VCU Radiation Oncology

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1 Quantitative Dosimetry Methods for Monte Carlo and Experimental Dosimetry Brachytherapy of Low-energy Brachytherapy Sources AAPM Summer School 19 July 2005 Jeffrey F. Williamson, Ph.D. Jeffrey F. Williamson, Ph.D. Virginia Commonwealth University Mark R. Rivard, Ph.D. Tufts-New England Medical Center VCU Radiation Oncology Virginia Commonwealth University

2 What is Quantitative Dosimetry? Williamson s definition: absorbed dose estimation method providing Accurate representation of well-defined physical quality Rigorous uncertainty analysis <10% uncertainty 0.5 to 5 cm in liquid water Traceable to NIST primary standards (S K,N99 ) Applications Single-source dose-rate arrays for TG-43 parameter determination ( Reference quality dose distributions) Direct treatment planning Validating semi-empirical algorithms

3 Outline Experimental Techniques TLD dosimetry: current standard of practice Emerging experimental techniques Monte Carlo-based dosimetry Results of TLD and MC dosimetry Uncertainty analysis Agreement

4 Quantitative Dosimetry Era: Tochlin: Film Dosimetry 1966 Lin & Kenny: TLD dosimetry in medium 1983 Ling: Diode dosimetry of I-125 seeds 1985 Loftus: I-125 exposure standard 1986 NIH ICWG contract Nath, Anderson, Weaver: Validation of TLD dosimetry 1983 Williamson: Monte Carlo dosimetry 1994 Task Group 43 Report

5 TLD dose measurements around 226 Ra Needle Lin and Cameron: Univ. of Wisconsin, 1965

6 Dosimetric Environment Large Dose Gradients Wide Range of Dose Rates Positioning accuracy needed for 2 % dose accuracy 2 mm Distance ±20 μm 5 mm Distance ±50 μm 10 mm Distance ±100 μm Large Number of Measurements Needed Low Photon Energies Relatively Low Dose Rates

7 Criteria for experimental dosimeters Signal stability and reproducibility Spatially and temporally constant Sensitivity (signal/dose) Free of fading, dose-rate effects Good signal-to-noise ratio (SNR) Small size, high sensitivity, large dynamic range Small size: avoid averaging dose gradients Large size: Good signal at low doses Good positioning accuracy Support measurements at many points

8 Sensitivity (10 cm)/sensitivity (1 cm) vs energy Sensitivity (reading/d wat ): 10 cm/1 cm LiF TLD Polyvinyl Toluene Silicon diode Energy (KeV)

9 Localization via Digital Dosimeters 2D dose distribution Profile A X c = (X 2 -X 1 )/2 Y Axis (mm) Y c A Dose (Gy) X c B X Axis (mm) X X c X 2 X Axis (mm) μm positional accuracy achievable

10 Solid Water Phantoms for TLD Dosimetry Transverse Axis Measurement Phantom Polar Dose Profile Measurement Phantom 90 o 120 o 60 o 135 o 45 o 160 o 20 o 180 o 0 o μm positional accuracy achievable

11 TLD Detectors Use TLD-100 LiF extruded ribbons ( chips ) 1 x 1 x 1 mm 3 at distances < 2 cm 3 x 3 x 0.9 mm 3 at distances 2 cm Use RMI 453 Machined Solid Water Phantom Composition (CaCO 3 + organic foam) not stable Either perform chemical assay or use high purity PMMA Annealing protocol 1 hour 400 C followed by 24 hours of 80 C pre-irradiation OR 1 hour 400 C pre-irradiation followed by 10 minutes at 100 C Post-irradiation

12 Source Solid Water Phantom Brachytherapy Dosimetry Detector at (x,y,z) Dose rate to Water at (x,y,z) R det ( r ) Given: Relative solid state dosimeter reading (TLD or Diode) Desired: D wat ( r ) absorbed dose to water Corrected for: Detector sensitivity Measurement vs reference geometry Radiation field Perturbation Detector response artifacts Liquid Water Reference Sphere

