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Monte Carlo evaluation of tissue inhomogeneity effects in the treatment of the head and neck
Int. J. Radiation Oncology Biol. Phys., Vol. 50, No. 5, pp. 1339 –1349, 2001 Copyright © 2001 Elsevier Science Inc. Printed in the USA. All rights reserved 0360-3016/01/$–see front matter
PII S0360-3016(01)01614-5
PHYSICS CONTRIBUTION
MONTE CARLO EVALUATION OF TISSUE INHOMOGENEITY EFFECTS IN THE TREATMENT OF THE HEAD AND NECK LU WANG, PH.D.,* ELLEN YORKE, PH.D.,†
AND
CHEN-SHOU CHUI, PH.D.†
*University of Pennsylvania School of Medicine, Department of Radiation Oncology, Philadelphia, PA; †Memorial Sloan-Kettering Cancer Center, New York, NY Purpose: To use Monte Carlo dose calculation to assess the degree to which tissue inhomogeneities in the head and neck affect static field conformal, computed tomography (CT)-based 6-MV photon treatment plans. Methods and Materials: We retrospectively studied the three-dimensional treatment plans that had been used for the treatment of 5 patients with tumors in the nasopharyngeal or paranasal sinus regions. Two patients had large surgical cavities. The plans were designed with a clinical treatment planning system that uses a measurementbased pencil-beam dose-calculation algorithm with an equivalent path-length inhomogeneity correction. Each plan employs conformally-shaped 6-MV photon beams. Patient anatomy and electron densities were obtained from the treatment planning CT images. For each plan, the dose distribution was recalculated with the Monte Carlo method, utilizing the same beam geometry and CT images. The Monte Carlo method accurately accounts for the perturbation effects of local tissue heterogeneities. The Monte Carlo calculated dose distributions were compared with those from the clinical treatment planning system. Results: The degree to which tissue inhomogeneity affects the dose distributions of individual fields varies with the specific anatomic geometry, especially the size and location of air cavities in relation to the beam orientation and field size. Most of the beam apertures completely enclose the air cavities within or adjacent to the gross tumor volume (GTV). Equivalent squares (including blocking) ranged from approximately 5 to 9.5 cm. A common feature observed for individual fields is that the Monte Carlo calculated doses to tissue directly behind and within an air cavity are lower. However, after combining the fields employed in each treatment plan, the overall dose distribution shows only small differences between the two methods. For all 5 patients, the Monte Carlo calculated treatment plans showed a slightly lower dose received by the 95% of target volume (D95) than the plans calculated with the pencil-beam algorithm. The average difference in the target volume encompassed by the prescription isodose line was less than 2.2%. The difference between the dose–volume histograms (DVHs) of the GTV was generally small. For the brainstem and chiasm, the DVHs of the two plans were similar. For the spinal cord, differences in the details of the DHV and the dose to 1 cc (D1cc) of the structure were observed, with Monte Carlo calculation generally predicting increased dose indices to the spinal cord. However, these changes are not expected to be clinically significant. Conclusion: For 6-MV photons, the effects of both normal tissue inhomogeneities and surgical air cavities on the target coverage were adequately accounted for by conventional pencil beam methods for all of the cases studied. Although differences in details of the DVHs of the normal structures were observed, depending on whether Monte Carlo or pencil-beam algorithm was used for calculation, these differences are not expected to be clinically significant. In general, the pencil-beam calculation corrected for primary attenuation by the equivalent pathlength is a sufficiently accurate method for head-and-neck treatment planning using 6-MV photons. © 2001 Elsevier Science Inc. Monte Carlo, Tissue inhomogeneity, Air cavities, Dose distribution.
INTRODUCTION In the head-and-neck region, the presence of surface curvature, air cavities, and bony structures influences the dose distribution in a complex manner. The main physical processes involved are the changes in the primary transmissions, the range of secondary electrons, and the number of photons scattered in different media; which change the
radiation dose distribution. Whether the change is clinically significant is not well understood at present. Several groups (1–7) have made measurements to investigate the effect of air cavities on the dose distribution in tissue equivalent phantoms. They reported a varying degree of underdosing at the air-tissue interface, depending on geometry, beam energy, and field size. However, an investigation of air-cavity interface doses in a humanoid phantom, with beam energies
Reprint requests to: Lu Wang, Ph.D., Department of Radiation Oncology, Division of Medical Physics, 2 Donner Building, 3400 Spruce Street, Philadelphia, PA 19104. Tel: (215) 662-3088; Fax: (215) 349-5978; E-mail: [email protected]
Presented at the 42nd Annual Meeting of ASTRO, Hynes Convention Center, October 22–26, 2000, Boston, MA. Received Oct 30, 2000, and in revised form Apr 1, 2001. Accepted for publication Apr 17, 2001. 1339
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ranging from cobalt-60 (60Co) to 10 MV and field sizes of at least 6 ⫻ 6 cm2, found the underdose to be clinically insignificant (1, 3, 5). Doses near the interfaces of regularly shaped air cavities were also studied for single and parallelopposed fields with a variety of dose calculation algorithms, including Monte Carlo calculation (4, 5). Calculations based on tissue-air ratio (TAR) and the Batho power-law method (8) failed to predict the experimentally observed underdose beyond an air cavity (4). This is because empiric methods do not account for loss of electronic equilibrium or the influence of electron transport from one medium to another, both of which contribute to the buildup and build-down of dose near interfaces. Even with a calculation model in which the loss of lateral equilibrium is accounted for by scaling field size with the density of the material (9, 10), the results near an air-water interface are inaccurate. Advanced dose calculation methods that model the physical process of electron transport are available on some commercial treatment planning systems. These methods calculate dose distributions by convolution/superposition techniques (11–13) using Monte Carlo precalculated dose spread kernels in water. One of the limitations of the convolution methods is that electronic equilibrium is assumed when such kernels are generated; therefore, these methods also fail to predict accurate dose distributions at the boundaries of air cavities or inhomogeneities (14 –16). In a study of air-cavity interface doses, however, Monte Carlo simulations were found to match the measured results to within 1% (5). Although phantom studies are important and reveal the perturbation effects of air cavities under various conditions, studies using patient anatomy and including the combined dosimetric effects of all tissue inhomogeneities—air cavities, soft tissues, and bony structures—are of practical significance. The use of conformal radiation therapy for headand-neck tumors increases the need to understand the differences between the dose distribution calculated by the treatment planning system and the actual distribution, including inhomogeneity effects. The goal of conformal treatments is to tightly shape the dose distribution to the target while avoiding critical structures and thus improve local control while maintaining acceptable normal tissue morbidity. Therefore, the dose distribution that is presented for treatment plan evaluation should be an accurate representation of the patient’s treatment. The Monte Carlo method can rigorously account for tissue inhomogeneity effects. With Monte Carlo, the transport of each radiation particle is carried out in the given inhomogeneous medium according to the probabilities or cross-sections of the allowed interactions. In this manner, the behavior of each particle is traced and the discrete energy deposition steps are accumulated. The final dose distribution is the result of millions of accumulated energy deposition events. If enough photon histories are accumulated, the results computed are of superior accuracy compared to any approximate method employed in the treatment planning systems, provided that the radiation source and the patient anatomy are correctly simulated. For linear acceler-
