Treatment Planning Considerations of Brachytherapy Procedures · Treatment Planning Considerations of Brachytherapy Procedures Ali S. Meigooni, Ph.D. University of Kentucky, Lexington,

Treatment Planning Considerations of Brachytherapy Procedures

Treatment Planning Considerations of Brachytherapy Procedures

Ali S. Meigooni, Ph.D.

University of Kentucky, Lexington, KY

&

Robert E. Wallace, Ph.D.

Cedars-Sinai Medical Center, Los Angeles, CA

Ali S. Meigooni, Ph.D.

University of Kentucky, Lexington, KY

&

Robert E. Wallace, Ph.D.

Cedars-Sinai Medical Center, Los Angeles, CA

Table of ContentsTable of ContentsIntroductionCalculation Algorithm

Linear Source ApproximationPoint Source ApproximationCurvilinear Line source Approximation

Source Data EntryLinear Source ApproximationPoint Source Approximation

Specific Features in PlanningCalculation GeometriesImaging support

IntroductionCalculation Algorithm

Linear Source ApproximationPoint Source ApproximationCurvilinear Line source Approximation

Source Data EntryLinear Source ApproximationPoint Source Approximation

Specific Features in PlanningCalculation GeometriesImaging support

Table of Contents (continue)Quality Control of Treatment planning

systemsTG 43 RecommendationTG 53 RecommendationTG 56 RecommendationTG 64 Recommendation

Implementations and FactorsVarian Planning systemsProwess Planning system ADAC Pinnacle planning systemNucletron TheraplanTM and SPOTTM

brachytherapy planning systems

Quality Control of Treatment planning systems

TG 43 RecommendationTG 53 RecommendationTG 56 RecommendationTG 64 Recommendation

Implementations and FactorsVarian Planning systemsProwess Planning system ADAC Pinnacle planning systemNucletron TheraplanTM and SPOTTM

brachytherapy planning systems

Table of Contents (continue)

Shortcomings and Recommendations in the present planning systems

Linear Source calculationsPoint Source calculationsInterpolation and ExtrapolationsStrategies to implement TG43U1 parameters in systems that do not support the TG-43Nomogram

Shortcomings and Recommendations in the present planning systems

Linear Source calculationsPoint Source calculationsInterpolation and ExtrapolationsStrategies to implement TG43U1 parameters in systems that do not support the TG-43Nomogram

IntroductionIntroduction

Inaccurate dose calculation for an excellent implant procedureInaccurate dose calculation for an excellent implant procedure

Accurate dose calculation for a Terrible implant procedure

Accurate dose calculation for a Terrible implant procedure

May be as bad asMay be as bad as

Introduction (continue)Introduction (continue)

We need to improve our dose calculation technique as we are developing the implant procedures.

We need to improve our dose calculation technique as we are developing the implant procedures.

Calculation AlgorithmCalculation AlgorithmLinear Source Approximation r > 2LLinear Source Approximation r > 2L

),,()()2/,(

),(),(0

θπθ

θ rFrgrG

rGSrD LL

LK ⋅⋅⋅Λ⋅=& ),,()(

)2/,(),(),(

0

θπθ

θ rFrgrG

rGSrD LL

LK ⋅⋅⋅Λ⋅=& ),,()(

)2/,(),(),(

0

θπθ

θ rFrgrG

rGSrD LL

LK ⋅⋅⋅Λ⋅=& ),,()(

)2/,(),(),(

0

θπθ

θ rFrgrG

rGSrD LL

LK ⋅⋅⋅Λ⋅=&

L

P( x, y) or P( r,θ)

θ

β

X

Y

Brachytherapy Source r

y

where

SK = air-kerma strength, cGy cm2 hr-1= U

Λ = dose-rate constant, cGy hr-1 U-1

G(r,θ) = geometry function, cm –2

g(r) = radial dose function (unitless), and

F(r,θ) = anisotropy function (unitless).

where

SK = air-kerma strength, cGy cm2 hr-1= U

Λ = dose-rate constant, cGy hr-1 U-1

G(r,θ) = geometry function, cm –2

g(r) = radial dose function (unitless), and

F(r,θ) = anisotropy function (unitless).

