- Email: [email protected]
Strategy for Online Correction of Rotational Organ Motion for Intensity-Modulated Radiotherapy of Prostate Cancer
doi:10.1016/j.ijrobp.2007.08.042
PHYSICS CONTRIBUTION
STRATEGY FOR ONLINE CORRECTION OF ROTATIONAL ORGAN MOTION FOR INTENSITY-MODULATED RADIOTHERAPY OF PROSTATE CANCER ERIK-JAN RIJKHORST, PH.D., MARCEL VAN HERK, PH.D., JOOS V. LEBESQUE, M.D., PH.D., AND JAN-JAKOB SONKE, PH.D. Department of Radiation Oncology, The Netherlands Cancer Institute–Antoni van Leeuwenhoek Hospital, Amsterdam, The Netherlands Purpose: To develop and evaluate a correction strategy for prostate rotation using gantry and collimator angle adjustments. Methods and Materials: Gantry and collimator angle adjustments were used to correct for prostate rotation without rotating the table. A formula to partially correct for left–right (LR) rotations was derived through geometric analysis of rotation-induced clinical target volume (CTV) beam’s-eye-view shape changes. For 10 prostate patients, intensity-modulated radiotherapy (IMRT) plans with different margins were created. Simulating CTV LR rotation and correcting each beam by a collimator rotation, the corrected CTV dose was compared with the original and uncorrected dose. Effects of residual geometric uncertainties were assessed using a Monte Carlo technique. A large number of treatments representative for prostate patients were simulated. Dose probability histograms of the minimum CTV dose (Dmin) were derived, with and without online correction, resulting in a more realistic margin estimate. Results: Dosimetric analysis of all IMRT plans showed that, with rotational correction and a 2-mm margin, Dmin was constant to within 3% for LR rotations up to ±15 . The Monte Carlo dose probability histograms showed that, with correction, a margin of 4 mm ensured that 90% of patients received a Dmin $95% of the prescribed dose. Without correction a margin of 6 mm was required. Conclusions: We developed and tested a practical method for (online) correction of prostate rotation, allowing safe and straightforward implementation of margin reduction and dose escalation. Ó 2007 Elsevier Inc. Prostate cancer, Rotations, Margins, Geometric uncertainties, IMRT.
With the introduction of image-guided radiotherapy (IGRT), geometric variations, like setup error and organ motion, can be measured and used in correction protocols. This permits smaller clinical target volume (CTV) to planning target volume (PTV) margins, thereby reducing complications and/or allowing better local control through dose escalation. The first-generation IGRT systems typically only corrected for translations through a shift of the treatment table, although for the prostate for instance the dominant anatomic motion is rotation around the left–right (LR) axis (1). Because these rotations are normally too large to be compensated for by a tilt-and-roll table (2, 3), one could resort to a technique like adaptive radiotherapy (ART) (4, 5), which can correct for such large rotations. But because ART only compensates for systematic errors and significantly increases
the workload because it necessitates replanning, fast, online correction methods are preferred. Recently, a number of online correction strategies (6) have been proposed, ranging from approaches that correct for translations (7) and rotations (8) to elaborate methods that adapt collimator leaf positions to take anatomic deformations into account (9–12). In this article we propose a more simple correction strategy that applies gantry and collimator angle adjustments to correct for prostate rotations. We ignore table rotation because, with currently available hardware, this degree of freedom (DoF) can not be remotely controlled, and the corresponding prostate rotation is small (1). Although our method could also be used to avoid replanning in an ART protocol, we here assume an online setting. This implies that values for prostate translation and rotation should be available at treatment time, for example
Reprint requests to: Jan-Jakob Sonke, Ph.D., Department of Radiation Oncology, The Netherlands Cancer Institute–Antoni van Leeuwenhoek Hospital, Plesmanlaan 121, 1066 CX Amsterdam, The Netherlands. Tel: (+31) 20-512-1723; Fax: (+31) 20-6691101; E-mail: [email protected]
Conflict of interest: Part of this work was sponsored by Elekta. Acknowledgment—The authors thank Jasper Nijkamp for help with importing data into Pinnacle. Received June 1, 2007, and in revised form Aug 2, 2007. Accepted for publication Aug 2, 2007.
