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
Table of Contents
¾
¾
Introduction
Calculation Algorithm
z
z
¾
z
Source Data Entry
z
¾
Linear Source Approximation
Point Source Approximation
Curvilinear Line source Approximation
z
Linear Source Approximation
Point Source Approximation
Specific Features in Planning
z
z
Calculation Geometries
Imaging support
Table of Contents (continue)
¾ Quality Control of Treatment planning
systems
z
z
z
z
TG 43 Recommendation
TG 53 Recommendation
TG 56 Recommendation
TG 64 Recommendation
¾ Implementations and Factors
z
z
z
z
Varian Planning systems
Prowess Planning system
ADAC Pinnacle planning system
TM and SPOTTM
TM
Nucletron TheraplanTM
brachytherapy planning systems
Table of Contents (continue)
¾ Shortcomings and Recommendations
in the present planning systems
z Linear Source calculations
z Point Source calculations
z Interpolation and Extrapolations
z Strategies to implement TG43U1
parameters in systems that do not support
the TG-43
z Nomogram
Introduction
Inaccurate dose calculation for
an excellent implant procedure
May be as bad as
Accurate dose calculation for a
Terrible implant procedure
Introduction (continue)
We need to improve our dose
calculation technique as we are
developing the implant procedures.
G L ( r ,θ )
⋅ g L (r ) ⋅ F (r ,θ ),
D& (r ,θ ) = S K ⋅ Λ ⋅
G L (r0 , π / 2)
Calculation Algorithm
¾ Linear Source Approximation r > 2L
Y
P( x, y) or P( r,θ)
β
Brachytherapy
Source
y
r
θ
L
X
i.TG-43 Algorithm
D
Ḋ˙ ((rr ,, θθ)) == SSKK
G
G ((rr,, θθ ))
⋅⋅ Λ
⋅⋅ gg((rr )) ⋅⋅ FF (( rr,, θθ))
Λ ⋅⋅
G
G ((11,, ππ // 22))
where
SKK
-1= U
= air-kerma strength, cGy cm22 hr-1
Λ
-1 U-1
-1
= dose-rate constant, cGy hr-1
G(r,θ)
–2
= geometry function, cm –2
g(r)
= radial dose function (unitless), and
F(r,θ)
= anisotropy function (unitless).
i.TG-43 Algorithm (continue)
Geometry
Geometry Function
Function
−2
r
⎧⎪
G( r, θ) = ⎨ β
⎪⎩ L⋅ y
Point Source Approximation
Linear Source Approximation
ii. Sievert Integral
L
I(x, y) =
MY .Γ
eq
Ly
P(r,θ ) or
P(x,y)
Ra μ t
e
'
'
θ − μ t secθ
dθ
∫θ 2 e
1
y
r
t
θ
L
θ'
dl
X
ii. Sievert Integral (continue)
M
I (x,
y)
=
.Γ
eq
Ra
e
μ t
'
Ly
where
I(x, y) =
M .Γ
eq
Ly
∫
Ra μ t
e
'
θ2
e
− μ t sec θ
'
d θ’
θ1
'
θ − μ t secθ
dθ
∫θ 2 e
1
Meq
eq = Source strength, mg Ra Eq
22 hr-1
-1 mg-1
-1
ΓRa
=
Gamma-rate
constant,
R.cm
Ra
μ
= Linear attenuation coefficient of capsule
-1
materials, cm-1
t
= thickness of the capsule, (cm)
iii. 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.
Calculation Algorithm (continue)
¾ Point Source Approximation
i.TG-43 Algorithm
.
D (r ) =
S k ⋅Λ
r2
π
φ an (r ) =
an
∫0
0
⋅ g ( r ) ⋅ φ an ( r )
.
D(r ,θ ) ⋅ sin θ ⋅d θ
.
2 ⋅ D(1, π / 2)
i.TG-43 Algorithm (continue)
It is OK to have
G
GLL((rr,, θθ ))
˙
˙
D
(r)
⋅Λ⋅
⋅⋅ ggLL((rr ))⋅⋅ φφ an
D ((rr )) == SSK
an ( r )
K ⋅Λ⋅G
GLL((11,, ππ // 22))
But not
˙˙ ((rr ))
D
D
== SSK
⋅Λ⋅
K ⋅Λ⋅
11
rr 22
(r)
⋅⋅ ggLL((rr ))⋅⋅ φφ an
an ( r )
ii.Traditional Algorithm
(r
T
˙ (r ) = A
⋅ ( Γδδ ) xx ⋅ f med
⋅ 22
D
app
app
med
r
)
⋅ φanan
Where
•Aapp
app = Apparent activity, mCi
• ( Γδδ)xx = Exposure rate constant, R m22 h-1-1 mCi-1-1
• fmed
med
=Exposure-to-dose conversion factor,, in cGy/R
• T(r) =Tissue attenuation factors,
• φan
an
=Anisotropy constant
Calculation Algorithm (continue)
¾ Curvilinear source Approximation
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.
¾ 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.