˙̇D D (( rr ,, θθ )) == SS KK ⋅⋅ ΛΛ ⋅⋅GG (( rr ,, θθ ))

GG ((11,, ππ // 22 ))⋅⋅ gg (( rr )) ⋅⋅ FF (( rr ,, θθ ))

i.TG-43 Algorithmi.TG-43 Algorithm

GG((rr,,θθ)) ==rr−− 22

ββLL ⋅⋅ yy

⎧ ⎧ ⎨ ⎨ ⎪ ⎪

⎩ ⎩ ⎪ ⎪

Geometry FunctionGeometry Function

Linear Source Approximation

Point Source ApproximationPoint Source Approximation

i.TG-43 Algorithm (continue)i.TG-43 Algorithm (continue)

∫−= 2θ

1θ

'secθtμ'tμRaeq dθeeLy

.ΓMy)I(x,

ii. Sievert Integralii. Sievert Integral

L

L dlX

Y

r

P(r,θ) orP(x,y)

tθ'θ

y

∫−= 2θ

1θ

'secθtμ'tμRaeq dθeeLy

.ΓMy)I(x,

ii. Sievert Integral (continue)ii. Sievert Integral (continue)

∫−

= θ2

'sec θtμ

'tμRaeq

d θ’eeLy

. ΓM

y)I (x,

θ1

where

Meq = Source strength, mg Ra Eq

ΓRa = Gamma-rate constant, R.cm2 hr-1 mg-1

μ = Linear attenuation coefficient of capsule materials, cm-1

t = thickness of the capsule, (cm)

where

Meq = Source strength, mg Ra Eq

ΓRa = Gamma-rate constant, R.cm2 hr-1 mg-1

μ = Linear attenuation coefficient of capsule materials, cm-1

t = thickness of the capsule, (cm)

iii. Interpolation Methodsiii. Interpolation Methods

a. The Along and Away Tables by Krishnaswamy

A matrix of dose rate per mg Ra Eq in

Cartesian Coordinate format, for Cs-137 tube.

b. Paterson & Parker system

A table of mg hrs that is needed to create 1000 cGy

At a given distance, as a function of active length

of the source, for any Radium equivalent source.

c. Quimby system

Same as Paterson & Parker system.

φφanan

((rr )) ==DD..((rr ,,θθ )) ⋅⋅ sinsinθθ ⋅⋅ddθθ

00

ππ

∫∫22 ⋅⋅ DD

..((11,, ππ // 22))

DD..

((rr )) ==SS kk ⋅⋅ ΛΛ

rr 22 ⋅⋅ gg (( rr)) ⋅⋅ φφanan (( rr ))

Point Source Approximation

i.TG-43 Algorithmi.TG-43 Algorithm

Calculation Algorithm (continue)Calculation Algorithm (continue)

˙̇D D (( rr )) == SS KK ⋅⋅ ΛΛ ⋅⋅GLGL(( rr ,, θθ ))

GLGL((11,, ππ // 22 ))⋅⋅ gLgL(( rr ))⋅⋅ φφ anan ( r( r ))

i.TG-43 Algorithm (continue)i.TG-43 Algorithm (continue)It is OK to have

But not

˙̇D D (( rr )) == SS KK ⋅⋅ ΛΛ ⋅⋅11

r 2r 2 ⋅⋅ gLgL(( rr ))⋅⋅ φφ anan ( r( r ))

ii.Traditional Algorithmii.Traditional Algorithm˙̇D D (( rr )) == AA appapp ⋅⋅ (( ΓΓδδ )) xx ⋅⋅ ff medmed ⋅⋅ TT(( rr ))

rr22 ⋅⋅ φ φ anan

Where•Aapp = Apparent activity, mCi

• ( Γδ)x = Exposure rate constant, R m2 h-1 mCi-1

• fmed =Exposure-to-dose conversion factor,, in cGy/R

• T(r) =Tissue attenuation factors,

• φan =Anisotropy constant

Where•Aapp = Apparent activity, mCi

• ( Γδ)x = Exposure rate constant, R m2 h-1 mCi-1

• fmed =Exposure-to-dose conversion factor,, in cGy/R

• T(r) =Tissue attenuation factors,

• φan =Anisotropy constant

Curvilinear source Approximation

Calculation Algorithm (continue)Calculation Algorithm (continue)

i. Ir-192 wire

“snail” isodose

Each curve corresponds to a given dose rate (cGy/day) for sources of unit linear reference kerma rate in central plane of the wire.

