Prostate motion and isocenter adjustment from ultrasound-based localization during delivery of radiation therapy

Int. J. Radiation Oncology Biol. Phys., Vol. 61, No. 4, pp. 984 –992, 2005 Copyright © 2005 Elsevier Inc. Printed in the USA. All rights reserved 0360-3016/05/$–see front matter

doi:10.1016/j.ijrobp.2004.07.727

CLINICAL INVESTIGATION

Prostate

PROSTATE MOTION AND ISOCENTER ADJUSTMENT FROM ULTRASOUNDBASED LOCALIZATION DURING DELIVERY OF RADIATION THERAPY ALBERT Y. C. FUNG, PH.D., CHARLES A. ENKE, M.D., KOMANDURI M. AYYANGAR, PH.D., NATARAJAN V. RAMAN, M.D., WEINING ZHEN, M.D., ROBERT B. THOMPSON, M.D., SICONG LI, PH.D., RAMASAMY M. NEHRU, PH.D., AND SUSHAKUMARI PILLAI, M.S. Department of Radiation Oncology, University of Nebraska Medical Center, Omaha, NE Purpose: To study prostate motion from 4,154 ultrasound alignment fractions on 130 prostate patients treated with conformal radiotherapy or intensity-modulated radiation therapy at the University of Nebraska Medical Center. Methods and Materials: Each prostate patient was immobilized in a vacuum cradle. Daily treatment was verified by ultrasound scan after laser setup with skin marks and before radiation delivery by the same physician responsible for anatomic delineation during planning. Directional statistics were employed to test the significance of shift directions. Results: Polar histograms showed the prevalence of prostate motion in superior-posterior directions. The average direction was about 27° from the superior axis. The average changes of prostate position in superior to inferior (SI), anterior-posterior (AP), and left to right (LR) directions and in radial distance were 0.25, ⴚ0.13, 0.03, and 0.92, cm respectively. Our data indicated that prostate motion was not patient specific, and its average magnitude remained virtually unchanged over time. Recommended planning target volume (PTV) margins for use without ultrasound localization were 0.90 cm in SI, 1.02 cm in AP, and 0.80 cm in LR directions. Conclusion: Ultrasound localization revealed a predominance of prostate shift from planning position in the superior-posterior direction, with an average closer to the superior axis. The motion data provides recommended margins for PTV. © 2005 Elsevier Inc. Prostate, Motion, Isocenter, Localization, Ultrasound, Adjuvant.

Prostate cancer is a deadly form of cancer, and 221,000 new cases occurred in the United States in 2003, accounting for 33% of all new male cancer (1). Radiation therapy, especially three-dimensional conformal therapy and intensity-modulated radiation therapy (IMRT), is a main treatment modality in localized as well as regional disease (2– 4). The movement of the prostate organ during radiation beam delivery has been a major concern in radiation therapy (5, 6). Typical magnitude of shift can be from 0 to 1.5 cm in seemingly random direction. Movement is usually accounted for in treatment planning by adding some margins around prostate clinical target volume (CTV) to form a planning target volume (PTV). With modern IMRT, the tendency is to prescribe ever tighter margins to reduce the toxicity to rectum and bladder. The existence of prostate motion will always involve the possibility of underdosing the target. Currently, the most popular method of treatment local-

ization is portal imaging, either by use of radiographic films or by electronic means. Although effective in detecting setup error relative to bony structure, portal images do not show the anatomy of soft tissue and cannot pinpoint the exact position of organs during radiation treatment. Imageguided localization during beam delivery is a new concept in minimizing the chance of target miss, thereby improving the cure probability of prostate treatment. Image-guided radiation therapy can be performed in several ways. Some techniques include placing an ultrasound scanner on the patient’s anterior pelvis (7–9), installing a CT machine inside the linear accelerator vault (10 –12), using the electronic portal images to generate cone-beam CT images (13–15), and implanting radiopaque fiducial markers, which are visible in portal images, into the prostate (16 –18). In our institution, an ultrasound-based repositioning system (BAT; Nomos Corporation, Chatsworth, CA [19]) has been in use since March 2000, to guide our radiation delivery for most daily fractions of prostate treatment (20). This

