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CHAPTER 9

INFLUENCE OF SMOOTHING ALGORITHMS IN MONTE

CARLO DOSE CALCULATIONS OF CYBERKNIFE

TREATMENT PLANS: A LUNG PHANTOM STUDY

9.1 INTRODUCTION

9.1.1 Dose Calculation Algorithms

Dose calculation algorithms are used in the TPS for determining the

dose distribution in radiotherapy. Accuracy of the treatment dose calculations

is determined by the algorithm used in the TPS. In a homogeneous medium

these algorithms are calculating nearly similar dose distributions. However

they are not yielding similar results in heterogeneous media (Fotina et al

2009; Knöös et al 1995). There are several algorithms introduced to improvise

the dose calculations in a heterogeneous interface or medium (Krieger and

Sauer 2005; Vanderstraeten et al 2006; Carrasco et al 2004; Deng et al 2003;

Deng et al 2004; Francescon et al 2009). Monte Carlo algorithm is considered

to be the finest of the dose calculating algorithms among all other

commercially available algorithms (Wilcox et al 2010; Wilcox and Daskalov

2008).

CyberKnife radiosurgery is performed for intracranial as well as

extra cranial targets. Lung target is one among the extracranial site which is

treated with dedicated tracking methods. Anatomy of lung is highly

inhomogeneous and it requires accurate dose calculation algorithms like

Monte Carlo algorithm.

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9.1.2 Monte Carlo Dose Calculation Algorithm in CyberKnife

Treatment Planning

Multiplan is the dedicated CyberKnife stereotactic radiosurgery

TPS. Multiplan TPS is one among the treatment planning systems which uses

Monte Carlo dose calculation algorithm. Multiplan system has Ray Tracing

dose calculations algorithm also, in addition with the Monte Carlo algorithm.

There are few studies available on implementation of Monte Carlo

algorithms in CyberKnife treatment planning (Wilcox et al 2010; Wilcox and

Daskalov 2008; Yamamoto et al 2002; Sánchez-Doblado et al 2003; Yu et al

2004, Araki 2006; Sharma et al 2010; Sharma et al 2011; Craig et al 2008).

According to Wilcox et al (2010) the discrepancies between the Ray tracing

and Monte Carlo algorithms are larger for plans using smaller collimator

sizes.

Depth dose studies of Yamamoto et al (2002) state that the

discrepancy between the Monte Carlo calculated and measured depth dose

curve increases with decreasing field size. According to Sharma et al (2010)

there can be significant differences between Ray tracing and Monte Carlo

calculations in a heterogeneous medium.

9.1.3 Monte Carlo Dose Smoothing Algorithms

The Monte Carlo calculations in the Multiplan treatment planning

system are associated with a smoothing algorithm. These algorithms are prone

to create discrepancy in the final dose distribution as the smoothing principles

are different in each smoothing algorithm. The influence of these Monte Carlo

dose smoothing algorithms are not yet studied in depth. The present study is

to analyze the influence of these Monte Carlo dose smoothing algorithms in a

lung phantom which has the greater extent of heterogeneity.

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9.2 MATERIALS AND METHODS

9.2.1 The Lung Phantom

The X-sight® Lung Tracking lung phantom (Computerized

Imaging Reference Systems, Norfolk, VA, USA) which is used for

performing the end to end test of dynamic lung tumor tracking in CyberKnife,

was considered for this study. This XLT lung phantom (Figure 9.1) contains

anthropomorphic spine with cortical and trabecular bone, ribs, lung lobes and

a lung tumor-simulating target.

Figure 9.1 X-sight lung phantom with the insert which contains the

lung target

The CT images of this phantom were acquired in 1mm thickness

and loaded into the Multiplan TPS. The lung target which is the target

mimicked ball in the XLT phantom was contoured. The volume of the target

was 7023.81mm3.The organs at risk (OAR) ipsi-lateral (Left) lung, contra-

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lateral (Right) lung, and spine were also marked on the CT images. The

treatment plans were made for this target with proper constraints to the OARs.

9.2.2 Treatment Planning and the Dose Calculations for the Lung

Phantom in the Multiplan TPS

All the CyberKnife treatment plans are associated with a tracking

method. The lung tumors having definite size can also be used as a tracking

object and this lung tracking method is called as X-sight lung tracking.

