Inverse planning optimization for hybrid prostate permanent-seed implant brachytherapy plans using two source strengths.

Abstract

The purpose is to demonstrate the ability to generate clinically acceptable prostate permanent seed implant plans using two seed types which are identical except for their activity. The IPSA inverse planning algorithms were modified to include multiple dose matrices for the calculation of dose from different sources, and a selection algorithm was implemented to allow for the swapping of source type at any given source position. Five previously treated patients with a range of prostate volumes from 20-48 cm3 were re-optimized under two hybrid scenarios: (1) using 0.32 and 0.51 mGy m2 / h 125I, and (2) using 0.64 and 0.76 mGy m2 / h 125I. Isodose lines were generated and dosimetric indices , V150Prostate, D90Prostate, V150Urethra, V125Urethra, V120Urethra,V100Urethra, and D10Urethra were calculated. The algorithm allows for the generation of single-isotope, multi-activity hybrid brachytherapy plans. By dealing with only one radionuclide, but of different activity, the biology is unchanged from a standard plan. All V100Prostate were within 2.3 percentage points for every plan and always above the clinically desirable 95%. All V150Urethra were identically zero, and V120Urethra is always below the clinically acceptable value of 1.0 cm3. Clinical optimization times for the hybrid plans are still under one minute, for most cases. It is possible to generate clinically advantageous brachytherapy plans (i.e. obtain the same quality dose distribution as a standard single-activity plan) while incorporating leftover seeds from a previous patient treatment. This method will allow a clinic to continue to provide excellent patient care, but at a reduced cost. Multi-activity hybrid plans were equal in quality (as measured by the standard dosimetric indices) to plans with seeds of a single activity. Despite the expanded search space, optimization times for these studies were still under two minutes on a modern day laptop and can be reduced to below one minute in a clinical setting. With the typical cost of a set of PPI seeds on the order of thousands of dollars, it is possible to reduce the cost of brachytherapy treatments by allowing for easier use of seeds left over from a previous patient or unused due to a cancelled treatment.

Full text

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Inverse planning optimization for hybrid prostate
permanent-seed implant brachytherapy plans using two
source strengths
J. Adam M. Cunha,a Barby Pickett, Jean Pouliot
Physics Division, Department of Radiation Oncology, The University of California,
San Francisco, CA 94115 USA
Adam.Cunha@UCSF.Edu
Received 15 May, 2009; accepted 22 February, 2010
The purpose is to demonstrate the ability to generate clinically acceptable prostate
permanent seed implant plans using two seed types which are identical except for
their activity. The IPSA inverse planning algorithms were modified to include mul-
tiple dose matrices for the calculation of dose from different sources, and a selection
algorithm was implemented to allow for the swapping of source type at any given
source position. Five previously treated patients with a range of prostate volumes
from 20–48 cm3 were re-optimized under two hybrid scenarios: (1) using 0.32 and
0.51 mGy ⋅ m2 / h 125I, and (2) using 0.64 and 0.76 mGy ⋅ m2 / h 125I. Isodose lines
were generated and dosimetric indices , V150
V100
single-isotope, multi-activity hybrid brachytherapy plans. By dealing with only one
radionuclide, but of different activity, the biology is unchanged from a standard plan.
All V100
clinically desirable 95%. All V150
below the clinically acceptable value of 1.0 cm3. Clinical optimization times for
the hybrid plans are still under one minute, for most cases. It is possible to gener-
ate clinically advantageous brachytherapy plans (i.e. obtain the same quality dose
distribution as a standard single-activity plan) while incorporating leftover seeds
from a previous patient treatment. This method will allow a clinic to continue to
provide excellent patient care, but at a reduced cost. Multi-activity hybrid plans
were equal in quality (as measured by the standard dosimetric indices) to plans
with seeds of a single activity. Despite the expanded search space, optimization
times for these studies were still under two minutes on a modern day laptop and
can be reduced to below one minute in a clinical setting. With the typical cost of
a set of PPI seeds on the order of thousands of dollars, it is possible to reduce the
cost of brachytherapy treatments by allowing for easier use of seeds left over from
a previous patient or unused due to a cancelled treatment.
Prostate, D90
Prostate, V150
Urethra, V125
Urethra, V120
Urethra,
Urethra, and D10
Urethra were calculated. The algorithm allows for the generation of
Prostate were within 2.3 percentage points for every plan and always above the
Urethra were identically zero, and V120
Urethra is always
PACS number: 87.55.D-, 87.55.Kd, 87.55.ne
Key words: brachytherapy, prostate cancer, hybrid plans, prostate permanent-seed
implant (PPI), optimization, IPSA
I. IntroductIon
Current permanent prostate implant brachytherapy (PPI) dose plans use one type of radioactive
seed per treatment plan, all with the same activity. Radioactive seeds must be ordered from a
vendor and used before the radioactivity dissipates. The half-life of one of the more common
a
Corresponding author: J. Adam M. Cunha, Physics Division, Department of Radiation Oncology, The University
of California, 1600 Divisadero St., San Francisco, CA 94115 USA; phone: 415-353-7031; fax: 415-353-9883
email: Adam.Cunha@UCSF.Edu
JournAL oF APPLIEd cLInIcAL MEdIcAL PHYSIcS, VoLuME 11, nuMBEr 3, SuMMEr 2010
64 64