Reprint requests to: Albert Y. C. Fung, Ph.D., Department of Radiation Oncology, University of Nebraska Medical Center, Omaha, NE 68198-7521. Tel: (402) 552-2012; Fax: (402) 5523926; E-mail: [email protected]

Presented at the 46th Annual ASTRO Meeting, October 3–7, 2004, Atlanta, GA. Received Apr 28, 2004, and in revised form Jul 15, 2004. Accepted for publication Jul 23, 2004.

INTRODUCTION

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Fig. 1. Daily prostate isocenter shift for 1 patient in the anterior-posterior direction, showing the randomness of movement.

article presents results from data analysis. The aspects we look into include the magnitude and direction of prostate movement, whether it is patient specific, and whether a trend over time is apparent. METHODS AND MATERIALS The standard prescription dose for prostate tumor irradiation at our institution was 7,920 cGy in 180-cGy fractions. Patients undergoing prostatectomy or seed implant received a lower prescription dose. A physician delineated the contours for prostate, seminal vesicles, intrapelvic nodes, rectum, bladder, and penile bulb, and a planner drew the femurs. ICRU definitions for CTV and PTV were used (21). For planning purpose, the patients had CT as well as MRI. MRI was employed to indicate local regions of higher tumor concentration, in which we would try to deposit higher doses of radiation (22–24). The T2 MRI slices were fused with the CT cross sections by fiducial-points matching and rigid-body transformation. Planning was usually performed by application of the Nomos Corvus software (19). The patients for the BAT study were all treated in the supine position. Beam arrangement was 7 gantry angles equally spaced around the patient, starting at 180° (posterior). Planning goal was to have 95% of the prostate volume covered by the prescribed dose (i.e., V100 ⫽ 95) and higher dose to the target area revealed by MRI. We would attempt to give the seminal vesicles and the intrapelvic nodes the prescribed dose, but some noncoverage by 100% prescribed dose could be accepted if that was needed to keep the rectum and bladder from being

overdosed. The accuracy of the Corvus dose calculation had been validated by independent software (25). Each prostate patient, treated in the supine position, was immobilized by Vac Lock (26). Our method of immobilization was state of the art but not superior in any way to other popular devices of immobilization. The device consisted of tiny beads held in a plastic coating. When air was pumped out of the bag to create a vacuum inside, the sheet “locked” onto the shape of the patient’s body and formed a cradle. The patient’s feet were taped with a piece of Styrofoam between them. The patient’s arm rested on his chest and he held a stretchy foam ring. No sponge was placed under the patient’s knees. Ultrasound localization was performed with the Nomos BAT equipment (19). After a plan was approved by the physician, the contours were transferred to the BAT computer. During each treatment fraction, a radiation therapist first aligned the patient according to skin marks vs. sagittal and side lasers. The BAT probe was then registered onto a cradle permanently installed at the linear accelerator gantry, to calibrate the location of the isocenter. The probe was put on the patient’s pelvis, and transverse and sagittal ultrasound images were obtained. The planning volumes were then overlaid on the ultrasound images and adjusted until they matched. At that time, the computer automatically deduced the offset necessary to move the patient so that the treatment area was in the correct location. The probe was docked to the couch, which was translated as needed. New ultrasound images were taken to confirm that the anatomic images at the new position agreed with the planning contours. The physician who had delineated the planning volumes was called in to check that the