Curvilinear source Approximation

ii. Stranded Sources: Point Source approx.

A tandem of N sources in a strand form compared with an Ir-192 wire with continuous activity distribution.

Linear Source Approximation Source Data EntrySource Data Entry

i. 2D TG43U1 parameters Λ = Consensus of measured and calculated data

by TG43U1 and U2

GL (r,θ) = If it is not included in the planning algorithm, enter the tabulated data.

gL(r) = Tabulated data or fitted parameters

F(r,θ) = 2D Anisotropy Function (Tabulated data or fitted parameter)

i. 2D TG43U1 parameters (Continue)

55

44

33

2210 rararararaa)r(g +++++= 5

54

43

32


44

33

2210 rararararaa)r(g +++++=

Note that you may need to use

Λ∗ = Λ / G(ro , θo)

For some planning systems.

In order to enter the 2D anisotropy functions,1) There are fixed angles and radial distances

that you have to provide the values for

2) The planning system requires the angles and radial distances that you have the values for.

i. 2D TG43U1 parameters (Continue)

55

44

33


54

43

32


44

33

2210 rararararaa)r(g +++++=

The Original TG43 recommended

g(r) = ao + a1r + a2r2+ a3r3+ a4r4+ a5r5

Double exponential fit suggested by Furhang and Anderson:

g(r) = C1 e−μ1r+ C2 e−μ2r

Modified polynomial suggested by Meigooni et al :

g(r) = (ao + a1r + a2r2+ a3r3+ a4r4+ a5r5)e−br

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

Rad

ial D

ose

Func

tion,

g(r

)

Distance (cm)

- - - - - - 5th order polynomial fitModified Polynomial

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

Rad

ial D

ose

Func

tion,

g(r

)

Distance (cm)

- - - - - - 5th order polynomial fitDouble-Exponential fit

5th order Polynomial fit of g(r) vs Double exponential and Modified polynomial fit

For one of the I-125 seed models

5th order Polynomial fit of g(r) vs Double exponential and Modified polynomial fit

For one of the I-125 seed models

ii.Traditional Formalism Physical Length

Active length

Attenuation Coefficient of the Core of the source

Attenuation Coefficient of the source capsule

Tissue Attenuation Coefficient:

Meisberger Coefficient

(A + B r + C r2 + Dr3)Exposure Rate Constant.

Exposure to Dose Conversion Factor

Half Life

Point Source Approximation

ii.1D TG43U1 parameters Λ = Consensus of measured and calculated data

by TG43U1 and U2

GL (r,θ) or Gp (r,q) = If it is not included in the planning algorithm, enter the tabulated data.

gL(r) or gp(r) = Corresponding to Geometry Function (Tabulated data or fitted parameters)

φan (r) = 1D Anisotropy Function (Tabulated data or fitted parameter)

TG43U1 Recommends:

No Anisotropy Constant

Λ = Consensus of measured and calculated data by TG43U1 and U2

GL (r,θ) or Gp (r,q) = If it is not included in the planning algorithm, enter the tabulated data.

gL(r) or gp(r) = Corresponding to Geometry Function (Tabulated data or fitted parameters)

φan (r) = 1D Anisotropy Function (Tabulated data or fitted parameter)

TG43U1 Recommends:

