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Photon Beam Dose Calculation Algorithms

Photon Beam Dose Calculation Algorithms. Kent A. Gifford, Ph.D. Medical Physics III Spring 2010. Dose Computation Algorithms. Correction-based (Ancient!) Convolution (Pinnacle,Eclipse,…) Monte Carlo (Stochastic) Deterministic (Non-stochastic). Photon Source. Standard SSD. Patient

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Photon Beam Dose Calculation Algorithms

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  1. Photon Beam Dose Calculation Algorithms Kent A. Gifford, Ph.D. Medical Physics III Spring 2010

  2. Dose Computation Algorithms • Correction-based (Ancient!) • Convolution (Pinnacle,Eclipse,…) • Monte Carlo (Stochastic) • Deterministic (Non-stochastic)

  3. Photon Source Standard SSD Patient composition Patient SSD, Thickness Measurements Calculations (Correction Factors) Correction-based algorithms Water

  4. Correction-based:Semi-empirical • Empirical: Standard measurements • Analytical: Correction factors for: • Beam modifiers: shaped blocks, wedges… • Patient contours • Patient heterogeneities

  5. Measurements • Percent Depth Dose • Lateral Dose Profiles • Beam Output Measurements • Wedge Factor Measurements

  6. Generating Functions • Convert phantom dose to patient dose Examples: • Tissue-Phantom Ratio - Attenuation • Inverse square factor – Distance • Lookup tables, e.g. off-axis factors

  7. Generating Functions • Accurate ONLY in case of electronic equilibrium • Dmax and beyond • Far from heterogeneities Issues: • Small tumors in presence of heterogeneities • Small field sizes

  8. Beam Modifier Corrections • Must correct for attenuation through beam modifiers: 1. Wedges- WF, wedged profiles 2. Compensators- attenuation measurements 3. Blocks- OF

  9. Contour Corrections Attenuation corrections due to “missing” tissue • Effective SSD Method • Uses PDD. Assumes PDD independent of SSD. Scales Dmax with inverse square factor.

  10. Contour Corrections • TMR (TAR) Ratio Method • Exploits independence of TMR and SSD • More accurate than Effective SSD method.

  11. Contour Corrections • Isodose Shift Method • Pre-dates modern treatment planning systems • Manual method; generates isodose curves for irregular patient contours • Greene & Stewart. Br J Radiol 1965; SundblomActa Radiol 1965

  12. Contour Corrections

  13. Contour corrections • Effective attenuation method • Corrects for average attenuation along beam direction • Least accurate and easiest to apply

  14. Heterogeneity Corrections • One dimensional: 1. TMR ratio: CF=TMReff /TMRphysical • Corrects for primary photon attenuation • Not as accurate in heterogeneity proximity

  15. Heterogeneity CorrectionsBatho power law

  16. Problems with correction-based algorithms • Usually assume electronic equilibrium • Inaccurate near heterogeneities • Errors as large as 20% • Require copious measurements

  17. Convolution Algorithms • Rely on fewer measurements • Measured data: • Fingerprint to characterize beam • Model beam fluence • Energy deposition at and around photon interaction sites is computed

  18. Convolution: Explicitly Modeled Beam Features • Source size • Extrafocal radiation: • flattening filter, jaws,... • Beam spectrum– change with lateral position (flattening filter) • Collimator transmission • Wedges, blocks, compensators…

  19. r’ r Primary and Scatter Concepts • Two types of energy deposition events • Primary photon interactions. • Scatter photon interactions.

  20. Dose from Scatter Interactions • To calculate dose at a single point: • Must consider contributions of energy scattered from points over the volume of the patient. r’ r’ r’

  21. Convolution: Volume segmented into voxels (volume elements) Primary fluence(dose) Interaction sites Dose spread array

  22. Convolution Algorithm:Heterogeneities Radiological path length

  23. Convolution Algorithm

  24. Primary Energy Fluence - Y(r’) • Product of primary photons/area and photon energy • Computed at all points within the patient from a model of the beam leaving the treatment head

  25. Mass Attenuation Coefficientm / r (r’) • Fraction of energy removed from primary photon energy fluence per unit mass • Function of electron density

  26. TERMA - T(r’) • Product of Ψ(r’) and μ/ρ(r’) • Total radiation Energy Released per MAss • It represents the total amount of radiation energy available at r’ for deposition

  27. Convolution Kernel • Gives the fraction of the TERMA from a primary interaction point that is deposited to surrounding points • Function of photon energy and direction primary Iso energy distribution lines.2’ interactions

  28. Convolution Superposition Algorithm • Convolution equation is modified for actual radiological path length to account for heterogeneities

  29. Pinnacle Convolutions • Collapsed-cone (CC) convolution • Most accurate, yet most time consuming • Adaptive convolution • Based on gradient of TERMA, compromise • Fast convolution • Useful for beam optimization and rough estimates of dose