INTRODUCTION
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Correction of rotational organ motion for IMRT d E.-J. RIJKHORST et al.
by using cone-beam computed tomography (CT) to planning CT grey-value registration (13, 14). We start with a geometric analysis of the problem at hand and derive a formula to adapt the collimator angle. Using data of 10 patients, this formula is applied to intensity-modulated radiotherapy (IMRT) plans, to give achievable margin reduction when only LR rotations were compensated for. Finally, using a Monte Carlo technique, a large number of treatments and corrections taking residual uncertainties into account are simulated, resulting in a more realistic margin estimate.
METHODS AND MATERIALS Patient data Planning CT and delineations of 10 patients previously treated for prostate cancer at our institution were used. The prostate and seminal vesicles (SV), referred to as CTV for the remainder of this article, were contoured as a single organ. The rectal wall was contoured from the anal verge up to the sigmoid flexure.
To find g(a, b), we need to compare Eq. 1 with the BEV of the original CTV, given by Ry(b)r, corrected by a collimator rotation over an angle g:
0
1 xcosbcosg þ ysing zsinbcosg Rz ðgÞRy ðbÞr ¼ @ xcosbsing þ ycosg þ zsinbsing A: xsinb þ zcosb (2) Note that, to find Eq. 1, the CTV was first rotated and then transformed to the gantry coordinate system, whereas to find Eq. 2 the inverse sequence was needed. We now demand that a BEV point inside the rotated CTV (Eq. 1) corresponds to its equivalent location in the BEV of the original CTV corrected by a collimator rotation (Eq. 2). Equating the first components of Eq. 1 and Eq. 2 gives
g ¼ asinb;
Because the largest rotations of the prostate occur around the LR axis (1), we aim our correction strategy at this DoF. A full geometric correction can in principle be achieved for all beam directions by combining appropriate gantry, collimator, and table rotations (12). However, because table rotations can not be controlled remotely and may induce additional setup errors due to patient movement, we wish not to use this DoF. Nevertheless, an approximate LR correction using the collimator rotation is still possible. Furthermore, a gantry rotation can correct for prostate cranial–caudal (CC) rotation. The change in CTV shape in the beam’s-eye view (BEV) of a particular beam due to prostate LR rotation over an angle a depends on the gantry angle b. Obviously, for lateral beams (b = 90 , 270 ), prostate LR rotation can be fully compensated for by a collimator rotation g = a. In contrast, for beams along the anterior–posterior (AP) direction (b = 0 , 180 ), prostate LR rotation will only result in a rescaling of its shape as seen from the BEV, and no collimator correction is possible (g = 0 ). For intermediate beams, a combination of these two effects occurs. In general, the optimal collimator correction angle g will lie somewhere between zero and a and is a function of gantry angle b, that is g = g(a, b). To derive the dependency of the collimator angle g on the prostate angle a and the gantry angle b, consider an arbitrary point r = (x, y, z)T located inside the CTV. Using the coordinate system introduced by Siddon (15) (see also the International Electrotechnical Commission coordinate system convention [16]), and ignoring divergence of the beam, we first rotate r over a around the LR axis to describe organ motion, after which it is transformed to the gantry coordinate system by rotating over gantry angle b around the CC axis. This results in
0
1 xcosb þ ysinasinb zcosasinb A; (1) Ry ðbÞRx ðaÞr ¼ @ ycosa þ zsina xsinb ysinacosb þ zcosacosb with Rx(a) and Ry(b) rotation matrices as defined in (15). The first two components of this equation give the BEV coordinates of the rotated CTV, whereas the third gives the position along the beam axis.
(3)
and, by using this result, the second component of Eqs. 1 and 2 results in
xsinb þ zcosb ¼ 0 ðfor bs90 ; 180 Þ; Correcting prostate LR rotation
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(4)
whereas the third component gives
acosb ¼ 0:
(5)
We assumed that both a and g were small (i.e. sinaxa, cosax1, singxg, and cosgx1). Eq. 3 is the desired collimator correction angle. Eq. 4 tells us that this correction is only exact for points in the plane through the origin of the coordinate system perpendicular to the beam axis. Eq. 5 is true for lateral beams and represents a measure of the rotational mismatch occurring for other beam directions. Note that formally, the system of Eqs. 1 and 2 has an approximate solution only, which is derived by rewriting it as a least-squares problem, resulting also in Eq. 3. Furthermore, when considering prostate AP rotation instead of LR rotation, a similar derivation as above leads to an equation for the collimator angle correcting for AP rotation given by
gAP ¼ aAP cosb;
(6)
with aAP the CTV rotation around the AP axis.
