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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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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 SSD,



Calculations (Correction Factors)

Correction-based algorithms



  • Empirical: Standard measurements

  • Analytical:

    Correction factors for:

    • Beam modifiers: shaped blocks, wedges…

    • Patient contours

    • Patient heterogeneities


  • Percent Depth Dose

  • Lateral Dose Profiles

  • Beam Output Measurements

  • Wedge Factor Measurements

Generating Functions

  • Convert phantom dose to patient dose


    • Tissue-Phantom Ratio - Attenuation

    • Inverse square factor – Distance

    • Lookup tables, e.g. off-axis factors

Generating Functions

  • Accurate ONLY in case of electronic equilibrium

    • Dmax and beyond

    • Far from heterogeneities


    • Small tumors in presence of heterogeneities

    • Small field sizes

Beam Modifier Corrections

  • Must correct for attenuation through beam modifiers:

    1. Wedges- WF, wedged profiles

    2. Compensators- attenuation measurements

    3. Blocks- OF

Contour Corrections

Attenuation corrections due to “missing” tissue

  • Effective SSD Method

    • Uses PDD. Assumes PDD independent of SSD. Scales Dmax with inverse square factor.

Contour Corrections

  • TMR (TAR) Ratio Method

    • Exploits independence of TMR and SSD

    • More accurate than Effective SSD method.

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

Contour Corrections

Contour corrections

  • Effective attenuation method

    • Corrects for average attenuation along beam direction

    • Least accurate and easiest to apply

Heterogeneity Corrections

  • One dimensional:

    1. TMR ratio: CF=TMReff /TMRphysical

    • Corrects for primary photon attenuation

    • Not as accurate in heterogeneity proximity

Heterogeneity CorrectionsBatho power law

Problems with correction-based algorithms

  • Usually assume electronic equilibrium

  • Inaccurate near heterogeneities

    • Errors as large as 20%

    • Require copious measurements

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

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…



Primary and Scatter Concepts

  • Two types of energy deposition events

  • Primary photon interactions.

  • Scatter photon interactions.

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.




Convolution: Volume segmented into voxels (volume elements)

Primary fluence(dose)

Interaction sites

Dose spread array

Convolution Algorithm:Heterogeneities Radiological path length

Convolution Algorithm

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

Mass Attenuation Coefficientm / r (r’)

  • Fraction of energy removed from primary photon energy fluence per unit mass

  • Function of electron density

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

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


Iso energy distribution lines.2’ interactions

Convolution Superposition Algorithm

  • Convolution equation is modified for actual radiological path length to account for heterogeneities

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

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

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)

Virtual phantom/irradiation geometry

Types of algorithms considered

  • Type A: Electron (energy) transport not modeled

  • Type B: Electron transport accounted for (Pinnacle CC and Eclipse AAA).

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.


  • 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

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

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


Monte Carlo(Gambling)



Particle Interaction


Monte Carlo


  • 100 20 MeV photons interacting with water. Interactions:

    • τ, Photoelectric absorption (~0)

    • σ, Compton scatterings (56)

    • π, Pair production events (44)

Monte Carlo

Indirect Use of Monte Carlo

  • Energy deposition kernels

Comparisons of Algorithms Monte Carloand Convolution

Direct Monte Carlo Planning

FundamentalsLinear Boltzmann Transport Equation (LBTE)




↑direction vector

↑Angular fluence rate

↑position vector

↑particle energy

↑macroscopic total cross section

extrinsic source ↑

↑scattering source

  • Obeys conservation of particles

    • Streaming + collisions = production

Transport ExamplesMethods and Materials (External beam-Prostate)

Transport ExamplesMethods and Materials (External beam-Prostate)

Transport ExamplesResults (External beam-Prostate)

Transport ExamplesMethods and Materials (Brachytherapy-HDR)

Dimensions in cm

ResultsAttila (S16) vs. MCNPX

Run time*: 13.7 mins, 97% points w/in 5%, 89% w/in ±3%

*MCNPX: 2300 mins

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.

References (2/2)

  • Fogliatta A, et al. On the dosimetric behaviour of photon dose calculation algorithms in the presence of simple geometric heterogeneities: comparison with Monte Carlo calculations. Phys Med Biol. 2007; 52:1363-1385.

  • Knöös T, et al. Comparison of dose calculation algorithms for treatment planning in external photon beam therapy for clinical situations. Phys. Med. Biol. 2006; 51:5785-5807.

  • CC Convolution

  • Ahnesjö A, Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media. Med. Phys. 1989; 16(4):577-592.

  • Mackie TR, Scrimger JW, Battista JJ. A convolution method of calculating dose for 15-MV x-rays. Med Phys 1985; 12:188.

  • Mohan R, Chui C, Lidofsky L. Differential pencil beam dose computation models for photons. Med Phys 1986; 13:64.

  • Lovelock DMJ, Chui CS, Mohan R. A Monte Carlo model of photon beams used in radiation therapy. Med Phys 1995;22:1387.

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