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Journal of Applied clinical Medical Physics, Vol. 11, no. 3, Summer 2010
radionuclides, 125I, is approximately 60 days; therefore, if the seeds are not used within one
week, the activity will have decreased by approximately 10%. For seeds like 103Pd and 131Cs,
with half lives of 17 and 10 days respectively, the decrease is even greater (Table 1). Thus, if a
treatment is missed, seeds — and therefore money — are wasted. These seeds are not entirely
unusable and may be used for a different patient by generating a plan using the partially-decayed
activity†; however, this can only be done if there are enough seeds for an entire plan.
Table 1. Half-lives for commonly-used PPI seeds: 0.76 mGy ⋅ m2 / h (0.6 mCi) 125I = 0.65 mGy ⋅ m2 / h (0.51 mCi)
125I after two weeks.
Seed Type

Half Life

Activity after
7 days 14 days
Iodine-125
Palladium-103
Cesium-131
59.9 days
17.0 days
9.7 days
92%
75%
62%
85%
57%
38%
In addition, it has been reported that it is important to account for differences in the seeds
supplied by different manufacturers when generating treatment plans and calculating dosim-
etry. Identical plans using the same radionuclide but from different vendors will have different
dosimetry due to different dose rate constants, anisotropy factors, and radial dose functions of
each vendor’s seeds.(1,2,3)
There has been recent interest in generating dose plans with two different radionuclides.
In their 2002 paper on the feasibility of 192Ir seeds for PPI, Glasgow et al.(4) proposed that
combinations of 192Ir and 125I seeds can provide adequate coverage of the prostate and spar-
ing of the organs at risk. In this case, the argument is that 192Ir and 125I have similar half lives
(73.83 days verses 59.40 days) and similar absorbed doses delivered in the permanent implant.
Therefore, the radiobiological effects of using two different radionuclides is negligible for cases
which used up to 40 mGy ⋅ m2 / h (10 mCi) 192Ir. In 2007, Chaswal et al.(5) expanded on the
forward planning-based work of Glasgow and used a Greedy Heuristic algorithm to optimize
the treatment plans. They showed that there can be dosimetric and trauma-reducing benefits
to using plans with a combination of 192Ir and 125I. These studies are promising in that they
show a clinical benefit can be derived from including more than one radionuclide in a given
brachytherapy plan. However, the results are dependent on knowing and understanding the
biology of the superposition of two different radiation delivery mechanisms.
There has been progress made recently in our understanding of the biological responses to
different dose delivery characteristics of different radionuclides. In fact, some recent studies
have shown no significant difference between biochemical failure and control as a function
of biological equivalent dose (BED), equivalent uniform dose (EUD), or tumor control prob-
ability (TCP) when comparing plans using 125I and 103Pd.(6) However, even setting aside the
uncertainty in CT-reconstructed target volumes, there is a lack of consensus about the actual
value of the biological parameters that govern the definition of the BED, EUD, and TCP, with
values of α/β differing by more than a factor of 2.(7) The uncertainty in the models that predict
the biological effect of the specific characteristics naturally propagates to the dosimetry of
brachytherapy plans that incorporate multiple radionuclides.
However, assuming the uncertainty in the biology is acceptable, there does appear to be a
benefit to using multiple types of seeds (each with a different dosimetry) in one brachytherapy
plan.(4,5) In this work, we aim to avoid the biology-based uncertainties attached to the use of
two different radionuclides. It would be beneficial to be able to generate clinically-acceptable
† We use will use partial activity or fractional activity to describe a seed that has only a fraction of their original
activity. Usually this is a seed that was not used immediately after ordering from a vendor (e.g. those left over
from a cancelled treatment or from ordering too many seeds for a given implant).

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66 cunha et al.: Inverse planning optimization 66
Journal of Applied clinical Medical Physics, Vol. 11, no. 3, Summer 2010
hybrid plans that incorporate seeds of the same radionuclide, but with different characteristics
— be they different activity or slightly different dosimetric geometry. In contrast to plans using
multiple radionuclides, single radionuclide hybrid plans are free from the biological uncertain-
ties associated with the efficacy combining characteristically different radiation.
We present an algorithm that allows for the generation of single-isotope, multi-activity
hybrid brachytherapy plans. By dealing with only one radionuclide, but of different activity, it
is possible to generate clinically advantageous brachytherapy plans: i.e. obtain the same quality
dose distribution as a standard single-activity plan while incorporating left over seeds from
a previous patient treatment. This method will allow a clinic to continue to provide excellent
patient care, but at a reduced cost.
II. MAtErIALS And MEtHodS
A. code development rational
The algorithms developed for this work augment the IPSA inverse planning algorithms.(8,9,10,11)
While the core optimization engine remains unchanged, the code was modified in three ways:
(1) more than one radionuclide source can be specified using the TG-43 formalism;(12) (2) the
system for evaluating the dose delivered to the target and surrounding organs was expanded to
incorporate two separate radionuclide dose profiles; and (3) the optimization engine can switch
the seed type at each source position at specific moments during the iteration process.
As in the original algorithm, to determine the dose, Dj, delivered to unit volume (voxel) j of
an organ, the contributions from the ith source position, Dij, are summed:






(1)
Dij;Dj =Σ
Np
i
Np is the number of source positions. The total dose, D, to an organ is the sum of the dose
at each voxel within that organ, Nv is the number of voxels in the organ.