Treatment planning We created step-and-shoot IMRT plans using the Pinnacle3 (version 7.6c, Philips Medical Systems, Eindhoven, The Netherlands) treatment-planning system (TPS). Each plan had five coplanar beams with our clinically used gantry angles of 0 , 40 , 100 , 260 , and 320 . The TPS optimization resulted in approximately 10 segments per beam. For each patient five plans with isotropic CTV-to-PTV margins of 2, 4, 6, 8, and 10 mm were calculated, resulting in a total of 50 plans. The objectives used to optimize these plans resulted in a conformal and homogeneous PTV dose of 70 Gy, while minimizing the rectum dose. Although in clinical practice at our institution simultaneous integrated boost IMRT plans (17) are used, we chose in this study a homogeneous dose instead. This simplified interpretation of dose differences occurring when parts of the CTV move out of the PTV owing to prostate LR rotation. For dosimetric evaluation of our correction method it is important to obtain accurate margins. Because expansion in Pinnacle resulted in margins that are slightly larger (approximately 1 mm) than required, we used more accurate, in-house-developed expansion
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software instead. Furthermore, using a PTV objective restricting the maximum dose, the 95% isodose surface tightly enclosed the PTV without the need for manual tweaking.
Geometric analysis To assess the geometric effectiveness of our method, we obtained the CTV surface overlap index (OI) as seen from the BEV of a particular beam. To this end, the intersection of the rotated CTV area orig Arot was calculated: a,b with respect to the original CTV area Ab
OIrot a;b ¼
orig Arot a;b XAb ; Aorig b
(7)
where we explicitly stated the dependence on the LR rotation a and gantry angle b. A similar quantity was calculated when the collimator correction (Eq. 3) was applied:
OIcorr a;b ¼
orig Acorr a;b XAb
Aorig b
:
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Table 1. Systematic and random rotation SDs (in degrees) used in the Monte Carlo simulations
Rotational organ motion (1) Rotational setup errors (21) Case A: without correction Case B: with correction Case C: ‘‘golden standard’’
SRLR
SRCC
SRAP
sRLR
sRCC
sRAP
5.1
2.2
1.3
3.6
2.0
1.6
0.9
0.6
0.8
1.1
0.6
0.5
5.2
2.3
1.5
3.8
2.1
1.7
5.2* 1.0
1.0y 1.0
1.5 1.0
3.8* 1.0
1.0y 1.0
1.7 1.0
Organ motion SDs from (1) were quadratically summed with rotational setup SDs from (21). * Left–right rotations corrected by calculating the appropriate beam doses using Eq. 3. y Cranial–caudal rotations corrected by a gantry rotation leaving a residual SD of 1 .
(8)
We compared, for the whole patient group, the OI of the rotated prostate with the OI when correcting for LR rotation, resulting in a quantitative measure for the gain in CTV BEV coverage our method can achieve. Note that the CTV is rotated around its center of gravity instead of around the apex, to ensure that a lower limit to the geometric error is found. Also, for online correction, this rotation point would be chosen as well (by adjusting the table shift), to minimize the impact of prostate rotations.
Dosimetric effects To investigate the dosimetric effect of our method, we obtained three-dimensional dose distributions from each IMRT plan for every single beam. By adding individual beam doses using in-housedeveloped software, the total CTV dose, indicated by Dorig, was constructed. The CTV was rotated around the LR axis over a, with the center of gravity as its rotation point. The dose delivered to the rotated CTV is indicated by Drot. To apply the collimator correction, we needed to adapt the total dose using the known prostate LR rotation a. Assuming rotational invariance, each beam was rotated according to Eq. 3. The resulting beam doses were accumulated and, using the rotated CTV, the corrected total dose Dcorr was found. For a single plan, rotational invariance was checked by computing the corrected dose using Pinnacle by setting the collimator angles to their appropriate values. The dose distributions Dorig, Drot, and Dcorr were obtained for all 50 plans, for each of which the mean CTV dose and SD were calculated. Furthermore, dose–volume histograms (DVHs) were constructed, from which the minimum CTV dose Dmin was derived. orig rot orig The differences DDrot min = (Dmin – Dmin)/Dmin for the uncorrected corr orig corr orig and DDmin = (Dmin – Dmin )/Dmin for the corrected case were also calculated. By averaging over the patient group, a margin estimate was derived for the cases with and without rotation correction. Finally, we also assessed the effect of our strategy on the rectum dose. Because the amount of rectal filling is known to drive prostate LR rotation, the anterior rectal wall is expected to be in close proximity of the posterior side of the prostate. As a first-order approximation, we chose the rectum to co-rotate with the CTV. Therefore the rectum DVH is most accurate for high doses, delivered to the rectal wall section close to the prostate, and less accurate for low doses.