Source Data Entry
¾ Linear Source Approximation
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)
Note that you may need to use
Λ∗ = Λ / G(ro , θo)
For some planning
systems.
g (r ) = a + a r + a r + a r + a r
2
0
1
2
3
3
4
4
+ a 5r 5
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)
The Original TG43 recommended
g(r) = ao + a1r + a2r2+ a3r3+ a4r4+ a5r5
g (r ) = a 0 + a 1 r + a 2 r 2 + a 3 r 3 + a 4 r 4 + a 5 r 5
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
5th order Polynomial fit of g(r) vs Double
exponential and Modified polynomial fit
For one of the I-125 seed models
1.2
- - - - - - 5th order polynomial fit
Modified Polynomial
1
Radial Dose Function, g(r )
Radial Dose Function, g(r )
1.2
0.8
0.6
0.4
0.2
0
0
2
4
6
Distance (cm)
8
10
- - - - - - 5th order polynomial fit
Double-Exponential fit
1
0.8
0.6
0.4
0.2
0
0
2
4
6
Distance (cm)
8
10
ii.Traditional Formalism
ƒ
Physical Length
ƒ
Active length
ƒ
Attenuation Coefficient of the Core of the source
ƒ
Attenuation Coefficient of the source capsule
ƒ
Tissue Attenuation Coefficient:
Meisberger Coefficient
(A + B r + C r2 + Dr3)
ƒ
Exposure Rate Constant.
ƒ
Exposure to Dose Conversion Factor
ƒ
Half Life
¾ Point Source Approximation
ii.1D TG43U1 parameters
Λ
= Consensus of measured and calculated data
by TG43U1 and U2
GLL (r,θ) or Gpp (r,q) = If it is not included in the planning
algorithm, enter the tabulated data.
gLL(r) or gpp(r)
φan
an (r)
= Corresponding to Geometry Function
(Tabulated data or fitted parameters)
= 1D Anisotropy Function (Tabulated data or
fitted parameter)
TG43U1 Recommends:
No Anisotropy Constant
Specific Features in Planning
A. Calculation Geometries
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
i. Orthogonal films
Pt. A
Origin
Flange
AP
Lat
ii. Linear Stereo-shift
T1
T2
d
F
A
B
Z
f
A2
B2
B1
A1
Y1
Y2
S
Film
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 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
iv. Radiographic reconstruction:
Three or more film non-coplanar film & fiducial jigs
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.
iv. Radiographic reconstruction:
Three or more film non-coplanar film & fiducial jigs
Single film seed overlap
from Su, et al., Med Phys 31:1277-1287 (2004)
iv. Radiographic reconstruction:
Three or more film non-coplanar film & fiducial jigs
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 alegebraic
estimation fits the visualized jig markers into the known
jig geometry to provide a fixed coordinate system.
iv. Radiographic reconstruction:
Three or more film non-coplanar film & fiducial jigs
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.
v.
Volumetric reconstruction: DICOM Image source
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
vi. Volumetric reconstruction: from CT image series
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.
vi. Volumetric reconstruction: from CT image series
7 seed sinogram
(from Tubic & Beaulieu, Med Phys 32:163-174 (2005).
vii. Real time (RT) planning (for prostate)
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 session
Assume that seeds land where intended – idealized plan
or Use imaging (US, flouro, CT,…) to obtain actual seed locations
Use 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.
Quality 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 brachytherapy
planning systems, BtTPS, in particular.
The general recommendation is that each
component of the system be tested with
independent and standard methods.
Quality Control of Tx Planning Systems
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.
Quality Control of Tx Planning Systems
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 Systems
AAPM 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
Quality Control of Tx Planning Systems
AAPM Task Group Recommendations
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 Systems
TG43/U1 Benchmark dose-rate table
MED3631
-A/M
Bebig
model
I25.S06
Imagyn
model
IS12501
3.978
4.112
3.922
3.426
3.014
3.184
0.911
1.004
0.986
0.95
0.815
0.587
0.626
0.413
0.368
0.419
0.42
0.398
0.334
0.199
0.215
2
0.213
0.186
0.217
0.207
0.205
0.169
0.0837
0.0914
3
0.0768
0.0643
0.0783
0.0746
0.0733
0.0582
0.0206
0.0227
4
0.0344
0.0284
0.0347
0.0325
0.0323
0.0246
0.00634
0.00697
5
0.0169
0.0134
0.0171
0.0157
0.0157
0.0118
0.00221
0.00247
6
0.0089
0.00688
0.00908
0.00811
0.0084
0.00592
0.000846 0.000933
7
0.0049
0.00373
0.00506
0.00429
0.00459
0.00328
0.000342 0.000364
r (cm)
Amersham
model
6702
Amersham
model
6711
Best
model
2301
0.5
4.119
3.937
1
0.995
1.5
NASI
model
Therageni
NASI
cs
model
model 200 MED3633
Quality Control of Tx Planning Systems
AAPM Task Group Recommendations
TG53 Treatment Planning QA
General considerations
Validation 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
Quality Control of Tx Planning Systems
AAPM Task Group Recommendations
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
Quality Control of Tx Planning Systems
AAPM Task Group Recommendations
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 Æ 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)
Quality Control of Tx Planning Systems
AAPM Task Group Recommendations
TG56, additional recommendation
Verification by secondary calculation of:
treatment specifications,
times,
positions,
and dose
in a planned therapy.
Like a second Monitor Unit check for EBRT.
Quality Control of Tx Planning Systems
AAPM Task Group Recommendations
TG64 Permanent prostate seed implant brachytherapy
Recommendations echo those of the TG56 repot
Adds the requirement that the Medical Physicist shall
verify 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 Factors
Recommendations for Data Entry in
Planning Systems
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
Implementations and Factors
Data 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 & recommendations
Linear Source calculations
TG43 formulation is intended for short brachytherapy
sources, 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.
Shortcomings & recommendations
Point 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.
Shortcomings & recommendations
Interpolation and Extrapolation
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.
Shortcomings & recommendations
Implementation strategies in non-TG43 BtTPS
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.
Shortcomings & recommendations
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, multi-planar or ellipsoidal.
Shortcomings & recommendations
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,… .
Shortcomings & recommendations
Other planning tools: Nomograms
(from Anderson el al 1985), for planar implant with
192Ir ribbons with peripheral dose rate of 10 Gy d-1
Hope this helps!
Thank you