# Pencil Beam and Collapsing Cone

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```					                Pencil Beam and Collapsed Cone Algorithm Calculations for a

Lung-type Volume Using CT and the OMP Treatment Planning System

Methods

Measurements have been carried out in both phantom and a specifically designed phantom

which simulated human lung volume. Samples were taken from the Lung Planning CT

images for 15 patients using the Oncentra Masterplan OMP Treatment Planning System.

The X-axis was, following convention, taken to be horizontal, and the Y-axis to be vertical;

accordingly, abscissa and ordinate distances to the skin, heart and the lungs were measured

(see figure 8). Figures 4 and 5 show typical CT images for a patient’s lungs, while Tables 1

and 2 give the beam information and dose information for typical patients. The X-ray

images were taken using CT-SIM: Philips Brilliance Big Bore. A print out of the planning

CT images was produced by the Oncentra Masterplan OMP treatment Planning system (see

section 3.3).

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Figure 4: Lungs Image for Patient by CT-SIM: Philips Brilliance Big Bore

Beam Information
Beam                  1ANT            2RPO          3RPO                  4ARO
Nom. Acc. Pot.(MV or MeV)           6              6              6                    6
FX (cm)                   8.2            8.2           8.6                   8.6
FY (cm)                   9.4           10.6           8.2                   8.6
SSD (cm)                  87.2           86.8          85.6                  84.7
Gantry (degrees)               0            223            267                  320
Wedge Angle(degrees)           60/60          60/33         60/25
Dose Information: Absolute dose 5500 cGy (275 cGy / fraction)
Number of Fraction              20             20             20                  20
IN = 424.77    IN = 185.78    IN = 92.85
MU or min / Fraction                                                              16.39
OUT = 0      OUT = 85.22 OUT = 69.34
Table 1: Beam Information and Dose Information for Patient

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Figure 5: Lungs Image for Patient by CT-SIM: Philips Brilliance Big Bore

Beam Information
3LPO
Beam                                      4ANT           5MINI-ANT            6LAO
THORAX
Nom. Acc. Pot.
6              6               6               6
(MV or MeV)
FX (cm)               10.6           10.1             9.7            14.2
FY (cm)                9.7           14.3             11             10.1
SSD (cm)              86.3           87.2            87.2            82.4
Gantry (degrees)         120              0               0              60
Wedge Angle(degrees)      60/25          60/28           60/60            60/9
Dose Information: Absolute dose 4000 cGy (267 cGy / fraction)
Number of Fraction         15             15              15              15
IN = 2291.07   IN = 1277.72 IN = 1974.08        IN = 476.08
MU or min / Fraction
OUT = 1711.09 OUT = 793.65       OUT = 0       OUT = 1301.50

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Table 2: Beam Information and Dose Information for Patient

Design of multi-block chest phantoms

The first phantom was introduced to the experiment as shown in figure 7, in order to reduce

the uncertainty within the results and to increase the accuracy all that because of the very

inhomogeneous lung region that may led to poor dose distribution.

Figure 7: for Design 1 of the Multiblock phantom (first phantom)

The specially designed phantom

Using measurements taken from 15 patients, who had previously been scheduled for lung

radiotherapy, a second phantom consisting of multi-block components was designed. A

multi-block phantom is essentially a phantom containing a number of blocks with different

shapes and materials used to form an approximate cross-section of the patient. This

facilitates taking measurements on the phantom volume to confirm the prescribed dose. A

plan for the phantom was designed using similar field parameters, for example collimator

settings, beam weightings, wedge fractions, and gantry angles as the clinical plan. The two

lungs are presented in a lateral position, as shown in Figure 8 the heart is represented in the

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middle to reflect the correct anatomy and the lighter color in both Figures 7 and 8 represent

the lungs.

Figure 8: Design 2 for the Multiblock phantom (second phantom), where (S-L) is skin and lung, and

(L-H) is lung and heart.

Table 3 shows the average distance between the skin, lungs and heart of the patient from

the X-ray for the X and Y axes. The table also illustrates the maximum and minimum

values for the X and Y axes, as well as the range of maximum and minimum values. Figure

8 illustrates the distance for X and Y axes between the skin, lungs and heart in the Multi-

Block Phantom. The phantom blocks designed for the experiments were 30 cm in length,

having square or right angled triangular cross-sections and 4 cm sides. They were made of

an epoxy resin-based tissue-equivalent material to represent water (WT1, density=1.02

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gcm-3), lung (LN10 density=0.27 gcm-3) and bone (IB7, density=1.13 gcm-3). Some of the

square blocks of WT1 were drilled to accommodate a 0.6 cm3 graphite ionisation chamber.

The phantoms were composed by putting the epoxy blocks within an adjustable wooden

frame in desired configurations. The frame was held together using a series of small

wooden pins with diameters of 5 mm.