No Anisotropy Constant

A. Calculation GeometriesSpecific Features in PlanningSpecific Features in Planning

Λ = Consensus of measured and calculated data by TG43U1 and U2

B. Imaging support

i. Radiographic reconstruction: Orthogonal films

ii. Radiographic reconstruction: Linear Stereo-shift

iii.Radiographic reconstruction: Rotation Stereo-shift

Pt. A

AP Lat

Flange

Origin

i. Orthogonal films

A B

T1T2d

A1B1B2

A2

Z

Y1Y2

S

F

Film

f

ii. Linear Stereo-shift

Special Jig for Stereo-shift film

Fiducial Marker

iii. Rotation Stereo-shift

Dr. Robert Wallace

will present other Imaging modalities and QA procedures

Specific Features in PlanningSpecific Features in Planning

B. Imaging support (continued)

iv. Radiographic reconstruction:

Three or more film non-coplanar film & fiducial jigs

v. Volumetric reconstruction: DICOM Image source

vi. Volumetric reconstruction: from CT image series

vii. Real time planning



In complex implants having many sources, any individual source may be hidden in one or both of the two films in the techniques just discussed. Sources may be hidden by: anatomical structures or by other sources.

Using more views (i.e. films) can help sort sources

Using non–coplanar views also can help.

But the imaging geometry becomes complicated for a strictly defined set-up (e.g. stereo-shift) due to the variability in direction in which films may be taken.



Single film seed overlap from Su, et al., Med Phys 31:1277-1287 (2004)



Several authors reported generalized methods that determine film orientations related to each other, to patient anatomy, and to the implant source array.

Common to these (automated) methods are:

The use of a fiducial jig that lays out orthogonal axes using four or more radio-opaque markers. The jig geometry is known a priori.

The use of minimum least-squares or alegebraicestimation fits the visualized jig markers into the known jig geometry to provide a fixed coordinate system.



The sources are more easily sorted with an increased number of views.

BUT

There often remain ambiguities that confound complete source localization.

This problem is also evident in reconstruction of source positions from slice image sets, trans-axial CT for example.

In order to use volume image sets, one first needs to get them into a brachytherapy planning system.

Several methods exist, including digitizing hard-copy films, but the most robust and faithful methods use direct data transfer over wire or by digital media.

The Digital Imaging and Communications in Medicine, “DICOM,” standard was created to allow interchange of medical images (and related information) of all types.

The standard defines:

Electrical and signaling standards

Media, file, and data format standards

v. Volumetric reconstruction: DICOM Image source

Finding and sorting implanted objects and sources in CT image sets has been a popular and important subject of research. This is principally due to the use of CT sets to provide seed locations for retrospective dosimetry of prostate implants.

Many approaches have been forwarded to automate the process of identifying, sorting, and culling potential source locations in a CT data set.

Ultimately, all are hampered by sampling issues where the spatial sampling frequency (i.e. the “voxel” size) is of the order of that which distinguishes sources.

Recent work using CT sinograms shows promise.


7 seed sinogram (from Tubic & Beaulieu, Med Phys 32:163-174 (2005).


Non-real-time planning (about two to four weeks to complete):Pre-plan ultrasound,Predictive planning for source distribution, strengths, needle loading,Implant procedure replicating position in US space.

Real-time planning (one day to complete)Plan and implant during one US imaging sessionAssume that seeds land where intended – idealized plan

or Use imaging (US, flouro, CT,…) to obtain actual seed locationsUse flexible & RT needle loading machinery for fixed needles

or a variable seed implantation system (I.e a “Mick” applicator)or use needles of various standard loading patterns.

Planning system that supports RT dosimetry, reading US plane locations from positioning and imaging transducers.

vii. Real time (RT) planning (for prostate)

Quality Control of Tx Planning SystemsQuality Control of Tx Planning Systems

Several AAPM Task Groups provide general guidance on quality assurance (QA) for clinical treatment planning systems (TPS).

Little mention is made regarding brachytherapyplanning systems, BtTPS, in particular.

The general recommendation is that each component of the system be tested with independent and standard methods.


In each clinical use of BtTPS, plans should be verified using an independent, if idealized, system.

Hand calculations of dose to selected points.

