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Dose Computation Algorithms

- Correction-based (Ancient!)
- Convolution (Pinnacle,Eclipse,…)
- Monte Carlo (Stochastic)
- Deterministic (Non-stochastic)

Photon Source

Standard SSD

Patient

composition

Patient SSD,

Thickness

Measurements

Calculations (Correction Factors)

Correction-based algorithmsWater

Correction-based:Semi-empirical

- Empirical: Standard measurements
- Analytical:

Correction factors for:

- Beam modifiers: shaped blocks, wedges…
- Patient contours
- Patient heterogeneities

Measurements

- Percent Depth Dose
- Lateral Dose Profiles
- Beam Output Measurements
- Wedge Factor Measurements

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 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

- 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

- 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

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…

r’

r

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.

r’

r’

r’

Convolution: Volume segmented into voxels (volume elements)

Primary fluence(dose)

Interaction sites

Dose spread array

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

primary

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)

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.

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

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

Example:

- 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

- Energy deposition kernels

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

Transport ExamplesMethods and Materials (External beam-Prostate)

Transport ExamplesMethods and Materials (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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