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ators, the radiation source can be accurately modeled (14, 17–20). Anatomy, including the electron density and an approximate atomic number distribution, is accurately represented by the patient-specific computed tomography (CT) images. Therefore, patient-specific external beam dosimetry that correctly accounts for inhomogeneities can be confidently based on Monte Carlo techniques (21–26). In this work, we used the Monte Carlo method (26) in a retrospective dosimetric study of treatment planning in the head and neck. Five patients who had been treated for carcinoma in the nasopharyngeal region or the paranasal sinus were selected. Monte Carlo– calculated dose distributions in the target and surrounding normal tissues were compared to those calculated with a clinical treatment planning system that uses a measurement-based pencil-beam dose-calculation algorithm with an equivalent pathlength inhomogeneity correction for the same beams. METHODS AND MATERIALS Treatment plan selection We selected the treatment plans of 5 patients who had been treated with three-dimensional (3D) conformal radiation therapy for carcinoma in the head and neck. The plans include a variety of static field techniques commonly used in head-and-neck treatments. To accentuate tissue inhomogeneity effects, two of the chosen patients (#1 and #4) had large post-surgical air-filled cavities. We chose patients treated with two-, three-, four-, and seven-field techniques, all with 6-MV photons. Specifically, patients #1, #2, and #3 had paranasal sinus malignancies and were treated with a three-field technique (heavily weighted anterior field with or without wedge and lightlyweighted, 60° wedged, parallel-opposed laterals) (27). For patient #1, an additional small, unwedged anterior field augmented the dose between the eyes, allowing the eyes to be blocked in the lateral beams. Patient #4 had cancer of the jaw and cheek and was treated with a wedged pair (anterior and left lateral, 45° wedges). Patient #5 had nasopharyngeal cancer and was treated with a seven-field technique. This technique (28, 29) consists of seven fields separated by 30°: an unwedged posterior field and opposed-lateral and four posterior-oblique fields, each with a 45° wedge. The cord is blocked in each field. This beam arrangement was developed as a static field technique for sparing the brainstem and spinal cord while conforming the dose to a target volume that has wrapped around these structures (28, 29). Clinical planning process Each patient was immobilized with a custom Aquaplast mask for the planning CT scan and for treatment. The planning CT scans were acquired for each patient at 3-mm intervals. The gross tumor volume (GTV) and the planning target volume (PTV) (30) were outlined by a physician. In general, the GTV was expanded by 1 cm to derive the PTV; however, tighter margins were used near the brainstem or in the buildup region. Normal structures of interest such as
Monte Carlo evaluation of tissue inhomogeneity effects in the head and neck
eyes, optic chiasm, brainstem, and spinal cord were also outlined on the images. The beam directions were selected by experienced planners and the aperture of each beam was designed with a 6-mm margin around the PTV (except where tighter margins were used to protect normal structures). The beam weights were selected to satisfy the physician’s objectives relative to target coverage and normal tissue sparing. Our clinical convention is to normalize all plans so that 100 cGy is delivered to the 100% isodose line in the graphic display. The physician prescribes the treatment dose to the percent isodose line that meets treatment objectives. Subsequently, final graphic displays and dose– volume histograms (DVHs) for both percent and cumulative absolute dose are generated. All treatment plans were generated on the Memorial Sloan-Kettering Cancer Center (MSKCC) treatment planning system. This dose calculation algorithm is based on measured depth doses and cross-field profiles over a range of depths and square fields. It corrects for tissue inhomogeneities by computing the equivalent pathlength along each ray direction. For irregularly-shaped fields, a correction factor generated by convolution of a pencil beam kernel with the primary fluence distribution defined by the aperture is applied at each point (31, 32). In this algorithm, the changes of lateral electron scattering in media differing from water are ignored. All plans were judged to be suitable for treatment delivery. Below, we refer to them as the “standard plans.” Monte Carlo calculations Monte Carlo algorithms simulate radiation interactions and perform ray-tracing for both primary and scattered radiation through the patient geometry, as defined by the CT images. The Monte Carlo method we used employs the EGS4 system (33) for radiation simulation and handles transport by the user code MCPAT (26). This code contains several variance reduction techniques to improve computational efficiency, including a more efficient ray-trace between photon interactions, the use of a kerma approximation for dose deposition by photons below a user-selected energy, and an analytic determination of the number of primary photon interactions in each voxel, which gives the same statistics for low- and high-density media. The code was validated by measurement in homogeneous and inhomogeneous phantoms. Further details on the method and measurement validation are provided in Refs. (26, 34). The beam information from the clinical treatment plans (e.g., energy, orientation, aperture, fluence distribution, and wedge angle) was entered into the Monte Carlo dose calculation module. The patient-specific CT images were employed to describe the computational geometry and to define the electron density ratio, e. To improve ray-trace efficiency, the MCPAT code also determines an approximate effective atomic number for the medium in each voxel from the CT images by treating voxels above a user-specified electron density as bone and below as water. The image voxel size was 3 mm on each side. This density array was used both to evaluate the equivalent pathlength and to flag
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the change of medium. Because local electron density derived from the CT image data was incorporated into the Monte Carlo calculation, the perturbation effects of local tissue heterogeneities were automatically accounted for. More than 1,000 first interactions were sampled in each image voxel, and a statistical uncertainty of 1.5% in the target volume was achieved. The calculation was performed on a (500-MHz) DEC Alpha workstation. Comparison of Monte Carlo and standard plans The comparison between the pencil-beam and Monte Carlo calculations was carried out in terms of absolute absorbed dose. The Monte Carlo algorithm produces results in units of dose/fluence. To convert to dose per monitor unit (dose/MU), we first performed the Monte Carlo dose calculation in a homogeneous water phantom with a reference field size (10 ⫻ 10 cm) and a source-axis distance (SAD) of 100 cm. The central axis dose per unit fluence at Dmax was derived from this simulation. The inverse of this factor gives the fluence to produce a dose of 1 cGy at Dmax under the reference field size and SAD conditions, which is the same as the fluence per MU. Having the conversion factor of fluence/MU for the reference conditions, it is straightforward to derive the dose/MU by multiplying the Monte Carlo calculated dose/fluence data by the conversion factor. The standard plan was normalized to deliver 100 cGy to the 100% isodose line, and the beam weights of the standard plan were copied to the Monte Carlo plan. Therefore, the beam-on-time for each beam is the same for both plans. Because contaminant electrons are not included in the current version of the Monte Carlo module, the study was performed only for tumors and normal structures lying beyond Dmax (1.5 cm). We therefore modified the GTV contours to exclude the portion in the buildup region. Because the PTVs require more drastic alteration to avoid the buildup region, we did not evaluate changes in dose distribution in the PTV between the two calculation techniques. The average volume of the modified GTVs was 108 cc (range 74 –145 cc). RESULTS Dose distributions for single fields To more clearly demonstrate the differences between the standard and Monte Carlo calculations, we first compared dose distributions of individual treatment fields. Figures 1 and 2 show the dose distributions in three orthogonal views through isocenter of the main anterior and the right-lateral field, respectively, for patient #1, who had a previous maxillectomy. The surgery created a larger air cavity than the normal anatomic cavities present in nonsurgical patients (4.5-cm superior to inferior, 4.0-cm anterior to posterior, and 2.0 cm left to right). Small soft tissue protrusions were visible inside the cavity. The inhomogeneity effects in this patient should be more pronounced, and represent an extreme case. The collimator settings for the anterior and lateral fields were 11.5 ⫻ 9.2 cm2 and 13.5 ⫻ 9.2 cm2,
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Fig. 1. Comparison of the isodose distributions for AP field from transverse, coronal, and sagittal views. The dose distributions based on the equivalent pathlength method are shown on the upper panel. The Monte Carlo calculated dose distributions are shown on the lower panel.
