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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 l.jpg

Photon Beam Dose Calculation Algorithms

Kent A. Gifford, Ph.D.

Medical Physics III Spring 2010


Dose computation algorithms l.jpg
Dose Computation Algorithms

  • Correction-based (Ancient!)

  • Convolution (Pinnacle,Eclipse,…)

  • Monte Carlo (Stochastic)

  • Deterministic (Non-stochastic)


Correction based algorithms l.jpg

Photon Source

Standard SSD

Patient

composition

Patient SSD,

Thickness

Measurements

Calculations (Correction Factors)

Correction-based algorithms

Water


Correction based semi empirical l.jpg
Correction-based:Semi-empirical

  • Empirical: Standard measurements

  • Analytical:

    Correction factors for:

    • Beam modifiers: shaped blocks, wedges…

    • Patient contours

    • Patient heterogeneities


Measurements l.jpg
Measurements

  • Percent Depth Dose

  • Lateral Dose Profiles

  • Beam Output Measurements

  • Wedge Factor Measurements


Generating functions l.jpg
Generating Functions

  • Convert phantom dose to patient dose

    Examples:

    • Tissue-Phantom Ratio - Attenuation

    • Inverse square factor – Distance

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


Generating functions7 l.jpg
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


Beam modifier corrections l.jpg
Beam Modifier Corrections

  • Must correct for attenuation through beam modifiers:

    1. Wedges- WF, wedged profiles

    2. Compensators- attenuation measurements

    3. Blocks- OF


Contour corrections l.jpg
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 l.jpg
Contour Corrections

  • TMR (TAR) Ratio Method

    • Exploits independence of TMR and SSD

    • More accurate than Effective SSD method.


Contour corrections11 l.jpg
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 l.jpg
Contour corrections

  • Effective attenuation method

    • Corrects for average attenuation along beam direction

    • Least accurate and easiest to apply


Heterogeneity corrections l.jpg
Heterogeneity Corrections

  • One dimensional:

    1. TMR ratio: CF=TMReff /TMRphysical

    • Corrects for primary photon attenuation

    • Not as accurate in heterogeneity proximity



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Problems with correction-based algorithms

  • Usually assume electronic equilibrium

  • Inaccurate near heterogeneities

    • Errors as large as 20%

    • Require copious measurements


Convolution algorithms l.jpg
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 l.jpg
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 l.jpg

r’

r

Primary and Scatter Concepts

  • Two types of energy deposition events

  • Primary photon interactions.

  • Scatter photon interactions.


Dose from scatter interactions l.jpg
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’


Convolution volume segmented into voxels volume elements l.jpg
Convolution: Volume segmented into voxels (volume elements)

Primary fluence(dose)

Interaction sites

Dose spread array


Convolution algorithm heterogeneities radiological path length l.jpg
Convolution Algorithm:Heterogeneities Radiological path length



Primary energy fluence y r l.jpg
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 l.jpg
Mass Attenuation Coefficientm / r (r’)

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

  • Function of electron density


Terma t r l.jpg
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 l.jpg
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


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Convolution Superposition Algorithm

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


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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 l.jpg
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 l.jpg
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 l.jpg
Virtual phantom/irradiation geometry geometric heterogeneities


Types of algorithms considered l.jpg
Types of algorithms considered geometric heterogeneities

  • 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 l.jpg
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.


Conclusions l.jpg
Conclusions Several algorithms

  • 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 l.jpg
Comparison of algorithms in clinical treatment planning Several algorithms

  • 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 l.jpg
Conclusions – Algorithm comparisons for clinical cases Several algorithms

  • 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 l.jpg

e- Several algorithms

Monte Carlo(Gambling)

σ

γ

Particle Interaction

Probabilities


Slide39 l.jpg

Monte Carlo Several algorithms

Example:

  • 100 20 MeV photons interacting with water. Interactions:

    • τ, Photoelectric absorption (~0)

    • σ, Compton scatterings (56)

    • π, Pair production events (44)


Monte carlo l.jpg
Monte Carlo Several algorithms


Indirect use of monte carlo l.jpg
Indirect Use of Monte Carlo Several algorithms

  • Energy deposition kernels


Comparisons of algorithms monte carlo and convolution l.jpg
Comparisons of Algorithms Monte Carlo Several algorithmsand Convolution


Direct monte carlo planning l.jpg
Direct Monte Carlo Planning Several algorithms


Fundamentals linear boltzmann transport equation lbte l.jpg
Fundamentals Several algorithmsLinear 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


Transport examples methods and materials external beam prostate l.jpg
Transport Examples Several algorithmsMethods and Materials (External beam-Prostate)


Transport examples methods and materials external beam prostate46 l.jpg
Transport Examples Several algorithmsMethods and Materials (External beam-Prostate)


Transport examples results external beam prostate l.jpg
Transport Examples Several algorithmsResults (External beam-Prostate)


Transport examples methods and materials brachytherapy hdr l.jpg
Transport Examples Several algorithmsMethods and Materials (Brachytherapy-HDR)

Dimensions in cm


Results attila s 16 vs mcnpx l.jpg
Results Several algorithmsAttila (S16) vs. MCNPX

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

*MCNPX: 2300 mins


References 1 2 l.jpg
References (1/2) Several algorithms

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 l.jpg
References (2/2) Several algorithms

  • 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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