(2)
Dj.D =Σ
Nv
j
However, in the new algorithm, the dose matrix (Dij) used depends on which seed is present
at position i. During the initialization phase of the optimization process, the algorithm com-
putes a separate dose matrix for each seed type. Then an initial configuration of seeds is placed
in the target. This configuration is random, but the user has the ability to specify a desired
number of each seed type. The user also has the ability to permanently set the seed type at any
source position.
The algorithm then proceeds to the iteration phase, during which the search space is probed
by placing or removing seeds of either type at randomly selected source positions. The new
configuration is then (1) evaluated to determine the value of the objective function‡, (2) compared
to the best configuration yet attained, and (3) kept or rejected based on the result of No. 2.
‡
As described in Lessard et al.,(8) Lessard and Pouliot,(9) Lessard(10) and Pouliot et al.,(11) the objective function
is computed by assessing penalties to doses delivered to organs which are out of the range desired by
the medical physicist. The objective function is the main criteria for evaluating plans during the
optimization process.

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67 cunha et al.: Inverse planning optimization 67
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In order to maximize clinical relevance, the optimization parameters were chosen from the
class solution developed in Lessard et al.(8) and Pouliot.(13) This class solution was shown to
mimic an experienced dosimetrist by consistently producing dose plans equivalent (as measured
by common dosimetric indices) to those created by a dosimetrist in our clinic. This allows for
better isolation of the variables which control the use of partial-activity seeds in the optimiza-
tion. Two limits on the number of needles allowed per plan are included: a soft penalty and an
upper limit. The soft penalty is a weight multiplied by the total number of needles and then
added into the objective function of the optimization. The upper limit restricts the number of
needles allowed in one implant. Throughout the studies in this paper, the upper limit is set to
30. This is the limit our clinic imposes, since our clinical experience has led to the conventional
wisdom that, as the number of needles in one implant approaches 30, the complications due to
edema, erectile dysfunction and other trauma begin to have unacceptably deleterious effects
on the post-treatment quality of life of the patient. On average our clinic uses 25 needles per
treatment plan for a 40 cm3 prostate gland.
B. dosimetric analysis
The quality of the plans generated in this analysis will be graded using the standard dosimetric
indices developed by the American Association of Physicists in Medicine (AAPM), the American
Brachytherapy Society (ABS), and our clinic. For brachytherapy treatment of prostate cancer,
Stock et al.(14) have demonstrated that the minimum dose delivered to at least 90% of the gland
(D90
recurrence. The American Brachytherapy Society has published general guidelines for differ-
ent anatomical sites(15) that consist of a set of dose limit specifications. Our clinic incorporates
these recommendations and imposes even stricter limits for the target coverage and urethra
dose,(8) which have yielded reproducible results: mature five-year biochemical control rates
of 96% (median follow-up 63 months) reported for 118 consecutive patients.(16) Plan quality
was evaluated by the UCSF clinical physicist with experience generating over 1500 plans. For
the purposes of this study, the single-activity plans were considered the control sample against
which the dosimetry of the multiple-activity plans was judged. The validity of the standard
(single-activity) plans was examined and established in previous work.(8)
Prostate) had a critical impact on the subsequent risk of prostate-specific antigen-diagnosed
B.1 Target dose coverage
The target coverage was compared across plans by examining volume of the prostate
receiving at least the prescription dose (V100
(V150
strive to achieve V100
coverage of the target, but will encourage a value of D90
Because this is a not a post-implant dosimetry analysis, but rather a pre-implant dosimetry
analysis, it is important to see the D90
this amount,(2,3) since the dosimetry generally sees a decrease in post-implant D90
respect to the pre-implant D90
Prostate), at least 150% of the prescription dose
Prostate), and the minimum dose that covers 90% of the prostate (D90
Prostate > 95% and V150
Prostate). In general, we
Prostate < 65%. A V100
Prostate above 95% ensures complete
Prostate 10%–20% above the prescription dose.
Prostate higher than the prescription dose by approximately
Prostatewith
Prostate.
B.2 Urethral dosimetry
One of the most common side effects of prostate brachytherapy (urethral stricture) is caused
by excessive dose delivered to the urethra. The urethral volume receiving at least 100%, 120%,
125%, and 150% of the presection dose (V100
as well as the minimum dose delivered to 10% of the urethra (D10
the dose delivered to the urethra. To adequately protect the urethra, we strive to obtain V125
< 1.0 cm3 and V120
Urethra, V120
Urethra, V125
Urethra, and V150
Urethra), can be used to monitor
Urethra, respectively)
Urethra
Urethra < 1.0 cm3.

