Monte Carlo methods in proton beam radiation therapy. Harald Paganetti

Transcription

1 Monte Carlo methods in proton beam radiation therapy Harald Paganetti

2 Introduction: Proton Physics Electromagnetic energy loss of protons Distal distribution Dose [%] p e p Ionization Excitation Interaction probability is proportional to proton energy depth [mm] Peak broadening due to range straggling

3 Introduction: Proton Physics Electromagnetic energy loss of protons Lateral distribution Multiple Coulomb scattering (small angles) p θ p 160 MeV 200 MeV

4 Introduction: Proton Physics p Nuclear interactions of protons p p p γ, n Elastic nuclear collision (large θ) Inelastic int. Nuclear interactions cause a decrease in fluence Nuclear interactions lead to secondary particles and thus to local dose deposition (secondary protons) non-local dose deposition (secondary neutrons)

5 Introduction: Monte Carlo Probability Density Function expresses the relative likelihood that a variable will have a certain value p p Monte Carlo f ( x) 0 on [ a, b] f ( x) dx= 1 e θ p p b a p p p p γ, n

6 Introduction: Monte Carlo

7 Introduction: Monte Carlo step size definition Condensed history algorithms group many charged particles track segments into one single condensed step grouped interactions elastic scattering on nucleus multiple Coulomb scattering soft inelastic collisions collision stopping power etc discrete interactions hard d-ray production energy > cut hard bremstrahlung emission energy > cut etc

8 Monte Carlo applications to proton radiation therapy Quality assurance Treatment head simulation Patient dose calculations Treatment head simulation Phase space calculations Patient (CT) simulations Clinical implementation Neutron dose calculations Treatment head simulation Patient simulations

9 Treatment Head Simulation Double scattering system Beam Aperture High-Density Structure Body Surface Target Volume Critical Structure Modulator Dose [%] Depth [mm]

10 Treatment Head Simulation Monte Carlo model of the nozzle (~1000 objects)

11 Monte Carlo model of the nozzle at the FHBPTC Treatment Head Simulation

12 Monte Carlo model of the nozzle at the FHBPTC Treatment Head Simulation

13 Treatment Head Simulation 4D Monte Carlo: Geometry changes during the simulation via C++ class architecture High Z Low Z

14 Range Modulator Wheel Issues Treatment Head Simulation 1. Beam Gating Dose [%] 2. Beam Current Modulation Beam range: cm Modulation: 6.78 cm Depth [mm] Dose [%] Beam range: cm Modulation: 6.78 cm Depth [mm]

15 Treatment Head Simulation Parameters to characterize the beam at nozzle entrance 1. Beam size and spread (IC measurement) 2. Beam angular spread (manufacturer info) 3. Beam energy (range!) (control system) 4. Beam energy spread (manufacturer info, measured) Are these parameters correlated?

16 Dose [%] N N D e p th [m m ] am Be 5 10 Si z e ma Sig am Be Siz ] [cm d] 0 a igm es [ra d] [ ra ] [cm 0.2 Beam Size Sigma [cm] Depth [cm] Angular Spread [rad] ad ad re Sp re Sp 40 Angular Spread [rad] 0 l ar gu An Dose [%] 20 l ar gu An Treatment Head Simulation Commissioning of the Monte Carlo Beam Size Sigma [cm] 30

17 Treatment Head Simulation Dose [%] Dose [%] Dose [%] Dose [%] depth [cm]

18 Aperture and Compensator Treatment Head Simulation

19 Aperture and Compensator Treatment Head Simulation Monte Carlo simulation based on milling machine files

20 Example: Quality Assurance / Tolerance Studies Alignment of second scatterer 120 Quality Assurance Dose [%] second scatterer aligned Depth [mm] Dose [%] Lateral distance to isocenter [mm] Dose [%] Dose [%] second scatterer tilted by 5 o Depth [mm] Lateral distance to isocenter [mm]

21 Treatment Head Simulation Phase Space plane Phase Space Format Example: (part, x, y, p x, p y, p z, flags )

22 Treatment Head Simulation Absolute dosimetry (output factor prediction) by simulating the ionization chamber output charge Volume for absolute dosimetry Output Factor [cgy / MU] cm < SOBP r < 15 cm Output Factor i Output Factor [cgy / MU] ic D cal i ic cgy MU e ε ic de = p dξdf W dx air 20 cm < SOBP r < 24 cm air (SOBP r - SOBP m ) / SOBP m (SOBP r - SOBP m ) / SOBP m

23 Monte Carlo dose calculation Patient Simulation Simulate a large number of particle histories until all primary and secondary particles are absorbed or have left the calculation grid Calculate and store the amount of absorbed energy of each particle in each region (voxel) The statistical accuracy of the dose is determined by the number of particle histories

24 HP1 Patient Simulation Patient information Example: CT scan: 134 CT slices, voxels/slice mm mm 1.25/2.5 mm Treatment planning grid: 2.0 mm 2.0 mm 2.5 mm Challenges: - Memory Consumption - Many boundary crossings

25 Slide 24 HP1 Harald Paganetti, 3/14/2008

26 CT conversion Hounsfield Units (HU) Patient Simulation HU Photon Planning System HU versus electron density Dose-to-water Density; Material comp. Density; Material comp. Proton Planning System HU versus rel. stopping power Dose-to-water Monte Carlo HU versus mass density HU versus material Dose-to-medium (tissue)