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shift was correct. The physician would sometimes readjust the position with new ultrasound scans. Every time the treatment table was moved, the computer recorded the magnitude of displacement in three orthogonal directions. The motion of prostate isocenter was the opposite of couch shift in each case. Our result was based on the premise that the BAT ultrasound scanner was accurate and reproducible. The ultrasound device was calibrated with manufacturer-specified procedures and phantom and was found accurate within 1 to 2 mm at a target depth of 10 to 15 cm. We collected data for 4,154 daily treatments of 130 prostate patients. The time for a therapist to perform a BAT localization averaged 3 min, and a physician required an additional 4 min to double check—a total of 7 min. The prostate and couch motion data were recorded by the BAT computer. This methods was more reliable than manual recording, which was more likely prone to missing and incorrect information. Nevertheless, computer recording was not without problems. The shift sometimes consisted of unusually large magnitude (e.g., 48 cm) that could occur when the couch position was accidentally registered before any skin mark and laser alignment. Most of the recorded data points were concentrated 1 cm around the origin, with sparsely located points spread out to great distance. The outliers did not affect the value of average displacement very much but had a huge effect on the standard deviation calculation, which intrinsically emphasized the far away points. Therefore, a somewhat arbitrary cutoff maximum distance (dm) had to be imposed. We took dm to be 3 cm in each direction, as explained in the “Discussion”. With directional data, ordinary statistical analysis suitable for linear data did not apply. However, a statistical method existed that was tailored for directional data (27–29). We defined the shift angles ␪ in the range from 0° to 360° counterclockwise as viewed from RL (see Fig. 2b), with 0° specified as the anterior direction and ⫹90° specified as the superior direction. To test the random-

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ness in shift directions, the angles were sorted into ascending linear order, as indicated by the following equations: ␪1 ⬍ ␪2 ⬍ ␪3 · · · ⬍ ␪n ,

(1)

where n was the number of data. To test the hypothesis vigorously, we calculated: D⫹ ⫽ maximum of 兵i/n ⫺ ␪i ⁄ 360其;

(2a)

D⫺ ⫽ maximum of 兵␪i ⁄ 360 ⫺ (i ⫺ 1) ⁄ n其 ,

(2b)

and the statistic from (25): V ⫽ (D⫹ ⫹ D⫺)

冉兹

n ⫹ 0.155 ⫹

0.24

兹n

冊

.

(3)

To find the mean direction, each shift was weighted by the radial distance of motion. In other words, x¯ ⫽

兺 r cos␪ ;

(4a)

兺 r sin␪ ,

(4b)

i

i

i

y¯ ⫽

i

i

i

where r ⫽ 兹共x2⫹y 2⫹z2兲 was the radial distance. Then the mean direction equaled tan⫺1(yi/xi). In the following, all the results of “prostate motion” were relative to the isocenter of the linear accelerator. Some authors defined “internal organ motion” as relative to bony anatomy. Because ultrasound localization did not involve bony anatomy, we did not invoke internal organ motion, bony anatomy, or setup

Fig. 2. Polar histograms of the number of treatment fractions (radial axis) with prostate shift direction falling into each 10-degree interval (angular axis). (a) The view from anterior-posterior (AP) shows a spike along the superior (S) direction, (c) from inferior to superior (IS) (from patient’s feet) shows a spike along the posterior (P) direction, and (b) from right to left (RL) shows the prevalence of shift along S and P, with mean direction along the arrow M. The labels S, I, A, P, L, and R stand for superior, interior, anterior, posterior, left, right, respectively, and positive directions were toward S, A, and L.

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variation (movement of bony anatomy relative to the linac isocenter). In the data and figures, the labels S, I, A, P, L, and R, are for superior, interior, anterior, posterior, left, right, respectively, and positive directions are toward S, A, and L.

RESULTS The random nature of daily shift for 1 patient in the AP direction is illustrated in Fig. 1. To study the direction of prostate displacement, we divided the 360° circle in each orthogonal view into 10-degree intervals and plotted the polar histograms of the number of treatment fractions, with prostate motion falling into each 10-degree interval. The result is shown in Fig. 2. Spikes appear to occur along the S and the P directions but do not imply that the shifts were concentrated near the cardinal axes. Each diagram concealed the direction perpendicular to the sheet of paper. Figure 2b reveals that the shifts were predominantly in a direction between S and P. As described in “Methods and Materials” for directional data analysis, the shift angle values [i/(n ⫹ 1), ␪i] as viewed from RL were plotted in Fig. 3. True directional randomness would generate points that fluctuated about the dashed diagonal line. The curve deviated from the diagonal line, which indicates that the directions were not random. Using the sta-

