1

Experimental verification of 4D Monte Carlo simulations of dose delivery to a

moving anatomy

S. Gholampourkashi Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

M. Vujicic Department of Medical Physics, The Ottawa Hospital Cancer Centre, 501 Smyth Road, Box 927, Ottawa, Ontario K1H 8L6, Canada

J. Belec Department of Medical Physics, The Ottawa Hospital Cancer Centre, 501 Smyth Road, Box 927, Ottawa, Ontario K1H 8L6, Canada

Joanna. E. Cygler Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

Department of Medical Physics, The Ottawa Hospital Cancer Centre, 501 Smyth Road, Box 927, Ottawa, Ontario K1H 8L6, Canada

E. Heath Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

Purpose: To evaluate a novel 4D Monte Carlo simulation tool by comparing calculations to physical

measurements using a respiratory motion phantom.

Methods: We used a dynamic Quasar phantom in both stationary and breathing states (sinusoidal motion of

amplitude of 1.8 cm and period of 3.3 sec) for dose measurements on an Elekta Agility linear accelerator.

Gafchromic EBT3 film and the RADPOS 4D dosimetry system were placed inside the lung insert of the

phantom to measure dose profiles and point-dose values at the center of the spherical tumour inside the insert.

Both a static 4x4 cm2 field and a VMAT plan were delivered. Static and 4D Monte Carlo simulations of the

treatment deliveries were performed using DOSXYZnrc and a modified version of the defDOSXYZnrc user

code that allows modeling of the continuous motion of both machine and patient. DICOM treatment plan files

and linac delivery log files were used to generate corresponding input files. The phantom motion recorded by

RADPOS during beam delivery was incorporated into the input files for the 4DdefDOSXYZnrc simulations.

Results: For stationary phantom simulations, all point-dose values from MC simulations at the tumour center

agreed within 1% with film and within 2% with RADPOS. More than 98% of the voxels from simulated dose

profiles passed a 1D gamma of 2%/2 mm criteria against measured dose profiles. Similar results were

observed when applying 2D gamma of 2%/2 mm to compare 2D dose distributions of Monte Carlo

simulations against measurements. For simulations on the moving phantom, MC simulated dose values at the

center of the tumour were found to be within 1% of film and within 2 of experimental uncertainties (2.8%)

of RADPOS measurements. 1D gamma comparisons of the dose profiles were better than 91% and 2D gamma

comparisons of the 2D dose distributions were found to be better than 94%.

Conclusion: Our 4D Monte Carlo method using defDOSXYZnrc can be used to accurately calculate the dose

distribution in continuously moving anatomy for various treatment techniques. This work, if extended to

2

deformable anatomies, can be used to reconstruct patient delivered dose for the purpose of adaptive

radiotherapy techniques.

Key words: Monte Carlo, respiratory motion, 4D dose calculation, VMAT

I. INTRODUCTION

The ultimate goal of radiation therapy is to deliver a planned dose to a target volume while minimizing dose to

normal tissue. This objective, however, is limited by the fact that the dose distribution from the treatment plan is

based on a single state of the patient anatomy while patient’s anatomy and position often vary between treatment

fractions (inter-fraction motion) or during one fraction (intra-fraction motion).1-3

As a result of these positional

uncertainties, a significant deviation could be observed between the dose prescribed and received by a target

volume.3

Respiratory motion is an intra-fraction motion that contributes largely to the geometric uncertainties in

thoracic and abdominal sites.2-4

The main impact of the respiratory motion is the blurring of the dose distribution

along the path of the motion. The amount of this blurring is independent of the treatment technique and depends

on the properties of the respiratory motion.1,2

Localized deformations in the dose distribution are another effect

that occur due to the motion and deformation of the internal anatomy during respiration and can result in up to 5%

error in the localized dose values.1,5

When dynamic beam delivery techniques are used, an additional effect caused

by the interplay between motion of the machine components (e.g. multi-leaf collimators) and target motion is

observed inducing further deviation of 1%-10% in the delivered dose compared to the prescribed dose1,2,6-13

Many researchers have developed methods to account for these effects in the calculation of dose distributions.