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68 cunha et al.: Inverse planning optimization 68
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c. Procedure
Five previously treated patients with a range of prostate volumes from 20 to 48 cm3 were chosen
and reoptimized using the hybrid-activity optimization. Different clinics use different seed
activities — 0.3–0.5 mCi and up to 0.7 mCi are common.(17) Since our clinic uses 0.39 mCi,
we performed this work using two different sets of seed activity. Four studies were organized
into two scenarios. Of course the work presented here should not be considered indicative of
the clinical work done at any institution; since many factors go into generating plans, these
studies were kept as general as possible. In Scenario I, we generate hybrid plans using 0.32 and
0.51 mGy ⋅ m2 / h (0.25 and 0.40 mCi) 125I seeds (A/A0 = 62.5%). In Scenario II, we generate
hybrid plans using 0.64 and 0.76 mGy ⋅ m2 / h (0.50 and 0.60 mCi) 125I seeds (A/A0 = 83.3%).
Table 2 outlines the parameters of the studies performed.
For each study, five plan types were generated with a prescription dose of 144 Gy:
• Uni-activity–full activity: Only one seed type (the full activity) is available to theoptimization
• 30 partial activity: The optimization is requested to use 30 of the partial activity seeds plus
any number of the full activity seeds
• 60 partial activity: The optimization is requested to use 60 of the partial activity seeds plus
any number of the full activity seeds
• Uni-activity–partial activity: Only one seed (the partial activity) available to the optimization
• Unrestricted mix (pure hybrid): Allow the optimization to employ any number of each
seed type
The soft needle penalty encourages the optimization to minimize the number of needles in
addition to optimizing the dose distribution. For Study 1 in Scenario I and II, this needle penalty
is set to the value used in our clinic. For Study 2 in Scenario I and II, this was removed and the
optimization was run with no per-needle penalty.
Table 2. A summary of the studies performed.


Study

Air Kerma Rate
125I (U)
Per-needle Penalty

Results Table
Scenario I; Study 1
Scenario I; Study 2
Scenario II; Study 1
Scenario II; Study 2
0.32 & 0.51
0.32 & 0.51
0.64 & 0.76
0.64 & 0.76
On
Off
On
Off
Table 3
Table 4
Table 5
Table 6
For each study five plan types were generated
III. rESuLtS
The dosimetric results for Scenario I are presented in Tables 3 and 4, and a set of isodose
lines are shown in Fig. 1. The same are presented for Scenario II in Tables 5 & 6 and Fig. 2.
The number of seeds of each activity is listed along with the standard dosimetric indices for
the prostate (V100
D10
Prostate, V150
Prostate, and D90
Prostate) and for the urethra (V100
Urethra, V120
Urethra, V125
Urethra, and
Urethra). VUrethra150 is identically zero for all cases and is, therefore, not listed in the Tables.

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69 cunha et al.: Inverse planning optimization 69
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Table 3. Scenario I; Study 1. Data showing five separate plans generated for each patient case. Plans were
generated with: (1) only one seed activity available to the optimization, 0.51 U 125I; (2) a requested 30 seeds of
0.32 U 125I activity plus any number of seeds of 0.51 U 125I; (3) a requested 60 seeds of 0.32 U 125I plus any number of
seeds of 0.51 U 125I; (4) only 0.32 U 125I seeds available to the optimization; (5) an unrestricted hybrid mix of 0.32 and
0.51 U 125I. Per-needle penalty is on.
Target
Volume Type Needles Seeds
(cm3)
Plan # of Total Low
Act.
#(%)
V100
(%)
Prostate

V150
(%)
Prostate

D90
(Gy)
Prostate

D100
(cm3)
Urethra

V120
(cm3)
Urethra

V125
(cm3)
Urethra

D10
(Gy)
Urethra














































48

48

48

48

48 Pure hybrid 29
47 Only
0.51 U
47 30
0.32 U
47 60
0.32 U
47 Only
0.32 U
47 Pure hybrid 25
36 Only
0.51 U
36 30
0.32 U
36 60
0.32 U
36 Only
0.32 U
36 Pure hybrid 28
29 Only
0.51 U
29 30
0.32 U
29 60
0.32 U
29 Only
0.32 U
29 Pure hybrid 25
20 Only
0.51 U
20 30
0.32 U
20 60
0.32 U
20 Only
0.32 U
20 Pure hybrid 19
Only
0.51 U
30
0.32 U
60
0.32 U
Only
0.32 U
26 85 0(0) 96.9 64.0 178 0.6 0.4 0.1 184
29 94 28(30) 99.2 56.4 174 0.6 0.1 0.1 184
29 105 57(54) 98.2 59.6 178 0.6 0.2 0.1 186
30 130 130(100) 98.6 57.2 178 0.6 0.3 0.1 186
94
89
24(26)
0(0)
98.2
99.4
57.3
61.4
180
179
0.6
0.8
0.1
0.1
0.0
0.0
177
17423
26 100 30(30) 99.6 59.5 173 0.8 0.1 0.0 171
26 109 58(53) 99.2 59.3 175 0.8 0.1 0.0 175
30 137 137(100) 98.8 61.9 175 0.9 0.1 0.0 175
100
73
32(32)
0(0)
97.6
96.6
60.2
63.9
173
173
0.8
0.5
0.1
0.1
0.0
0.0
173
17728
30 85 30(35) 97.3 63.7 181 0.5 0.1 0.0 177
30 94 58(62) 98.2 62.0 176 0.5 0.0 0.0 173
39 111 111(100) 97.6 59.8 176 0.6 0.0 0.0 173
82
63
25(30)
0(0)
97.1
98.2
61.6
62.7
178
178
0.5
0.9
0.1
0.2
0.0
0.0
178
17822
25 74 29(39) 98.0 61.5 180 0.8 0.2 0.0 177
30 85 59(69) 97.9 61.6 176 0.8 0.2 0.0 177
30 97 97(100) 97.4 56.7 176 0.8 0.0 0.0 177
71
47
22(31)
0(0)
97.8
96.9
58.7
64.7
177
175
0.9
0.4
0.0
0.2
0.0
0.2
174
189 18
18 57 29(51) 96.6 62.3 174 0.4 0.2 0.1 183
22 66 57(86) 96.7 64.1 173 0.4 0.2 0.1 188
22 70 70(100) 97.3 62.7 173 0.4 0.2 0.1 188
51 12(24) 96.7 60.4 175 0.4 0.2 0.1 184