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tistic in Eq. 3, we calculated an acceptance level ␣ ⫽ 0.01 that corresponded to V ⫽ 2.001. Our data had V ⫽ 9.2. Hence, the p value was much less than 0.01, which was statistically significant. From our data, the mean direction as calculated by Eq. 4 (a, b) was 27° from the superior toward the posterior direction, as illustrated by the arrow M in Fig. 2b. Traditional linear histograms of prostate movement in three major directions and in radial distance are shown in Fig. 4. The shifts clustered around 5 to 7 mm. Figure 5 shows scatter plots of the data points viewed from the same angles as in Fig. 2. Figure 5b shows the slight preference of motion toward superior-posterior directions, although it is not as revealing as the polar histogram. Table 1 lists the averages and standard deviations (SD) of prostate motion in the SI, AP, and LR directions and in three-dimensional radial distance. To detect patient-specific movement, the radial distance data were analyzed. We found the average, Ai, and standard, Si, deviation (over all fractions) of radial distances for each patient i. The standard deviation of Ai was 0.35 cm, which represented the interpatient variation. The average deviation of Si was 0.47 cm, which represented the intrapatient variation. Because intrapatient variation was larger than the interpatient variation, prostate motion was not patient spe-

Fig. 3. Linear order plot of the shift angle data. If the shift directions are random, the plotted line will fluctuate about the dashed diagonal line. Our line differs significantly from the diagonal line, which indicates that the shift has a systematic direction.

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Fig. 4. Linear histograms of prostate shift in three major directions and in radial distance. The number of treatments in the 0-cm bin is exceptionally large, more than can be explained by a Gaussian distribution. This finding represents a tendency for the physician to keep the position unchanged when the required shift is not far from zero.

Fig. 5. Scatter plots of the data points viewed from the same angles as in Fig. 2. Panel (b) shows slight preference of motion toward superior-posterior directions. The labels S, I, A, P, L, and R stand for superior, interior, anterior, posterior, left, right, respectively, and positive directions were toward S, A, and L.

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Table 1. Average and standard deviation of prostate shift SI Average Standard deviation

0.25 cm 0.60 cm

AP ⫺0.13 cm 0.68 cm

LR

3D Radial distance

0.03 cm 0.53 cm

0.92 cm 0.57 cm

Abbreviations: AP ⫽ anterior to posterior; LR ⫽ left to right; SI ⫽ superior to interior; 3D ⫽ three-dimensional.

cific. Observation of the direction of movement and its magnitude parallel to the three major axes did not discern any patient specificity. The radial distance of prostate shift over time from March 2000 to December 2002, pooling all patients together, is shown in Fig. 6. The plot does not manifest any perceivable trend. Testing for randomness gives z ⫽ ⫺4.97, which meant a p value much less than 0.001. However, fitting of a straight line gave an increase of 0.1 mm/y, which was practically negligible.

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DISCUSSION The recorded measurements of BAT system localizations for 4,154 events presented here demonstrate that the shifts of our prostate patients are predominantly in a direction between the superior and the inferior (Fig. 2b). The standard deviations of movement in Table 1 agree well with data from other studies. In addition, the analysis of radial distance shift information indicates that the direction and magnitude of these movements have no discernable patient specificity. One major cause for the varying position of prostate every day is the filling in the patient’s bladder and rectum. Studies demonstrate correlation of prostate location with bladder and rectum fullness (30 –32). A full bladder facilitates prostate visualization in ultrasound images, and our patients are instructed to keep a full bladder. However, a full bladder is most irritating to the patients and tends to increase the difficulty for patients trying to hold still. On the other hand, an empty rectum is most comfortable and reproducible. However, for most people, voiding the rectum is not something achievable on demand. Another possible

Fig. 6. The radial distance of prostate shift over time from March 2000 to December 2002. All patients are pooled together. The plot does not show any perceivable trend.