One early approach is convolution14-16

of the static dose distribution with a probability distribution function (PDF)

that describes the characteristics of the respiratory motion. Although this approach sufficiently models the blurring

effect of the respiratory motion, it is limited by certain assumptions. One assumption is that the dose distribution

is shift invariant which results in inaccuracies at tissue interfaces.17,18

To accurately model the spatial dependence

of the dose distribution, a fluence-convolution method to convolve the incident beam fluence with the PDF of the

motion was suggested and implemented into Monte Carlo-based dose calculation algorithms.17,19,20

However, the

limitation that remained unresolved is that the patient motion can only be modeled as rigid body translation and

deformations in the anatomy are not considered.1,17

A more accurate approach to calculate the dose distribution, while accounting for the effects of respiratory

motion, is to accumulate the dose distributions calculated on different respiratory phases. This approach accounts

for the motion and deformation of the anatomy. The concept of 4D dose accumulation was initially introduced by

Brock et al.21

. Many other groups4,22-26

have investigated the reconstruction of accumulated dose in a deforming

anatomy using deformable image registration (DIR) to map dose calculated in each respiratory phase to a

3

reference (planning) phase. Although DIR provides a more realistic modeling of the respiratory motion, these

groups did not model the interplay effect in their dose calculations. Studies conducted by Rao et al.13

and

Paganetti et al.27

investigated 4D dose calculations with interplay effect during lung treatments. The first study

(Rao et al.) focused on IMRT and VMAT deliveries and determined the beam segment corresponding to each

respiratory phase. The dose from each segment was calculated on the appropriate respiratory phase. The second

study (Paganetti et al.) modeled proton therapy delivery. They used a Monte Carlo (MC) simulation method

where both the beam delivery and dose calculation geometries were continuously updated as a function of time

spent in each respiratory phase.

All of the previously mentioned 4D dose accumulation studies made use of dose interpolation methods in

combination with DIR to map the dose back to the reference geometry.22-27

Previous studies have assessed the

accuracy of dose interpolation methods for dose accumulation.28-31

Deformable image registration algorithms

might split or merge voxels while determining the correlation between images and thus cause a lack of a one-to-

one voxel correspondence between each respiratory phase and the reference phase (i.e. dose calculation grid is not

conserved). As pointed out by Siebers et al.28

, this can lead to inaccuracies when dose interpolation is used in

regions of dose or density gradients. More accurate approaches are the energy/mass transfer (EMT)28,29

and voxel

warping methods (VWM)30

. EMT uses deformation vector fields (DVFs) generated by DIR to map energy

deposited on each respiratory phase to a reference phase. VWM uses DVFs to deform voxels from the reference

geometry to reproduce each respiratory phase. Both methods assure conservation of the energy deposited as well

as the mass on each respiratory phase and as a result a more accurate cumulative dose calculation on the reference

phase.

A previous study by Belec et al.32

used the EMT method adopted from Siebers et al.28

and Zhong et al.29

to

calculate accumulated dose distributions from VMAT lung treatments. They modeled the continuous motion of

the beam during VMAT treatments using a position-probability sampling (PPS) technique.33

A randomly sampled

time variable between 0 and 1 was associated with each particle. This time variable was used to sample linac

geometry settings specified as a function of normalized cumulative MU. The time variable was then used to

interpolate DIR vectors and the voxel densities to more closely model changes associated with continuous motion.

The authors acknowledged the limitation of using this linear interpolation of the voxel densities and attempted to

minimize its impact by reducing the motion between respiratory phases to be smaller than voxel sizes. They

reported results from comparison of simulation with measurements for a sweeping field delivered to a respiratory

motion phantom moving a sinusoidal motion with 2 cm amplitude and 8 sec period. Delivery log files recorded at

a sampling interval of 250 ms were captured using an iCom listening software. The log files contained planned

and actual values for gantry, multi-leaf collimator leaves, jaws and table settings, cumulative MU delivered, dose

rate, and linac status (beam holds). The authors also applied the same MC method to calculate cumulative

delivered dose for VMAT plans for several lung patients. For these studies plan information was extracted from

the treatment planning system (TPS) and MC calculated dose were compared against the TPS dose.

4

Recently, we have developed a 4D Monte Carlo simulation tool34

for reconstructing the delivered dose

accounting for respiratory motion. This approach uses the voxel warping method and delivery log files to model

continuous motion of machine components and patient voxel boundaries. The aim of the current work was to

validate this simulation tool using a lung motion phantom. Dose delivery was performed on an Elekta Agility

linac for both static and dynamic (VMAT) delivery techniques. Dose distributions from Monte Carlo simulations

were compared with measurements to evaluate the accuracy of simulations. We demonstrate how motion recorded

during dose delivery as well as the delivery log files, using a 4D dosimetry system, are incorporated into our

simulations.

II. MATERIALS AND METHODS

II. A. Measurements

II. A.1. Quasar respiratory motion phantom

Measurements were performed in a Quasar respiratory motion phantom (Modus Medical, London, ON,

Canada), containing a cylindrical lung insert made of cedar wood with a 3 cm diameter solid water sphere to

imitate a tumour (Fig. 1).

FIG. 1. (a) The Quasar respiratory motion phantom, (b) wooden lung insert, (c) solid water tumour.

The Quasar phantom simulates the breathing motion by allowing the lung insert to move rigidly in one

direction according to a programmed motion function. A single, reproducible, sinusoidal motion function was

used for all experiments.

