Photon Beam Dose Calculation
Kent A. Gifford, Ph.D.
Medical Physics III Spring 2010
Dose Computation Algorithms
Correction-based (Ancient!)
II. Convolution (Pinnacle,Eclipse,…)
III. Monte Carlo (Stochastic)
IV. Deterministic (Non-stochastic)
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
1. Wedges- WF, wedged profiles
2. Compensators- attenuation measurements
3. Blocks- OF
Contour Corrections
Attenuation corrections due to
“missing” tissue
1. Effective SSD Method
• Uses PDD. Assumes PDD independent of
SSD. Scales Dmax with inverse square factor.
Contour Corrections
2. TMR (TAR) Ratio Method
Exploits independence of TMR and SSD
More accurate than Effective SSD method.
Contour Corrections
3. Isodose Shift Method
Pre-dates modern treatment planning systems
Manual method; generates isodose curves for
irregular patient contours
Greene & Stewart. Br J Radiol 1965; Sundblom
Acta Radiol 1965
Contour Corrections
Contour corrections
4. Effective attenuation method
Corrects for average attenuation along beam
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 Corrections
Batho power law
Problems with correction-based
• 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
• Scatter photon
Dose from Scatter Interactions
• To calculate dose at a
single point:
– Must consider
contributions of energy
scattered from points
over the volume of the
Convolution: Volume segmented
into voxels (volume elements)
Dose spread array
Convolution Algorithm:
Heterogeneities Radiological path length
Convolution Algorithm
D r  
( r ' )  r '    ( r  r ' )d r '
Primary Energy Fluence - (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
D r  
( r ' )  r '    ( r  r ' )d 3r '
Mass Attenuation Coefficient
 /  (r’)
Fraction of energy removed from primary
photon energy fluence per unit mass
Function of electron density
D r  
( r ' )  r '    ( r  r ' )d 3r '
TERMA - T(r’)
Product of Ψ(r’) and μ/ρ(r’)
Total radiation Energy Released per MAss
T (r ' )  (r ' )  (r ' )
It represents the total amount of radiation energy
available at r’ for deposition
D r   
( r ' )  r '    ( r  r ' )d 3r '
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
D r  
( r ' )  r '    ( r  r ' )d 3r '
Iso energy distribution
lines.2’ interactions
Convolution Superposition
• Convolution equation is modified for actual
radiological path length to account for
Dr  
( r ' r ' )  r 'r '    ( r  r '( r  r ' ))d r '
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
•Energy that should be deposited
in voxel B’ from interactions at
the vertex of the lower cone is
deposited in voxel B and vice
•Approximation is less accurate at
large distances from cone vertex.
•Errors are small due to rapid falloff of point-spread functions
Behavior of dose calculation
algorithms near simple geometric
• 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
• 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
equilibrium? No
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
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
D r  
( r ' )  r '    ( r  r ' )d r '
Comparisons of Algorithms
Monte Carlo
and Convolution
Direct Monte Carlo Planning
Can model “everything”
Requires lots of histories
Accuracy improved by
tracing lots of particle
Computation times,
limited by computer
Linear Boltzmann Transport Equation (LBTE)
cross section
Obeys conservation of particles
• Streaming + collisions = production
Transport Examples
Methods and Materials (External beam-Prostate)
Transport Examples
Methods and Materials (External beam-Prostate)
Transport Examples
Results (External beam-Prostate)
Transport Examples
Methods and Materials (Brachytherapy-HDR)
Dimensions in cm
Attila (S16) vs. MCNPX
Run time*: 13.7 mins, 97% points w/in 5%, 89%
w/in ±3%
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 9 th international conference on the use of
computers in radiation therapy, Scheveningen, The Netherlands. North Holland: The Netherlands,
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.

Photon Beam Dose Algorithms