respectively. Blocking reduced the equivalent areas by approximately 30%. In these figures, the portion of the GTV lying beyond Dmax is outlined in orange. The isodose lines represent the absolute doses in cGy delivered with 100 MU from a beam which delivers 1 cGy/MU at Dmax under the calibration conditions. Isodoses calculated with the equivalent-pathlength method are shown on the upper row, and with Monte Carlo on the lower row. Comparing the rows of images, it is obvious that the air cavity produces differences between the two dose distributions. For example, the Monte Carlo 70-cGy isodose line near the inferior edge of the AP field is pulled in (as seen in the sagittal and coronal views of Fig. 1), while the 10- and 5-cGy isodose lines bulge out (as seen in the transverse cut of Fig. 1). For the lateral field, the effect of the air cavity is even greater, as the longer dimension of the air cavity lies across the beam, leaving little soft-tissue margin over the anterior edge of the cavity. As a result, the Monte Carlo isodose lines in the range of 25–35 cGy (shown by yellow, green, and light-blue lines in Fig. 2) penetrate less deeply than the corresponding lines generated by the standard calculation. The Monte Carlo calculation
predicts a lower dose to soft tissue lying within and immediately downstream of the cavity than the standard calculation. This effect, as well as the constriction of higher isodose lines within the cavity, is caused by the loss of electronic equilibrium. The bulge of the lower dose lines is attributed to the larger lateral scattering of electrons in an air cavity located at the beam edge. The inhomogeneity effect of bone in the low megavoltage energy range is mainly a change of transmission (34) which is accounted for by the equivalent pathlength method. The individual fields for the other four patients were also evaluated. The observed difference between the Monte Carlo and standard calculations varies from patient-to-patient, depending on the volume and location of the air cavities relative to the beam, as well as field size and beam orientation. For the patients with only normal anatomic cavities in the treatment volume, the differences are less notable than those shown in the figures. However, common features are observed that the dose to tissue downstream and within an air cavity is lower in the Monte Carlo calculation, and beam penumbra is increased in the Monte Carlo plan if
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Fig. 2. Comparison of the isodose distributions for right-lateral field from transverse, coronal, and sagittal views. The dose distributions based on the equivalent pathlength method are shown on the upper panel. The Monte Carlo-calculated dose distributions are shown on the lower panel.
the beam edge lies in an air cavity. The impact of these effects on GTV coverage when the individual beams are combined to form the treatment plan will be addressed in the following evaluations. Dose distribution for the plans Figure 3 compares the relative isodose distributions for the standard and Monte Carlo calculations for patient #1. The relative isodose distributions were normalized so that 100% ⫽ 100 cGy, as is the practice in MSKCC. Because the main anterior field was heavily weighted relative to the two lateral-wedged fields, with a beam-on-time ratio of approximately 3:1:1, and the small anterior field between the eyes was weighted about 12% of the main field, the overall dose distribution is dominated by the main anterior field, and shows less difference between Monte Carlo and standard calculations than the single lateral field. For patient #1, the prescription level was the 87% isodose line (represented by yellow line). Figure 3 shows only slight difference between the two calculations in the shape of the 87% isodose lines, with the GTV coverage in the Monte Carlo calculation being slightly tighter. Relatively larger differences are noted
in the higher- (95–100%) and the lower-dose region (10 – 30%). Overall, the beams in the Monte Carlo calculation deliver lower dose behind the air cavity, creating a lower dose to the target. Comparing the standard calculations with the Monte Carlo calculations for all five patients, we observed that, in general, the difference in the appearance of the prescription isodose line was small. Dose–volume histograms GTV. A comparison of the DVHs for patient #1’s modified GTV (beyond Dmax) is shown in Fig. 4. The Monte Carlo DVH shows that a lower dose is delivered than is expected from the standard calculations. D95, the dose encompassing 95% of the structure, is 87% for the Monte Carlo calculation vs. 88.3% for the standard. D05, the isodose level encompassing 5% of the GTV, is an indicator of the high-dose region within the GTV. It differs by 2.3%, with the Monte Carlo value being smaller (98.9% vs. 101.2%). We report the maximum and minimum doses because, while they are determined by only a few points and thus may be misleading measures of dosimetric differences,
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Fig. 3. Comparison of the isodose distributions of the three-composite fields from the transverse, coronal, and sagittal views for patient #1. The standard plan based on the equivalent pathlength method is shown on the upper panel. The Monte Carlo plan is shown on the lower panel.
they are often examined in plan evaluation. The differences in the maximum and the minimum doses were 2.3% (106.07% in the standard calculation vs. 103.7% in the Monte Carlo calculation) and 4.3% (73.7% vs. 76.9%). The Monte Carlo mean dose is 2.4% lower than the standard calculation mean dose (93.8% vs. 96.1%). The steep slope of the integral DVH in the high-dose region makes the volume covered by a particular dose level a sensitive indicator of the difference between the two calculation techniques. For example, Monte Carlo calculations predict that a considerably smaller fraction of the GTV is encompassed by the 95% isodose level (V95 ⫽ 42.4%) than the standard calculations (V95 ⫽ 65.7%). For the prescribed isodose level (87%), the percentage of the GTV encompassed (Vp) was 97.4% in the standard plan and 95.2% in the Monte Carlo plan. As previously noted, there was little change in the shape of the prescription isodose. Table 1 lists the differences in the dose parameters discussed above for each of the five patients’ modified GTVs. The average differences in the mean dose to GTV and D05 were 1.3% and 1.0%, respectively. Table 2 summarizes the average and associated standard deviations of D05, D95, Vp,
and the maximum dose (Dmax), for the modified GTV from the Monte Carlo and standard plans. The ratios of these parameters between the Monte Carlo and standard plans were calculated for each patient, to reduce the effect of individual anatomy. Average ratios of these dose indices were derived from the ratios for each patient and are listed in the last column of Table 2. Although the ratios of each dose parameter are close to unity, they are less than 1 for four of the five patients. This indicates that the dose to the hot spot, the target coverage and the maximum dose within the GTV are generally less than expected from the standard treatment plan. Critical structures. The critical normal structures in the head-and-neck region include spinal cord, brainstem, chiasm, lenses, retinas, and eyes. Because the lenses, retinas, and eyes are located partly in the buildup region, we cannot properly compare the Monte Carlo and standard plan predictions for these structures, as noted above. Therefore, we limit our discussion to the spinal cord, brainstem, and chiasm. Spinal cord. Figure 5 compares the DVHs for the three patients (#1, #4, and #5) for whom the cord were close
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Fig. 4. A comparison of the DVH for the modified GTV of patient #1 using the two dose-calculation methods: the Monte Carlo and the equivalent-pathlength methods. The solid line represents the Monte Carlo plan and the dashed line represents the standard plan.
