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J Appl Clin Med Phys. Author manuscript; available in PMC 2010 August 20.

Published in final edited form as:

J Appl Clin Med Phys. 2010 June 8; 11(3): 3182.

PMCID: PMC2924766

NIHMSID: NIHMS206537

Hyejoo Kang,^{1} Ellen Yorke,^{1} Jie Yang,^{1} Chen-Shou Chui,^{1} Kenneth Rosenzweig,^{2} and Howard Amols^{1}

See other articles in PMC that cite the published article.

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.

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 institution^{1} and others^{2} for treatment of inoperable early stage non-small cell lung cancer (NSCLC) using treatment schedules such as 30 Gy×1 fraction^{3}^{,}^{4}, 20 Gy×3 fractions^{5}, 15 Gy×3 fractions^{6},12 Gy×4 fractions^{7}. 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.

‘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 investigations^{12}^{,}^{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.

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 ( V_{20} (percentage of structure receiving >20% of the prescribed dose) ≤25%,), total lungs (V_{20}≤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 toxicity^{1}. 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 outcomes^{18}.

All calculations were done on an in-house treatment planning system^{19}^{,}^{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 constraints^{21}. 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

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.

We used the methods of Chui *et al*^{13} 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

$${\phi}_{p}={\int}_{t=0}^{T}I({\chi}_{rk}(t)-X(t+{t}_{0};\tau ;\text{A}))I(X(t+{t}_{0};\tau ;\text{A})-{\chi}_{lk}(t))dt$$

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,

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 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. D_{max}, D_{min}, and D_{mean} (maximum, minimum and average structure doses respectively); D_{95} and D_{05} (dose encompassing the hottest 95% and 5% of the structure) and V_{95} (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 R_{Dmax}, R_{D95}, 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.

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.

DVH’s for the PTV, CTV and ITV for a lung IMHFRT treatment plan of 20 Gy×1 fraction. Prescription dose corresponds to 100%.

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.

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.

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.

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 **...**

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 R_{Dmin}, R_{D95} and R_{V95} 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. D_{min}, D_{95} and V_{95} are sensitive to dose gradients at field edges or in regions of large modulation and are more sensitive to motion effects. Average R_{Dmin} 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 D_{min}. Average R_{Dmin} for the ITV is 0.98 (range 0.91–1.06) indicating little change in delivered dose. For the PTV, the average R_{D95} and R_{V95} with *A*=1.26 cm are reduced to 0.81 and 0.78. For the CTV there is only a 6% reduction in R_{D95} and R_{V95}, and for the ITV only 2% reduction, indicating that the CTV-PTV margin chosen is sufficient.

Average R_{Dmin}, R_{D95} and R_{V95} 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 **...**

Average± standard deviation of R_{D95} and R_{V95} 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 D_{mean}, D_{max} and D_{05} 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 D_{mean} is <5%, and D_{max} and D_{95} 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.

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.

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.

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 R_{Dmean} for *A*=1.28cm are 0.89 and 0.92 for the CTV and GTV, with average R_{Dmax} and R_{D05} reduced to 0.94 and 0.95 for the CTV, and 0.95 and 0.96 for the GTV. The average R_{D95} falls to 0.83 and 0.85 for the CTV and GTV. The average R_{Dmin} and R_{V95} 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.

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 studies^{12}^{,}^{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.

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. D_{min} 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 calculation^{24}. A more accurate study on tumor motion effects should be performed using these algorithms.

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.

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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