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Table 4. Scenario I; Study 2. Data showing five separate plans generated for each patient case. Plans were
generated with: (1) only one seed activity available to the optimization, 0.51 U 125I; (2) a requested 30 seeds of
0.32 U 125I activity plus any number of seeds of 0.51 U 125I; (3) a requested 60 seeds of 0.32 U 125I plus any number of
seeds of 0.51 U 125I; (4) only one seed activity available, 0.32 U 125I; (5) unrestricted hybrid mix of 0.32 U and
0.51 U 125I. Per-needle penalty is off.
Target
Volume Type Needles Seeds
(cm3)
Plan # of Total Low
Act.
#(%)
V100
(%)
Prostate

V150
(%)
Prostate

D90
(Gy)
Prostate

D100
(cm3)
Urethra

V120
(cm3)
Urethra

V125
(cm3)
Urethra

D10
(Gy)
Urethra















































48

48

48

48

48 Pure hybrid 30
47 Only
0.51 U
47 30
0.32 U
47 60
0.32 U
47 Only
0.32 U
47 Pure hybrid 29
36 Only
0.51 U
36 30
0.32 U
36 60
0.32 U
36 Only
0.32 U
36 Pure hybrid 30
29 Only
0.51 U
29 30
0.32 U
29 60
0.32 U
29 Only
0.32 U
29 Pure hybrid 29
20 Only
0.51 U
20 30
0.32 U
20 60
0.32 U
20 Only
0.32 U
20 Pure hybrid 21
Only
0.51 U
30
0.32 U
60
0.32 U
Only
0.32 U
30 86 0(0) 97.9 63.9 179 0.6 0.3 0.1 183
30 97 30(31) 99.0 56.2 181 0.6 0.1 0.0 176
30 105 58(55) 99.0 58.6 179 0.6 0.2 0.1 181
30 129 129(100) 99.1 54.1 179 0.6 0.2 0.0 181
96
88
29(30)
0(0)
99.3
99.4
56.5
62.4
180
178
0.6
0.8
0.1
0.1
0.0
0.0
178
17629
30 100 30(30) 99.6 60.5 173 0.8 0.0 0.0 173
30 110 60(55) 98.5 58.8 171 0.8 0.1 0.0 175
30 136 136(100) 99.3 61.0 171 0.9 0.1 0.0 175
100
74
29(29)
0(0)
99.0
96.9
57.1
63.5
176
173
0.8
0.6
0.1
0.0
0.0
0.0
174
174 30
30 85 29(34) 97.5 61.4 179 0.5 0.1 0.0 176
30 95 59(62) 98.2 61.2 176 0.6 0.0 0.0 174
30 111 111(100) 98.2 59.3 176 0.6 0.1 0.0 174
85
64
31(36)
0(0)
96.7
97.7
60.8
62.7
178
178
0.5
0.8
0.1
0.1
0.0
0.0
175
17629
30 74 29(39) 97.9 59.6 179 0.8 0.1 0.0 173
30 85 60(71) 98.9 62.3 175 0.9 0.1 0.0 173
30 96 96(100) 97.7 59.0 175 0.9 0.0 0.0 173
75
47
31(41)
0(0)
97.9
97.6
59.4
66.6
176
182
0.8
0.4
0.0
0.2
0.0
0.2
172
194 19
22 68 30(52) 97.6 63.7 179 0.4 0.2 0.1 183
24 66 57(86) 96.9 64.7 175 0.4 0.2 0.2 189
25 71 71(100) 96.9 63.8 175 0.4 0.2 0.1 189
53 16(30) 96.4 62.1 177 0.4 0.2 0.0 180

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Fig. 1. Scenario I, Study 1: Isodose lines for one slice of the 48 cm3 prostrate. Isodose lines (outside in) are 50% (purple),
100% (red), 125% (orange), 150% (yellow), 150% (black).