Spreadsheet embodiments of the hand calculations

Second, independently accepted/verified BxTPS

With appropriate patient and treatment specific data, an end-to-end calculation can validate more complex plans from dedicated BtTPS.


General recommendation: Prudence and Caution

QA of parts of a BtTPS may prove only the internal consistency of the system

Goal: ensure all parts work as intended & expected

Test parts individually and as part of the whole.

Unit and “End-to-end” testing.

Quality Control of Tx Planning SystemsAAPM Task Group Recommendations


TG43/U1 Brachytherapy Source Dosimetry

TG53 Treatment Planning QA

TG56 Brachytherapy Physics Code of Practice

TG64 Permanent Prostate Seed Implants

TG40 Comprehensive QA for Radiation Oncology

TG100 Update TG40, in committee, may address treatment planning systems as equipment



TG43/U1 Brachytherapy Source Dosimetry

Single source dosimetry testing:

Calculation using parameters and TG43U1 formulas

Comparison of planning system generated dose-rate distribution to benchmarks provided in the report

Acceptability: 2% limit for agreement (larger near source and source ends in high dose-gradient regions)

Evaluation of isodose distributions by evaluating numerical values of the 2D/3D dose distribution, not the graphical output

Quality Control of Tx Planning SystemsTG43/U1 Benchmark dose-rate table

Quality Control of Tx Planning SystemsTG43/U1 Benchmark dose-rate table

0.0003640.0003420.003280.004590.004290.005060.003730.00497

0.0009330.0008460.005920.00840.008110.009080.006880.00896

0.002470.002210.01180.01570.01570.01710.01340.01695

0.006970.006340.02460.03230.03250.03470.02840.03444

0.02270.02060.05820.07330.07460.07830.06430.07683

0.09140.08370.1690.2050.2070.2170.1860.2132

0.2150.1990.3340.3980.420.4190.3680.4131.5

0.6260.5870.8150.950.9861.0040.9110.9951

3.1843.0143.4263.9224.1123.9783.9374.1190.5

NASI model

MED3633

Theragenics

model 200

Imagynmodel

IS-12501

Bebigmodel

I25.S06

NASI model

MED3631-A/M

Best model2301

Amershammodel 6711

Amershammodel 6702r (cm)



TG53 Treatment Planning QAGeneral considerationsValidation of subsystems:I/O: Imaging, numerical (dosimetric and other) data, graphical output, numerical output, electronic output

Anatomy: integrity of all graphical and display tools, anatomy database (store & recall), image fusion and registration

Beam/source design tools: placement, identification, modification, shielding

Dose calculation: models, data

Plan tools: evaluation (DVH…), implementation, review



TG56 Brachytherapy Physics Code of Practice

“Relatively little has been written on QA of clinical treatment planning systems in general and even less is available specifically for brachytherapy treatment planning systems.”

Most comprehensive of the TG reports on BtTXP QA



TG56, areas of concern (Table VIII in report)

Source position reconstruction methods from images

Catheter trajectory analysis tools

Linearity & correctness of graphical & image display

Methods to assign source strengths & durations (HDR perm)

Dose calculation algorithms

Dose distribution optimization, evaluation, and presentation

Hard copy documentation numerical and graphical fidelity

What might be added:

Methods to use shields or filters from images

Integrity of data transfer to treatment systems (e.g. HDR)



TG56, additional recommendationVerification by secondary calculation of:

treatment specifications, times,positions, and dose

in a planned therapy.

Like a second Monitor Unit check for EBRT.



TG64 Permanent prostate seed implant brachytherapy

Recommendations echo those of the TG56 repotAdds the requirement that the Medical Physicist shallverify that the treatment planning system reproduces the TG43 (orig. and U1) values for single sources.Adds recommendations for QA of imaging sources, equipment, implant templates, applicators and accessories, and physical dosimeters (GM counters, ion and well chambers).Particular reassertion of ultrasound QA (TG01) in phantom including template registration.