13 Brachytherapy Dose Measurement r r D (r) R (r) g(t) r S S E(r) BRx & wat det = K ε meas K λ ε λ = [ R det D med ] λ meas [ ] BRx at r E( r ) = R det D wat ε λ is measured Response in calibration beam, λ is relative detector response at r in Brachytherapy geometry S K = Measured Air-Kerma Strength g(t) = 1/effective exposure time (decay correction)

14 r R (r) = 1/n TLD TLD readings TL i is Measured Response of i-th detector at r F lin (TL) is non-linearity correction for net response TL S i is relative sensitivity of i-th detector derived from reading TLDs exposed to uniform doses TG-43 recommends n = 5-15 n i= 1 (TL TL ) i F lin S bkgd i

15 Relative Energy Response r E(r) = = [ TL(r) / D ] wat [ TL / D ] ε r BRx 0 ελ (TL 0 ) r (r) for Brachy Source med for Calibration Beam r (TL,r) for same TL 0 λ E(d) obtained by Measuring TLD response in free air as function of average energy in low energy x-ray beams Monte Carlo calculations Analytic calculations Generally assumed to be independent of position

16 ted ion chamber Scintillator Detector Compare detector to matched X-ray Beam calibration in Free-Air hυ = kvp TL = TLD mean net reading FS air K = measured air kerma hν Meas hν wat MC ( K D ) TL air E(r) = FS K c air repl c disp(r) ε λ D in medium crepl = 0.97 K in cavity wat FS wat r 1 c disp(r) D wat(r) at point r = r D wat(r')dv' ( ) V(r) r V(r)

17 Measured E factors Relative Energy Response Best fit line Reft 1988 Muench 1991 Hartmann 1983 Weaver 1984 Meigooni 1988b Photon energy (KeV) Conventional choice: E=1.4 w/o regard to details Hence, 2004 TG-43 has assigned 5% uncertainty to E 0.9

18 Monte Carlo Evaluation of E(d) E(d) Corrects for Measurement medium and geometry vs water Calibration medium vs. water Detector artifacts: Energy response, volume averaging, angular anisotropy, self attenuation Assume: Detector response energy imparted to active volume for beam qualities λ If R λ det r Then E(r) = =α D λ det [ ΔD (r)/ ΔD (r)] det r wat [ Δ Δ ] r D det / Dmed λ MC BRx MC

19 Measured vs. Calculated E(d) Davis 2003 and Das 1995 Relative Energy Response Measured/Monte Carlo Davis (3x3x0.4 mm 3 ) Das (3x3x0.9 mm 3 ) Das (1x1x1 mm 3 ) R = TL at energy λ λ λ air K = measured air α = λ kerma ( TL K ) λ air Meas λ air MC ( D K ) TLD Photon Energy (kev) Energy linearity of TLD is controversial

20 I-125 Seed E(d) in Solid Water Relative Energy Response: E(d) Chemical Analysis: 1.6% Ca RMI Specifications: 2.3% Ca { LiF Point Detector 1x1x1 mm 3 TLD-100 1x1x1 mm 3 TLD Distance (cm), d Solid-to-Liquid Water correction: 4%-15% at 1-5 cm 10-30% variations in SW composition reported: 5%-20% dosimetric errors

21 Summary: TLD phantom dosimetry 1-3 mm size precision: 2-5% above 1 cgy Energy response corrections Distance independent, excluding phantom corrections Energy linearity is controversial (<10%) Many corrections routinely ignored Widely-used SW phantom has uncertain composition High-purity industrial plastics recommended Extensive benchmarking of TLD vs Monte Carlo 3-10% agreement for Pd-103 and I-125 sources 7%-10% absolute dose measurement uncertainty

22 Other dosimetry systems Plastic scintillator (PS) and diode probes High sensitivity, small size, good SNR, and waterproof Single element detectors requiring water scanning system PS: established as transfer/relative dosimeter for beta sources» Large (30%) energy nonlinearity Diode: underutilized in presenter s opinion Energy linearity well established Large E(d) variation for medium energy sources Well established as relative dosimeter