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Table 5. Scenario II; Study 1. Data showing five separate plans generated for each patient case. Plans were
generated with: (1) only one seed activity available to the optimization, 0.76 U 125I; (2) a requested 30 seeds of
0.64 U 125I activity plus any number of seeds of 0.60 mCi 125I; (3) a requested 60 seeds of 0.64 U 125I plus any number of
seeds of 0.76 U 125I; (4) only 0.64 U 125I seeds available to the optimization; (5) an unrestricted hybrid mix of 0.64 and
0.76 U 125I. Per-needle penalty is on.
Target
Volume Type Needles Seeds
(cm3)
Plan # of Total Low
Act.
#(%)
V100
(%)
Prostate

V150
(%)
Prostate

D90
(Gy)
Prostate

D100
(cm3)
Urethra

V120
(cm3)
Urethra

V125
(cm3)
Urethra

D10
(Gy)
Urethra














































48

48

48

48

48 Pure hybrid 23
47 Only
0.76 U
47 30
0.64 U
47 60
0.64 U
47 Only
0.64 U
47 Pure hybrid 28
36 Only
0.76 U
36 30
0.64 U
36 60
0.64 U
36 Only
0.64 U
36 Pure hybrid 30
29 Only
0.76 U
29 30
0.64 U
29 60
0.64 U
29 Only
0.64 U
29 Pure hybrid 27
20 Only
0.76 U
20 30
0.64 U
20 60
0.64 U
20 Only
0.64 U
20 Pure hybrid 18
Only
0.76 U
30
0.64 U
60
0.64 U
Only
0.64 U
22 58 0(0) 98.6 50.3 174 0.6 0.2 0.0 179
23 62 29(47) 99.3 50.9 172 0.6 0.1 0.1 181
23 68 60(88) 98.4 53.8 178 0.7 0.2 0.1 183
25 69 69(100) 99.6 57.0 178 0.7 0.1 0.1 183
63
61
33(52)
0(0)
99.1
98.7
56.0
59.9
177
169
0.6
0.9
0.1
0.1
0.1
0.0
181
173 28
30 65 30(46) 98.0 56.8 175 0.8 0.1 0.0 175
29 70 59(84) 98.5 62.4 175 0.8 0.1 0.0 176
28 72 72(100) 96.9 56.9 175 0.8 0.1 0.0 176
65
51
33(51)
0(0)
98.2
96.9
57.1
57.7
171
176
0.8
0.5
0.0
0.2
0.0
0.2
172
18628
29 55 29(53) 95.7 56.4 178 0.5 0.1 0.0 178
28 60 59(98) 96.1 60.1 176 0.5 0.1 0.0 175
28 60 60(100) 97.0 58.4 176 0.5 0.2 0.0 175
55
43
28(51)
0(0)
96.3
97.3
58.0
57.6
180
177
0.5
0.8
0.2
0.2
0.0
0.0
179
17726
25 48 29(60) 96.5 53.9 174 0.7 0.0 0.0 171
26 52 52(100) 97.6 58.5 179 0.7 0.1 0.0 176
28 52 52(100) 97.0 57.1 179 0.9 0.0 0.0 176
47
32
19(40)
0(0)
97.9
94.7
53.3
62.0
179
172
0.8
0.4
0.0
0.2
0.0
0.1
172
18517
18 37 29(78) 97.3 58.8 173 0.4 0.2 0.0 181
18 39 39(100) 94.7 62.0 172 0.4 0.2 0.1 185
18 39 39(100) 93.7 59.6 172 0.4 0.2 0.1 185
35 17(49) 95.1 56.1 171 0.4 0.2 0.0 181

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73 cunha et al.: Inverse planning optimization 73
Journal of Applied clinical Medical Physics, Vol. 11, no. 3, Summer 2010
Table 6. Scenario II; Study 2. Study of 0.635 U vs. 0.6 mCi and hybrid plans. Data showing five separate plans
generated for each patient case – Prostate dosimetric indices. Plans were generated with: (1) only one seed activity
available to the optimization, 0.76 U 125I; (2) a requested 30 seeds of 0.64 U 125I activity plus any number of seeds of
0.60 mCi 125I; (3) a requested 60 seeds of 0.64 U 125I plus any number of seeds of 0.76 U 125I; (4) only 0.64 U 125I seeds
available to the optimization; (5) an unrestricted hybrid mix of 0.64 and 0.76 U 125I. Per-needle penalty off.
Target
Volume Type Needles Seeds
(cm3)
Plan # of Total Low
Act.
#(%)
V100
(%)
Prostate