Implementations and FactorsImplementations and Factors

Seven systems reviewed:

Varian Planning systems: VarisSeed, BrachyVision

Prowess Planning systems: 2D, 3D

ADAC planning system: Pinnacle p3

Nucletron planning systems: Theraplan, SPOT

Specific information in the proceedings chapter

Recommendations for Data Entry in Planning Systems

Implementations and FactorsImplementations and FactorsData Entry: General Observations:

Not all of the systems reviewed provide full support for TG43U1 data specification and formulary

Some require manipulation of TG43U1 style data to fit the calculation models to achieve TG43 formulation

Some provide interoperability with legacy formulations

Thus data entry becomes a significant QC/QA issue.

One may need to combine TG43U1 style data for a given source into surrogate functions to enter into a given treatment planning system.

In this case, clear documentation is recommended.

Shortcomings & recommendationsShortcomings & recommendations

TG43 formulation is intended for short brachytherapysources, few mm in length

Elongated source extensions to TG43 needed

Near-field electron fluence from 192Ir sources not explicitly considered with mixed-beam models

Tissue heterogeneity corrections generally not available

Where functional fitting is used in planning, the 5th order polynomial of TG43 may not be as accurate as products of polynomial and exponential functions.

Linear Source calculations


Point source based distribution calculations are common particularly where source center location but not 3D orientation is known and where orientations are assumed to be randomly distributed.

Point source anisotropy corrections simply scale the transverse radial dose distribution in isotropic (spherical) geometry.

Linear source models provide more accurate anisotropy in single source dose distributions and for ensembles of implanted sources.

Fixed geometry implants, including ribbons and plaques, lend to linear source (TG43 “2D” formula) models

When better methods of imaging, identifying, sorting, and culling sources from clinical images are available, then linear source models could be used.

Point Source calculations


There exist no clear recommendations regarding the methods to be used to interpolate single source or multiple source dose distribution data.

This is a sampling problem in the range of evaluated single source data.

Beyond that range ( “clinical range”), linear extrapolation often leads to confounding dose distributions.

One solution is to model single source data at large distances. Another solution would approach zero dose asymptotically by exponential or Build-up factor functional extrapolation.

Interpolation and Extrapolation


As mentioned earlier, if a planning system supports only the outdated TG43 anisotropy constant, one can populate the system’s radial dose function table with the product on the actual radial dose function and the anisotropy factor:

gentered(r) = gP(r) * φan(r)

This is an example.

See Appendix D of TG43U1.

Implementation strategies in non-TG43 BtTPS


Prior to robust and available computerized planning systems for brachytherapy, numerical tables (i.e. the Manchester, Quimby, Paris systems) and graphical nomograms were developed to assist in planning and implementing brachytherapy.

All are based on idealized geometries, yet are robust.

A graphical nomogram relates therapy parameters to each other under a set of assumptions and are much like a fixed form of a duty-specific slide rule.

Nomograms developed by Anderson for 192Ir, 125I, and 103Pd provide the number, strength, and implanted spatial separation of sources for provided dimensions of a target volume, multi-planar or ellipsoidal.

Other planning tools: Nomograms


Prior to robust and available computerized planning systems for brachytherapy, numerical tables (i.e. the Manchester, Quimby, Paris systems) and graphical nomograms were developed to assist in planning and implementing brachytherapy.

All are based on idealized geometries, yet are robust.

A graphical nomogram relates therapy parameters to each other under a set of assumptions and are much like a fixed form of a duty-specific slide rule.

Nomograms developed by Anderson for 192Ir, 125I, and 103Pd provide the number, strength, and implanted spatial separation of sources for provided dimensions of a target volume in an assumed geometry, planar, ellipsoidal,… .

Other planning tools: Nomograms

Shortcomings & recommendationsShortcomings & recommendationsOther planning tools: Nomograms

(from Anderson el al 1985), for planar implant with192Ir ribbons with peripheral dose rate of 10 Gy d-1

Hope this helps!

Thank you

Documents

Treatment Planning Considerations of Brachytherapy Procedures · Treatment Planning Considerations of Brachytherapy Procedures Ali S. Meigooni, Ph.D. University of Kentucky, Lexington,