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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

Photon Beam Dose Calculation Algorithms

Kent A. Gifford, Ph.D.

Medical Physics III Spring 2010

dose computation algorithms
Dose Computation Algorithms
  • Correction-based (Ancient!)
  • Convolution (Pinnacle,Eclipse,…)
  • Monte Carlo (Stochastic)
  • Deterministic (Non-stochastic)
correction based algorithms

Photon Source

Standard SSD



Patient SSD,



Calculations (Correction Factors)

Correction-based algorithms


correction based semi empirical
  • 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
Generating Functions
  • Convert phantom dose to patient dose


    • Tissue-Phantom Ratio - Attenuation
    • Inverse square factor – Distance
    • Lookup tables, e.g. off-axis factors
generating functions7
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
Beam Modifier Corrections
  • Must correct for attenuation through beam modifiers:

1. Wedges- WF, wedged profiles

2. Compensators- attenuation measurements

3. Blocks- OF

contour corrections
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 corrections10
Contour Corrections
  • TMR (TAR) Ratio Method
    • Exploits independence of TMR and SSD
    • More accurate than Effective SSD method.
contour corrections11
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 corrections13
Contour corrections
  • Effective attenuation method
    • Corrects for average attenuation along beam direction
    • Least accurate and easiest to apply
heterogeneity corrections
Heterogeneity Corrections
  • One dimensional:

1. TMR ratio: CF=TMReff /TMRphysical

      • Corrects for primary photon attenuation
      • Not as accurate in heterogeneity proximity
problems with correction based algorithms
Problems with correction-based algorithms
  • Usually assume electronic equilibrium
  • Inaccurate near heterogeneities
    • Errors as large as 20%
    • Require copious measurements
convolution algorithms
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
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



Primary and Scatter Concepts
  • Two types of energy deposition events
  • Primary photon interactions.
  • Scatter photon interactions.
dose from scatter 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
Convolution: Volume segmented into voxels (volume elements)

Primary fluence(dose)

Interaction sites

Dose spread array

primary energy fluence y r
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 coefficient m r r
Mass Attenuation Coefficientm / r (r’)
  • Fraction of energy removed from primary photon energy fluence per unit mass
  • Function of electron density
terma t r
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
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 Superposition Algorithm
  • Convolution equation is modified for actual radiological path length to account for heterogeneities
pinnacle convolutions
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
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
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)
types of algorithms considered
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
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
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
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


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)
indirect use of monte carlo
Indirect Use of Monte Carlo
  • Energy deposition kernels
fundamentals linear boltzmann transport equation lbte
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
results attila s 16 vs mcnpx
ResultsAttila (S16) vs. MCNPX

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

*MCNPX: 2300 mins

references 1 2
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
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.