V150
(%)
Prostate

D90
(Gy)
Prostate

D100
(cm3)
Urethra

V120
(cm3)
Urethra

V125
(cm3)
Urethra

D10
(Gy)
Urethra














































48

48

48

48

48
47

47

47

47

47
36

36

36

36

36
29

29

29

29

29
20

20

20

20

20
Only
0.76 U
30
0.64 U
60
0.64 U
Only
0.64 U
Mix
Only
0.76 U
30
0.64 U
60
0.64 U
Only
0.64 U
Mix
Only
0.76 U
30
0.64 U
60
0.64 U
Only
0.64 U
Mix
Only
0.76 U
30
0.64 U
60
0.64 U
Only
0.64 U
Mix
Only
0.76 U
30
0.64 U
60
0.64 U
Only
0.64 U
Mix
30 57 0(0) 99.3 52.6 177 0.6 0.1 0.0 181
30 62 29(47) 99.3 46.2 173 0.6 0.1 0.1 181
30 68 60(88) 99.0 56.7 180 0.6 0.1 0.0 177
30 69 69(100) 99.3 50.1 180 0.6 0.1 0.1 177
30
28
64
62
36(56)
0(0)
99.5
98.0
47.6
58.7
174
174
0.6
0.8
0.1
0.2
0.1
0.1
182
176
30 66 30(45) 98.1 57.2 165 0.8 0.1 0.0 175
29 70 59(84) 98.0 55.5 167 0.9 0.1 0.0 175
28 73 73(100) 98.4 52.8 167 0.8 0.1 0.0 175
28
28
65
51
29(45)
0(0)
97.9
96.2
55.7
57.3
171
176
0.9
0.5
0.1
0.1
0.0
0.0
173
180
29 55 29(53) 97.3 57.4 175 0.5 0.2 0.1 184
28 60 58(97) 96.4 61.7 176 0.5 0.1 0.0 180
28 60 60(100) 96.5 56.5 176 0.5 0.2 0.1 180
30
26
55
44
26(47)
0(0)
96.7
96.0
59.8
56.8
180
170
0.5
0.4
0.1
0.2
0.0
0.0
180
177
25 49 29(59) 96.3 60.7 170 0.4 0.2 0.1 183
26 52 52(100) 96.0 56.8 170 0.4 0.2 0.0 177
28 53 53(100) 98.3 64.6 170 0.4 0.2 0.1 177
27
17
47
33
20(43)
0(0)
96.7
98.3
60.9
57.4
168
181
0.4
0.8
0.2
0.1
0.1
0.0
182
176
18 38 30(79) 96.7 58.5 181 0.8 0.0 0.0 173
18 38 38(100) 98.1 58.7 176 0.8 0.0 0.0 174
18 38 38(100) 97.3 54.2 176 0.8 0.1 0.0 174
18 36 18(50) 97.0 60.0 181 0.8 0.1 0.0 176

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74 cunha et al.: Inverse planning optimization 74
Journal of Applied clinical Medical Physics, Vol. 11, no. 3, Summer 2010
A. Activities 0.32 u and 0.51 u
Note that for any one case in Scenario I, Study 1 (Table 3), the target volume receiving 100% of
the prescribed dose (V100
the clinically desirable 95%. The D90
dose. This is to be expected when evaluating the preplan dosimetry as opposed to the post-plan
dosimetry.(2,3)
Also note that the V120
under this scenario shows the effect of removing the per-needle penalty compared to Study 1,
which preserves it. Note that the effect of removing the needle penalty is to increase the number
of needles and obtain a slight increase in target coverage. Comparing Table 3 with Table 4 (and
Table 5 with Table 6 in Scenario II) shows the effect of the per-needle penalty. In general, this
penalty allows for a decrease in the number of needles needed independent of the hybrid status
of the plan. It is interesting to note that, even in the case where the per-needle penalty is turned
on (Tables 3 and 5), the plans generated with an unrestricted mix of seeds still preferred using
some partial-activity seeds. For the studies with the per-needle penalty turned on, the number
of needles recommended for each implant is consistent with the number of needles routinely
used for actual implants performed at our clinic.
Prostate) is within 2.3 percentage points for every plan and always above
Prostate for all plans hovers around 120% of the prescription
Urethra is always below the clinically acceptable value of 1.0 cm3. Study 2
B. Activities 0.64 u and 0.76 u
The results are similar in Scenario II for both Study 1 (Table 5) and Study 2 (Table 6) across
all plans. It is clear from these results that it is possible to achieve clinically acceptable dose
distributions with hybrid plans that incorporate different-activity seeds. Across all four studies
of each of the five patients, there is no evidence that the prostate size (which ranges from 20
to 48 cc) has an effect on the dosimetry of the hybrid plans.
Fig. 2. Scenario II, Study 1: Isodose lines for one slice of the 48 cm3 prostate. Isodose lines (outside in) are 50% (purple),
100% (red), 125% (orange), 150% (yellow), 150% (black).

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75 cunha et al.: Inverse planning optimization 75
Journal of Applied clinical Medical Physics, Vol. 11, no. 3, Summer 2010
Studies were performed on the geometric distribution of each seed type. The density of seeds
as a function of distance from the center of mass of the prostate was examined. The prostate was
divided in octants with the origin placed at the center of the prostate∫, and the density of seeds
in each octant was evaluated. No correlation was found between seed location and seed type.
A final study was performed in order to determine whether the optimized configuration of
seed types is independent of the initial configuration. The initial configuration of seed types was
set to be all of one activity or the other (as opposed to randomly chosen for each seed position,
as was done in the main studies). The plans were then optimized requesting an unrestricted mix
of the two seed types. The final configuration was found to have no correlation to the initial
configuration of seed types.
c. cPu time
Table 7 shows the time needed to process the optimization in Scenario I Study 1 (all studies
had similar results). The baseline IPSA(8,9,10,11) optimization for a single-activity varies from
51–155 s. The hybrid optimization incorporates an increase in the degrees of freedom that must
be probed, so an increase in optimization time is expected. The increase in optimization time
varies from 17%–35%; however, this translates into only a 16–37 s increase in real time. Thus,
the optimization time is still on the order of two minutes for all cases. Our clinical protocol
for the baseline optimization uses a factor of five fewer iterations than used in this study. The
optimizations were stable after a two-fold increase in the number of iterations over the clinical
baseline; so the times listed here should be considered an upper limit which can be reduced
without any clinically noticeable loss in plan quality by a factor of 2.
Table 7. Scenario I; Study 1. CPU time required for optimization using a MacBook Pro running Mac OS 10.5.5 with
a 2.33 GHz Intel Core 2 Duo processor and 3 GB RAM. On average there is a 25% increase in CPU time needed
for the hybrid plan optimization; however, in real time this only amounts to at most about an 26-second increase in
optimization time. This can be further reduced by a factor of two when implemented on a clinical system where fewer
iterations are needed than in this proof of hypothesis study.


