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Evaluation of tumor motion effects on dose distribution for

hypofractionated intensity modulated radiotherapy of non-small

cell lung cancer

Hyejoo Kang1, Ellen Yorke1, Jie Yang1, Chen-Shou Chui1, Kenneth Rosenzweig2, and

Howard Amols1

1 Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, NY

10065, USA

2 Department of Radiation Oncology, Memorial Sloan-Kettering Cancer Center, New York, NY

10065, USA

Abstract

Respiration-induced tumor motion during intensity modulated radiotherapy (IMRT) of non-small

cell lung cancer (NSCLC) could cause substantial differences between planned and delivered

doses. However, it has been shown that for conventionally fractionated IMRT motion effects

average out over the course of many treatments, but this might not be true for hypofractionated

IMRT (IMHFRT). Numerical simulations were performed for 9 NSCLC patients (11 tumors) to

evaluate this problem. Dose distributions to the Clinical Target Volume (CTV) and Internal Target

Volume (ITV) were retrospectively calculated using the previously calculated leaf motion files but

with the addition of typical periodic motion (i.e., amplitude 0.36–1.26 cm, 3–8 sec period). A

typical IMHFRT prescription of 20 Gy×3 fractions was assumed. For the largest amplitude (1.26

cm), the average±standard deviation of the ratio of simulated to planned mean dose, minimum

dose, D95 and V95 were 0.98±0.01, 0.88±0.09, 0.94±0.05 and 0.94±0.07 for the CTV, and

0.99±0.01, 0.99±0.03, 0.98±0.02 and 1.00±0.01 for the ITV. There was minimal dependence on

period or initial phase. For typical tumor geometries and respiratory amplitudes changes in target

coverage are minimal but can be significant for larger amplitudes, faster beam delivery, more

highly modulated fields, and smaller field margins.

Keywords

Hypofractionation; Lung cancer; IMRT; Organ motion effects

1. Introduction

Highly conformal photon dose distributions generated with Intensity-Modulated Radiation

Therapy (IMRT) often improve the therapeutic ratio, permitting higher tumor doses while

respecting normal tissue tolerance. Recently there has been increasing use of

hypofractionated IMRT (IMHFRT) at our institution1 and others2 for treatment of

inoperable early stage non-small cell lung cancer (NSCLC) using treatment schedules such

as 30 Gy×1 fraction3,4, 20 Gy×3 fractions5, 15 Gy×3 fractions6,12 Gy×4 fractions7. Early

studies report better local control than conventional multi-fractionated treatments, with

acceptable morbidity. The amplitude of lung tumor respiratory motion is typically 0.5–2.5

cm with periods of 3–8 seconds 8,9,10. To improve dose coverage of the Gross and Clinical

Tumor Volume (GTV and CTV) an Internal Target Volume (ITV) is often defined but dose

calculations usually do not account for motion-related effects such as interplay and blurring.

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Published in final edited form as:

J Appl Clin Med Phys. ; 11(3): 3182.

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‘Blurring’11,12,13,14,15,16,17 refers to changes in dose to a target voxel caused by motion to a

region where the dose is very different from what was planned. It is dependent on

respiration amplitude and the degree of modulation in the plan. For target voxels near the

beam penumbra blurring results in dose reduction even for non-IMRT treatments. IMRT

‘interplay’ refers to a change in delivered dose caused by tumor motion relative to MLC leaf

motion. During delivery, a target voxel, assumed to be stationary for treatment planning

dose calculations, may move relative to the moving MLC leaves and receive a significantly

different dose. Interplay effects also increase with respiratory amplitude and may also

depend on the breathing period and the breathing phase at the start of each beam. For

identical treatment plans the expectation value of a patient’s dose distribution is a function

mostly of blurring, while statistical variation is mostly determined by interplay.

Previous investigations12,13,14,15 showed that blurring and interplay effects average out for

IMRT consisting of >10 fractions. For IMHFRT, however, there are far fewer treatment

fractions but more breathing cycles per treatment field and the statistics are very different.

This treatment planning study attempts to answer whether these averaging effects also result

in only small perturbations to delivered dose for IMHRFT.