27 Patient Simulation HU conversion Group HU range Density Density Material [g/cm3] correction composition weights [%] (center of HU bin) H C N O Na Mg P S Cl Ar K Ca Ti 1 [ ; -951 ] [ -950 ; -121 ] [ -120 ; -83 ] [ -82 ; -53 ] [ -52 ; -23] [ -22 ; 7 ] [ 8 ; 18 ] [19 ; 79 ] [ 80 ; 119 ] [ 120 ; 199 ] [ 200 ; 299 ] [ 300 ; 399 ] [ 400 ; 499 ] [ 500 ; 599 ] [ 600 ; 699 ] [ 700 ; 799 ] [ 800 ; 899 ] [ 900 ; 999 ] [ 1000 ;1099 ] [ 1100 ; 1199 ] [ 1200 ; 1299 ] [ 1300 ; 1399 ] [ 1400 ; 1499 ] [ 1500 ; 1599 ] [ 1600 ; 1999 ] [ 2000 ; 3060 ] [ 3061 ; ] HU space is divided into 27 groups with members of each group sharing the same element composition but differ in mass density (4000 densities)

28 Patient Simulation Gantry Angle Position XYZ Rotation Pitch Roll Air Gap Gantry Couch ISO AP1A 0º 0º 1 AS1A 65º 270º 1 RS1A 305º 50º 1 RA1A 295º 0º 2 RS2A 300º 60º 2 AS2B 90º 270º 3

29 Patient Database Treatment Planning FOCUS/XiO Clinical Implementation Treatment Control System Treatment Head Geometry Beam Setup Patient Geometry Patient Setup Phase Space Calculation Dose Calculation Monte Carlo Dose Cube Monte Carlo Dose Cube FOCUS/XiO format FOCUS and XiO: Computerized Medical Systems Inc.

30 Example 1 Clinical Examples Case 1: Para-spinal tumor 176 x 147 x 126 slices voxels: x x mm 3

31 Proton dose in the presence of range uncertainty Clinical Examples

32 Proton dose in the presence of range uncertainty Clinical Examples

33 Clinical Examples Monte Carlo Pencil Beam 1 Gy(RBE) 3 Gy(RBE) 5 Gy(RBE) 7 Gy(RBE) 9 Gy(RBE) 11 Gy(RBE) 13 Gy(RBE) 15 Gy(RBE) 17 Gy(RBE) Range

34 Clinical Examples 10 Gy(RBE) 20 Gy(RBE) 30 Gy(RBE) 35 Gy(RBE) 40 Gy(RBE) 42 Gy(RBE) 44 Gy(RBE) 46 Gy(RBE) 48 Gy(RBE) Penumbra Dose homogeneity Range 1 Gy(RBE) 2 Gy(RBE) 3 Gy(RBE) 4 Gy(RBE) Dose-to-water Dose-to-tissue

35 Planned SOBP versus delivered SOBP Clinical Examples Dose [relative] Depth [cm] Dose [relative] Depth [cm]

36 Total DVH MC XiO Clinical Examples

37 Example 2 Clinical Examples Case 3: Maxillary sinus 121x121x101 slices voxels: x x mm 3 PTV A Critical Structure B C

38 PTV A Critical Structure B C Clinical Examples Monte Carlo Pencil Beam 2 Gy(RBE) 6 Gy(RBE) 10 Gy(RBE) 14 Gy(RBE) 18 Gy(RBE) 20 Gy(RBE) 22 Gy(RBE) 24 Gy(RBE) 26 Gy(RBE)

39 Clinical Examples 5 Gy(RBE) 10 Gy(RBE) 15 Gy(RBE) 20 Gy(RBE) 22 Gy(RBE) 24 Gy(RBE) 26 Gy(RBE) 28 Gy(RBE) 30 Gy(RBE) 1 Gy(RBE) 1.5 Gy(RBE) 2 Gy(RBE) 2.5 Gy(RBE) 3 Gy(RBE)

40 Clinical Examples 10 Gy(RBE) 20 Gy(RBE) 30 Gy(RBE) 40 Gy(RBE) 50 Gy(RBE) 60 Gy(RBE) 65 Gy(RBE) 70 Gy(RBE) 75 Gy(RBE) 2 Gy(RBE) 4 Gy(RBE) 6 Gy(RBE) 8 Gy(RBE) MC XiO

41 Neutron Dose Simulation Scattered dose as a function of lateral distance

42 Simulation of the radiation field entering the patient Neutron Dose Simulation External Internal Output: Neutrons leaving the treatment head Protons leaving the treatment head

43 Pediatric phantoms Lee, Lee, Williams, et al. Whole-body voxel phantoms of paediatric patients - UF Series B. Phys Med Biol. 51, (2006) Neutron Dose Simulation phantom number of voxels voxel dim (mm) X Y Z X Y Z 9 month old year old year old year old year old Adult

44 Neutron Dose Simulation From: Annals of the ICRP; ICRP Publication 92; Relative Biological Effectiveness (RBE), QualityFactor (Q), and Radiation Weighting Factor (w R )

45 Neutron Dose Simulation

46 Neutron Dose Simulation Organ equivalent dose thyroid (circles) lung (squares) liver (triangles)

47 References Proton Therapy Paganetti and Bortfeld: Proton Therapy. In: New Technologies in Radiation Oncology (Series: Medical Radiology; Subseries: Radiation Oncology); Eds. Schlegel, W.; Bortfeld, T.; Grosu, A.L.; ISBN ; Springer Verlag, Heidelberg 2005: Monte Carlo dose calculation Chetty et al., Report of the AAPM Task Group No. 105: issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning. Med Phys 2007: 34, Proton treatment head simulation Paganetti et al: Accurate Monte Carlo simulations for nozzle design, commissioning, and quality assurance in proton radiation therapy. Med Phys 2004: 31, Simulation of neutron doses in proton therapy Zacharatou Jarlskog et al: Assessment of organ specific neutron equivalent doses in proton therapy using computational whole-body agedependent voxel phantoms. Phys Med Biol 2008: 53, Monte Carlo code Geant4