Monte Carlo simulation of correction strategy To determine the required margin more accurately, the effects of geometric interfraction uncertainties on the total CTV dose were modeled using a Monte Carlo technique similar to the one used by Van Herk et al. (18). Instead of applying just the LR rotation, as described in the previous section, all translational and rotational DoF were taken into account. For each patient a large number (4000) of treatments was simulated by generating systematic (preparation) errors from a 6D Gaussian distribution with SDs STLR, STCC, and STAP for translations and SRLR, SRCC, and SRAP for rotations. To minimize the impact of discretization errors, we used a high-resolution grid with 2-mm voxels. To represent the fractions in each simulated treatment, a set of 35 random (execution) errors was drawn from another 6D Gaussian distribution with SDs sTLR, sTCC, and sTAP for translations and sRLR, sRCC, and sRAP for rotations. By combining the systematic error of a particular treatment with the random errors, the total CTV translations and rotations for every single fraction were obtained. The CTV dose was accumulated, from which Dmin was extracted. By binning the values of Dmin, cumulative dose probability histograms (DPHs) (19) were calculated. Such a DPH plots, as a function of Dmin, the probability that patients will receive at least that value of Dmin. Because we are primarily interested in margin reduction in an online setting, we assumed translational errors to be compensated for by a table shift, leaving small residual SDs of STLR = STCC = STAP = sTLR = sTCC = sTAP = 1 mm (20). For rotations we considered three different cases (Table 1). Case A: without rotation correction, for which we used prostate rotation SDs from Hoogeman et al. (1). Case B: with rotation correction, whereby the appropriate gantry and collimator corrections were applied to every fraction. Collimator corrections were performed by adapting the beam doses according to Eq. 3, while allowing for a discretization error of 1 . For gantry ‘‘correction’’ only small residual SDs of SRCC = sRCC = 1 were applied. Case C: a ‘‘golden standard,’’ whereby we assumed all rotation SDs to be equal to 1 . Note that for Case B we did not apply Eq. 6 to correct for prostate AP rotations. Tests using 2-mm margin plans showed that such a correction did not improve Dmin because, for our type of plans, the two most lateral beams can hardly be corrected for prostate AP rotation. On the other hand for LR correction only one beam (AP) remains uncorrected, and our method performs well.
Correction of rotational organ motion for IMRT d E.-J. RIJKHORST et al.
Dose probability histograms of Dmin were obtained for different margins. By demanding that 90% of treatments should result in a Dmin of at least 95% of the prescribed dose, margins for Cases A, B, and C were obtained.
RESULTS Geometric correction For each patient, we obtained values for OIrot a,b and OIcorr a,b (Eqs. 7 and 8) as a function of gantry angle b for prostate LR rotations of a = 15 . We chose these rather large angles to obtain a measure for the maximum OI mismatch. The influence of positive and negative LR rotation was studied separately, because for positive rotations the SV and apex rotate out, whereas for negative rotations they rotate into the AP beam. Figure 1 shows BEV overlap images of the orig-
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inal and rotated CTV for a single patient. Figure 2 plots the mean OI over the patient group as a function of gantry angle.
Dosimetric effects Figure 3 presents color-coded images of the uncorrected and corrected dose distribution in a sagittal slice through the center of the CTV for a single IMRT plan with a 2-mm margin. The CTV dose difference between the rotated dose and the uncorrected/corrected dose is also shown. The corresponding CTV and rectum DVHs are shown in Fig. 4. The CTV mean dose and SD were found to remain virtually constant for LR rotation in the range of [–15 , +15 ], when correction was applied. Therefore, for our type of step-and-shoot IMRT plans, the LR correction can be safely
Fig. 1. Clinical target volume (CTV) beam’s-eye views for a single patient and several beam directions (left to right: gantry angle b = 0 , 30 , 60 , 90 ). In panel (A) (top) no collimator correction was applied, whereas for panel (B) (bottom) results with collimator correction are shown. In the top rows of panels (A) and (B), the prostate was rotated over a = +15 , and in the bottom rows the case for a = –15 is shown. The part of the rotated CTV that is being fully covered is shown in black. The part of the CTV that is geometrically missed is shown in dark grey, whereas the light grey area is irradiated without any part of the CTV being present.