Though it is lung tracking method the initial alignment is done by aligning the

spine. As the part of the planning, the initial Spine Tracking Volume was

contoured. Then the alignment of the spine in the DRR (generated by the

TPS) was confirmed. The lung tumor simulating the target was taken as the

Tumor Tracking Volume. The sequential optimization was selected for the

treatment planning. The collimators were selected by the automatic collimator

selection tool for optimal conformity.This tool suggested 10mm and 15mm

collimator for the lung target. Then four dose limiting shell volumes were

created around the target.

The first shell covered a radial width of 2 mm around the target.

The second shell covered 3mm radial width around the first shell. The third

shell covered 5mm from the second shell. Similarly the final fourth shell

covered a radial with of 15mm around the third shell. The dose limit set for

the first shell was 100% of the target dose. Similarly the limiting dose of 85%,

60% and 25% of the target dose were set for the second shell, third shell and

the fourth shell respectively. The goal to the target dose coverage was set as

60Gy in 4 fractions and it was set for optimal conformity. The Ray tracing

algorithm was selected for the dose calculations. The optimization was

executed in low resolution. Once the optimization was completed the high

resolution calculations were performed. In Multiplan planning system the

maximum dose was taken as the default normalization dose. The isodose

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covering the 95% of the target was selected for prescription and the

prescription dose in this study was 60 Gy.

In CyberKnife the Monte Carlo dose calculations are performed

after the basic dose calculations by the Ray tracing algorithm. Hence the high

resolution Ray tracing doses were introduced for Monte Carlo calculations

with the same beam parameters estimated by the basic Ray tracing based

sequential optimization. The Monte Carlo doses were smoothed by the

smoothing algorithms. The smoothing algorithms available in Multiplan TPS

are Average, Weighted average, Gaussian, Clipped Gaussian and Desparkled-

Only algorithm.

9.2.3 Principles of the Dose Smoothing Algorithms

The average smoothing algorithm computes the average value

within a 3x3x3- voxel cube surrounding the calculation voxel.

Weighted averagealso does the same but with weighting factors

which decreases with distance from the central voxel.

Gaussian algorithm gives the convolution of the dose distribution

with a 3D Gaussian function and the standard deviation � of the Gaussian

function can be selected by the user. Two different standard deviations (� =

0.2 and � = 3) are taken for the present study.

Clipped Gaussian also does the same but the outcome of the

Gaussian function is modified so that the difference between the raw dose and

the smoothed dose exists within the statistical uncertainty in dose calculation

at each voxel.

Desparkled-Only algorithm removes the artificial hot spots at

voxels with greater uncertainty.

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All the smoothing algorithms were introduced in the Monte Carlo

dose calculations independently and the results were analyzed and compared.

9.2.4 Treatment Plan Evaluation for Comparison

The CyberKnife treatment plans of different Monte Carlo dose

smoothing algorithms were evaluated for target coverage and sparing of the

OAR.

The formulae used to calculate the conformity index and the

homogeneity index are given below.

Conformity index CI = (VRI / TVRI) x (TV/ TVRI)

Where, VRI is the actual volume including the target, receiving the

prescription isodose or more, TV is the volume of the target, and TVRI is the

volume of the target which receives the prescription isodose or more.

The homogeneity index is given by,

Homogeneity Index HI = (D2% -D 98%)/ D 50%

Where, D2% is the dose received by only 2% of the target volume, D98% is the

dose received by 98% of the target volume and D 50% is the dose received by

50% of the target volume.

For the OARs spine, ipsi- lateral lung and contra lateral lung the

V100%, V80%, V50%, V30%, V10%, V5% were evaluated in terms of the volume in

cubic millimeters.

The P-values were calculated from the two tailed Student’s T test

and tabulated accordingly.

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9.3 RESULTS

The target doses D98%, D95%, D90%, D50%, D10% and D2% are shown in

Table 9.1 for the Ray tracing algorithm and for all the Monte Carlo smoothing

algorithms. Monte Carlo smoothed doses were found to be lesser than the

doses calculated by the Ray tracing algorithm. The Ray tracing calculated

dose distribution is shown in Figure 9.2.

Figure 9.2 Dose distribution calculated by the Ray tracing algorithm

Gaussian, Clipped Gaussian and Desparkled-only algorithms were

showing same results when the standard deviations selected was low.