Skin to        Lung to         Heart       Heart to      Lung to
X,Y axis
Lung (cm)      heart (cm)       (cm)       Lung (cm)     Skin (cm)
Average for
2.8        4.2                  4.2           3.3           3.1            17.4
patient(Lateral)
Average for patient
2.3        1.9                  4.4           1.3           2.6            11.1
(Ant-post)
Average for
4          8                    4             8             4             28
Phantom(X)
Average for
4          4                    6             2             4             20
Phantom(Y)
MAX in X axis for patients (Lateral)                                                                    19
MIN in X axis for patients (Lateral)                                                                    15
MAX in Y axis for patients (Ant-post)                                                                  13.7
MIN in Y axis for patients (Ant-post)                                                                   9.6
RANGE in X axis for patients (Lateral)                                                                   4
RANGE in Y axis for patients (Ant-post)                                                                 4.1
Table 3: The area for Lateral and Ant-post in 15 Patients (average and range for 15 patients) and
average for Multiblock phantom

Figures 9 and 10 below depict various stages in the construction of the thorax phantom

within its frame. Expanded polystyrene spacer elements with triangular cross sections

stabilised the slanted surfaces.

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Import and Plan

After scanning the multi-blocks phantom using CT - SIM: Philips Brilliance Big- Bore, the

planning CT images were sent to the Oncentra Masterplan (OMP) Treatment Planning

System. The Oncology Management System: Impac, MOSAIQ was used to transfer the

data from the OMP treatment planning system to the Linac before running the Linac to

determine the points’ ISO center, Beam Information and Dose Information, as shown in

figure 14, 15, 16 and 17 for the first and second phantom.

The phantoms were positioned on the Elekta Precise linac, isocentre and aligned with

lasers, and the ion chamber was placed at each dose point, for example Iso, DP1, DP2, DP3

and DP4 (see figure 12 and 13). Doses were measured for the dosimeters and chambers.

The field size and gantry angles chosen are typical of clinical plans for the same 15 patients

as used to design phantom 2. A field size of 10 x 10cm, was used for all fields. Gantry

angles of 00-3150-2700 and 00-600-1200 were used for phantom 1 and 2 respectively. Tables

4 and 5 show beam information for the first and second phantoms, respectively. The energy

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used for the plans was 6MV because lung cancer is treated clinically with 6MV in HOF

Hospital 10 MV beam is not used because considered very high energy and risky to the

lungs. Wedges were used for beam one and three- the angle of the wedge is 60/60 for each

beam. Figure 12 and 13 show the plan for phantoms 1 and 2, with the isocentre and dose

points measured.

For the first phantom was generated using three 6 MV photon beams, all with a 10 x 10

cm2 field size, as shown in fig A.

Figure A. The plan used for first phantom.

The plan was isocentric and included an ANT beam with a 60º wedge and a right RAO

beam with no wedge. The third field was a right LAT oblique beam with a 60º wedge. The

first phantom was outlined and the total dose prescribed to the isocentre was 5492.8 cGy

(274.6 cGy / fraction).

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For the second phantom was generated using three 6 MV photon beams, all with a 10 x 10

cm2 field size, as shown in fig B.

Figure B. The plan used for second phantom.

The plan was isocentric and included an ANT beam with a 60º wedge and a left LAO beam

with no wedge. The third field was a left LPO oblique beam with a 60º wedge. The second

phantom was outlined and the total dose prescribed to the isocentre was 3971.8 cGy (264.8

cGy / fraction).

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Figure 12: Plan for the first phantom, showing isocentre and 3 dose points (DP1, DP2 and DP3)

(see appendix for large pictures).

Beam Information
Beam                           ANT                           RAO          LAT
Nom. Acc. Pot.(MV or MeV)        6                             6            6
Field size X (cm)               10                            10           10
Field size Y (cm)               10                            10           10
SSD (cm)                        90                            86           90
Gantry (degrees)                 0                           315          270
Table 4: Beam information for the first phantom.

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Figure 13: Plan for the second phantom, showing isocentre and 4 dose points (DP1, DP2, DP3 and
DP4) (see appendix for large pictures).

Beam Information
Beam                          ANT                        LAO            LPO
Nom. Acc. Pot.(MV or MeV)       6                          6              6
Field size X (cm)              10                         10             10
Field size Y (cm)              10                         10             10
SSD (cm)                       90                        88.5           91.3
Gantry (degrees)                0                         60            120
Table 5: Beam information for the second phantom.