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DISCUSSION
prostate rotation: +15o with correction without correction
1.05
Overlap Index
1 0.95 0.9 0.85 0.8 0.75 0.7
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-60
-40
-20
0
20
40
60
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gantry angle 1.1
prostate rotation: -15o with correction without correction
1.05
Overlap Index
1 0.95 0.9 0.85 0.8 0.75 0.7
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-40
-20
0
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gantry angle
Fig. 2. Mean overlap indexes (OIs) for prostate left–right rotation angles of +15 (top) and –15 (bottom) for the 10 patients studied. The error bars represent 1 SD. Solid lines indicate OIs calculated with, and dashed lines indicate OIs calculated without collimator rotation correction.
applied without introducing any significant cold or hot spots in the CTV dose. The dependence of Dmin on margin and prostate LR rotation for a single patient is shown in Fig. 5. Figure 6 shows the difference in Dmin averaged over the patient group as a function of margin for the uncorrected and corrected case. From this, the margin required to prevent CTV under-dosage when geometric uncertainties are assumed to be only due to LR rotations was estimated. Monte Carlo simulation of correction strategy For all 50 IMRT plans (10 patients with 5 margins each), we performed Monte Carlo simulations as described in Methods and Materials. This resulted in 50 DPHs of Dmin, which, for each margin were averaged over patients to find population DPHs. Figure 7 plots the results for 4- and 6-mm margins for the corrected, uncorrected, and ‘‘golden standard’’ (i.e., small residual errors) cases. From the DPHs Fig. 8 was derived, which shows Dmin corresponding to the 90% probability level as a function of margin.
Geometric correction By studying the OI as a function of gantry angle for different prostate LR rotations, an indication of applicability of our correction method was determined. To this end, we separated the analysis into two cases: one with positive, and one with negative prostate LR rotation. We first discuss positive rotation, whereby the SV and apex rotated out of the AP beam (a = +15 ; top row Fig. 1, top panel Fig. 2). Without collimator correction, the OI remained fairly constant at approximately 0.83, meaning the geometric mismatch between the BEVs of the original and the rotated prostate was almost independent of beam direction. With collimator correction however, the OI steadily improved with increasing gantry angle, to become equal to unity for fully lateral beams. For negative LR rotation (a = – 15 , bottom row Fig. 1, bottom panel Fig. 2), the OIs behave quite differently. Because of the direction of rotation of the prostate, it remained almost fully covered in the BEV of the AP beam, reflected in a high OI value of approximately 0.96. For non-zero gantry angles and without collimator correction the coverage reduced, and the OI deteriorated to approximately 0.83 for lateral beams. In contrast, with correction, the OI again improved with increasing gantry angle. These two cases clearly demonstrate the influence of the direction of prostate rotation on the quality of the correction. When the SV and apex rotated out of the AP beam, the OI was small for the AP direction. On the other hand, when they rotated into the AP beam, an almost complete correction was achieved for all beam directions. Court et al. (9) found a similar effect for which they compensated by opening extra multileaf collimator leaf pairs. In a correction strategy by Wu et al. (8), who compensated for LR rotations for lateral beams only, this effect was not important because their study excluded the SVs. In our case, for a treatment plan consisting of beams at different angles, the AP beam is expected to contribute most to a deterioration of CTV dose when the SVs and apex rotate out of this beam. Dosimetric effects After assessing the geometric properties of our method, we investigated its dosimetric performance by applying it to our set of IMRT plans. An example of one such plan is shown in Fig. 3 for a 2-mm margin and prostate LR rotation angles of a = 15 . For a = +15 , the resulting dose without collimator correction is shown in Fig. 3 (top row). A mismatch between the CTV and the 95% isodose line occurred, resulting in a CTV under-dosage of approximately 10 Gy. With collimator correction (Fig. 3, third row), the CTV coverage improved drastically, reducing the under-dosage to approximately 6 Gy. Note that the latter under-dosage occurred in a part of the SV that lay outside of the slice shown in Fig. 3. For a = –15 and no correction (Fig. 3, second row), the mismatch and under-dosage were similar to the case of
Correction of rotational organ motion for IMRT d E.-J. RIJKHORST et al.
Fig. 3. Sagittal slices of the dose distribution (left) and dose difference between uncorrected/corrected and rotated original dose (right) for prostate left–right rotation angles of a = 15 for a single patient. Contours of the clinical target volume (CTV) (dark blue), rectum (dark red), and 95% isodose line (yellow) are shown. For this example, a CTV to planning target volume margin of 2 mm was used. The top four panels show the result without, and the bottom four panels the result with collimator correction.