2. Methods and Material

2.1 Treatment Plans

Dose distributions from the clinical treatment plans for 9 early-stage NSCLC patients (11

tumors) previously treated at our institution with IMHFRT (20 Gy×3 or 12 Gy×4 fractions)

were retrospectively recalculated to assess perturbations in delivered doses resulting from

respiratory motion. At simulation patients were immobilized in a customized body cradle

and free breathing plus respiration correlated (4DCT) planning scans were acquired. The

physician delineated the GTV from the planning scan and expanded it to an ITV using the

4DCT. The CTV was defined as ITV plus 0 to 5 mm margin and the PTV encompassed the

CTV with 5 mm margin in all directions. Treatment plans were designed to give full dose

coverage to the PTV while respecting departmental normal tissue constraints: maximum

spinal cord dose (≤24 Gy/3 fractions), ipsilateral lung ( V20 (percentage of structure

receiving >20% of the prescribed dose) ≤25%,), total lungs (V20≤12%) and the mainstem

and distal bronchi (maximum dose ≤ 30 Gy/3 fractions and 60 Gy/3 fractions, respectively)

At each treatment fraction, a Kilovoltage Cone Beam CT (kVCBCT) was acquired and the

soft-tissue in the GTV region was registered to the planning CT for patient setup at each

treatment fraction. Department policy limits IMHFRT to patients whose respiratory motion

amplitude, tumor location and size are appropriate for the ensuing larger ITVs. Our

department’s technique for lung IMHFRT typically consists of 3–7 coplanar 6MV sliding

window IMRT beams, concentrated on the ipsilateral lung and delivered using a Varian

MLC with 5 mm leaf width running at a dose rate of 600 MU/min. For the past year, we

have taken care to ‘spread out’ the beams to reduce skin toxicity1. This differs from the ≥

10-field, non-coplanar, static field technique used by many others but, at ≥ 2 years, appears

to have similar local control/complication outcomes18.

All calculations were done on an in-house treatment planning system19,20 (written in Fortran

and C++ and currently running on a networked system of Windows-based PCs with ~ 4 GB

of memory and high end video cards). A radiological path-length corrected pencil beam

algorithm is used for tissue inhomogeneity correction. The IMRT optimization algorithm

uses an iterative gradient search method to minimize a quadratic objective function that

includes target dose uniformity and normal tissue maximum dose, mean dose and dose-

volume constraints21. A research module modifies the intensity profile incident on a tissue

voxel to account for relative motion between the voxel and the MLC as described below

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The NSCLC IMHFRT treatments typically require relatively modest beam modulation, but

we also examined the effect of respiratory motion on treatment plans with more highly

modulated beams.

2.2 Respiratory Motion Simulation

We used the methods of Chui et al13 which simulate one dimensional tumor motion, either

parallel or perpendicular to MLC leaf motion. Motion in lung is primarily in the cranial-

caudal direction and perpendicular to leaf motion which is typically in the axial plane 22,23.

Thus, respiration can displace a tumor voxel from beneath its planned leaf pair to an

adjacent pair where it will receive a different dose. Respiratory motion parallel to leaf

motion exposes a voxel to the open portion of the leaf pair for a different amount of time

than planned, also resulting in different delivered doses. This study concentrates and reports

in detail on motion perpendicular to the leaves although effects of periodic parallel motion

were also investigated.

The total beam intensity received at a point, X (x,y) is the integral over time or monitor units

(MU) of the product of the intensity I(X−χl,k(t)) for the kth left leaf and the intensity I(χr,k(t)

−X) for the kth right leaf (x and y coordinates parallel to and perpendicular to leaf motion).

χl,k and χr,k are the locations of the kth left and right MLC leaves where k is determined by

the point’s y coordinate. For stationary voxels the intensity at X(x,y) is a function only of the

speed (and hence gap width) of one leaf pair. But for a point moving periodically, with

period τ, amplitude A, initial phase t0, the intensity received depends on both leaf and voxel

motion. The intensity received at X(t+t0; τ; A), φp is given by:

1

where T is the total beam-on-time (in MU); I=1 if its argument is positive (X(x,y) is exposed

relative to that leaf) and is reduced by penumbra and leaf transmission for negative

argument. For motion parallel to the leaves the leaf index, k, does not change with time.

When motion is perpendicular, k varies with time and y. Target motion was assumed to be

periodic. We used the single periodic function obtained from a typical clinical breathing

trace (Fig. 1) for all simulations. Each respiratory cycle was divided into 13 equally-spaced

phases, and A and τ were scaled for investigation of the effects of amplitude and period on

the dose. The target was assumed to be a rigid-body and changes in tissue inhomogeneity

caused by tumor motion were not considered for the dose calculation.