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Measurements on the Linac

For the experiment with the phantoms, a Farmer dosimeter and an Ionisation Chamber with

a volume of 0.6cc, both from N E Technology were used. A 6MV X-Ray beam with a SSD

of 100cm and a depth of 5cm was used, along with a field size of 10 x 10cm and a Set Dose

(SD) of 400MU. For the first phantom, on the first day, the experiments were conducted at

room temperature of 20.5 oC, and at a pressure of 765.5 mmHg. For the second phantom,

on the second day, the experiments were conducted with the temperature at 20.2 oC and

pressure 759.2 mmHg. A temperature correction factor of 0.9945 was calculated using

equation 2.3, and a Depth Dose Correction to dmax of 0.863 was used for the calculations,

which is a constant for a 6MV linac in experiment. Further, the value of Wρ (density

correction) was taken as 1.000, which is a correction for Perspex to water. The calibration

factor for the ion chambers were 0.794 and 1.034, as two different chambers were used for

the two sets of measurement. The ion recombination factor, Pion, was 1.0042 in both cases.

The following equations were used to calculate the dose delivered:

Dose = Reading x ND x Pion x Ø (P, T) x Wρ / %DD             (2.1)

For Phantom: D (cGy) = Reading x ND x Pion x Ø (P, T) x daily calibration correction
factor                                                     (2.2)

Wρ is the density correction factor;

%DD is the percentage Depth Dose.

ND Calibration factor ion chamber and electrometer.

Pion ion recombination.

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First phantom- daily calibration correction factor   = (400MU / 401.9cGy)

Second phantom- daily calibration correction factor = (400MU / 399.1cGy)

Readings were obtained from the Dosemeter and converted to dose (401.9-399.1) using
Equation 2.1.

Ø (P, T) = (273 + T / 293) * (760 / P),                    (2.3)

Where Ø (P, T) is the temperature and pressure correction factor, given by equation 2.3

In the users’ beam, the correction factor for air temperature and air pressure Ø (P, T) is

given as:

273 .2  T P0
Ø (P, T) =                   ;
273 .2  T0 P

and is applied to convert the measured signal to the reference conditions used for the

chamber calibration at the standards laboratory. Note that P and T (in oC) are chamber air

pressure and temperature, respectively, at the time of measurement, while Po and To (in oC)

are the normal conditions used in the standards laboratory.

The temperature of the air in a chamber cavity should be taken as that of the phantom and

this is not necessarily the same as the temperature of the surrounding air. For measurements

in a water phantom the chamber waterproof sleeve should be vented to the atmosphere in

order to obtain a rapid equilibrium between the ambient air and the air in the chamber

cavity.

The ionisation chamber measurements were taken on linear accelerator A (Lin A). The

Linac was used to deliver the 6MV X-ray beam to each phantom separately. During this

process, the ionisation chamber was inserted within the phantom at each dose point, (Iso,

DP1, DP2, DP3 and DP4). Moreover, the radiation beam were delivered as per the plans in

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figure 12 and 13. The readings were taken with the ionisation chamber are shown in table 8

and 9. These measurements were used with equation 2.2 to calculate the dose in cGy. The

percentage difference between the measured dose and the dose calculated using the PB and

CC algorithms was calculated.

Table 6 shows the two models for Dosemeter and Chambers used to obtain the dose, while

Table 7 summaries the parameters used in the experimental measurements.

Manufacturer        Description          Part No.           Serial No.          Local
Description
Dosemeter:
NE Technology         Farmer            2570/1 B           944 & 1297       Field 2 & Field
3
Chambers:
NE technology      0.6 cc thimble     2571 & 2571 A      1884 & 2921       Mk3 & Mk4
& graphite
Table 6: Dosemeter and ionisation chambers used for the experimental measurements.

Sample depth dose chart for a 6 MV X-ray beam for a treatment distance of 100 cm SSD
First day       Second day
Field Size                               10 x 10 cm         10 x 10
Source to surface Distance (SSD)                        100 cm           100 cm
Depth                                     5 cm             5 cm
Set Dose (SD)                                400 mu           400 mu
ND (calibration factor ion chamber & electrometer)                0.794            1.034
Pion (ion recombination)                           1.0042           1.0042
Temperature                            20.5 Centigrade         20.2
Pressure                                765.50 mmHg       759.20 mmHg
Ø (P,T) (Temperature & Pressure correction)                 0.9945            1.0017
Wρ (density Correction)                            1.000             1.000
Depth Dose Correction to dmax                          0.863             0.863
Table 7: Parameters used in experimental measurements.

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4. Results and Discussion

4.1 Results

As describe in the Materials and Methods a Set Dose (SD) of 400MU was used. Readings

were obtained from the Dosimeter and converted to dose after accounting for daily

calibration correction factor for first and the second phantoms. Using Equation 2.1 and

Equation 2.2.the calculated values of 400MU=401.9cGy and 400MU=399.1cGy were

obtained respectively.

Table No 8 and Table No 9 summarize the Beam Information for Beams 1, 2 and 3 for

Phantom 1 and Phantom 2 respectively.