II. A.2. 3DCT acquisition

3DCT scans of the Quasar phantom were acquired using a helical CT scanner (Brilliance CT Big Bore,

Philips, Amsterdam, Netherlands). Reconstructed images had a standard resolution of 0.0625 0.0625 0.1 cm3

resulting in an image matrix of 512 512 246 voxels. The center of the sphere inside the lung insert was

(a) (b)

3 cm

(c)

5

positioned at the zero amplitude position. Pitch values and the gantry rotation times for the scans were 0.95 0.75

sec, respectively.

II. A.3. Treatment plans

Two treatment plans using a 6 MV photon beam were created on the static 3DCT scans of the Quasar phantom

to deliver 100 cGy to the center of the tumour. A GTV was created by delineating the tumour. No margins were

added to compensate for motion. Both treatment plans were designed to cover the GTV. The first treatment plan

was a static 4 4 cm2 square field that was created using XiO V.4.7 (Elekta AB, Stockholm, Sweden). The

resultant dose distribution, calculated using a superposition algorithm, is shown in Fig. 2.

FIG. 2. Static 4 4 cm2 square plan from XiO: dose distributions on (a) axial, (b) coronal and (c) sagittal planes.

The second treatment plan was a VMAT plan with 45 control points that was created in Monaco V.5.10.02.

The start and stop angles of the VMAT delivery arc were 180o with angular spacing of 8

o between most control

points. The dose calculation algorithm used by Monaco is XVMC35

(X-ray voxel Monte Carlo). A 2 mm dose

calculation grid with a statistical uncertainty of 1% was used to calculate the dose to water (Dw) to comply with

measurements (film and RADPOS) and MC calculations. Figure 3 shows the dose distribution corresponding to

the VMAT treatment on the static 3DCT image of the Quasar phantom.

(a) (b)

(c)

6

FIG. 3 Static VMAT plan from Monaco: dose distributions on (a) axial, (b) coronal and (c) sagittal planes.

II. A.4. Dose measurements: Film and RADPOS

Dose measurements inside the Quasar lung insert were performed using calibrated Gafchromic film (EBT3,

Ashland, Wayne, NJ, United States) and the RADPOS 4D dosimetry system36,37

. The RADPOS probe consists of

a microMOSFET dosimeter and an electromagnetic positioning sensor and is capable of simultaneous real-time

monitoring of dose and position. The MOSFET dosimeter and position sensor are separated by 8 mm to minimize

the perturbation of the incident radiation fluence at the MOSFET location.

RADPOS dose measurements are based on measuring the change in the threshold voltage (∆Vth) of the

MOSFET detector before and after irradiation. Hence, a calibration coefficient is required to convert readings in

mV to absorbed dose in cGy. The position sensor, preamplifier, transmitter and 3D-guidance tracker are

responsible for position tracking of RADPOS. The RADPOS transmitter generates a 3D DC magnetic field. This

signal is received by the position sensor and its response to the signal is amplified through a pre-amplifier and

monitored by the guidance tracker to determine the spatial coordinates of the RADPOS probe. More details about

the system can be found in the publication by Cherpak et al.37

The EBT3 film and RADPOS detector used in this work were cross-calibrated against an A1SL ionization

chamber (Standard imaging Inc., Middleton, WI, USA) in a 6 MV photon beam at a field size of 10 10 cm2. Film

and RADPOS were placed at a depth of 5 cm and the A1SL chamber was placed at a depth of 10 cm in a Solid

(a) (b)

(c)

7

Water (RMI457 Gammex, Wisconsin, USA) phantom at an SSD of 100 cm. After appropriate irradiations (three

irradiations of 100 MU for RADPOS and eight irradiations of 0, 5, 25, 50, 75, 119, 178, 240 MU’s for film), dose

to water (Dw) at the position of RADPOS and film was determined using the PDD curves available in the clinic.

The calibration coefficient ( for RADPOS was derived by calculating the ratio of the average dose

delivered to RADPOS (Dw) to the average change in the threshold voltage (∆Vth). Films were scanned (pre and

post-irradiation) using an Epson (10000XL, Suwa, Naogna, Japan) scanner. The film analysis and calibration (to

convert film readings to Dw) was performed according to the procedures described in Devic et al.38

using an in-

house MATLAB (R2013a, Mathworks, MA, USA) script.

For dose measurements with the Quasar phantom, film and RADPOS were placed inside the lung insert of the

phantom as shown in Fig. 4. The RADPOS probe was fixed in a special groove that was cut into the spherical

solid water tumour and the lung insert so that its point of measurement was located at the center of the tumour.

Film was placed and taped on top of the RADPOS probe.