However they were differing in smoothing when high standard deviation was

selected. D98% was the lowest for Clipped Gaussian algorithm and it was

50.56Gy. Except D98%, all other volume doses were smoothed for a lowest by

the Average smoothing algorithm. The dose distribution which was smoothed

by the Average algorithm is shown in Figure 9.3. The lowest values of the

volumes doses were 51.27Gy, 52.52Gy, 57.52Gy, 60.65Gy and 61.28Gy

respectively for D95%, D90%, D50%, D10% and D2%.The corresponding values

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calculated by the Ray tracing algorithms were 60.00Gy, 60.67Gy, 62.67Gy,

64.00Gy and 65.33Gy respectively. The DVHs of Average, Weighted

average, Gaussian with two � values, Clipped Gaussian with two � values and

Desparkled-only algorithms are shown in Figure 9.5, 9.6, 9.7, 9.8, 9.9, 9.10

and 9.11 respectively.

Figure 9.3 Monte Carlo dose distribution smoothed by the Average

smoothing algorithm

Similarly the highest value of D98% was obtained by the Weighted

Average smoothing algorithm and it was 50.82Gy. The highest values of

D95%, D90%, D50%, D10% and D2% were 52.03Gy, 53.40Gy, 58.20Gy, 61.63Gy

and 63.67Gy respectively. The volumes covered by 100% of the prescription

dose were vastly differing between the Ray tracing and Monte Carlo

smoothed doses. The V100% calculated by the Ray tracing algorithm was

94.31%. However the deviations between the Monte Carlo smoothed doses

were lesser.

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Figure 9.4 Monte Carlo dose distribution smoothed by the Gaussian

smoothing algorithm

The minimum V100% value was obtained for weighted average

algorithm and it was 15.78%. Gaussian, Clipped Gaussian algorithms with

low standard deviation and Desparkled-only algorithms were showing the

same maximum V100% and the value was 24.9%. The smoothed dose

distribution by Gaussian algorithm with �=0.2 is shown in Figure 9.4. Though

there was a huge difference between Ray tracing and Monte Carlo smoothed

doses in V100%, the deviations progressively reducing for V95%, V90%, V85% and

V80%. The minimum V80% was 99.90% and it was for weighted average

smoothing algorithm. The V100%, V95%, V90%, V85% and V80% of the target are

shown in Table 9.2. The target dose conformity index of the smoothed dose

distributions were between 4.01 and 6.34. However the conformity index of

Ray tracing dose distribution was 1.19. Similarly the homogeneity index of

the Monte Carlo smoothed doses were between 0.18 and 0.22 while it was

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0.11 for Ray tracing. The conformity index and homogeneity index are

tabulated in Table 9.3.

Table 9.1 Volume doses of the target calculated by different

smoothing algorithms

Dose calculation/smoothing

Algorithm

Target Volume doses in Gy

D98% D95% D90% D50% D10% D2%

Ray Tracing 58.67 60 60.67 62.67 64 65.33

Mo

nte

Car

lo s

mo

oth

ing

Alg

ori

thm

s

Average 50.64 51.27 52.52 57.52 60.65 61.28

Weighted Average 50.82 51.45 52.71 57.73 60.86 61.49

Gaussian(�=0.2) 50.67 52.03 53.4 58.2 61.63 63.67

Gaussian (�=3) 50.69 51.32 52.57 57.58 60.71 61.34

ClippedGaussian(�=0.2) 50.67 52.03 53.4 58.2 61.63 63.67

Clipped Gaussian (�=3) 50.56 51.87 52.53 57.78 61.07 61.72

Desparkled-only 50.67 52.03 53.4 58.2 61.63 63.67

P-value 0.0158 0.0173 0.0118 0.0006 <0.0001 0.0002

In the ipsilateral lung, the V100% was 123.98 mm3

for Ray tracing

while it was zero for all the Monte Carlo Smoothing algorithms. The

difference between the smoothed doses and Ray tracing was low for larger

volumes involving small doses. Though there was a difference between the

smoothed doses, the difference was very low. In the case of contra lateral lung

and spine the dose volumes from V100% to V30% were not appreciable to

quantify for both in Ray tracing and Monte Carlo calculations. V10% and V5%

analysis of contra lateral lung and spine are shown in Table 9.4. The dose

volumes of the ipsilateral lung are given in Table 9.5.

