Moyers

PTCOG 2010

Basic Interactions for Light Ion Beam Treatments: Penetration

Michael F. Moyers

Moyers

PTCOG 2010

Objectives

1. Describe the underlying physical processes that shape the depth dose curves for different particles.

2. Describe various parameters associated with energy and range.

3. Provide example sources and magnitudes of uncertainties for light ion penetration into a patient.

Moyers

PTCOG 2010

Assumptions

This presentation assumes the audience is familiar with:» ionization and stopping powers» multiple Coulombic scattering» bremstrahlung» nuclear reactions

The purpose of the presentation is to give the audience a "feel" for the magnitudes of the effects and how they influence light ion treatments.

Moyers

PTCOG 2010

Material for Presentation

Much of the material used in this presentation was taken from the forthcoming book:» Moyers, M. F. Vatnitsky, S. M. "Practical

Implementation of Light Ion Beam Treatments" (Medical Physics Publishing, Wisconsin, 2011)

Moyers

PTCOG 2010

Rationale for Light Ion Treatments

1. The dose delivered to non-target tissues relative to the dose delivered to target tissues is lower than for other radiation beams due to the depth dose distribution.

2. The lateral and distal dose gradients are higher than for other radiation beams enabling better splitting of the target and normal tissues.

3. For ions heavier than helium, a differential RBE with depth results in a higher effective dose in target tissues compared to surrounding normal tissues.

Moyers

PTCOG 2010

Depth Dose Distributions - Non-modulated[all distributions normalized to maximum dose]

Moyers

PTCOG 2010

Processes that Determine theShape of the Depth Dose Distribution

++++++++++otail fromsecondary particles

++++++++++buildup fromsecondary particles

++++++onuclearattenuation

+++++++radiation head scatter

ooooo+bremstrahlung

++++++++++++++straggling from multiple heterogeneity paths

++++++++++straggling from multiple scattering paths

++++++straggling from stochasticenergy losses

ooooo+++increasing obliquityfluence buildup

++++++++++++++++increasing stopping power with decreasing energy

Fe-56C-12He-4anti-HH-1eParticle

Moyers

PTCOG 2010

Electronic Stopping PowerVersus Energy and Particle

rule of thumb -

Stopping power of highest energy (clinically used) proton beam is

twice that of electrons; i.e.

4 MeV/cm instead of 2 MeV/cm.

Moyers

PTCOG 2010

Speed of Particles

1070.7350924.240.58216.62.191.0088.830.0

1540.5826216.560.45115.12.051.0021.810.0

2470.44131410.90.3458.61.901.005.903.0

3950.3471117.80.2531.81.820.982.041.0

6770.2536430.50.1816.31.920.910.740.3

11190.1819649.70.148.832.090.800.340.1

stoppingpower

[MeV/cm]

relativespeed [v/c]

energy[MeV]

stoppingpower

[MeV/cm]

relativespeed [v/c]

energy[MeV]

stoppingpower

[MeV/cm]

relativespeed [v/c]

energy[MeV]

range[cm]

carbon-12protonelectron

Moyers

PTCOG 2010

Proton Depth Dose Curve -Ionization Loss Only Along Path

max S / ent S≈ 185:1

CSDApeak/entrance

≈ 29:1

measuredpeak/entrance

≈ 4:1

Moyers

PTCOG 2010

Electron Depth Dose Curve -Ionization Loss Only Along Path

max S / ent S≈ 27:1

CSDApeak/entrance

≈ 2.5:1

measuredpeak/entrance

≈ 1.1:1

Moyers

PTCOG 2010

Straggling from StochasticEnergy Losses

ICRU 36 / Paretzke 1980

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PTCOG 2010

Straggling from MultipleParticle Paths

10 MeV electrons50 histories

80 MeV protons50 histories

150 MeV/n carbon ions500 histories

MCNPX simulations

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PTCOG 2010

Straggling from MultiplePaths Through Heterogeneities

ions traversing different paths encounter different water equivalent materialsions scattered toward the CAXhave traversed equivalent water equivalent pathlengths but stop at different physical depths; i.e. the dose deposition with respect to depth is not coherent