enough to the GTV to be a concern. Because different extents of the spinal cord was outlined among these patients, the DVHs plot absolute rather than relative volumes. Figure 5 shows differences in details of the DVH, depending on the dose calculation technique. However, when comparing the dose parameters (such as the maximum dose, Dmax, and the dose to hottest 1 cc of volume, D1cc) quantitatively, the changes are found to be fairly small. For example, the largest absolute increase in D1cc was 4.7% of the dose to the 100% line (patient #1); the largest increase in Dmax was 6% (patient #5). This may attribute to fact that only part of the spinal cord is involved and it is either under the block (patient #7) or in only one of the treatment fields (AP field for patients #1 and #4). Table 2 lists the dose indices averaged among the five patients. Ratios were taken for each dose index and each patient to reduce the effect of patient-specific anatomy and the position of the critical structure in respect to the target. The average ratios were listed in the last column of Table 2. Although the ratios are approximately 10%, the absolute dose difference is small because the cord dose is only a small fraction of dose to the
GTV. Therefore, we do not expect the difference to be clinically significant. Brainstem. The DVHs of brainstem calculated by the two methods for each patient are almost identical. Hence, no graphical comparison is presented here. Because, in general, brainstem is well separated from any air cavities and is surrounded by soft tissue, it is anticipated that the tissue inhomogeneity effect is small and the two dose-calculation methods should give similar results for this structure. Table 2 lists the averaged dose indices for brainstem. The differences in the dose indices derived from two plans are negligible. Optic chiasm. The DVHs of optic chiasm for patient #1 are shown in Fig. 6. Most of the chiasm was located within the fields, but it is well separated from air cavities. However, a piece of the chiasm is at the edge of the two lateral fields, where there is loss of electronic equilibrium. For this reason, the Monte Carlo plan presents a notable drop in the shoulder of the DVH. The Monte Carlo calculated dose to the chiasm was slightly smaller than expected from the conventional treatment plan. However, the difference in the
Table 1. Differences between the standard plan and Monte Carlo plans for the important dose distribution parameters of the GTV Statistics
Dmax (%)
Dmean (%)
D95 (%)
D05 (%)
V95 (%)
Vp (%)
Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Average
2.3 ⫺2.7 2.4 0.6 1.3 0.8
2.4 0.4 0.8 1.8 1.3 1.3
1.5 1.6 1.2 1.7 1.5 1.5
2.3 ⫺0.9 0.7 2.0 0.9 1.0
35.5 2.8 3.7 32.4 6.8 16.3
2.3 3.7 0.7 1.4 3.3 2.2
The negative sign represents that the data of the Monte Carlo plan are larger than those of the standard plans.
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Table 2. Summary of the dose distributions averaged over 5 patients for the Monte Carlo and standard plans
GTV
Spinal cord Brainstem Chiasm
D05 (%) D95 (%) Vp Dmax (%) D1cc Dmax (%) D05 (%) Dmax (%) D05 (%) Dmax (%)
Monte Carlo
Standard
Ratio*
106.0 ⫾ 6.9 90.0 ⫾ 3.9 91.4 ⫾ 8.5 111.1 ⫾ 8.6 19.6 ⫾ 11.9 41.7 ⫾ 13.5 63.8 ⫾ 30.7 73.6 ⫾ 30.9 79.6 ⫾ 27.4 84.5 ⫾ 28.2
107.0 ⫾ 5.6 91.3 ⫾ 3.9 93.5 ⫾ 7.4 112.0 ⫾ 7.1 18.1 ⫾ 12.8 40.1 ⫾ 11.2 64.3 ⫾ 30.8 74.1 ⫾ 31.9 79.2 ⫾ 30.0 85.0 ⫾ 31.0
0.990 ⫾ 0.013 0.985 ⫾ 0.002 0.977 ⫾ 0.012 0.992 ⫾ 0.021 1.14 ⫾ 0.14 1.03 ⫾ 0.11 0.99 ⫾ 0.01 0.99 ⫾ 0.04 1.02 ⫾ 0.08 1.01 ⫾ 0.06
* Monte Carlo/Standard. D05 ⫽ Dose encompassing 5% of volume. D1cc ⫽ Dose encompassing 1 cc of volume. D95 ⫽ Dose encompassing 95% of volume. Vp ⫽ Percent volume receiving at least the prescribed percent dose.
dose indices, such as D05 and Dmax, are negligible given the fact that uncertainty in dose calculation is 1.5%. For four patients, the chiasm was close enough to the PTV to be a concern. Two of the patients have almost identical DHVs between the Monte Carlo and the standard plans. The largest change (an increase) was seen for patient #4, for whom the chiasm is bisected by one field edge and is about 2 cm outside the edge of the other. For this patient, the absolute increase in D05 is about 4.5% and is 3.6% for Dmax. DISCUSSION As most head-and-neck cancers originate from the mucosa of the upper aerodigestive tract, these tumors are either in contact with or surround air cavities. The competing effects of increased transmission, decreased photon scatter, and the loss of electronic equilibrium in an air cavity determine the overall dose distribution. Modern treatment planning systems are able to account for the change of primary transmission in heterogeneous media with relatively simple algorithms, but most cannot account for loss of electronic equilibrium near tissue-air interfaces. We performed Monte Carlo calculations to assess the accuracy of dose distributions calculated by standard methods in the presence of typical head-andneck tissue inhomogeneities. The presence of bony structures mainly reduces the transmission of the primary beam. The increased scatter by high-density material (bone) for 6-MV photons is insignificant (34). The effect of electronic disequilibrium and variation of photon scatter near air-tissue interfaces depends strongly on cavity volume, field size, and beam energy (5). As normal anatomic air cavities in the head and neck region have dimensions less than 3 cm in diameter (5), and the treatment field sizes are often greater than 6 ⫻ 6 cm2, electronic equilibrium is retained for intermediate photon energies, such as 6 MV. If patients have large surgical cavities (patients #1 and #4),
tissue surrounding the cavity is considered to be at risk and is included in the GTV or CTV. For our patients, GTV was expanded to PTV by 1 cm in most directions, providing a larger volume of irradiated soft tissue surrounding the cavity. Therefore, even for simple field arrangements, the most heavily-weighted fields fully enclose the cavity, preventing large underdose for tissue surrounding and protruding into the cavity. We find that, although tissue inhomogeneities in head and neck alter features of the dose distribution, when the effect of inhomogeneity is assessed by Monte Carlo dose calculation, the target coverage and normal organ doses do not differ greatly from the predictions of the equivalent pathlength corrected pencil-beam method. As shown in Table 1, Monte Carlo and standard calculations of the average maximum and mean doses to the GTV beyond the buildup region differ, on average, by less than 2%. The average volume of GTV encompassed by the prescribed isodose level is lower by Monte Carlo calculation, but only by approximately 2%. The average decrease in the dose encompassing the hottest 5% and 95% of the GTV is only 1.0% and 1.5%, respectively. Our results indicate that the dose coverage of the target predicted by the approximate inhomogeneity correction method implemented in our treatment planning system (equivalent pathlength corrected pencil beam) is very similar to that obtained by Monte Carlo calculation. The electron transport accounted for in the Monte Carlo calculation has small influence on the dose distribution in the target for 6-MV photons. Hence, the loss of electronic equilibrium does not have a severe effect on the coverage of targets near normal, or even surgically-enlarged nasopharyngeal, air cavities. Although the Monte Carlo results may slightly overestimate the dose at the surface of a cavity build-up region due to the 3 mm3 voxel size, we believe that this is sufficiently fine resolution to detect significant underdoses. Our results agree with the mea-
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Fig. 5. A comparison of the DVH of the spinal cord for patients #1, #4, and #5.