Table No 8:

Table No 1 demonstrates percentage difference between Pencil Beam (PB) with Experiment

Measured and Collapsed Cone (CC) with Experiment Measured for first phantom. The results are

as follows:

a. For Isocenter:

i.      Experiment Measure for Isocenter ANT Beam one is 106.93 while for CC it is

107.9 and for PB it is 106.9. The % difference between the experiment measure

and that of CC is -0.02 % and between the experiment measure and that of PB is

0.9%.

ii.      Experiment Measure for Isocenter RAO Beam two is 60.9 while for CC it is 61

and for PB it is 61.1. The % difference between the experiment measure and that

of CC is 0.1 % and between the experiment measure and that of PB is 0.3%.

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iii.       Experiment Measure for Isocenter LAT Beam three is 104.7 while for CC it is

105.7 and for PB it is 106.9. The % difference between the experiment measure

and that of CC is 0.9% and between the experiment measure and that of PB is

2.1%.

b. For DP 1:

i.   Experiment Measure for DP1 ANT Beam one is 112.05 while for CC it is

112.7 and for PB it is 112.4. The % difference between the experiment

measure and that of CC is 0.5 % and between the experiment measure and

that of PB is 0.3%.

ii.    Experiment Measure for DP1 RAO Beam two is 64.07 while for CC it is

64.7 and for PB it is 65.3. The % difference between the experiment

measure and that of CC is 0.9 % and between the experiment measure and

that of PB is 1.9%.

iii.   Experiment Measure for DP1 LAT Beam three is 95.88 while for CC it is

97.3 and for PB it is 98.6. The % difference between the experiment

measure and that of CC is 1.4 % and between the experiment measure and

that of PB is 2.8%.

c. For DP2:

i.   Experiment Measure for DP2 ANT Beam one is 98.7 while for CC it is 78.3

and for PB it is 80. The % difference between the experiment measure and

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that of CC is 0.5 % and between the experiment measure and that of PB is

2.7%.

ii.   Experiment Measure for DP2 RAO Beam two is 90.7 while for CC it is 71.1

and for PB it is 73.3. The % difference between the experiment measure and

that of CC is -0.6 % and between the experiment measure and that of PB is

2.4%.

iii.   Experiment Measure for DP2 LAT Beam three is 117.74 while for CC it is

119.7 and for PB it is 120.6. The % difference between the experiment

measure and that of CC is 1.6 % and between the experiment measure and

that of PB is 2.4%.

d. For DP3:

i.   Experiment Measure for DP3 ANT Beam one is 139.04 while for CC it is

139.6 and for PB it is 140.8. The % difference between the experiment

measure and that of CC is 0.4 % and between the experiment measure and

that of PB is 1.2%.

ii.   Experiment Measure for DP3 RAO Beam two is 20.12 while for CC it is 27

and for PB it is 28.4. The % difference between the experiment measure and

that of CC is 34.1 % and between the experiment measure and that of PB is

41.1%.

iii.   Experiment Measure for DP3 LAT Beam three is 6.7 while for CC it is 6.1

and for PB it is 6.7. The % difference between the experiment measure and

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that of CC is -8.9 % and between the experiment measure and that of PB is

0%.

Table 8: Dosimeter Readings and percentage difference between PB with measured and CC
with measured for first phantom.

ANT Beam        Beam 1       RAO Beam         Beam 2      LAT Beam        Beam 3       Total Dose at
one        % Different      two         % Different      three      % Different      Isocentre
MU or min / Fraction       IN = 451.9                     78.4                       IN = 487.8
PB             IN = 106.9      - 0.02%        61.1            0.3%       IN = 106.9       2.1%             274.9
CC             IN = 107.9        0.9%          61             0.1%       IN = 105.7       0.9%             274.6
so
135.5                         77.2                        132.7
Dosemeter
experiment Measure        106.93                        60.9                        104.7                           272.53
PB               IN = 112.4         0.3%         65.3           1.9%       IN = 98.6        2.8%
CC              IN = 112.7         0.5%         64.7           0.9%       IN = 97.3        1.4%
P1
142                          81.2                        121.5
Dosemeter
experiment Measure         112.05                       64.07                       95.88
PB                 IN = 80          2.7%          73.3          2.4%       IN = 120.6       2.4%
CC               IN = 78.3         0.5%          71.1         - 0.6%      IN = 119.7       1.6%
P2
98.7                         90.7                        149.2
Dosemeter
experiment Measure         77.88                         71.57                       117.74
PB               IN = 140.8         1.2%          28.4         41.1%        IN = 6.7         0%
CC               IN = 139.6         0.4%           27          34.1%        IN = 6.1       - 8.9%
P3
176.2                         25.5                         8.5
Dosemeter
experiment Measure        139.04                         20.12                       6.7
Percentage difference = [(PB/Measure) * 100] – 100%
Percentage difference = [(CC/Measure) * 100] – 100%

For the First Phantom the isocentre plans includes an ANT beam with a 60º wedge, a right
RAO beam with no wedge and a LAT oblique beam with a 60º wedge. The Isocentre dose
for PB and CC algorithms were provided by the OMP treatment planning system. The first
phantom was outlined and the total dose prescribed to the isocentre for CC was 5492.8 cGy
(274.6 cGy / fraction) and for PB the total dose prescribed was 274.9 cGy / fraction. (Table
No 8). Dosimeter and ionization chamber were used to arrive at the Iso- Reading value of
135.5 cGy. Equation 2.2 was used to obtain the Iso Measure value of 106.93 cGy (Fig No
14 & 15, Table No 8).