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Fig. 7. Standard deviation (SD) in the SI direction vs. upper cutoff limit, dm. A plateau of SD occurs between 2 and 5 cm, outside of which the SD changes rapidly. We take dm to be 3 cm.

reason for prostate shift is the force of the ultrasound probe on the pelvis; that is, the act of scanning itself changes the position of the organ being scanned (33). This result is not something detectable with rigid phantom measurement. Our physicians and therapists try not to press any more than necessary in performing the scans. To find the magnitude of pressure-induced movement will require investigation by another independent imaging method. Studies in the literature estimated that the BAT procedure itself induced an average motion of 1 to 2 mm (8, 34). To set a reasonable cutoff distance dm for the data, we plot the dm in the SI direction vs. the resulting SD value in that direction in Fig. 7. A plateau of SD occurs between 2 and 5 cm, outside of which the SD changes rapidly. We take dm to be 3 cm in each direction, which, hopefully, includes most of the meaningful points. In other words, our presented data are calculated to exclude all points more than 3 cm in any direction. As a corollary, we do not think that providing information on the maximum shift is useful, because the magnitude will be larger with more daily treatment fractions in the data set. BAT ultrasound imaging is limited in a number of ways. First, it allows only rigid-body translational movement. It does not permit rotation, the change in volume, or the deformation of prostate shapes, which may happen in real-

ity. Second, prostate volumes observed in CT images tend to be larger than the same prostate observed in transrectal ultrasound (35–37). The same difference may exist between CT at planning and BAT ultrasound at treatment. Our physicians try to take this difference into account when evaluating the matching of positions. Third, the displacement is a compromise on all the delineated organs and does not, for example, separate the motion of seminal vesicle from the prostate. Postprostatectomy patients are a challenge. We delineate a prostate bed and have the physicians recognize it the best they can. Another hospital uses the bladder neck as the primary reference structure (38). Interuser variability can be as much as the prostate motion itself (9, 20). We try to minimize this effect by having the same physician who has delineated the planning contours do the ultrasound localization at radiation delivery. Nevertheless, even the same person may have slight variation from day to day. The ultrasound procedure observes only interfractional motion, so any intrafractional motion, such as respiration, is ignored. For prostate treatment, the magnitude of intrafractional motion averages about 2 mm (39, 40), which is much less than interfractional motion. Hence, the employment of BAT ultrasound will still be useful.

Prostate motion from ultrasound localization

From the histograms in Figs. 4a to 4c, one observes that the number of treatments in the 0-cm bin is exceptionally large, which is not totally consistent with a Gaussian distribution. In Fig. 4d, of the 304 treatments in the 0-cm bin (i.e., with less than 1 mm shift) in radial distance, 298 of them are exactly zero (i.e., no modification). This finding signifies a tendency to keep the position unchanged when the required displacement is not far from zero. The reasons can be that (1) 1 to 2 mm is within the uncertainty of the BAT alignment system, and (2) moving the patient and reacquiring ultrasound images for 1 to 2 mm is not “worth the effort.” This practice has the effect of slightly underestimating the true SD of prostate movement. The scatter plots of Fig. 5 were dominated by the outlying points with maximum displacement and did not portray well the varying concentration of data near the origin. The averages in Table 1, about 0 to 2 mm in each direction, were an indication of our systematic error. We did not know the exact cause of the small systematic uncertainty. The fact that prostate shift is not patient specific is a tribute to our therapists’ consistent skill in minimizing uncertainty. We also caution against attempts to design patient-specific PTV margins. If exceptional deviation of positioning is found on a particular patient, one should

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investigate the cause and try to eliminate it before setting margins different than those of other patients. Our motion results provide guidance in setting the margins around the CTV to generate the PTV, to be used in radiation delivery without the ultrasound system. A 1.5 SD has been suggested to be a good compromise between underdosing the target and irradiating too much of the critical organ (41). A 1.5 SD corresponds to 93% confidence interval that the CTV is within the PTV. With 1.5 SD, our margins are 0.90 cm in SI, 1.02 cm in AP, and 0.80 cm in LR directions. These values should be viewed as a minimum, conservative suggestion. With systematic uncertainty, intrafractional movement, and interuser variability, the realistic margins for prostate irradiation should be larger. CONCLUSION We have performed BAT ultrasound localization of radiation delivery on 4,154 treatments on 130 patients with prostate cancer. The data indicate a statistically significant directional prevalence, with a mean direction on the superior-posterior direction, closer to the superior. The systematic uncertainty is small, and the SD of motion agrees with the results from other studies. The shift is not patient specific and is practically unchanged over the time period of study.