surement results obtained in a cubic air cavity in solid water phantom by Kan et al. (5). For the critical structures, the dose difference between the two calculation methods varies with the location of the structure relative to the air cavities and field edges. If the structure lies within the fields and well separated from air cavities (e.g., brainstem), the difference in the dose distribution is small and may be attributed to statistical variation in the Monte Carlo calculations. If the structure is at a beam edge and is surrounded by soft tissue or is adjacent to air cavities, the dose
calculated by Monte Carlo is slightly higher than obtained by conventional calculation. We expect that the observed differences are clinically insignificant. Although electron contamination was not included in the current version of the Monte Carlo dose calculation, our conclusions are not altered, as neither the modified GTV nor the critical structures analyzed include volumes within Dmax of the skin. Nonetheless, it would be useful to modify the Monte Carlo code to include an accurate assessment of the dose in the buildup region.
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Fig. 6. A comparison of the DVH for the chiasm of patient #1.
CONCLUSION We compared the dose distributions for 5 patients with head-and-neck cancer calculated by the Monte Carlo method and by a measurement-based pencil-beam algorithm. We assessed the accuracy of the latter for conformal, CT-based treatment plans in the presence of tissue inhomogeneities in the head and neck, especially air cavities. A variety of conformal static field arrangements with 6-MV photons were used. For all patients studied, the Monte Carlo calculations showed a slight decrease in the target coverage (about 1–2%) in terms of Vp from that of the standard calculations based on the pencil-beam algorithm. Dose distributions of individual fields were altered to different extents, depending on the size and
location of the air cavities relative to the beam geometry, including field size and beam orientation. However, upon combining the multiple fields employed in the treatment plan, the overall dose distribution showed only small differences. For the cord, the Monte Carlo calculation indicates that the dose to the hottest 1 cc is generally increased by a small fraction. For the brainstem and the optic chiasm, the differences are minimal. Our results indicate that conformal 6-MV photon treatment plans for head-and-neck tumors, designed with a pathlengthcorrected, measurement-based pencil-beam algorithm, give adequate target coverage and sparing of normal organs at risk, even in the presence of large surgical air cavities.
REFERENCES 1. Epp ER, Lougheed MN, McKay JW. Ionization build-up in upper respiratory air cavities during teletherapy with cobalt 60 radiation. Br J Radiol 1958;31:361–367. 2. Epp ER, Boyer AL, Doppke KP. Underdosing of lesions resulting from lack of electronic equilibrium in upper respiratory air cavities irradiated by 10-MV x-ray beams. Int J Radiat Oncol Biol Phys 1977;2:613– 619. 3. Niroomand-Rad A, Harter KW, Thobejane S, et al. Air cavity effects on the radiation dose to the larynx using Co-60, 6 MV, and 10 MV photon beams. Int J Radiat Oncol Biol Phys 1994;29:1139 –1146. 4. Klein EE, Chin LM, Rice RK, et al. The influence of air cavities on interface doses for photon beams. Int J Radiat Oncol Biol Phys 1993;27:419 – 427. 5. Kan WK, Wu PM, Leung HT, et al. The effect of the nasopharyngeal air cavity on x-ray interface doses. Phys Med Biol 1998;43:529 –537. 6. Shahine BH, Al-Ghazi MSAL, El-Khatib E. Experimental evaluation of interface does in the presence of air cavities compared with treatment planning algorithms. Med Phys 1999;26:350 –355.
7. Beach JL, Mendiondo MS, Mendiondo OA. A comparison of air-cavity inhomogeneity effects for cobalt-60, 6-, and 10-MV x-ray beams [published erratum appears in Med Phys 1987;4: 691]. Med Phys 1987; 14:140 –144. 8. Khan FM. The physics of radiation therapy. Baltimore: Williams and Wilkins; 1992. 9. Petti PL, Rice RK, Mijnheer BJ, et al. Heterogeneity model for photon beams incorporating electron transport. Med Phys 1987;14:349 –354. 10. Petti PL, Siddon RL, Bjarngard BE. A multiplicative correction factor for tissue heterogeneities. Phys Med Biol 1986;31: 1119 –1128. 11. Mohan R, Chui C, Lidofsky L. Differential pencil beam dose computation model for photons. Med Phys 1986;13:64 –73. 12. Mackie TR, Scrimger JW, Battista JJ. A convolution method of calculating dose for 15-MV x rays. Med Phys 1985;12: 188 –196. 13. Ahnesjo A, Andreo P, Brahme A. Calculation and application of point spread functions for treatment planning with high energy photon beams. Acta Oncol 1987;26:49 –56. 14. Liu HH, Mackie TR, McCullough EC. A dual source photon
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beam model used in convolution/superposition dose calculations for clinical megavoltage X-ray beams. Med Phys 1997; 24:1960 –1974. Knoos T, Ahnesjo A, Nilsson P, et al. Limitations of a pencil beam approach to photon dose calculations in lung tissue. Phys Med Biol 1995;40:1411–1420. Hurkmans C, Knoos T, Nilsson P, et al. Limitations of a pencil beam approach to photon dose calculations in the head and neck region. Radiother Oncol 1995;37:74 – 80. Rogers DW, Faddegon BA, Ding GX, et al. BEAM: A Monte Carlo code to simulate radiotherapy treatment units. Med Phys 1995;22:503–524. Lovelock DMJ, Chui CS, Mohan R. A Monte Carlo model of photon beams used in radiation therapy. Med Phys 1995;22: 1387–1394. Chaney EL, Cullip TJ, Gabriel TA. A Monte Carlo study of accelerator head scatter. Med Phys 1994;21:1383–1390. Mohan R, Chui CS, Lidofsky L. Energy and angular distributions of photons from linear accelerators. Med Phys 1985;12: 592–597. Cox LJ, Schach von Wittenau AE, Bergstrom PMJ, et al. Photon beam description in PEREGRINE for Monte Carlo dose calculations. Lawrence Livermore National Laboratory; 1997. Schach von Wittenau AE, Cox LJ, Bergstrom PMJ, et al. Treatment of patient-dependent beam modifiers in photon treatments by the Monte Carlo dose calculation code PEREGRINE. Lawrence Livermore National Laboratory;1997. Ma CM, Reckwerdt P, Holmes M, et al. DOSXYZP users manual. Ottawa, Canada: National Research Council of Canada; 1995. Briesmeister JF. MCNP. A general Monte Carlo N-particle
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transport code, Version 4A. Los Alamos National Laboratory; 1993. DeMarco JJ, Solberg TD, Smathers JB. A CT-based Monte Carlo simulation tool for dosimetry planning and analysis. Med Phys 1998;25:1–11. Wang L, Chui CS, Lovelock DMJ. A patient-specific Monte Carlo dose-calculation method for photon beams. Med Phys 1998;25:867– 878. Bentel G. Treatment planning - head and neck region. New York: McGraw Hill; 1996. p. 307–310. Leibel SA, Kutcher GJ, Harrison LB, et al. Improved dose distributions for 3D conformal boost treatments in carcinoma of the nasopharynx. Int J Radiat Oncol Biol Phys 1991;20: 823– 833. Hunt MA, Kutcher GJ, Burman C, et al. The effect of setup uncertainties on the treatment of nasopharynx cancer. Int J Radiat Oncol Biol Phys 1993;27:437– 447. ICRU-50. Prescribing, recording, and reporting photon beam therapy. Bethesda, MD; 1993. Mohan R, Barest G, Brewster LJ, et al. A comprehensive three-dimensional radiation treatment planning system. Int J Radiat Oncol Biol Phys 1988;15:481– 495. Mohan R, Antich PP. A method of correction for curvature and inhomogeneities in computer aided calculation of external beam radiation dose distributions. Comput Progr Biomed 1979;9:247–257. Nelson WR, Hirayama H, Rogers DWO. The EGS4 code system. Stanford, CA: Stanford Linear Accelerator Center; 1985. Wang L, Lovelock M, Chui CS. Experimental verification of a CT-based Monte Carlo dose-calculation method in heterogeneous phantoms. Med Phys 1999;26:2626 –2634.