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Table 9.2 Dose volumes of the target calculated by different

smoothing algorithms

Dose calculation/smoothing

algorithm

Target Dose Volumes in percentage

V100% V95% V90% V85% V80%

Ray Tracing 94.31 99.93 100.00 100.00 100.00

Mo

nte

Car

lo s

mo

oth

ing

Alg

ori

thm

s

Average 17.24 54.13 82.59 96.10 100.00

Weighted Average 15.78 58.52 83.50 97.79 99.90

Gaussian(�=0.2) 24.90 58.98 86.46 96.58 99.92

Gaussian (�=3) 16.58 57.79 82.76 96.12 99.96

Clipped Gaussian(�=0.2) 24.90 58.98 86.46 96.58 99.92

Clipped Gaussian (�=3) 23.26 58.72 84.62 96.74 99.97

Desparkled-only 24.90 58.98 86.46 96.58 99.92

P-value 0.8931 0.4863 0.0329 <0.0001 <0.0001

Table 9.3 Conformity and homogeneity indices calculated by different

smoothing algorithms

Dose calculation/smoothing algorithm Conformity

Index

Homogeneity

Index

Ray Tracing 1.19 0.11

Mo

nte

Car

lo s

mo

oth

ing

Alg

ori

thm

s

Average 5.80 0.18

Weighted Average 6.34 0.18

Gaussian(�=0.2) 4.01 0.22

Gaussian (�=3) 6.03 0.18

Clipped Gaussian(�=0.2) 4.01 0.22

Clipped Gaussian (�=3) 4.30 0.19

Desparkled-only 4.01 0.22

p value 0.6544 0.4210

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Table 9.4 Spine and contra-lateral lung dose volumes for different

Monte Carlo smoothing algorithms and Ray tracing

calculation algorithm

Dose calculation/smoothing

algorithm

Dose volumes in mm3

Spine Contra-lateral (Right)Lung

V10% V5% V10% V5%

Ray Tracing 858.31 4404.07 77903.75 185400.01

Mo

nte

Car

lo s

mo

oth

ing

Alg

ori

thm

s

Average 30.52 367.69 3196.72 86472.51

Weighted Average 32.42 3616.33 3557.21 87102.89

Gaussian(�=0.2) 268.94 4141.81 7039.07 112191.20

Gaussian (�=3) 29.56 3656.39 3275.87 86572.65

Clipped Gaussian(�=0.2) 268.94 4141.81 7039.07 112191.20

Clipped Gaussian (�=3) 196.46 3403.66 5495.07 78414.92

Desparkled-only 268.94 4141.81 7039.07 112191.20

P- value 0.8808 0.6576 0.9259 0.6047

Table 9.5 Ipsi-lateral lung dose volumes for different Monte Carlo

smoothing algorithms and Ray tracing calculation algorithm

Dose calculation/smoothing

algorithm

Ipsi-lateral (Left) Lung dose volumes in mm3

V100% V80% V50% V30% V10% V5%

Ray Tracing 123.98 6729.13 21890.64 52158.36 331079.50 574212.11

Mo

nte

Car

lo s

mo

oth

ing

Alg

ori

thm

s

Average 0.00 531.20 16341.21 44845.58 260334.97 555864.32

Weighted Average 0.00 521.60 16209.60 47410.01 259840.97 554157.28

Gaussian(�=0.2) 0.00 905.04 16349.79 49522.40 270144.40 613836.32

Gaussian (�=3) 0.00 527.38 16305.92 47614.10 260173.81 555432.30

Clipped

Gaussian(�=0.2) 0.00 905.04 16349.79 49522.40 270144.40 613836.32

Clipped Gaussian

(�=3) 0.00 678.06 16048.43 49477.58 279426.56 526952.76

Desparkled-only 0.00 905.04 16349.79 49522.40 270144.40 613836.32

P-value 0.9529 0.9089 0.1823 0.0056 0.0832 0.0214

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Figure 9.5 DVH of the treatment plan smoothed by the average algorithm

Figure 9.6 DVH of the treatment plan smoothed by the weighted

average algorithm

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Figure 9.7 DVH of the treatment plan smoothed by the Gaussian

(�=0.2) algorithm

Figure 9.8 DVH of the treatment plan smoothed by the Gaussian (�=3)

algorithm

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Figure 9.9 DVH of the treatment plan smoothed by the Clipped

Gaussian (�=0.2) algorithm

Figure 9.10 DVH of the treatment plan smoothed by the Clipped

Gaussian (�=3) algorithm

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Figure 9.11 DVH of the treatment plan smoothed by the Desparkled-

only algorithm

9.4 DISCUSSION

Monte Carlo algorithm is the proven algorithm for accurate dose

calculations in radiotherapy (Krieger T. and Sauer O.A2005; Vanderstraeten

et al 2006; Wilcox et al 2010;Sharma et al 2011; Craig et al 2008). Sharma et

al (2011) studied the dose calculation accuracy of CyberKnife Monte Carlo

dose calculation algorithm with other commercially available algorithms.