FIG. 4. Film and RADPOS inside the lung insert of the Quasar phantom. RADPOS was placed inside a special groove and film was

placed on the top of RADPOS probe.

The total dosimetric uncertainty of RADPOS measurements was determined to be 1.40%, including the

uncertainties in the dosimeter calibration and beam delivery conditions. Sources that contributed to the dosimeter

calibration uncertainty (1.39%) included uncertainties corresponding to IC calibration (NDw from clinical data

~1%, kQ from literature39

), IC reading (0.16%), RADPOS reproducibility (0.48%) and Solid Water phantom

material variability40

. With respect to the beam delivery conditions, uncertainties corresponding to SSD, depth and

field size settings as well as temperature and pressure correction factors were the main contributors to the total

uncertainty of 0.25%.39

The total dosimetric uncertainty of the film measurements was determined to be 2.3%.

Items such as scanner uniformity, lateral correction, film inhomogeneity, energy and angular dependence, fit

accuracy (netOD to Dose) and intra-batch variations were considered to be main contributions to uncertainty

associated with EBT3 films (1.83%).41

Regarding the calibration, total uncertainty (1.3%) was determined based

on parameters such as IC calibration (NDw from clinical data ~1%, kQ from literature39

) and Solid Water phantom

material variability40

. The uncertainty related to beam delivery (0.25%) was determined to be similar for film and

Film

RADPOS probe

8

RADPOS measurements. Total dosimetric uncertainties of film and RADPOS measurements were obtained by

quadrature sum of all contributing sources of uncertainty.

II. A.5. Quasar phantom irradiations

The treatment plans described in section II.A.3 were transferred to the Elekta MOSAIQ RadOnc system and

delivered to the Quasar phantom on an Agility linac (Elekta AB., Stockholm, Sweden). The 4 4 cm2 square plan

delivered 123.2 MU at a nominal dose rate of 600 . The VMAT plan delivered 172.3 MU at a varying

dose rate. Delivery log files (IAN V.2, Elekta AB., Stockholm, Sweden) containing cumulative delivered MU,

gantry, multi-leaf collimator, jaws and table positions at 40 ms intervals were saved after each delivery and

processed as explained in section II.B.1.

For both treatment plans, irradiations were performed with the Quasar in stationary (no motion) and breathing

(sinusoidal motion, 1.8 cm respiratory amplitude, 3.3 s period) states. To align the phantom, the center of the

sphere inside the lung insert was positioned at the zero amplitude position and was aligned with the beam

isocenter. During all irradiations, film and RADPOS were placed inside the lung insert (as explained in section

II.A.4) to measure the point dose at the center of the tumour (film and RADPOS) as well as dose profile (film)

along the motion path of the tumour. For irradiations with breathing motion, the RADPOS positioning sensor was

used to record the motion at a sampling interval of 100 ms. In order to synchronize the beam-on time with the

starting phase of the Quasar motion, it was assured that computer clock times of both MOSAIQ and RADPOS

were synchronized.

II. B. Monte Carlo simulations

II. B.1. Monte Carlo user codes and their simulation parameters

All Monte Carlo simulations were performed using EGSnrc42

(V4-2.4.0, National Research Council of

Canada, Ottawa, ON, Canada). The BEAMnrc43

user code was used to model the Elekta Agility linear accelerator.

Dose distributions on stationary and moving phantoms were calculated with the DOSXYZnrc44

and

defDOSXYZnrc30

user codes, respectively. Calculated dose from Monte Carlo simulations was converted to

absolute dose using the following formulation:

(1)

where, is the monitor units (MU) delivered by a linear accelerator. In this formula

represents the dose scored per number of incident particles in a Monte Carlo simulation. The calibration

simulation was performed in water for a square field of 10 10 cm2 and SSD of 100 cm and dose was scored at a

depth of 10 cm.

9

DICOM plan files exported from the TPS as well as the linac delivery log files were used to generate all the

input files required for Monte Carlo simulations. An in-house Python script was written to perform these

functions. The photon cutoff energy (PCUT) and electron cutoff energy (ECUT) were set to 0.01 and 0.7 MeV,

respectively and the electron range rejection was set to 2 MeV for all Monte Carlo simulations. Dose calculations

were performed with 300,000,000 histories to achieve a mean relative statistical uncertainty45

of 0.4% over all

voxels with doses greater than 50% of the maximum dose.