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
Figure 14: First phantom calculated with Pencil Beam (PB)

Figure 15: First phantom calculated with Collapsed Cone (CC)

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Table No 9:

Table No 9 demonstrates percentage difference between Pencil Beam (PB) with Experiment

Measured and Collapsed Cone (CC) with Experiment Measured for Second phantom. The results

are as follows:

a. For Isocenter:

i.     Experiment Measure for Isocenter ANT Beam one is 89.3 while for CC it is 90

and for PB it is 90.5. The % difference between the experiment measure and that

of CC is 0.7 % and between the experiment measure and that of PB is 1.3%.

ii.     Experiment Measure for Isocenter LAO Beam two is 117.7 while for CC it is

119.3 and for PB it is 120.6. The % difference between the experiment measure

and that of CC is 1.3 % and between the experiment measure and that of PB is

2.4%.

iii.     Experiment Measure for Isocenter LPO Beam three is 50.5 while for CC it is

55.5 and for PB it is 55.6. The % difference between the experiment measure

and that of CC is 9.9% and between the experiment measure and that of PB is

10.09%.

b. For DP1:

i.     Experiment Measure for DP1 ANT Beam one is 94.7 while for CC it is 94.4

and for PB it is 95.1. The % difference between the experiment measure and

that of CC is -0.1 % and between the experiment measure and that of PB is

0.6%.

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ii.    Experiment Measure for DP1 LAO Beam two is 121.9 while for CC it is

121.6 and for PB it is 121.4. The % difference between the experiment

measure and that of CC is -0.2 % and between the experiment measure and

that of PB is -0.4%.

iii.   Experiment Measure for DP1 LPO Beam three is 50.03 while for CC it is

50.9 and for PB it is 50.8. The % difference between the experiment

measure and that of CC is 1.7 % and between the experiment measure and

that of PB is 1.5%.

c. For DP 2:

i.   Experiment Measure for DP2 ANT Beam one is 82.3 while for CC it is 82.5

and for PB it is 83.5. The % difference between the experiment measure and

that of CC is 0.2 % and between the experiment measure and that of PB is

1.4%.

ii.    Experiment Measure for DP2 LAO Beam two is 125.6 while for CC it is

125.6 and for PB it is 127.5. The % difference between the experiment

measure and that of CC is -0.1 % and between the experiment measure and

that of PB is 1.5%.

iii.   Experiment Measure for DP2 LPO Beam three is 52.8 while for CC it is

55.5 and for PB it is 55.6. The % difference between the experiment

measure and that of CC is 5.1 % and between the experiment measure and

that of PB is 5.3%.

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d. For DP3:

i.   Experiment Measure for DP3 ANT Beam one is 106.3 while for CC it is

107.4 and for PB it is 110.4. The % difference between the experiment

measure and that of CC is 1.03 % and between the experiment measure and

that of PB is 3.8%.

ii.   Experiment Measure for DP3 LAO Beam two is 100.7 while for CC it is

101.9 and for PB it is 102. The % difference between the experiment

measure and that of CC is 1.1 % and between the experiment measure and

that of PB is 1.2%.

iii.   Experiment Measure for DP3 LPO Beam three is 34.9 while for CC it is 54

and for PB it is 55. The % difference between the experiment measure and

that of CC is 54.7 % and between the experiment measure and that of PB is

57.5%.

e. For DP4:

i.   Experiment Measure for DP4 ANT Beam one is 132.5 while for CC it is

136.7 and for PB it is 139.3. The % difference between the experiment

measure and that of CC is 3.1 % and between the experiment measure and

that of PB is 5.1%.

ii.   Experiment Measure for DP4 LAO Beam two is 20.8 while for CC it is 24.4

and for PB it is 26.4. The % difference between the experiment measure and

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that of CC is 17.3 % and between the experiment measure and that of PB is

26.9%.

iii.   Experiment Measure for DP4 LPO Beam three is 38.7 while for CC it is 39

and for PB it is 39. The % difference between the experiment measure and

that of CC is 0.7 % and between the experiment measure and that of PB is

0.7%.