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100
100
Dminrot/Dminorig [%]
Volume [%]
80
CTV
60 rectum 40 prostate rotation: +15° original with correction without correction
20
0
0
10
20
30
95 90 without correction 10 mm 8 mm 6 mm 4 mm 2 mm
85 80 75
40
50
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70 -20
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Dmincorr/Dminorig [%]
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Volume [%]
0
5
10
15
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10
15
20
100
100
60
CTV rectum
40 prostate rotation: -15° original with correction without correction
20
0
-5
prostate angle α
0
10
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30
95 90 with correction 10 mm 8 mm 6 mm 4 mm 2 mm
85 80 75 70 -20
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Dose [Gy]
-15
-10
-5
0
5
prostate angle α
Fig. 4. Dose–volume histograms (DVHs) for the clinical target volume (CTV) and rectum for prostate left–right rotation angles of a = +15 (top) and a = 15 (bottom) for a single patient. Different line types indicate whether the original (solid), corrected (dashed), or uncorrected (dotted) dose distribution was used to create the DVHs.
Fig. 5. Normalized Dmin as a function of prostate left–right rotation angle for a single patient. Clinical target volume to planning target volume margins used to create the individual intensity-modulated radiotherapy plans are indicated by different line types. The top panel shows results without, and the bottom panel shows results with applying the collimator correction.
positive rotation. However, with collimator correction (Fig. 3, bottom row), the under-dosage reduced to only approximately 2.5 Gy, confirming our expectation that negative rotations are better corrected for than positive ones. Similar trends were observed in the DVHs (cf. Fig. 4). For positive rotation considerable improvement in the CTV DVH was achieved when the collimator correction was applied. For negative rotations, this improvement became almost 100%, with the original and corrected DVHs almost fully overlapping. For the rectum DVH we observed only small differences, which were smallest when the correction was applied. Furthermore, the maximum rectum dose did not change. As mentioned before, because of our simplistic modeling of rectum motion, the low-dose part of the rectum DVHs is less reliable. To check rotational invariance of the dose, we compared the corrected dose calculated with our in-house-developed software, with the dose calculated using Pinnacle. For a single plan with a 2-mm margin and LR rotation a = 15 , the maximum CTV dose difference was approximately 1 Gy, indicating that we may safely assume rotational invariance.
orig corr orig In Fig. 5 we plot the ratios Drot min/Dmin and Dmin /Dmin for the same single patient we have been considering so far. Without collimator correction and small margins, Dmin rapidly decreased when the LR rotation deviated from zero, independent of the rotation direction. With correction however, Dmin decreased much less rapidly for positive angles and stayed almost constant for negative ones, even up to unrealistic LR rotations of a = –20 . For the 2-mm plan, there orig was even a slight improvement of Dcorr min over Dmin for negative LR rotation angles (see Fig. 5, bottom panel). This was due to the TPS optimization procedure, which had difficulty in achieving the required Dmin for such a tight 2-mm margin. Figure 6 shows DDmin averaged over the patient group as a function of margin. In the top panel no correction was used, resulting in an increasing hDDrot min i with decreasing margin, up to hDDrot ix20 5% for a 2-mm margin and LR rotation min of a = 15 . With correction (bottom panel) these values were again much smaller: hDDcorr min ix8 2:5% for a = +15 and hDDcorr min ix2 2% for a = –15 for a 2-mm margin. If LR rotation of the prostate would be the only error present, these results imply that, with correction, a 2-mm margin
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4mm margin without correction with correction golden standard
0.3 0.2 0.1 0 85
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0.7 0.6 0.5 0.4
6mm margin without correction with correction golden standard
0.3 0.2 0.1 0 85
87.5
90
92.5
Dmin/Dpres [%]
Fig. 7. Cumulative dose probability histograms averaged over the patient group of the probability hPi as a function of Dmin/Dpres for clinical target volume to planning target volume margins of 4 mm (top) and 6 mm (bottom). Different line types indicate uncorrected (dashed), corrected (solid), and ‘‘golden standard’’ (dotted) cases.
TPS to create the plan, resulting in a rotated dose distribution. Thus, instead of correcting the dose by using Eq. 3, we should now use g ¼ ða dÞ sin b; Fig. 6. Normalized DDmin as a function of margin averaged over the patient group, without (top) and with (bottom) collimator correction. Error bars indicate 1 SD. Different line types show results for left– right rotation angles of a = 15 (solid), a = 10 (dashed), and a = 5 (dotted). CTV = clinical target volume; PTV = planning target volume.