23 Emerging Dosimetry Systems 2D RadioChromic Film Ir-192 HDR Source

24 Absolute RCF Dose Measurement vs Monte Carlo HDR 192 Ir Source RCF 2σ uncertainty: 4.6% 1.05 Dose [Gy] Away [cm]

25 Absolute RCF dosimetry for LDR Sources Cs-137: RCF/MC vs. Exposure-to-densitometry time interval Mean error vs dose 6 day exposure Very high 100 μm spatial resolution Fading artifacts not significant Energy linearity within 5%

26 Monte Carlo Simulation Typical Trajectory (r 1,Ω 1,E 1,W 1 ) r 1 Photon Collision (r 0,Ω 0,E 0,W 0 ) Ω 0,E 0 Ω 1,E 1 Ag Ag core r 3 Ω 2,E 2 Heterogeneity Ti capsule I-125 Seed Ω 3,E 3 Scoring Bin, ΔV

27 Monte Carlo Technical Issues Particle Collision Dynamics Total and differential cross sections for all collision processes and media Geometric Model Size, location, shape, composition and topology of of each material object Detector Model relationship between dose and collision density

28 Collisional Physics Requirements for Low- Energy Brachytherapy Only photon transport needed Secondary CPE obtains (Dose Kerma) Neutral-particle variance reduction techniques useful Comprehensive model of photon collisions NIST EXCOM or EPDL97 Cross sections are essential!! Coherent scattering and electron binding corrections» Use molecular/condensed medium form factors Characteristic x-ray emission from photo effect Approximations OK for some RTP applications Options: MCNP, EGSnrc and VCU s PTRAN_CCG

29 6711 silver rod end Electron microscopy Geometric Model Validation DraxImage I-125 Seed 6711 contact radiographs Contact Radiograph Final Model

30 300mm 250 mm diameter 153mm Long Wide-angle Free Air Chamber 80mm 150mm NIST Primary Standard interstitial sources photons < 50 kev Source 0.08 mm Al filter 1 mm thick tungsten collimator V V/2 0 (Guard Ring) K,99N 2 (I153 I 11)d = ρ air(v153 V 11) i S (W/e) k i 11 mm long, 250 mm ID electrode

31 Analog and Tracklength Dose Estimation Need cubic array of voxels: 3 3 1x1x1 mm to 2x2x2 mm j=1 S 1,4 ΔS 1,4 Analogue Estimator (EGS method) 2 3 r n+1 ( Ω n+1,e n+1 ) D2,3 from n+1 = Energy in - Energy out voxel mass 4 r n Expected Value Tracklength Estimator ( Ω n,e n ) Δs1,4 D 1,4 from n En vo xel volume ( ρ) μ en

32 Estimator Use Tracklength estimators 20-50X more efficient than analog Models volume averaging and medium replacement by extended detectors 3D patient (voxel array) calculations Next flight estimators: dose-at-a-point Condensed-medium dose calculations at least 1-2 mm from interfaces Dilute-medium (air) kerma calculations 0.1% - 2% statistical precision for I-125 dosimetry Kalli/Cashwell Once-more-collided Flux Point doses near media interfaces Energy imparted to small detectors

33 onte Carlo quantities for typical seed study ΔD (cgy/simulated photon): wat ab Bounded next-flight estimator for most distances { Transverse axis angular dose profiles ΔE Energy imparted to WAFAC volume/simulated photon Track-length estimator when fluence varies over detector Next-flight point dose estimator for TLD/diode detectors > 2 cm from source Δ K at geometric points { air in free air Transverse-axis angular fluence profile ( 30 cm) Track length for WAFAC Next-flight for transverse axis distribution

34 Calculation of TG-43 Parameters by MCPT MCPT calculates per disintegration within source: - Dose to medium, ΔD med (r), near source in phantom geometry: usually 30 cm liquid water sphere - Air-kerma strength, ΔS K, in free-air geometry usually 5 m air sphere or detailed model of calibration vault Λ= Δ D (r= 1cm, θ=π/2) wat wat ΔS K ΔD wat(r, π/2) G(1cm, π/2) g(r) = Δ D (1cm, π /2) G(r, π /2)