For the Second Phantom

The isocentric plan includes an ANT beam with a 60º wedge and a left LAO beam with no

wedge. The third field is a left LPO oblique beam with a 60º wedge. The second phantom

was outlined and the total dose prescribed to the isocentre was 3971.8 cGy (264.8 cGy /

fraction) and for PB the total dose prescribed was 266.7 cGy. Dosimeter and ionization

chamber were used to arrive at the Iso- Reading value of 135.5 cGy. Equation 2.2 was used

to obtain the Iso Measure value of 106.93 cGy.

The Isocentre dose for PB and CC algorithms were provided by the OMP treatment

planning system. The first phantom was outlined and the total dose prescribed to the

isocentre for CC was 5492.8 cGy (274.6 cGy / fraction) and for PB the total dose

prescribed was 274.9 cGy / fraction. (Table No 8). Dosimeter and ionization chamber were

used to arrive at the Iso- Reading value of 85.7 cGy and the ISO Measure value of 89.3 cGy

was obtained using Equation 2.2 (Fig No 16 & 17, Table No 9)

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Figure 16: Second phantom calculated with Pencil Beam (PB)

Figure 17: Second phantom calculated with Collapsed Cone (CC)

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Table 9: Dosimeter Readings and percentage difference between PB with measured and CC with measured for second phantom.

ANT Beam         Beam 1       LAO Beam         Beam 2     LPO Beam       Beam 3      Total Dose at    Isocentre
one       % Different        two        % Different      three     % Different    Isocentre      % Different
MU or min / Fraction     IN = 382.4                      144.1                     IN = 229.2
Iso               PB            IN = 90.5        1.3%          120.6           2.4%       IN = 55.6     10.09%         266.7           3.5%
CC             IN = 90         0.7%          119.3           1.3%       IN = 55.5      9.9%          264.8           2.8%
Reading from          85.7                         113.0                         48.5
Dosemeter
experiment Measure      89.3                          117.7                       50.5                       257.5
DP1              PB             IN = 95.1         0.6%          121.4         - 0.4%      IN = 50.8      1.5%
CC            IN = 94.4        - 0.1%         121.6         - 0.2%      IN = 50.9      1.7%
Reading from         90.7                          117.0                       48.0
Dosemeter
experiment Measure      94.5                          121.9                       50.03
DP2              PB             IN = 83.5        1.4%           127.5          1.5%       IN = 55.6      5.3%
CC            IN = 82.5        0.2%           125.4         - 0.1%      IN = 55.5      5.1%
Reading from         79.0                          120.5                        50.7
Dosemeter
experiment Measure      82.3                          125.6                      52.8
DP3              PB            IN = 110.4        3.8%            102           1.2%       IN = 55       57.5%
CC           IN = 107.4        1.03%          101.9          1.1%       IN = 54       54.7%
Reading from        102.0                           96.7                      33.5
Dosemeter
experiment Measure     106.3                          100.7                      34.9
DP4               PB           IN = 139.3        5.1%            26.4          26.9%      IN = 39        0.7%
CC            IN = 136.7        3.1%            24.4          17.3%      IN = 39        0.7%
Reading from        127.2                           20.0                      37.2
Dosemeter
experiment Measure      132.5                          20.8                       38.7
Percentage different = [(PB/Measure) * 100] – 100%
Percentage different = [(CC/Measure) * 100] – 100%

25 |
4.2 Discussion

4.2.1 Comparison between Pencil beam (PB) VS Collapsed Cone (CC):

Table 10 shows a comparison between PB and CC data for the First Phantom. As can be

seen in the above table, most of the beam values calculated by the two algorithms show a

variation of between 0 to 3%, except for the DP3 Doses in the case of the RAO and the

lateral beam 3, which show a variation in the range of 5% and 10%, respectively.

Table 10: Comparison of PB and CC algorithms for the First Phantom

Beam                  ANT Beam 1                 RAO Beam 2                LAT Beam 3
PB    CC      %            PB    CC      %           PB    CC      %

Iso Dose
106.9    107.9     -0.9    61.1      61      0.1     106.9    105.7     1.1
(cGy/Fraction)

DP1 Dose
112.4    112.7     -0.2    65.3     64.7     0.9      98.6     97.3     1.3
(cGy/Fraction)

DP2 Dose
80      78.3     2.1     73.3     71.1     3.1     120.6    119.7     0.7
(cGy/Fraction)

DP3 Dose
140.8    139.6     0.8     28.4      27      5.1      6.7      6.1      9.8
(cGy/Fraction)

Figures 14 and 15 demonstrate position of DP 1, DP 2 and DP 3 related to the beams. It is

evident that DP 3 is closer to ANT Beam 1 but away from the RAO Beam 2 and LAT beam

3. The beams 2 and beam 3 reach DP 3 at a tangent. In case of Iso dose there is little

difference in the algorithm for Beam 2 and Beam 3. For DP 1 there is no significant

difference in the algorithm for any of the beams. In case of DP 2 there is a slight variation

in the algorithm for Beam 1 and Beam 2 with a difference of 2.1 % and 3.1 % respectively.