2.3 Calculations and Analysis

The average ITV, CTV, and PTV were 9.9 (range, 1.5–27.3), 33 (range 10.2–75.7), and 70.7

(range 27.8–141.5) cc. Average field sizes were 7.7 (range 5–13) and 6.4 (range 4.5–8.5) cm

parallel and perpendicular to leaf motion. The average±standard deviation (σ) beam-on-time

per beam was 1184±456 (range 513–2506) MU, and average±σ leaf gap was 2.4±0.8 (range

0.7–3.5) cm. Depending on the breathing period, each treatment field included 13–36

breathing cycles.

Eq.1 was evaluated for dose prescriptions of 20 Gy×1 and 20 Gy×3 fractions using leaf-

sequence files from the original treatment plans modified by the respiratory motion of Fig. 1

with respiratory amplitudes 0.36, 0.9 and 1.26 cm (peak-to-peak excursions 0.68, 1.7 and

2.38 cm), and periods of 3, 5, and 8 seconds. The initial respiration phase for each fraction

was chosen randomly from points 1–13 in Fig. 1 and T in Eq.1 was set to the corresponding

MU. Doses calculated via Eq. 1 are denoted as Respiration Correlated Dose (RCD). To test

the effects of initial respiratory phase additional simulations were performing using 3

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different starting phases: at the rising slope (θ=1 in Fig. 1), maximum amplitude (θ=5), and

minimum amplitude (θ=12). For a given treatment fraction, the same initial phase was used

for each beam. Dmax, Dmin, and Dmean (maximum, minimum and average structure doses

respectively); D95 and D05 (dose encompassing the hottest 95% and 5% of the structure) and

V95 (percentage of structure receiving >95% of the prescribed dose) were calculated for the

ITV and CTV. Ratios of all dosimetric parameters to the planned quantity, designated as

RDmax, RD95, etc, were also calculated. A ratio of 1.0 means that respiratory motion does not

change the quantity, <1 means that it is reduced by motion, and >1 that it is increased.

Although the PTV is a geometric construct that is not subject to motion, dose parameters

were also calculated for the PTV to estimate the upper limit of respiration artifacts on

delivered target dose.

3. Results

3.1 Hypofractionated NSCLC plans

The RCD was insensitive (<1%) to period and initial phase for all simulations, but amplitude

effects could be large. Fig. 2(a) compares the planned PTV, CTV and ITV DVH’s (black

curves) for a 20 Gy×1 fraction treatment of Tumor#5 (4-fields, average 1157 MU, 81.9, 40.2

and 13.0 cc for PTV, CTV and ITV) with the corresponding RCD (red curves) for A=0.9

cm, perpendicular to leaf motion. The red DVHs were generated by starting the motion at

each of the 13 different phases shown in Fig. 1. The narrow spread of these DVHs shows the

small statistical deviation due to different initial phases. The expectation value of the RCD

lies within the bundle of red curves. For the PTV, it differs from the planned distribution,

with dose uniformity degraded and the sharp shoulder of the planned DVH rounded by

respiration induced dose blurring at the field edges. Dose to the CTV is minimally reduced

while dose to the ITV is unchanged. Qualitatively similar motion effects were seen for

parallel leaf and tumor motions.

Fig. 3 shows the planned and the effective intensity profiles for one field from this case.

Respiration-induced smearing of the profile in the direction perpendicular to the leaf motion

is evident.

Fig. 4 compares the planned and motion–affected isodose distributions for this case for three

fractions (60 Gy) with randomly chosen initial phase at each fraction. Penumbra broadening

in the cranial-caudal direction and smoothing of the lower isodose lines are seen for the

moving tumor. For organ motion parallel to leaf motion, the penumbra broadening is in the

anterior-posterior and left-right directions. The penumbra broadening is responsible for the

degradation of the PTV and CTV coverage.