REFERENCES 1. Cancer facts and figures 2003. Atlanta: American Cancer Society; 2003. 2. Leibel SA, Fuks Z, Zelefsky MJ, et al. Technological advances in external-beam radiation therapy for the treatment of localized prostate cancer. Semin Oncol 2003;30:596 – 615. 3. Pollack A, Hanlon A, Horwitz EM, et al. Radiation therapy dose escalation for prostate cancer: A rationale for IMRT. World J Urol 2003;21:200 –208. 4. Saw CB, Ayyangar KM, Zhen W, et al. Clinical implementation of intensity-modulated radiation therapy. Med Dosim 2002;27:161–169. 5. Langen KM, Jones DT. Organ motion and its management. Int J Radiat Oncol Biol Phys 2001;50:265–278. 6. Booth JT, Zavgorodni SF. Set-up error and organ motion uncertainty: A review. Australas Phys Eng Sci Med 1999;22: 29 – 47. 7. Chandra A, Dong L, Huang E, et al. Experience of ultrasoundbased daily prostate localization. Int J Radiat Oncol Biol Phys 2003;56:436 – 447. 8. Trichter F, Ennis R. Prostate localization using transabdominal ultrasound imaging. Int J Radiat Oncol Biol Phys 2003; 56:1225–1233. 9. Langen KM, Pouliot J, Anezino C, et al. Evaluation of ultrasound-based prostate localization for image-guided radiotherapy. Int J Radiat Oncol Biol Phys 2003;57:635– 644. 10. Fung AY, Grimm SY, Wong JR, et al. Computed tomography localization of radiation treatment delivery versus conventional localization with bony landmarks. J Appl Clin Med Phys 2003;4:112–119. 11. Court LE, Dong L. Automatic registration of the prostate for computed-tomography-guided radiotherapy. Med Phys 2003; 30:2750 –2757. 12. Shiu AS, Chang EL, Ye JS, et al. Near simultaneous computed tomography image-guided stereotactic spinal radiotherapy:

13.

14.

15.

16.

17.

18.

19. 20.

21.

22.

An emerging paradigm for achieving true stereotaxy. Int J Radiat Oncol Biol Phys 2003;57:605– 613. Letourneau D, Watt L, Gulam M, et al. Implementation of an on-board kilovoltage cone-beam CT imaging system for clinical applications [Abstract]. Int J Radiat Oncol Biol Phys 2003;57(Suppl.):S185. Pouliot J, Xia P, Aubin M, et al. Low-dose megavoltage cone-beam CT for dose-guided radiation therapy [Abstract]. Int J Radiat Oncol Biol Phys 2003;57(Suppl.):S183–184. Seppi EJ, Munro P, Johnsen SW, et al. Megavoltage conebeam computed tomography using a high-efficiency image receptor. Int J Radiat Oncol Biol Phys 2003;55:793– 803. Nederveen AJ, Dehnad H, van der Heide UA, et al. Comparison of megavoltage position verification for prostate irradiation based on bony anatomy and implanted fiducials. Radiother Oncol 2003;68:81– 88. Pouliot J, Aubin M, Langen KM, et al. (Non)-migration of radiopaque markers used for on-line localization of the prostate with an electronic portal imaging device. Int J Radiat Oncol Biol Phys 2003;56:862– 866. Litzenberg D, Dawson LA, Sandler H, et al. Daily prostate targeting using implanted radiopaque markers. Int J Radiat Oncol Biol Phys 2002;52:699 –703. B-mode Acquisition and targeting. Chatsworth, CA: Nomos Corporation. Enke C, Ayyangar K, CB Saw CB, et al. Inter-observer variation in prostate localization utilizing BAT. Int J Radiat Oncol Biol Phys 2002;54(Suppl.):S269. ICRU Report 50: Prescribing, recording, and reporting photon beam therapy. Bethesda, MD: International Commission on Radiation Units and Measurements; 1993. Hricak H, Schoder H, Pucar D, et al. Advances in imaging in the postoperative patient with a rising prostate-specific antigen level. Semin Oncol 2003;30:616 – 634.