PII S0360-3016(01)01614-5
PHYSICS CONTRIBUTION
MONTE CARLO EVALUATION OF TISSUE INHOMOGENEITY EFFECTS IN THE TREATMENT OF THE HEAD AND NECK LU WANG, PH.D.,* ELLEN YORKE, PH.D.,†
AND
CHEN-SHOU CHUI, PH.D.†
*University of Pennsylvania School of Medicine, Department of Radiation Oncology, Philadelphia, PA; †Memorial Sloan-Kettering Cancer Center, New York, NY Purpose: To use Monte Carlo dose calculation to assess the degree to which tissue inhomogeneities in the head and neck affect static field conformal, computed tomography (CT)-based 6-MV photon treatment plans. Methods and Materials: We retrospectively studied the three-dimensional treatment plans that had been used for the treatment of 5 patients with tumors in the nasopharyngeal or paranasal sinus regions. Two patients had large surgical cavities. The plans were designed with a clinical treatment planning system that uses a measurementbased pencil-beam dose-calculation algorithm with an equivalent path-length inhomogeneity correction. Each plan employs conformally-shaped 6-MV photon beams. Patient anatomy and electron densities were obtained from the treatment planning CT images. For each plan, the dose distribution was recalculated with the Monte Carlo method, utilizing the same beam geometry and CT images. The Monte Carlo method accurately accounts for the perturbation effects of local tissue heterogeneities. The Monte Carlo calculated dose distributions were compared with those from the clinical treatment planning system. Results: The degree to which tissue inhomogeneity affects the dose distributions of individual fields varies with the specific anatomic geometry, especially the size and location of air cavities in relation to the beam orientation and field size. Most of the beam apertures completely enclose the air cavities within or adjacent to the gross tumor volume (GTV). Equivalent squares (including blocking) ranged from approximately 5 to 9.5 cm. A common feature observed for individual fields is that the Monte Carlo calculated doses to tissue directly behind and within an air cavity are lower. However, after combining the fields employed in each treatment plan, the overall dose distribution shows only small differences between the two methods. For all 5 patients, the Monte Carlo calculated treatment plans showed a slightly lower dose received by the 95% of target volume (D95) than the plans calculated with the pencil-beam algorithm. The average difference in the target volume encompassed by the prescription isodose line was less than 2.2%. The difference between the dose–volume histograms (DVHs) of the GTV was generally small. For the brainstem and chiasm, the DVHs of the two plans were similar. For the spinal cord, differences in the details of the DHV and the dose to 1 cc (D1cc) of the structure were observed, with Monte Carlo calculation generally predicting increased dose indices to the spinal cord. However, these changes are not expected to be clinically significant. Conclusion: For 6-MV photons, the effects of both normal tissue inhomogeneities and surgical air cavities on the target coverage were adequately accounted for by conventional pencil beam methods for all of the cases studied. Although differences in details of the DVHs of the normal structures were observed, depending on whether Monte Carlo or pencil-beam algorithm was used for calculation, these differences are not expected to be clinically significant. In general, the pencil-beam calculation corrected for primary attenuation by the equivalent pathlength is a sufficiently accurate method for head-and-neck treatment planning using 6-MV photons. © 2001 Elsevier Science Inc. Monte Carlo, Tissue inhomogeneity, Air cavities, Dose distribution.