According to that study the gamma analysis shows a better match in more

than 97% area with 3% dose difference and 3mm distance to agreement

criteria. Another study by Sharma et al (2010) shows a greater degree of

difference between Ray tracing and Monte Carlo doses especially in lung

target. According to that study the target coverage is 97.3% for Ray tracing

while it is only 71.3% for Monte Carlo calculations. The results of the present

study show that the Ray tracing dose coverage is 94.31% while the average

dose coverage value of all smoothing algorithm is only 21.08% only. This

difference is much higher than that reported in their study.

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Studies by Wilcox et al (2010) say that the maximum doses

calculated by the Ray tracing are higher than the Monte Carlo plans by up to a

factor of 1.63. In the present study the D98% of Ray tracing dose is 97.8% and

the mean D98% value of all smoothing algorithms is 84.5%. This difference is

lesser than the difference quoted by Wilcox et al (2010).

Gaussian smoothing algorithm with standard deviation of 1 is taken

in those studies by Sharma et al (2010). However the role of all other dose

smoothing algorithms in CyberKnife Monte Carlo calculations is not

addressed explicitly in any of the Monte Carlo studies reported till now. The

present study shows that there is a disparity in the conformity index among

the different dose smoothing algorithms.

The dose conformity index is the measure of conformity of the

prescribed dose to the target. Variation in the conformity index shows that

there is a non-uniformity in the dose coverage between the Monte Carlo

smoothed dose distributions. The values are more than 4 indicate the degree

of under coverage of the prescribed dose. The weighted average algorithm

gives the least dose conformity with a maximum conformity index of 6.34.

For an ideal dose distribution, the conformity index should be 1. Interestingly

the conformity index of Ray tracing calculation is closer to 1 and it is 1.19.

Homogeneity in dose distribution within the target is quantified

with the homogeneity index. For an ideal dose distribution the homogeneity

index should be zero. This means the D2% and D98% should be the same for an

ideal dose distribution. In reality for a good plan the homogeneity index

should be closer to zero. In the present study the homogeneity index for the

Ray tracing algorithm is 0.11. However the homogeneity index for all the

Monte Carlo smoothing algorithms it is about 0.20. The least value of

homogeneity index is obtained for Average, Weighted average and Gaussian

(�=3) algorithms with a homogeneity index of 0.18. Though there is a

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difference in the target covering dose, the difference among the smoothing

algorithms in the D95%, D90%, D50% and D2% are found to be small.

Disparity between the Monte Carlo smoothing algorithms is higher

for V100% values than the V80% values. This is seen in the OAR dose

distributions too. These results are showing that the smoothing algorithms are

creating appreciable discrepancies in the higher dose regions than in the lower

dose regions.

According to Sharma et al (2010) the difference between the Ray

tracing and Monte Carlo doses are also decided by the location of the tumor in

the lung. The present study is a phantom study and the target position at

different places couldn’t be accounted. Further studies on real patient should

be made to analyze the role of location in Monte Carlo Smoothing algorithms.

8.5 CONCLUSION

Monte Carlo smoothed doses for all the five available algorithms in

the Multiplan treatment planning system are resulting in reduced doses when

compared with the Ray tracing doses. The differences between the algorithms

are predominant in the higher doses regions and in the target dose conformity

index. In regions of lower doses the smoothing algorithms are giving similar

results with lesser discrepancy. Desparkled only and Gaussian, Clipped

Gaussian algorithms with smaller standard deviation are yielding same

results. However they are differing when the selected standard deviation is in

the higher side. As the dose smoothing algorithms are creating discrepancies

in the final dose distributions in lung targets, it is essential to select an

accurate and optimal dose smoothing algorithm in Monte Carlo dose

calculations of CyberKnife radiosurgery treatment planning of lung cancer.

Inappropriate choice of smoothing algorithm may lead to under or over

dosage in lung targets.