II. B.2. Monte Carlo model of Elekta Agility linear accelerator

Figure 5 shows an illustration of the Elekta Agility linac model in BEAMnrc including the patient independent

(target, flattening filter, etc.) and patient dependent (160 multi-leaf collimators, lower jaws) components. To

model the multi-leaf collimators and lower jaws, the SYNCMLCE and SYNCMLCQ component modules (CMs)

were used, respectively. The ‘SYNC’ versions of these component modules enable synchronization of the motion

of the multi-leaf collimators, gantry and jaws in the linac model and dose calculation geometry by using a

common, randomly generated MU index which lies between 0 and 1, to sample the configuration of the linac

components for each particle history. This was required for the VMAT delivery simulations which used Source

2146

in DOSXYZnrc. A ‘SYNC’ version of the MLCQ component module was created by modifying this CM to

read the MU index generated in the SYNCMLCE CM. The SYNCMLCE module was also modified to account

for the defocusing of the leaf bank with respect to the focal spot to limit interleaf transmission.

FIG. 5. BEAMnrc preview of the Elekta Agility linac model showing the various component modules.

The linac model was constructed based on the technical data provided by the manufacturer and previously

published work47

. Details of the model parameters and validation have been presented elsewhere48

. For the

BEAMnrc simulations, bremsstrahlung cross-section enhancement was turned on while other transport parameters

were set to default values.

Primary collimator

Flattening filter

Target

Backscatter plate

Multi-leaf collimator

Lower jaws

Monitor Ion chamber

10

II. B.3. Dose calculation geometry

The voxelized geometry for dose calculations (egsphant file) was created from the 3DCT scans of the Quasar

phantom using an in-house software. Voxel densities were assigned using the HU/density calibration data for the

Big Bore CT scanner. For material assignment to the voxels, the approach introduced by Seco et al.49

was

followed to define voxels inside the phantom as water with densities derived from the CT image. With this

approach we can calculate Dw in MC simulations which allows direct comparison against film and RADPOS

measurements. All voxels outside the phantom were assigned as air with default density. The original CT image

was re-sampled to a resolution of 0.125 0.125 0.2 cm3 to generate the dose calculation geometry as shown in

Fig. 6.

FIG. 6. Dose calculation geometry (egsphant file) generated using static CT scans of the Quasar phantom.

II. B.4. Monte Carlo simulations of stationary phantom

Two sets of input files for DOSXYZnrc were created for simulations of the 4 4 cm2 and VMAT plan

deliveries on the stationary state of the phantom. The first set of simulations used input files generated from the

DICOM plan files as described in section II.B.1. Linac delivery log files were used to generate input files for

second set of simulations.

For simulation of the 4 4 cm2 square plan delivery, the linac model described in section II.B.2 was used as a

particle source (Source 9) thus eliminating the need to store a separate phase space file44

. Source 2146

was used to

simulate the VMAT beam delivery. Source 21 also uses a full BEAMnrc linac model as a particle source, but

additionally, as mentioned earlier in section II.B.2, it uses an MU index to synchronize the motion of dynamic

components of the linac in BEAMnrc. This MU index is then used to interpolate between the control points

specifying the gantry, collimator and couch angle in the treatment plan or delivery log file (extracted as explained

in section II.B.1) as a function of fraction of the delivered monitor units to determine the source settings in

DOSXYZnrc. A photon splitting value of 10 and default values for other transport parameters were used for all

DOSXYZnrc simulations.

11

II. B.5. 4D Monte Carlo simulations of moving phantom

Simulations of plan delivery on the breathing motion state of the Quasar phantom were performed using a

modified version of the defDOSXYZrc user code30

. Organ motion is modeled in defDOSXYZnrc by displacing

the voxel nodes of the reference dose calculation geometry using displacement vectors. These displacement

vectors may be generated from a motion model or deformable image registration. New densities are calculated for

each deformed voxel to ensure conservation of mass between the reference and deformed geometries. Incident

particles are transported and their energy depositions are scored in the deformed geometry. No mapping of doses

between geometries is required since the same dose calculation grid is retained for all motion phases simulated.

The output of a defDOSXYZnrc simulation is the dose distribution in the reference geometry coordinates, which

was the stationary state of the Quasar phantom in this work.

The modified version of the defDOSXYZnrc, which we refer to as 4DdefDOSXZYnrc, enables simulation of

a continuously deforming geometry by sampling a new geometry for each incident particle. The MU index

defined in source 21 is used to determine the corresponding motion phase from a user-specified respiratory motion

trace. The voxel node displacements are linearly interpolated from a set of displacement vectors which the user

provides as input to the simulation.

The input files generated for the 4DdefDOSXYZnrc simulations used the beam delivery information from

linac delivery log files as well as the Quasar respiratory motion recorded by RADPOS. The RADPOS motion was

re-sampled to match the resolution of the log file and then normalized to give a displacement vector scaling factor

that ranged between -1 and 1 as a function of cumulative MU (Figure 7). For each incident particle, the MU index

used in source 21 is used to interpolate a vector scaling factor to be applied to the displacement vectors. Since the

Quasar lung insert moves rigidly, displacement vectors that exactly modeled this rigid translation (peak-to-peak

amplitude and direction) were generated with an in-house Python script using the recorded motion trace data.