INTRODUCTION In the head-and-neck region, the presence of surface curvature, air cavities, and bony structures influences the dose distribution in a complex manner. The main physical processes involved are the changes in the primary transmissions, the range of secondary electrons, and the number of photons scattered in different media; which change the
radiation dose distribution. Whether the change is clinically significant is not well understood at present. Several groups (1–7) have made measurements to investigate the effect of air cavities on the dose distribution in tissue equivalent phantoms. They reported a varying degree of underdosing at the air-tissue interface, depending on geometry, beam energy, and field size. However, an investigation of air-cavity interface doses in a humanoid phantom, with beam energies
Reprint requests to: Lu Wang, Ph.D., Department of Radiation Oncology, Division of Medical Physics, 2 Donner Building, 3400 Spruce Street, Philadelphia, PA 19104. Tel: (215) 662-3088; Fax: (215) 349-5978; E-mail: [email protected]
Presented at the 42nd Annual Meeting of ASTRO, Hynes Convention Center, October 22–26, 2000, Boston, MA. Received Oct 30, 2000, and in revised form Apr 1, 2001. Accepted for publication Apr 17, 2001. 1339
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ranging from cobalt-60 (60Co) to 10 MV and field sizes of at least 6 ⫻ 6 cm2, found the underdose to be clinically insignificant (1, 3, 5). Doses near the interfaces of regularly shaped air cavities were also studied for single and parallelopposed fields with a variety of dose calculation algorithms, including Monte Carlo calculation (4, 5). Calculations based on tissue-air ratio (TAR) and the Batho power-law method (8) failed to predict the experimentally observed underdose beyond an air cavity (4). This is because empiric methods do not account for loss of electronic equilibrium or the influence of electron transport from one medium to another, both of which contribute to the buildup and build-down of dose near interfaces. Even with a calculation model in which the loss of lateral equilibrium is accounted for by scaling field size with the density of the material (9, 10), the results near an air-water interface are inaccurate. Advanced dose calculation methods that model the physical process of electron transport are available on some commercial treatment planning systems. These methods calculate dose distributions by convolution/superposition techniques (11–13) using Monte Carlo precalculated dose spread kernels in water. One of the limitations of the convolution methods is that electronic equilibrium is assumed when such kernels are generated; therefore, these methods also fail to predict accurate dose distributions at the boundaries of air cavities or inhomogeneities (14 –16). In a study of air-cavity interface doses, however, Monte Carlo simulations were found to match the measured results to within 1% (5). Although phantom studies are important and reveal the perturbation effects of air cavities under various conditions, studies using patient anatomy and including the combined dosimetric effects of all tissue inhomogeneities—air cavities, soft tissues, and bony structures—are of practical significance. The use of conformal radiation therapy for headand-neck tumors increases the need to understand the differences between the dose distribution calculated by the treatment planning system and the actual distribution, including inhomogeneity effects. The goal of conformal treatments is to tightly shape the dose distribution to the target while avoiding critical structures and thus improve local control while maintaining acceptable normal tissue morbidity. Therefore, the dose distribution that is presented for treatment plan evaluation should be an accurate representation of the patient’s treatment. The Monte Carlo method can rigorously account for tissue inhomogeneity effects. With Monte Carlo, the transport of each radiation particle is carried out in the given inhomogeneous medium according to the probabilities or cross-sections of the allowed interactions. In this manner, the behavior of each particle is traced and the discrete energy deposition steps are accumulated. The final dose distribution is the result of millions of accumulated energy deposition events. If enough photon histories are accumulated, the results computed are of superior accuracy compared to any approximate method employed in the treatment planning systems, provided that the radiation source and the patient anatomy are correctly simulated. For linear acceler-
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ators, the radiation source can be accurately modeled (14, 17–20). Anatomy, including the electron density and an approximate atomic number distribution, is accurately represented by the patient-specific computed tomography (CT) images. Therefore, patient-specific external beam dosimetry that correctly accounts for inhomogeneities can be confidently based on Monte Carlo techniques (21–26). In this work, we used the Monte Carlo method (26) in a retrospective dosimetric study of treatment planning in the head and neck. Five patients who had been treated for carcinoma in the nasopharyngeal region or the paranasal sinus were selected. Monte Carlo– calculated dose distributions in the target and surrounding normal tissues were compared to those calculated with a clinical treatment planning system that uses a measurement-based pencil-beam dose-calculation algorithm with an equivalent pathlength inhomogeneity correction for the same beams. METHODS AND MATERIALS Treatment plan selection We selected the treatment plans of 5 patients who had been treated with three-dimensional (3D) conformal radiation therapy for carcinoma in the head and neck. The plans include a variety of static field techniques commonly used in head-and-neck treatments. To accentuate tissue inhomogeneity effects, two of the chosen patients (#1 and #4) had large post-surgical air-filled cavities. We chose patients treated with two-, three-, four-, and seven-field techniques, all with 6-MV photons. Specifically, patients #1, #2, and #3 had paranasal sinus malignancies and were treated with a three-field technique (heavily weighted anterior field with or without wedge and lightlyweighted, 60° wedged, parallel-opposed laterals) (27). For patient #1, an additional small, unwedged anterior field augmented the dose between the eyes, allowing the eyes to be blocked in the lateral beams. Patient #4 had cancer of the jaw and cheek and was treated with a wedged pair (anterior and left lateral, 45° wedges). Patient #5 had nasopharyngeal cancer and was treated with a seven-field technique. This technique (28, 29) consists of seven fields separated by 30°: an unwedged posterior field and opposed-lateral and four posterior-oblique fields, each with a 45° wedge. The cord is blocked in each field. This beam arrangement was developed as a static field technique for sparing the brainstem and spinal cord while conforming the dose to a target volume that has wrapped around these structures (28, 29). Clinical planning process Each patient was immobilized with a custom Aquaplast mask for the planning CT scan and for treatment. The planning CT scans were acquired for each patient at 3-mm intervals. The gross tumor volume (GTV) and the planning target volume (PTV) (30) were outlined by a physician. In general, the GTV was expanded by 1 cm to derive the PTV; however, tighter margins were used near the brainstem or in the buildup region. Normal structures of interest such as
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eyes, optic chiasm, brainstem, and spinal cord were also outlined on the images. The beam directions were selected by experienced planners and the aperture of each beam was designed with a 6-mm margin around the PTV (except where tighter margins were used to protect normal structures). The beam weights were selected to satisfy the physician’s objectives relative to target coverage and normal tissue sparing. Our clinical convention is to normalize all plans so that 100 cGy is delivered to the 100% isodose line in the graphic display. The physician prescribes the treatment dose to the percent isodose line that meets treatment objectives. Subsequently, final graphic displays and dose– volume histograms (DVHs) for both percent and cumulative absolute dose are generated. All treatment plans were generated on the Memorial Sloan-Kettering Cancer Center (MSKCC) treatment planning system. This dose calculation algorithm is based on measured depth doses and cross-field profiles over a range of depths and square fields. It corrects for tissue inhomogeneities by computing the equivalent pathlength along each ray direction. For irregularly-shaped fields, a correction factor generated by convolution of a pencil beam kernel with the primary fluence distribution defined by the aperture is applied at each point (31, 32). In this algorithm, the changes of lateral electron scattering in media differing from water are ignored. All plans were judged to be suitable for treatment delivery. Below, we refer to them as the “standard plans.” Monte Carlo calculations Monte Carlo algorithms simulate radiation interactions and perform ray-tracing for both primary and scattered radiation through the patient geometry, as defined by the CT images. The Monte Carlo method we used employs the EGS4 system (33) for radiation simulation and handles transport by the user code MCPAT (26). This code contains several variance reduction techniques to improve computational efficiency, including a more efficient ray-trace between photon interactions, the use of a kerma approximation for dose deposition by photons below a user-selected energy, and an analytic determination of the number of primary photon interactions in each voxel, which gives the same statistics for low- and high-density media. The code was validated by measurement in homogeneous and inhomogeneous phantoms. Further details on the method and measurement validation are provided in Refs. (26, 34). The beam information from the clinical treatment plans (e.g., energy, orientation, aperture, fluence distribution, and wedge angle) was entered into the Monte Carlo dose calculation module. The patient-specific CT images were employed to describe the computational geometry and to define the electron density ratio, e. To improve ray-trace efficiency, the MCPAT code also determines an approximate effective atomic number for the medium in each voxel from the CT images by treating voxels above a user-specified electron density as bone and below as water. The image voxel size was 3 mm on each side. This density array was used both to evaluate the equivalent pathlength and to flag
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the change of medium. Because local electron density derived from the CT image data was incorporated into the Monte Carlo calculation, the perturbation effects of local tissue heterogeneities were automatically accounted for. More than 1,000 first interactions were sampled in each image voxel, and a statistical uncertainty of 1.5% in the target volume was achieved. The calculation was performed on a (500-MHz) DEC Alpha workstation. Comparison of Monte Carlo and standard plans The comparison between the pencil-beam and Monte Carlo calculations was carried out in terms of absolute absorbed dose. The Monte Carlo algorithm produces results in units of dose/fluence. To convert to dose per monitor unit (dose/MU), we first performed the Monte Carlo dose calculation in a homogeneous water phantom with a reference field size (10 ⫻ 10 cm) and a source-axis distance (SAD) of 100 cm. The central axis dose per unit fluence at Dmax was derived from this simulation. The inverse of this factor gives the fluence to produce a dose of 1 cGy at Dmax under the reference field size and SAD conditions, which is the same as the fluence per MU. Having the conversion factor of fluence/MU for the reference conditions, it is straightforward to derive the dose/MU by multiplying the Monte Carlo calculated dose/fluence data by the conversion factor. The standard plan was normalized to deliver 100 cGy to the 100% isodose line, and the beam weights of the standard plan were copied to the Monte Carlo plan. Therefore, the beam-on-time for each beam is the same for both plans. Because contaminant electrons are not included in the current version of the Monte Carlo module, the study was performed only for tumors and normal structures lying beyond Dmax (1.5 cm). We therefore modified the GTV contours to exclude the portion in the buildup region. Because the PTVs require more drastic alteration to avoid the buildup region, we did not evaluate changes in dose distribution in the PTV between the two calculation techniques. The average volume of the modified GTVs was 108 cc (range 74 –145 cc). RESULTS Dose distributions for single fields To more clearly demonstrate the differences between the standard and Monte Carlo calculations, we first compared dose distributions of individual treatment fields. Figures 1 and 2 show the dose distributions in three orthogonal views through isocenter of the main anterior and the right-lateral field, respectively, for patient #1, who had a previous maxillectomy. The surgery created a larger air cavity than the normal anatomic cavities present in nonsurgical patients (4.5-cm superior to inferior, 4.0-cm anterior to posterior, and 2.0 cm left to right). Small soft tissue protrusions were visible inside the cavity. The inhomogeneity effects in this patient should be more pronounced, and represent an extreme case. The collimator settings for the anterior and lateral fields were 11.5 ⫻ 9.2 cm2 and 13.5 ⫻ 9.2 cm2,
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Fig. 1. Comparison of the isodose distributions for AP field from transverse, coronal, and sagittal views. The dose distributions based on the equivalent pathlength method are shown on the upper panel. The Monte Carlo calculated dose distributions are shown on the lower panel.