Moyers

PTCOG 2010

Straggling from MultiplePaths Through Heterogeneities

Urie et al., 1983

Moyers

PTCOG 2010

Electron Depth Dose Curve -Multiple Processes

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PTCOG 2010

Depth Number Distribution /Depth Dose Distribution

Moyers et al., 2007

Moyers

PTCOG 2010

End of Range / Peak Region Magnified

Moyers et al., 2007

Moyers

PTCOG 2010

Range of Protons in Non-modulatedBeam and Number of Protons Lost

rule of thumb -

for every cm of depth, ≈ 1% of

protons undergo nuclear reaction

Moyers et al., 2007

Moyers

PTCOG 2010

Range of Carbon Ions in Non-modulated Beam and Number of Carbon Ions Lost

rule of thumb -

for every cm of depth, ≈ 4% of

carbon ions undergo nuclear

reactions

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PTCOG 2010

Example Range Modulation Scheme

energy stacking from acceleratorenergy stacking via rangeshiftingrotating stepped propellorrotating stepped propellor with flux modulationstationary ridge filterstationary cones

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PTCOG 2010

Effect of Energy Spread on Depth Dose Distribution

increased energy spread →» increased entrance dose» rounding at proximal mesa» rounding at distal mesa» increased distal penumbra

Hsi et al., 2009

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PTCOG 2010

Distal Penumbra

250 MeVsynchrotron with direct energy extraction205 MeV cyclotron with rangeshifterand slit

Hsi et al., 2009

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PTCOG 2010

Various Range Parameters

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PTCOG 2010

Uncertainties in Penetration

patient information

beam delivery

mitigated by planning techniques

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PTCOG 2010

CT Number Dependencies

scanner calibrationkVp, filter, and FOVvolume and configuration of patientposition in scanartifactsimplants

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PTCOG 2010

CT Number Scaling

XCTNmat - XCTNwat SXCTN = + 1 x 1000

XCTNwat - XCTNair

Wrightstone et al., 1989

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PTCOG 2010

Uncertainties in Stopping Powers

range in water» ICRU 49 (1993) versus Janni (1982)

≈ 4 mm different at 250 MeV (≈1%)» several studies have shown the I-value is closer to the 81.77 eV

used by Janni than the 75.0 eV used by ICRU 49

Relative Linear Stopping Power for protons» Moyers et al. (1992): tissue substitutes and ancillary equipment -

calculated/literature versus measured 0.4 - 3.3%» Schneider et al. (1996): tissues - calculated/literature versus

measured 1.6%» small energy dependence (ignored in most TPSs)

≤ ±1% for z<13 between 30 and 250 MeV» almost no dependence on ion species

Moyers

PTCOG 2010

Uncertainties in Converting CT # to RLSP

for std. tissues, CT # to RLSP≤ 1.6%

for some other materials, CT # to RLSP>> 1.6%

Moyers

PTCOG 2010

Uncertainties in Penetration -Patient Information Related

± 2.2± 3.5--Total(soft tissues only)

± 0.5MC± 1.2-± 1.2%energy dependence ofRLSP for low Z

± 1.6± 1.6-± 1.6%WEQ vs RLSP(soft tissues only)

± 1.0%± 1.0%contour and substitute

± 0.0 to 3.0%RLSP of tissues anddevices

± 0.5%± 1.0%-± 1.0%stopping powerof water

± 5.0% metal*± 5.0% metal*z ≤ 22 - MVXCTz > 22 - substitution

100%metal implants

± 0.5% waterDE*± 0.8% tissueDE

> ± 1.0% boneDE*

± 1.5% water*± 2.5% tissue

> ± 3.0% bone*

-± 1.5% water± 2.5% tissue> ± 3.0% bone

position in scan

± 0.0%± 0.0%patient specificscaling

± 2.5%volume andconfiguration scanned

± 0.0%± 0.0%use only calibratedconditions

± 2.0% PMMA, PC> ± 2.0% bone

kVp, filter, andFOV selection

± 0.0%± 0.0%patient specificscaling

± 0.3% day-to-dayscanner calibration forstandard conditions

possible future uncertainty

uncertaintyafter mitigation

mitigationuncertaintybefore mitigation

cause

* ≡ not considered in totalDE ≡ dual energy CTMC ≡ Monte Carlo calc.