This variation in algorithm is expected and can be explained from the fact that Beam 1 and

26 |
Beam 2 have to pass through air. DP3 Beam 1 passes through only 3cm of water and no air

giving an accurate algorithm. Whereas in case of DP 3 Beam 2, there is a difference of 5.1

% suggesting that DP3 is situated in the low dose Penumbra. The algorithms are less

accurate in low dose areas with an absolute dose difference of less than 1.5 cGy, (Figure 14

and 15). Beam 3 does not pass through DP3 giving PB and CC algorithms values of 6.7

cGy and 6.1 cGy respectively demonstrating a difference of 9.8 % (Table 10). These

observations are similar to a retrospective treatment planning study conducted by

(ASPRADAKIS et al 2006)3, to evaluate the differences in the dose distributions and

monitor units predicted by CC and PB algorithms. They observed that the calculated dose

in unit density medium was within1% for the CC model and up to 2% for PB. In contrast in

low density medium and under full scatter conditions, CC overestimated the dose by 1%

whereas PB overestimated the dose by 9%. A negative value obtained while calculating the

percent difference is suggestive of a CC dose.

Table 11: A comparison between PB and CC data for the second Phantom

Beam                  ANT Beam 1                LAO Beam 2                LPO Beam 3
PB    CC      %           PB    CC      %           PB    CC      %
Iso Dose
90.5      90      0.5     120.6   119.3     1.08     55.6    55.5      0.1
(cGy/Fraction)

DP1 Dose
95.1     94.4     0.7     121.4   121.6     -0.1     50.8    50.9     -0.1
(cGy/Fraction)

DP2 Dose
83.5     82.5     1.2     127.5   125.4      1.6     55.6    55.5      0.1
(cGy/Fraction)

DP3 Dose
110.4   107.4     2.7     102.0   101.9     0.09     55.0    54.0      1.8
(cGy/Fraction)

DP4 Dose
139.3   136.7     1.9      26.4    24.4      8.1      39      39       0.0
(cGy/Fraction)

27 |
Table no 11 shows the beam values calculated by the two algorithms. For Iso dose the

variation is not significant for all the beams. In case of DP 1 LAO Beam 2 and LPO Beam

3 show a variation of -0.1%. For DPI 2 all the beams have an accurate algorithm with a

percent difference of 1.2 and 1.6 for Beam 1 and Beam 2. In case of DP3, Beam 1 has a

difference of 2.7 and Beam 3 has a difference of 1. 8 %. In case of DP4 LAO Beam 2,

shows a maximum variation of 8%. This could be explained by the fact that point DP4 is

located at the edge of beam 2 in the penumbra region.

4.2.2 Comparison between algorithms and experimental data:

Phantom 1

In order to investigate the comparative accuracy of the Pencil Beam and Collapsed Cone

algorithms, the percentage differences were calculated by dividing the dose for each

algorithm by the dose calculated from equation 2.2. Figure 18(a – d) illustrates the accuracy

of each algorithm for each beam for First Phantom.

a
Beam 1 (ANT)
2.722                                    Beam 1 (ANT)
3
percentage differences

Dose
2                                          Points
1.264
0.907                                 Measured   PB Series   CC Series   PB - CC
1       0.580.5390.402      PB Series
ISO         -0.028      0.907      -0.935
-0.028                    CC Series
0           0.312                       DP1          0.312       0.58      -0.268
ISO DP1 DP2 DP3                     DP2          2.722      0.539       2.183
-1                                       DP3          1.264      0.402       0.862
Dose Point measured

Fig: 18 a: Difference between PB and CC algorithm for Beam 1 (ANT) Phantom 1

28 |
The difference between PB and CC for Beam 1 (ANT) is maximum at DP2 where it is

found to be 2.183. For rest of the dosage points it is less than 1.

b                                     Beam 2 (RAO)
Beam 2 (RAO)
50                41.15
percentage differences

40                                                 Dose
30                    34.19                       Points    PB       CC
20                                 PB Series    Measured   Series   Series   PB - CC
1.919
10 0.328    2.417                 CC Series
ISO         0.328    0.164    0.164
0 0.164 0.983 -0.656                          DP1         1.919    0.983    0.936
-10 ISO DP1 DP2 DP3                             DP2         2.417   -0.656    3.073
Dose Point measured                       DP3         41.15    34.19    6.96

Fig: 18 b: Difference between PB and CC algorithm for Beam 2 (RAO) Phantom 1

The difference between PB and CC for Beam 2 (RAO) ranges from 0.164 to 6.96. It is

maximum at DP3 where it is found to be 6.96 showing a wide variation in the algorithm by

Pencil Beam (PB).