(9)
which automatically gives the required extra CC margin. In Fig. 9 we plot Dcorr min as function of LR rotation now using the adapted correction angle of Eq. 9. As expected, with increasing prerotation angle d, the value of Dcorr min decreases
Dmin/Dpres [%]
100
would be sufficient to compensate rotations within [15 , +10 ]. To obtain a better margin estimate when all geometric DoF are taken into account, we discuss Monte Carlo simulations of interfraction prostate motion in the next section. From the previous discussion it becomes clear that our strategy gives very good results for negative but is limited for positive LR rotation. For positive LR rotation, one would like to have a slightly larger margin in the CC direction only for those beam components not directed along the LR axis. This can be achieved by prerotating the PTV around the LR axis over a positive angle d and importing it into the
95 golden standard with correction without correction
90
85
2
4
6
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margin [mm]
Fig. 8. Dmin at hPi ¼ 90% averaged over the patient group as a function of margin. Different line types indicate uncorrected (dashed), corrected (solid), and ‘‘golden standard’’ (dotted) cases.
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tice at our institution. For plans with a different set of beams, we expect our method to work as well, as long as the majority of beams is oriented not too far away from the lateral direction.
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Dmincorr/Dminorig [%]
102 100 98 96 with correction 94
δ= 0o δ= 5o δ= 10o δ= 15o
92 90 -20
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-5
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prostate angle α
Fig. 9. Normalized Dcorr min as a function of prostate left–right rotation angle a for a single intensity-modulated radiotherapy plan with a 2mm margin. All results were obtained by applying Eq. 9 to rotate the collimator for each beam. Different line types indicate results for prerotated plans with d = 0 (solid), d = 5 (dashed), d = 10 (dotted), and d = 15 (short dashed).
Monte Carlo simulation of correction strategy Figure 7 shows results of the Monte Carlo simulations for 4- and 6-mm margins for the corrected, uncorrected, and ‘‘golden standard’’ cases. When we demand that 90% of the patients receive a Dmin of at least 95% of the prescribed dose, one sees that without correction (Fig. 7, top panel and Fig. 8) a margin of 4 mm will not suffice. In this case only approximately 60% of the patients would receive the required Dmin. However, with correction, a margin of 4 mm would ensure that 90% of patients receive Dmin/Dpres $ 95%. For a larger margin of 6 mm (Fig. 7, bottom panel), Dmin/Dpres = 95% is reached for 90% of patients without correction, and, with correction, for all patients. Because in this study intrafraction motion and target definition were ignored, the margins obtained represent a lower limit. CONCLUSIONS
for positive LR rotation. However, for negative LR rotation there is an increase of Dcorr min , and an appropriate intermediate value for d would be 10 , for which Dcorr min <3% for a within [–15 , +15 ]. In this section, we found that our correction strategy performs well for negative, and with some adaptation, for positive prostate LR rotation. It improves on the method of Wu et al. (8), who corrected only for lateral beams, whereas we correct for all beam directions and also take the SVs into account. Moreover, because prostate deformations are small (22), our method constitutes a much simpler approach than methods that adapt leaf positions (9–11, 23). To conclude, we note that our correction method was only tested for plans with beam orientations used in clinical prac-
We have developed a simple and practical strategy for the approximate correction of prostate rotations for online, as well as offline, IMRT protocols. Analysis of IMRT plans with different margins for our patient group showed that, with rotational correction and a 2-mm margin, Dmin is constant to within 3% for LR rotations up to 15 . When taking residual geometric uncertainties into account through Monte Carlo simulations, a CTV-to-PTV margin of 4 mm was sufficient to ensure that 90% of patients received a Dmin $ 95% of the prescribed dose. Without correction 6 mm was needed. By compensating for prostate rotations, our correction strategy permits safe and straightforward implementation of margin reduction and/or improved local control through dose escalation.