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23. Adusumilli S, Pretorius ES. Magnetic resonance imaging of prostate cancer. Semin Urol Oncol 2002;20:192–210. 24. el-Gabry EA, Halpern EJ, Strup SE, et al. Imaging prostate cancer: Current and future applications. Oncology (Huntingt) 2001;15:325–336. 25. Ayyangar KM, Nizin PS, Saw CB, et al. Independent dose calculations for the Corvus MLC IMRT. Med Dosim 2001; 26:135–141. 26. Vac-Lock, MED-TEC. Inc., Orange City, IA. 27. Fisher NI. Statistical analysis of circular data. Cambridge: Cambridge University Press; 1995. 28. Mardia KV, Jupp PE. Directional statistics. New York: Wiley; 1999. 29. Upton GJG, Fingleton B. Categorical and directional data. New York: Wiley; 1989. 30. Zellars RC, Roberson PL, Strawderman M, et al. Prostate position late in the course of external beam therapy: Patterns and predictors. Int J Radiat Oncol Biol Phys 2000; 47:655– 660. 31. Zelefsky MJ, Crean D, Mageras GS, et al. Quantification and predictors of prostate position variability in 50 patients evaluated with multiple CT scans during conformal radiotherapy. Radiother Oncol 1999;50:225–234. 32. Beard CJ, Kijewski P, Bussiere M, et al. Analysis of prostate and seminal vesicle motion: Implications for treatment planning. Int J Radiat Oncol Biol Phys 1996;34:451– 458. 33. Artignan X, Smitsmans MH, Lebesque JV, et al. Online ultrasound image guidance for radiotherapy of prostate cancer:

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34.

35. 36.

37. 38. 39. 40.

41.

Impact of image acquisition on prostate displacement. Int J Radiat Oncol Biol Phys 2004;59:595– 601. Serago CF, Chungbin SJ, Buskirk SJ, et al. Initial experience with ultrasound localization for positioning prostate cancer patients for external beam radiotherapy. Int J Radiat Oncol Biol Phys 2002;53:1130 –1138. Badiozamani KR, Wallner K, Cavanagh W, et al. Comparability of CT-based and TRUS-based prostate volumes. Int J Radiat Oncol Biol Phys 1999;43:375–378. Hoffelt SC, Marshall LM, Garzotto M, et al. A comparison of CT scan to transrectal ultrasound-measured prostate volume in untreated prostate cancer. Int J Radiat Oncol Biol Phys 2003; 57:29 –32. Helmick R, Tarver R, Chan R, et al. Evaluation of post-plan dosimetry using TRUS and CT after transperineal prostate seed implant. Med Dosim 2002;27:289 –293. Chinnaiyan P, Tomee W, Patel R, et al. 3D-ultrasound guided radiation therapy in the post-prostatectomy setting. Technol Cancer Res Treat 2003;2:455– 458. Mah D, Freedman G, Milestone B, et al. Measurement of intrafractional prostate motion using magnetic resonance imaging. Int J Radiat Oncol Biol Phys 2002;54:568 –575. Kitamura K, Shirato H, Seppenwoolde Y, et al. Three-dimensional intrafractional movement of prostate measured during real-time tumor-tracking radiotherapy in supine and prone treatment positions. Int J Radiat Oncol Biol Phys 2002;53: 1117–1123. Goitein M. Nonstandard deviations. Med Phys 1983;10: 709 –711.