FIG. 7 Normalized displacement (scaling factor for displacement vectors) recorded by RADPOS and re-sampled according to the

resolution of log files.

12

II.B.6. Monte Carlo simulation comparisons with measurements

2D dose distributions from film and MC simulations were extracted and compared using a 2D gamma

analysis50

with a 2% dose-difference and 2 mm distance-to-agreement criteria. The choice of these criteria was to

comply with the AAPM commissioning and QA guidelines51 for gamma comparisons of VMAT plan deliveries.

The film dose was used as the reference dose distribution for the gamma analysis. A dose calculation grid with 2

mm voxel size along the motion path of tumor was used for MC simulations. The dose grid resolution of film was

reduced (by applying a moving average filter) to match the resolution of the MC dose grid. Dose grids from film

and MC were aligned for the best agreement between the dose distributions. While this approach eliminates the

influence of setup errors, the alignment corrections were observed to never exceed 0.7 mm. Two different dose

thresholds, 5% and 50% of the evaluated maximum dose were tested to evaluate the agreement for all voxels or

only voxels in high dose regions, respectively

Dose profiles along the superior/inferior direction (motion path of the tumour) were extracted from film

measurements and were compared with profiles from MC simulations using an in-house Python script. A 1D

gamma analysis using the same parameters as the 2D analysis was performed on the dose profiles. Comparisons

of dose values at the center of the tumour were performed between measurements (film and RADPOS) and MC

simulations. RADPOS measurements were converted to absolute dose using the calibration coefficient acquired as

explained in section II.A.4.

13

III. RESULTS

III. A. Stationary phantom comparisons

Figure 8(a, b) shows the comparison of dose profiles from MC simulations using log files (MC-Log file) as

well as film for the 4 4 cm2 and VMAT plan deliveries on the stationary state of the Quasar phantom.

FIG. 8. Dose profile comparisons for 4×4 cm2 (Left) and VMAT (Right) plan deliveries on the stationary phantom along the

superior/inferior direction (Top row), 2D dose distribution (Middle row) and gamma comparison maps (Bottom row) from film

measurements and MC simulations (log file). Gamma comparison maps were generated using a dose threshold = 50% Dmax.

Good agreement was observed between the measured and simulated dose profiles with more than 99% of the

voxels passing the 1D gamma of 2%/2 mm criteria, for both plan deliveries when 5% Dmax threshold was applied.

For the 50% Dmax threshold, the agreements were observed to be higher than 99% for the VMAT delivery and

(b) (a)

(f) (e)

(d) (c)

2%/2 mm 2%/2 mm

14

98% for the static plan delivery. Also, a passing rate of 99.1% and 100% (i.e. all dose points) was observed

comparing MC simulations using log files (MC-Log files) against film measurements for the static and VMAT

plan deliveries, respectively. MC simulations using log files (MC-Log files) against film measurements were

found to have 100% passing rate for the 5% Dmax threshold. In Fig. 8(b), dose points in profiles from film and MC

simulations were observed to have a distance-to-agreement of less than 1 mm.

Table I shows the RADPOS and film dose measurements taken at the center of the tumour as well as the

corresponding dose values from MC simulations. Uncertainties reported on dose values are experimental (film

and RADPOS) or statistical (MC simulations). Percent difference comparisons for dose values were calculated as

well.

TABLE I. Dose values at the center of the tumour from RADPOS, film and MC simulations for static and VMAT beam deliveries on the

stationary phantom.

Dose (cGy)

Plan MC(DICOM) MC(log file) Measurements

Film RADPOS

Static 4 4 cm2 99.50.4% 99.30.4% 100.52.3% 101.61.4%

VMAT 99.50.4% 99.80.4% 99.02.3% 98.41.4%

All dose values from MC simulations were found to be within 1% of film and 2% of RADPOS for VMAT

plan delivery. The same was true for the static plan delivery with the exception of MC-Log file against film

measurements having a discrepancy of 1.2%. Film and RADPOS doses agreed with each other at 1.1% for the

static and 1% for the VMAT plan beam deliveries.

2D dose distributions from film and MC-Log file simulations for the 4 4 cm2 and VMAT plan deliveries, as

well as the 2D gamma comparison maps for a 2%/2 mm criteria are shown in Fig. 8(c, d) and Fig. 8(e, f),

respectively. Gamma comparison maps were generated for a dose threshold of 50% of the reference maximum

dose. The passing rates of the 2D gamma comparisons for both deliveries are shown in Table II.

15

TABLE II. Passing rate of 2D gamma comparison of 2%/2 mm criteria for MC simulations (DICOM and log files) against film

measurements for static and VMAT deliveries on the stationary phantom.