For each dosimetric parameter and amplitude, we averaged the RCD’s calculated with the 3

different initial phases and 3 motion periods for 20Gy×1 and 20Gy×3 fractions over all

tumors. Fig. 5 shows averaged RDmin, RD95 and RV95 for A=0.36, 0.9, and 1.26 cm

(perpendicular to leaf motion). Red error bars show the ranges of variation, blue error bars

the standard deviations. Dmin, D95 and V95 are sensitive to dose gradients at field edges or in

regions of large modulation and are more sensitive to motion effects. Average RDmin is 0.77

(range 0.62–1.11) and 0.89 (range 0.76–1.12) for the PTV and CTV for A=1.26 cm; large

motion amplitude could displace target edges beyond the aperture swept out by the leaves,

resulting, on average, in a reduction of Dmin. Average RDmin for the ITV is ≃ 0.98 (range

0.91–1.06) indicating little change in delivered dose. For the PTV, the average RD95 and

RV95 with A=1.26 cm are reduced to 0.81 and 0.78. For the CTV there is only a 6%

reduction in RD95 and RV95, and for the ITV only 2% reduction, indicating that the CTV-

PTV margin chosen is sufficient.

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Average± standard deviation of RD95 and RV95 for A=1.26 cm for the PTV for 6 randomly

selected patients are 0.8±0.06 and 0.75±0.10 for perpendicular, and 0.84±0.05 and

0.72±0.13 for parallel to leaf motions. These ratios show that the motion effects are

qualitatively similar for perpendicular and parallel motions.

Changes in Dmean, Dmax and D05 are <2% for the ITV and CTV even for large amplitudes

since most IMRT lung plans have relatively homogeneous dose distributions near the

isocenter. Even for the PTV decreases in Dmean is <5%, and Dmax and D95 are <2%, similar

to the observations of Ref. 13 for conventional multi-fractionated lung IMRT.

We also confirmed that for conventionally fractionated treatments these intensity

distributions behaved similarly to those studied by others 12,13,15. Specifically, for a single 2

Gy fraction, interplay effects are more important and lead to greater dependence on initial

phases, but the interplay effects average out for the 30 or more sessions that are typical for

conventional fractionation.

3.2 Highly modulated case

Finally we studied motion effects for a 20 Gy fraction of one highly-modulated 7-field

treatment plan. The increased modulation was designed to protect a critical “serial” structure

adjacent to the target volume. The planned and effective intensity profiles calculated from

Eq.1 for this intensity pattern differ greatly as shown in Fig. 6. Blurring inside the field is

increased because of larger differences in leaf motion profiles between adjacent leaf pairs.

Fig. 7 shows the DVH’s for the planned dose and 13 simulations of the RCD with random

initial phases for A=0.36 cm (Fig. 7(a)) and 0.9 cm (Fig. 7(b)), and τ=5 sec. There is a

noticeable change in the expectation value of the dose distribution to all structures (PTV,

CTV, and GTV – taken to equal the ITV) even for small motion amplitude (Fig 7(a)).

However there is little variation due to different initial phases (indicated by the small spread

of the motion-affected DVH’s), because treatment extends over many breathing cycles per

field, which averages out the interplay effects even for this highly modulated IMHFRT plan.

The average RDmean for A=1.28cm are 0.89 and 0.92 for the CTV and GTV, with average

RDmax and RD05 reduced to 0.94 and 0.95 for the CTV, and 0.95 and 0.96 for the GTV. The

average RD95 falls to 0.83 and 0.85 for the CTV and GTV. The average RDmin and RV95 are

0.80 and 0.41 for the GTV, and 1.38 and 0.19 for the CTV. These results indicate that

expectation values of dose depend strongly on the degree of modulation, but the interplay is

small even for highly modulated intensity patterns with IMHFRT treatment.

4. Discussion

When sliding window IMRT is delivered to a target that experiences respiratory motion, the

effective beam intensity distribution is a complicated function of the tumor motion relative

to that of the MLC leaves. For a single fraction at conventional dose and dose-rate (2 Gy, ~

300–600 MU/min), several studies12,13,14,15,16 show that the dose distribution can depend

on the initial breathing phase as well as the respiratory amplitude and period but the variance

of dose distribution from the many fractions is negligible The study of Seco et al 16 implied

that the overall dose error between delivered dose and the motion average dose for IMHFRT

could be small due to long beam delivery time of high dose. Our study shows that for

IMHFRT delivered with the sliding window technique at 600 MU/min or less, the variance

has minimal dependence on respiratory period or initial phase. In our simulations, there are

on the order of 10–50 breathing cycles per beam, thus mitigating any dependence on initial

phases.