Moyers et al., 2009

Moyers

PTCOG 2010

Uncertainties in MeasuringStandard Range in Water

• water tank window ± 0.008 mm• parallel plate chamber waterproof lid ± 0.036 mm• parallel plate chamber front wall ± 0.044 mm• setting of reference depth with spacer ± 0.3 mm• calibration of water tank scanning

mechanism ± 0.23 mm• backlash in water tank scanning

mechanism ± 0.3 mm• rigidity and tilt of ion chamber mount on

scanning mechanism ± 0.3 mm

• total range uncertainty ± 0.571 mm

Moyers

PTCOG 2010

Uncertainties in Bolus WaterEquivalent Thickness

bolus material density (with lot sampling) ± 0.5% → 0.4 mmbolus manufacturing ± 0.3 mmbolus voids (with CT sampling) and/or contamination ± 0.5 mm» will not be everywhere

total bolus: ((0.4 + 0.3)2 + 0.52)0.5 ± 0.9 mm

Moyers

PTCOG 2010

Alignment Devices

face masks» unlikely that holes and net will cover same anatomical

location as when CT scan and plan were performed » ± 1 mm

table tops and pods» materials often do not lie on the CT number to RLSP

conversion curve» ± 1 mm

Moyers

PTCOG 2010

Energy/Range Accuracy Requirements

absolute accuracy» Monte Carlo or analytical based planning

reproducibility» measured depth dose curve used in planning» TPS planned versus treatment delivered» adequate tumor coverage» distal blocking of normal tissues» patch field combinations

relative accuracy» energy stacking

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PTCOG 2010

Simulated Treatment IncludingVarious Errors

selection of average beam flux levelflux fluctuations during deliverynoise on flux monitor electronicsspot positionsbeam range

Yang et al., 2003

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PTCOG 2010

Sample Simulation Results[all curves for random energy error selected over 0.2 MeV]

Yang et al., 2003

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PTCOG 2010

Energy Accuracy Requirements

energy stacking for proton range modulation» uniform mesa requires relative accuracy of 0.1 MeV at 70

MeV and 0.25 MeV at 250 MeV (i.e. at 70 MeV a 2.3 MeVjump must actually be a 2.2 to 2.4 MeV jump)

Moyers

PTCOG 2010

Uncertainties in Delivering CorrectEnergy or Range During Treatment

• synchrotron under normal operation, small deviations (microns)

• when a component fails, can have large deviations (need interlocks)

Moyers et al., 2008

Moyers

PTCOG 2010

Uncertainties in Delivering CorrectEnergy or Range Each Treatment

• accelerator beam energy• variable scattering foils• green area represents

± 0.1 MeV (± 0.18 mm)

Moyers et al., 2008

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PTCOG 2010

Bolus Position Relative to Patient(Lateral Set-up Uncertainty Effect on Range)

nominal patient/bolus alignment 3 mm patient/bolus miss-alignment

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PTCOG 2010

Heterogeneous Material Straggling

use of multiple beam entry angles to reduce uncertainty of straggling and relocate localized regions of under and over dose

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PTCOG 2010

Patient Motion

bolus expansiontarget expansionRLSP assignmentsbreath holdgatingtrackingrescanning with synchronized delayapneic oxygenation

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PTCOG 2010

Summary of TypicalPenetration Uncertainties

standard energy (or range) ± 0.6 mmenergy (or range) reproducibility ± 0.1 to 2.0 mmbolus WET ± 0.9 mmalignment devices ± 1.0 mm

CT# accuracy (after scaling) ± 2.5%RLSP of tissues and devices ± 1.6%energy dependence of RLSP ± 1.0%CT# to RLSP (soft tissues only) ± 1.6%

bolus position relative to patient variableheterogeneity straggling variablepatient motion variable

Beam Delivery2.6 to 4.5 mm(linearly)

Patient Information3.5%(quadratically)

Planning Mitigationbolus expansionmultiple anglesbreathing control

Moyers

PTCOG 2010

Summary

The shape of light ion beam depth dose distributions is determined by multiple processes.There are multiple range parameters.The depth of penetration of a light ion beam in a patient is uncertain due to several factors. Allowances must be made to account for these factors.Delivery systems must be designed to detect/correct abnormal energy/range delivery.