As the values from Table II for VMAT delivery suggest, more than 99% of the dose points passed the 2D

gamma of 2%.2 mm for MC simulations against film measurements when a 50% dose threshold was used. At 5%

dose threshold, passing rate was reduced by less than 2% compared to a 50% threshold. With regards to the static

plan delivery, a passing rate of almost 99% was observed for both dose thresholds.

III. B. Moving phantom comparisons

For the moving state of the Quasar phantom, MC simulations used only delivery information from the log

files. Comparison of dose profiles from MC simulations using log files and film for both 4 4 cm2 and VMAT

plan deliveries on the moving state of the Quasar phantom is shown in Figure 9(a, b).

Plan Evaluated dose profile Reference dose profile

Threshold = 5%

Dmax

Threshold = 50%

Dmax

Film Film

Static 4 4 cm2

MC (DICOM) 99.5% 98.9%

MC (log file) 99.5% 98.9%

VMAT

MC (DICOM) 97.9% 99.5%

MC (log file) 97.9% 99.5%

16

FIG. 9. Dose profile comparisons for 4×4 cm2 (Left) and VMAT (Right) plan deliveries on the moving phantom along the

superior/inferior direction (Top row), 2D dose distribution (Middle row) and gamma comparison maps (Bottom row) from film

measurements and MC simulations (log file). Gamma comparison maps were generated using a dose threshold = 50% Dmax.

The level of agreement between dose profiles was verified using a 1D gamma criterion of 2%/2 mm and all

points from MC simulations agreed with the film for the static plan delivery. For VMAT delivery, the level of

agreement between MC simulation and film measurement was observed to be higher than 91% according to the

1D gamma comparisons for both dose thresholds. Discrepancies between measured and simulated profiles at the

vicinity of the maximum dose region for the VMAT delivery were found to be within the experimental

uncertainties (2.3%) and are attributed to film uncertainties.

(b) (a)

(d) (c)

(f) (e)

2%/2 mm 2%/2 mm

17

Dose values from MC simulations, film and RADPOS taken at the center of the tumor are shown in Table III.

Based on percent difference comparisons, MC simulations agreed within 1% with film and within 2 of

experimental uncertainties (2.8%) with RADPOS measurements. Film and RADPOS dose values were found to

be within 2% of each other.

TABLE III. Dose values at the center of the tumour from RADPOS, film and MC simulations for static and VMAT deliveries on the

moving phantom.

Dose (cGy)

Plan MC(log file) Measurements

Film RADPOS

Static 4 4 cm2 96.10.4% 96.42.3% 98.41.4%

VMAT 91.90.4% 91.12.3% 89.61.4%

Results of the 2D gamma comparisons with a 2%/2 mm criteria between the 2D dose distributions illustrated

in Figure 9(c, d) and Figure 9(e, f) are presented in Table IV. Gamma comparison maps were generated for a dose

threshold of 50% of the reference maximum dose.

TABLE IV. Passing rate of 2D gamma comparison of 2%/2 mm criteria for MC simulations (log files) against film measurements for static

and VMAT deliveries on the moving phantom.

2D dose distributions from MC simulations and film measurements had a good agreement and the passing rate

of gamma comparison was found to be higher that 94% for the VMAT delivery. The passing rate was found to be

slightly better when only dose points in the high dose region (i.e. 50% Dmax) were compared. All dose points (i.e.

100% passing rate) passed the gamma comparison when MC simulations were compared against films

measurements for the static plan delivery.

Plan Evaluated dose profile Reference dose profile

Threshold = 5%

Dmax

Threshold = 50%

Dmax

Film Film

Static 4 4 cm2

MC (log file) 100% 100%

VMAT

MC (log file) 94.6% 97.4%

18

IV. DISCUSSION

The aim of this study was to validate 4D Monte Carlo simulations of the dose delivered to a respiratory

motion lung phantom using the 4DdefDOSXYZnrc user code. A static 4 4 cm2 and a VMAT plan were delivered

to the phantom in stationary and breathing states. Our results show that the overall agreement of point dose values

at the center of the target volume (i.e. tumour) from MC simulations and film measurements is within 1.2%. Dose

differences between RADPOS and MC simulations are not larger than 2 of the experimental uncertainty, which

corresponds to 2.8%. These results apply to both plan deliveries and phantom motion states, i.e., stationary and

moving. Dose profiles and 2D dose distributions from film and MC simulations using delivery log files (MC-Log

file) were found to agree with more than 95% of the dose points, and hence passed the gamma comparison of

2%/2 mm placing the results in an acceptable clinical range. The level of agreement was observed to be higher for

the 4 4 cm2 square plan deliveries compared to VMAT; this can be related to the lower level of the treatment plan

complexity.