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A key point is that the total beam-on-time for an entire course of treatment is approximately

the same for IMHFRT (20 Gy×3 fractions) and conventionally fractionated IMRT (2 Gy×30

fractions). Thus the total number of breathing cycles during treatments is comparable which

in turn results in similar variances for the RCD. This result is not, however, apparent a

priori, but has been demonstrated by the simulations presented here. Further evaluation

should be made for sliding window treatments delivered with higher dose rates (e.g. 1000

MU/min) and/or delivery methods that reduce the MU, especially in patients with naturally

slow breathing periods or where 4DCT study shows large amplitude tumor motion. In such

cases, the variance in daily delivered dose can be large as it is for a single treatment with

low dose (2 Gy/fraction) and, although motion affects average out over a full course of

treatment, respiratory gating to limit the motion amplitude might be beneficial.

As discussed in previous studies, blurring effects depend on the proximity of the structure to

the field edges and the degree of in-field modulation. For modestly modulated NSCLC

treatment plans and ~ 5 mm margins, these effects are most evident for the PTV while they

are smallest for ITV which is furthest from the field edge. Dmin for the CTV can be reduced

by as much as 24% for large amplitude motion (e.g. 2.38 cm).

For more highly modulated fields than typically used for NSCLC treatments, respiratory

motion blurring could be problematic. If future lung or other thoracic cases require highly

modulated intensity patterns to protect a “serial” type normal structure (e.g. the esophagus or

mainstem bronchus) respiration effects should be evaluated by the planner.

We have also not studied the effects of respiratory motion on other treatment techniques

such as “step-and-shoot”, Tomotherapy, or volumetric arc treatment. We also approximated

tumor motion as one dimensional and periodic. In reality it is three dimensional and often

irregular. However, the weak dependence on period and phase and the qualitative similarity

of the effects of respiratory motion parallel and perpendicular to leaf motion suggest that

more accurately modeling these factors would not change our conclusions. Finally, we did

not account for deformation of the tumor or surrounding tissues.

It is well known that more advanced algorithms, superposition-convolution or Monte Carlo,

are preferable to the pencil beam algorithm for lung calculation24. A more accurate study on

tumor motion effects should be performed using these algorithms.

5. Conclusions

Respiratory motion effects depend primarily on motion amplitude with negligible

dependence on period or initial phase for the IMHFRT plans delivered for early-stage

NSCLC at our institution. For typical tumor geometries and respiratory amplitudes changes

in target coverage are minimal but can be significant for larger amplitudes, faster beam

delivery, more highly modulated fields, and smaller field margins.

Acknowledgments

This work was supported in part by Award Number T32-CA61801 from the National Cancer Institute. The content

is solely the responsibility of the authors and does not necessarily represent the official views of the National

Cancer Institute or the National Institutes of Health.

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Fig. 1.

Function used to simulate respiratory motion with an arbitrary unit of amplitude with 13

equal-spaced phases (θ) in time.

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Fig. 2.

DVH’s for the PTV, CTV and ITV for a lung IMHFRT treatment plan of 20 Gy×1 fraction.

Prescription dose corresponds to 100%.

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Fig. 3.

The planned intensity pro le (a) and the effective intensity profile for respiratory motion

with A=0.9 cm perpendicular to the leaf motion (b) for one lung HFRT field for single

fraction.

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Fig. 4.

The isodose distributions for the static tumor (left panels) and moving tumor with A=0.9 cm

perpendicular to leaf motion for 20 Gy×1 fraction (right panels). Yellow, pink and green

stars show the ITV, CTV and PTV respectively. Lines are percentages of prescription

isodose lines.

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Fig. 5.

Average RDmin, RD95 and RV95 over 132 simulations of various motion periods and initial

phases for moving tumor of all 11 HFRT treatment plans, PTV, CTV and ITV with the

standard deviation (blue bars), and range (red bars) of the ratios. The y-axis scaling does not

include the complete range for the largest amplitude PTV results.

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Fig. 6.

The intensity profile for static tumor (a) and effective intensity profile for a tumor moving

with A=0.36 cm (b) and 0.9 cm (c) perpendicular to the leaf motion for the highly modulated

intensity pattern for single fraction.

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Fig. 7.

DVH’s for the PTV, CTV and GTV for the highly modulated treatment plan for static tumor

(black) and for 13 simulation of a tumor moving (red) with A=0.36 cm (a) and 0.9 cm (b).

Prescription dose corresponds to 100%.

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