ model to the resulting cell survival curve Save fit parameters a H and H as a function of depth, initial carbon ion energy and po 2
49 4/2/2012 page 49 Table with a H and H HRF corrected a H as a function of depth for a 276 MeV/u carbon ions beam.
50 4/2/2012 page 50 PET intensity and voxel po 2 Currently used: Model by Chang et al. (2009) based on Fmiso PET localized Eppendorf electrode measurements in rats: xmax pi K 50 K 50 xi To calculate the po2 p i in voxel i. The PET value is x i and the maximum PET value in the tumor is x max Example from Chang et al. (2009)
51 4/2/2012 page 51 Summary Fast optimization method for ion beams based on the biological effect E=aD+bD² Multifield optimization improved sparing of normal tissues / OAR s possible for IM techniques Flexible biological input: a, b measured or from any radiobiological model can be used consideration of oxygen effect might be possible
52 4/2/2012 page 52 Challenges Robust biological optimization Organ motion, Setup uncertainties Uncertainties in biological input Locally variable RBE? Volume effect for photons? Do we need locally variable RBEs for protons?
53 4/2/2012 page 53 Risk adapted treatment planning Worst case optimization Uncertainties Range uncertainties Setup uncertainties Organ motion Dose calculations
54 4/2/2012 page 54 WCO -Idea Goal: Find a treatment plan which is still acceptable and robust under the influence of the anticipated uncertainties of treatment variables Example: Range uncertainties Calc. dose only for minimal, maximal and nominal range. Instead of calculating every possible combination of ranges, use worst case dose distribution as lower bound
55 4/2/2012 page 55 Worst Case Dose for range uncertainties Calculation of WorstCase Dose: Target: Store the minimal dose as WC-dose for each voxel OAR: Store maximal dose as WC-dose for each voxel
56 4/2/2012 page 56 Worst Case Optimization: To include the Worstcase dose distribution into the optimization, add another term to the objective function F: F new = F(dose) + wcp * F(wc_dose) F = standard objective function Dose =nominal dose distribution wc_dose=worstcase dose distribution wcp=worst case penalty (tuneable parameter)
57 4/2/2012 page 57 Example: 3 copl. IMPT beams Range uncertainty: 5 mm
58 4/2/2012 page 58
59 4/2/2012 page 59
60 4/2/2012 page 60 Range uncertainty: 5 mm pwc = 0 pwc = 1
61 4/2/2012 page 61 Setup uncertainties 2 mm pwc = 0 pwc = 1
62 4/2/2012 page 62 Range vs. Setup Uncertainties Range: 5 mm Setup: 0 mm
63 4/2/2012 page 63 Range vs. Setup Uncertainties Range: 5 mm Setup: 2 mm
64 4/2/2012 page 64 Range vs. Setup Uncertainties Range: 5 mm Setup: 5 mm
65 4/2/2012 page 65 Acknowledgement: J. J. Wilkens M. C. Frese
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