The validation work presented in this paper was performed in a rigidly moving phantom. We used manually

generated displacement vectors to accurately model the lung insert motion. The use of DIR algorithms was not an

appropriate choice considering that the motion was a purely rigid translation without any deformations occurring

in the lung insert. Work is currently underway to extend the validation work to a deformable phantom in order to

evaluate the accuracy of our 4DMC method to calculate dose delivered to a deforming anatomy. The use of DIR

to generate deformation vectors will be necessary to model deformations occurring in the phantom. This means

that the accuracy of simulation will depend on the accuracy of DIR algorithm as well. Thus, the challenge here

will be to generate DVFs that are as accurate as possible. Multiple sets of DVFs from registering different

respiratory phases (e.g. end-of-inhale or end-of-exhale) to the reference phase might be required to achieve the

most accurate model for the phantom motion and deformation.

A potential source of experimental uncertainty in this work is the temporal resolution of RADPOS and

delivery log files. The maximum sampling rate of the RADPOS position tracker is 100 ms and the sampling rate

for log files is 40 ms. Such sampling intervals act as system latencies of approximately 108 ms (summed in

quadrature) and limit our ability to accurately determine the starting phase of the respiratory cycle. Based on the

phantom motion used in these studies, this system delay was estimated to result in positional inaccuracies of about

1.1 mm. In addition to that, the uncertainty of the displacement measurements by RADPOS should be taken into

account. This uncertainty was measured to be about 0.2 mm and is in agreement with values reported by Cherpak

et al.37

. Another source of uncertainty is the accuracy of the PC clock synchronization between MOSAIQ and

RADPOS PCs. This synchronization is good to within ms and can also introduce positional uncertainties of less

than 1 mm when trying to detect the motion starting phase. Investigations of the impact of such positional

uncertainties showed that they lead to point dose uncertainties of 1%-2% at the center of the tumour. These

investigations indicate the sensitivity of our 4D dose calculations to interplay effect. For shorter delivery times

19

where only a few respiratory cycles are present or VMAT plans which are more highly modulated, accurate

detection of the starting phase of the respiratory cycle will become more important to assure better agreement

between 4DMC simulations and measurements.

A further source of uncertainty is the interpolation between the control points as performed by source 21 in

MC simulations. However, investigations showed that the effect of such interpolation is negligible. The high

sampling rate of the log files means that control points in MC input files are defined at every 40 ms and linear

interpolation occurs between these control points. Based on analyzing our log files, this corresponds to less than

0.2o of change in the gantry angle and maximum of 0.1 mm change in the MLC leaf positions between two

successive control points. This corresponds to the MU index (fraction) change of less than 0.001 between two

consecutive interpolation or control points, which minimizes the potential impact of interpolation on the dose

calculations.

The total uncertainty of the film dose measurements could have been reduced to about 1.6% if two films were

used for each individual Quasar irradiation. Using triple-channel rather than single channel film dosimetry is also

a potential film processing technique that can reduce the noise level of the film response and as a result the

dosimetric uncertainty52

.

V. CONCLUSIONS

The accuracy of a 4D Monte Carlo-based simulation tool to deliver dose to a Quasar respiratory motion

phantom using an Elekta Agility linac was investigated and verified. A sinusoidal motion with an amplitude of 1.8

cm and period of 3.3 sec was tested and RADPOS system was used to record this motion in real-time. Linac

delivery log files were used, along with the respiratory motion trace, to reproduce measurements during static 4 4

cm2 square plan and VMAT plan deliveries. Dose values at the center of the target volume inside the phantom

were observed to be within 1.2% compared to film measurements and not higher than 2 of the experimental

uncertainties (2.8%) with respect to RADPOS. Less than 5% of dose points from MC simulations using log files

failed a 2%/2 mm gamma comparison when compared against film measurements. This work has shown that our

4DMC simulations using the defDOSXYZnrc user code in combination with RADPOS (to measure motion) and

delivery log files (to reproduce beam delivery) accurately calculate realistic dose distributions in a moving

anatomy. Future work will focus on establishing the accuracy of our method in a deformable phantom as well as

investigating irregular respiratory motion patterns. If extended to deformable anatomies and more realistic

respiratory motions, this 4DMC simulation tool can be used for adaptive purposes by accurately calculating the

cumulative dose delivered to patients during treatments.

ACKNOWLEDGEMENTS

We would like to thank Jason Smale of Elekta for helping us with delivery log files. This project has been

supported by a grant from the Ontario Consortium for Adaptive Radiotherapy (OCAIRO).

20

DISCLOSURE OF CONFLICTS OF INTEREST

The authors have no relevant conflicts of interest to disclose.

21

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