35 Calculation of ΔS K Extrapolated Point-Kerma method Place sealed source model at center of large air sphere Calculate air-kerma/disintegration, ΔK air (d), as function transverse axis distance, d Extrapolate to free-space geometry by curve fitting 2 d K ΔK & (d) d = ΔS (1+αd) e μ air Where ΔS K and α are unknowns (1 + αd) - SPR accounts for scatter buildup μ = primary photon attenuation coefficient

36 Models 200 ( 103 Pd), 6702 ( 125 I) and 6711 ( 125 I) Seeds Pb marker Graphite pellet Ti Capsule Resin spheres Ag Rod Ag-halide layer Model Pd distributed in thin (2-25 μm) Pd metal coating of right circular graphite cylinder Model I distributed on surface of radio transparent resin spheres Model I distributed in thin ( 3 μm) silver-halide coating of right circular Ag cylinder

37 Sharp corners and opaque coatings Thin Highdensity coating Low-density core Near transverse-axis: Anisotropic at long distances Isotropic at short distances Inverse square-law deviations High-density cylinder Anisotropic at long and short distances Circular ends contribute at 8 d 1 cm θ= tan = 2 d 0.3 d = 30 cm 1 L = Low-density core Isotropic at both long and short distances

38 Polar Anisotropy in Air (30 cm) 1.25 Polar K air profile (30 cm in air) Model 6702 I-125 Model 6711 I-125 Model 200 Pd Polar angle (degrees)

39 ΔS K : Point-Extrapolation Method 1.20 ΔK air (d) d 2 cgy cm 2 h -1 /(mci h) Model 200 ( 2 μm Pd) Pd-103 Model 6702 I-125 Model 6711 I-125 Data Points: MCPT Solid Lines: Fit Distance (cm)

40 WAFAC: Wide Angle Free-Air Chamber 250 mm diameter 153mm Long Collecting volume 300mm 100mm 150mm Source Rotating Seed Holder 0.08 mm Al filter 1 mm thick tungsten collimator 80mm V V/2 0 (Guard Ring) I

41 x ab WAFAC Simulation Method ( ΔEab ΔE ab ) d K inv att ρair (V153 V 11) Δ S = k k where Δ E = Energy absorbed/disintegration in WAFAC volume of length x k k att 2 kinv inv d = 38 cm = seed-to-wafac volume center ( ΔS K) extr { = for a point source Pd-103 ( K d ) = Δ I-125 WFC Φ( l) da A = inverse square correction = = Φ(d) A

42 Pd-103 Dose-Rate Constants Source Investigator Λ xxd,n99s TLD MC Extrap. MC WAFAC Point This work Model 200 (light) Model 200 (heavy) This work Nath 2000 ICWG 1989 This work ICWG NAS MED 3633 Li Wallace

43 Monte Carlo vs. TLD: 125 I Seeds 14 Seed models, 38 Candidate datasets dose-rate ratios, Monte Carlo / experimental distance, r [cm]

44 Monte Carlo/TLD Dose Rates: 125 I Seeds

45 Monte Carlo/TLD Dose Rates: 125 I Seeds

46 TLD and Monte Carlo Uncertainty Analysis

47 Monte Carlo vs TLD Measurement Pros and Cons Large uncertainties and many artifacts Tests conjunction of all a priori assumptions: seed geometry, detector response corrections, etc Monte Carlo Pros and Cons Artifact free and low uncertainty Garbage in-garbage out» Seed geometry errors» Will not anticipate contaminant radionuclides etc., S K errors Does not model detector signal formation

48 Conclusions Low energy brachytherapy: main catalyst for improving dosimetry and source standardization for 30 years Single-source dose distributions have 5% uncertainty Both MC and measurement have important roles Current Role Monte Carlo: primary source of dosimetric data Measurement: Confirm assumptions underlying Monte Carlo model Major needs: more accurate and efficient dosemeasurement systems for low energy sources Test source-to-source variations during manufacturing process