Plan Type
CPU Time for Each Optimization
47 cm3
36 cm3
48 cm3
29 cm3
20 cm3
Only 0.51 U
30 0.32 U
60 0.32 U
Only 0.32 U
Pure Hybrid
Max Increase (s)
Max Increase (%)
90 s
104 s
106 s
97 s
100 s
16 s
17%
118 s
151 s
155 s
125 s
144 s
37 s
24%
100 s
135 s
131 s
104 s
122 s
35 s
35%
85 s
110 s
112 s
90 s
102 s
27 s
24%
51 s
68 s
67 s
51 s
61 s
17 s
25%
IV. dIScuSSIon
As noted in the Introduction, the effect of the radioactive decay half-life can have an impact
on the usability of seeds more than a week old. With activity reductions on the order of 40%
after one week (Table 1), it is necessary to incorporate this change in activity into the planning
workflow. In and of itself, this is not a problem since it is relatively simple to calculate the cur-
rent activity of the seeds available and build a treatment plan accordingly. But this only works
if there are enough seeds to accommodate an entire implant. If there are fewer partial-activity
seeds than is required for the implant, the partial-activity seeds are useless; the plan must be
discarded and a new plan using full-activity seeds must be generated.
∫
Since the prostate is generally of a regular geometry, this was defined by the intersection of the sagittal-,
coronal- and transverse-bisecting planes.

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76 cunha et al.: Inverse planning optimization 76
Journal of Applied clinical Medical Physics, Vol. 11, no. 3, Summer 2010
First and foremost, it is clear from Tables 3–6 that there is no degradation of plan quality
when using partial activity seeds — both coverage of the target and sparing of the urethra are
stable across plans. Given that plan quality is preserved, this algorithm would save both time
(by eliminating the possibility that a plan with too many partial-activity seeds must be dis-
carded) and money (by allowing for the use of any inventory of partial-activity seeds). Since
the algorithm includes input parameters to allow the user to chose a specific number of partial
activity seeds, this method will work for any number of partial activity seeds.

A. Post-implant dosimetry
From a clinical perspective, a challenging element of implementing the method presented in this
work is calculating the real dose delivered to the patient due to the actual (rather than planned)
implant. Since there is inherent seed placement error for PPI procedures, a post-implant dose
calculation is used to assess the potential efficacy of the implant.
It has been standard practice via the recommendations of the Radiation Therapy Oncology
Group (RTOG) for this procedure(18,19) to obtain a one-month, post-implant CT of the patient,
digitize the seeds, contour the organs and calculate the actual dose delivered. This may not be
sufficient in hybrid cases since there are visually identical seeds with different activities —
these must be identified. Thus it is necessary to create a one-to-one map between the planned
seed positions and the actual positions.
This procedure may be complicated by changes in the target volume and shape during the
intervening one month between delivery and post-implant imaging. However, a recent trend(20) in
PPI procedure is to obtain the post-implant CT immediately after the implant procedure (rather
than after one month). This would mitigate the difficulties in seed matching which stem from
debulking and edema. Obtaining the post-implant CT immediately after the procedure still would
not account for the uncertainty inherent in placing seeds, but recent advances in post-implant
seed identification show that a one-to-one map can be generated. Brunet-Benkhoucha et al.(21)
have shown that with only seven X-ray images taken with a cone-beam system subtending a
60° arc, seed detection rates of 96.7%, false negative rates of 3.3%, and false positive rates of
2.7% can be achieved. This is done by locating seeds to 0.4 ± 0.4 mm in 3D space, and resulted
in uncertainties in D90
Prostate and V100
Prostate of 1.5% and 0.3%, respectively.
V. concLuSIonS
An optimization algorithm that can generate hybrid brachytherapy plans was developed. Five
previously-treated PPI patients with a range of prostate volumes from 20 to 48 cm3 were chosen
and reoptimized using the hybrid-activity PPI optimization. These multi-activity hybrid plans
were equal in quality (as measured by the standard dosimetric indices) to plans with seeds of a
single activity. Potential gains achievable by using different radionuclides have recently been
explored in the literature; but, since the efficacy of incorporating the BED is still hotly debated
in the community, we have focused on the multi-activity hybrid plans. Despite the expanded
search space, optimization times for these studies were still under two minutes on a modern
day laptop and can be reduced to below one minute in a clinical setting. With the typical cost
of a set of PPI seeds on the order of thousands of dollars, it is possible to reduce the cost of
brachytherapy treatments by allowing for easier use of seeds left over from a previous patient
or unused due to a cancelled or postponed treatment.
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