REFERENCES 1. Hoogeman MS, van Herk M, de Bois J, et al. Strategies to reduce the systematic error due to tumor and rectum motion in radiotherapy of prostate cancer. Radiother Oncol 2005;74: 177–185. 2. Hornick DC, Litzenberg DW, Lam KL, et al. A tilt and roll device for automated correction of rotational setup errors. Med Phys 1998;25:1739–1740. 3. Litzenberg DW, Balter JM, Hornick DC, et al. A mathematical model for correcting patient setup errors using a tilt and roll device. Med Phys 1999;26:2586–2588. 4. Yan D, Lockman D, Brabbins D, et al. An off-line strategy for constructing a patient-specific planning target volume in adaptive treatment process for prostate cancer. Int J Radiat Oncol Biol Phys 2000;48:289–302. 5. Nuver TT, Hoogeman MS, Remeijer P, et al. An adaptive offline procedure for radiotherapy of prostate cancer. Int J Radiat Oncol Biol Phys 2007;67:1559–1567. 6. Ghilezan M, Yan D, Liang J, et al. Online image-guided intensity-modulated radiotherapy for prostate cancer: How much improvement can we expect? A theoretical assessment of clinical benefits and potential dose escalation by improving
7.
8.
9.
10.
11.
precision and accuracy of radiation delivery. Int J Radiat Oncol Biol Phys 2004;60:1602–1610. Lauve AD, Siebers JV, Crimaldi AJ, et al. A dynamic compensation strategy to correct patient-positioning errors in conformal prostate radiotherapy. Med Phys 2006;33:1879–1887. Wu Q, Ivaldi G, Liang J, et al. Geometric and dosimetric evaluations of an online image-guidance strategy for 3D-CRT of prostate cancer. Int J Radiat Oncol Biol Phys 2006;64: 1596–1609. Court LE, Dong L, Lee AK, et al. An automatic CT-guided adaptive radiation therapy technique by online modification of multileaf collimator leaf positions for prostate cancer. Int J Radiat Oncol Biol Phys 2005;62:154–163. Mohan R, Zhang X, Wang H, et al. Use of deformed intensity distributions for on-line modification of image-guided IMRT to account for interfractional anatomic changes. Int J Radiat Oncol Biol Phys 2005;61:1258–1266. Feng Y, Castro-Pareja C, Shekhar R, et al. Direct aperture deformation: An interfraction image guidance strategy. Med Phys 2006;33:4490–4498.
Correction of rotational organ motion for IMRT d E.-J. RIJKHORST et al.
12. Yue NJ, Knisely JP, Song H, et al. A method to implement full six-degree target shift corrections for rigid body in imageguided radiotherapy. Med Phys 2006;33:21–31. 13. Jaffray DA, Siewerdsen JH, Wong JW, et al. Flat-panel conebeam computed tomography for image-guided radiation therapy. Int J Radiat Oncol Biol Phys 2002;53:1337–1349. 14. Smitsmans MH, de Bois J, Sonke JJ, et al. Automatic prostate localization on cone-beam CT scans for high precision imageguided radiotherapy. Int J Radiat Oncol Biol Phys 2005;63: 975–984. 15. Siddon RL. Solution to treatment planning problems using coordinate transformations. Med Phys 1981;8:766–774. 16. International Electrotechnical Commission. Medical electrical equipment. Medical electron accelerators—Functional performance characteristics. IEC 60976 (1989-06). Geneva: IEC; 1989. 17. Bos LJ, Damen EM, de Boer RW, et al. Reduction of rectal dose by integration of the boost in the large-field treatment plan for prostate irradiation. Int J Radiat Oncol Biol Phys 2002;52: 254–265. 18. van Herk M, Remeijer P, Lebesque JV. Inclusion of geometric uncertainties in treatment plan evaluation. Int J Radiat Oncol Biol Phys 2002;52:1407–1422.
1617
19. van Herk M, Remeijer P, Rasch C, et al. The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy. Int J Radiat Oncol Biol Phys 2000;47:1121–1135. 20. Le´tourneau D, Martinez AA, Lockman D, et al. Assessment of residual error for online cone-beam CT-guided treatment of prostate cancer patients. Int J Radiat Oncol Biol Phys 2005; 62:1239–1246. 21. Remeijer P, Geerlof E, Ploeger L, et al. 3-D portal image analysis in clinical practice: An evaluation of 2-D and 3-D analysis techniques as applied to 30 prostate cancer patients. Int J Radiat Oncol Biol Phys 2000;46:1281–1290. 22. Deurloo KE, Steenbakkers RJ, Zijp LJ, et al. Quantification of shape variation of prostate and seminal vesicles during external beam radiotherapy. Int J Radiat Oncol Biol Phys 2005;61: 228–238. 23. Song WY, Wong E, Bauman GS, et al. Dosimetric evaluation of daily rigid and nonrigid geometric correction strategies during on-line image-guided radiation therapy (IGRT) of prostate cancer. Med Phys 2007;34:352–365.