c                                  Beam 3 (LAT)
Beam 3 (LAT)
5
2.1012.8362.429
percentage differences

1.4810.66 0                           Dose
0.955                                      Points     PB       CC
0
ISO DP1 DP2 DP3                           Measured   Series   Series   PB - CC
PB Series
ISO         2.101    0.955    1.146
-5                                 CC Series
DP1         2.836    1.481    1.355
-8.955
DP2         2.429     0.66    1.769
-10
Dose Point measured                       DP3             0   -8.955    8.955

Fig 18 c: Difference between PB and CC algorithm for Beam 3 (LAT) Phantom 1

29 |
For Beam 3 (LAT), the difference ranges from 1.146 to 8.955. The difference is maximum

for DP 3 (8.955) suggesting a very wide variation in the PB algorithm.

Phantom 2

The same exercise is repeated for Phantom 2, and the graphs are again plotted for Beam 1,
(ANT) Beam 2 (LAO) and Beam 3 (LPO) as shown in Figures 19 a – c.

Beam 1 (ANT)
a                                    Beam 1 (ANT)
Dose
6                                          Points     PB        CC
percentage differences

5.132
Measured   Series    Series    PB-CC
4                3.857
3.169                 Iso        1.343     0.783       0.56
2                           PB Series                0.634     -0.105
1.343 1.458                      DP1                             0.739
0.634 1.034
0.783
0.243        CC Series                1.458     0.243
0           -0.105                        DP2                             1.215
Dp4
Iso
DP1
DP2
DP3

DP3        3.857     1.034      2.823
-2
Dose Point measured                 Dp4        5.132     3.169      1.963

Fig 19 a: Difference between PB and CC algorithm for Beam 1 (ANT) Phantom 2

The difference between PB and CC for Beam 1 (ANT) ranges from 0.56 to 2.823. It is

maximum at DP3 where it is found to be 2.823 showing a slight variation in the algorithm

by Pencil Beam (PB).

Beam 2 (LAO)
30
b                                   Beam 2 (LAO)
Dose
percentage differences

26.92
Points   PB         CC
20                                                                                     Measured Series     Series    PB-CC
17.3
Iso         2.463    1.359     1.104
10                                                                        PB Series
2.463         1.29                    DP1         -0.41    -0.246   -0.164
-0.41 1.512          CC Series
0                                                        1.191                DP2         1.512    -0.159    1.671
1.359 -0.246 -0.159
Iso DP1 DP2 DP3 Dp4                        DP3          1.29    1.191     0.099
-10                                                                                                 26.92     17.3
Dose Point measured                   Dp4                             9.62

Fig 19 b: Difference between PB and CC algorithm for Beam 2 (LAO) Phantom 2

30 |
Difference for Beam 2 (LAO) is maximum in DP4 with a variation for PB to the tune of

9.62.

c                                                            Beam 3 (LPO)
Beam 3 (LPO)
80                               Dose Points   PB       CC
differences
Percentage

60          57.59
54.72
Measured      Series   Series   PB-CC
40                               Iso            10.09     9.9       0.19
20    10.095.303
1.539 0.775 PB Series
0   9.9 1.738 0.775             DP1            1.539    1.738    -0.199
5.113    CC Series
DP2            5.303    5.113      0.19
DP3            57.59    54.72      2.87
Dose Point measured
Dp4            0.775    0.775           0

Fig 19 c: Difference between PB and CC algorithm for Beam 3 (LPO) Phantom 2

The difference between PB and CC for Beam 3 (LPO) ranges from -0.199 to 2.87, it is

maximum at DP3 where it is found to be 2.87 showing a slight variation in the algorithm by

Pencil Beam (PB).

Using both the phantoms the difference in the algorithm for PB and CC is fairly

large in DP3 (Phantom 1) and DP 4 (Phantom 4) for Pencil Beam. These findings are

consistent with the conclusions of ASPRADAKIS et al (2006)3, who reported that PB

overestimated the dose by 9%. In this experiment it is apparent that PB tends to

overestimate the algorithm and therefore Collapsing Cone is a much preferred algorithm.

Nisbet et al (2004)27, had similar conclusion while comparing the accuracy of Pencil beam

with that of Collapsing Cone. They recommend usage of Collapsing Cone algorithm while

clinical treatment planning situations where lung is present.

31 |
Conclusion

1. This study was conducted to compare and contrast two algorithms Pencil Beam (PB)

and Collapsing Cone (CC).

2. Collapsing Cone is found to be more accurate when measured on two phantoms

suggesting that Collapsing cone is a much accurate algorithm for clinical treatment

planning scenario.

3. The experiment clearly shows that Pencil beam tends to overestimates the dose by 9.62

%.

4. Based on this study it is recommended that Collapsing Cone is used as the treatment

algorithm. Conclusions drawn in this study are consisted with findings of other studies.

32 |
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