  30. Collapsed cone approximation • All energy released from primary photons at elements on an axis of direction is rectilinearly transported and deposited on the axis. • Energy that should be deposited in voxel B’ from interactions at the vertex of the lower cone is deposited in voxel B and vice versa. • Approximation is less accurate at large distances from cone vertex. • Errors are small due to rapid fall-off of point-spread functions

  31. Behavior of dose calculation algorithms near simple geometric heterogeneities • Fogliatta A., et al. Phys Med Biol. 2007 • 7 algorithms compared • Included Pinnacle and Eclipse • Monte Carlo simulations used as benchmark • 6 and 15 MV beams • Various tissue densities (lung – bone)

  32. Virtual phantom/irradiation geometry

  33. Types of algorithms considered • Type A: Electron (energy) transport not modeled • Type B: Electron transport accounted for (Pinnacle CC and Eclipse AAA).

  34. Depth dose, 15 MV, 4 cm off-axis, through “light lung”, Several algorithms • Problems with algorithms that do not model electron transport. • Electronic equilibrium? No problem. • Better agreement between Pinnacle CC and Monte Carlo than between Eclipse AAA and Monte Carlo.

  35. Conclusions • Type A algorithms inadequate inside • heterogeneous media, • esp. for small fields • type B algorithms preferable. • Pressure should be put on industry to produce more accurate algorithms

  36. Comparison of algorithms in clinical treatment planning • Knoos T, et al. Phys Med Biol 2006 • 5 TPS algorithms compared (A & B) • CT plans for prostate, head and neck, breast and lung cases • 6 MV - 18 MV photon energies used

  37. Conclusions – Algorithm comparisons for clinical cases • Prostate/Pelvis planning: A or B sufficient • Thoracic/Head & Neck – type B recommended • Type B generally more accurate in the absence of electronic equilibrium

  38. e- Monte Carlo(Gambling) σ γ Particle Interaction Probabilities

  39. Monte Carlo Example: • 100 20 MeV photons interacting with water. Interactions: • τ, Photoelectric absorption (~0) • σ, Compton scatterings (56) • π, Pair production events (44)

  40. Monte Carlo

  41. Indirect Use of Monte Carlo • Energy deposition kernels

  42. Comparisons of Algorithms Monte Carloand Convolution

  43. Direct Monte Carlo Planning

  44. FundamentalsLinear Boltzmann Transport Equation (LBTE) Sources Collision Streaming ↑direction vector ↑Angular fluence rate ↑position vector ↑particle energy ↑macroscopic total cross section extrinsic source ↑ ↑scattering source • Obeys conservation of particles • Streaming + collisions = production

  45. Transport ExamplesMethods and Materials (External beam-Prostate)

  46. Transport ExamplesMethods and Materials (External beam-Prostate)

  47. Transport ExamplesResults (External beam-Prostate)

  48. Transport ExamplesMethods and Materials (Brachytherapy-HDR) Dimensions in cm

  49. ResultsAttila (S16) vs. MCNPX Run time*: 13.7 mins, 97% points w/in 5%, 89% w/in ±3% *MCNPX: 2300 mins

  50. References (1/2) The Physics of Radiation Therapy, 2nd Ed., 1994. Faiz M. Khan, Williams and Wilkins. Batho HF. Lung corrections in cobalt 60 beam therapy. J Can Assn Radiol 1964;15:79. Young MEJ, Gaylord JD. Experimental tests of corrections for tissue inhomogeneities in radiotherapy. Br J Radiol 1970; 43:349. Sontag MR, Cunningham JR. The equivalent tissue-air ratio method for making absorbed dose calculations in a heterogeneous medium. Radiology 1978;129:787. Sontag MR, Cunningham JR. Corrections to absorbed dose calculations for tissue inhomogeneities. Med Phys 1977;4:431. Greene D, Stewart JR. Isodose curves in non-uniform phantoms. Br J Radiol 1965;38:378 Early efforts toward more sophisticated pixel-by-pixel based dose calculation algorithms. Cunningham JR. Scatter-air ratios. Phys Med Biol 1972;17:42. Wong JW, Henkelman RM. A new approach to CT pixel-based photon dose calculation in heterogeneous media. Med Phys 1983;10:199. Krippner K, Wong JW, Harms WB, Purdy JA. The use of an array processor for the delta volume dose computation algorithm. In: Proceedings of the 9th international conference on the use of computers in radiation therapy, Scheveningen, The Netherlands. North Holland: The Netherlands, 1987:533. Kornelson RO, Young MEJ. Changes in the dose-profile of a 10 MV x-ray beam within and beyond low density material. Med Phys 1982;9:114. Van Esch A, et al., Testing of the analytical anisotropic algorithm for photon dose calculation. Med Phys 2006;33(11):4130-4148.

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