respectively. Blocking reduced the equivalent areas by approximately 30%. In these figures, the portion of the GTV lying beyond Dmax is outlined in orange. The isodose lines represent the absolute doses in cGy delivered with 100 MU from a beam which delivers 1 cGy/MU at Dmax under the calibration conditions. Isodoses calculated with the equivalent-pathlength method are shown on the upper row, and with Monte Carlo on the lower row. Comparing the rows of images, it is obvious that the air cavity produces differences between the two dose distributions. For example, the Monte Carlo 70-cGy isodose line near the inferior edge of the AP field is pulled in (as seen in the sagittal and coronal views of Fig. 1), while the 10- and 5-cGy isodose lines bulge out (as seen in the transverse cut of Fig. 1). For the lateral field, the effect of the air cavity is even greater, as the longer dimension of the air cavity lies across the beam, leaving little soft-tissue margin over the anterior edge of the cavity. As a result, the Monte Carlo isodose lines in the range of 25–35 cGy (shown by yellow, green, and light-blue lines in Fig. 2) penetrate less deeply than the corresponding lines generated by the standard calculation. The Monte Carlo calculation
predicts a lower dose to soft tissue lying within and immediately downstream of the cavity than the standard calculation. This effect, as well as the constriction of higher isodose lines within the cavity, is caused by the loss of electronic equilibrium. The bulge of the lower dose lines is attributed to the larger lateral scattering of electrons in an air cavity located at the beam edge. The inhomogeneity effect of bone in the low megavoltage energy range is mainly a change of transmission (34) which is accounted for by the equivalent pathlength method. The individual fields for the other four patients were also evaluated. The observed difference between the Monte Carlo and standard calculations varies from patient-to-patient, depending on the volume and location of the air cavities relative to the beam, as well as field size and beam orientation. For the patients with only normal anatomic cavities in the treatment volume, the differences are less notable than those shown in the figures. However, common features are observed that the dose to tissue downstream and within an air cavity is lower in the Monte Carlo calculation, and beam penumbra is increased in the Monte Carlo plan if
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Fig. 2. Comparison of the isodose distributions for right-lateral field from transverse, coronal, and sagittal views. The dose distributions based on the equivalent pathlength method are shown on the upper panel. The Monte Carlo-calculated dose distributions are shown on the lower panel.
the beam edge lies in an air cavity. The impact of these effects on GTV coverage when the individual beams are combined to form the treatment plan will be addressed in the following evaluations. Dose distribution for the plans Figure 3 compares the relative isodose distributions for the standard and Monte Carlo calculations for patient #1. The relative isodose distributions were normalized so that 100% ⫽ 100 cGy, as is the practice in MSKCC. Because the main anterior field was heavily weighted relative to the two lateral-wedged fields, with a beam-on-time ratio of approximately 3:1:1, and the small anterior field between the eyes was weighted about 12% of the main field, the overall dose distribution is dominated by the main anterior field, and shows less difference between Monte Carlo and standard calculations than the single lateral field. For patient #1, the prescription level was the 87% isodose line (represented by yellow line). Figure 3 shows only slight difference between the two calculations in the shape of the 87% isodose lines, with the GTV coverage in the Monte Carlo calculation being slightly tighter. Relatively larger differences are noted
in the higher- (95–100%) and the lower-dose region (10 – 30%). Overall, the beams in the Monte Carlo calculation deliver lower dose behind the air cavity, creating a lower dose to the target. Comparing the standard calculations with the Monte Carlo calculations for all five patients, we observed that, in general, the difference in the appearance of the prescription isodose line was small. Dose–volume histograms GTV. A comparison of the DVHs for patient #1’s modified GTV (beyond Dmax) is shown in Fig. 4. The Monte Carlo DVH shows that a lower dose is delivered than is expected from the standard calculations. D95, the dose encompassing 95% of the structure, is 87% for the Monte Carlo calculation vs. 88.3% for the standard. D05, the isodose level encompassing 5% of the GTV, is an indicator of the high-dose region within the GTV. It differs by 2.3%, with the Monte Carlo value being smaller (98.9% vs. 101.2%). We report the maximum and minimum doses because, while they are determined by only a few points and thus may be misleading measures of dosimetric differences,
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Fig. 3. Comparison of the isodose distributions of the three-composite fields from the transverse, coronal, and sagittal views for patient #1. The standard plan based on the equivalent pathlength method is shown on the upper panel. The Monte Carlo plan is shown on the lower panel.
they are often examined in plan evaluation. The differences in the maximum and the minimum doses were 2.3% (106.07% in the standard calculation vs. 103.7% in the Monte Carlo calculation) and 4.3% (73.7% vs. 76.9%). The Monte Carlo mean dose is 2.4% lower than the standard calculation mean dose (93.8% vs. 96.1%). The steep slope of the integral DVH in the high-dose region makes the volume covered by a particular dose level a sensitive indicator of the difference between the two calculation techniques. For example, Monte Carlo calculations predict that a considerably smaller fraction of the GTV is encompassed by the 95% isodose level (V95 ⫽ 42.4%) than the standard calculations (V95 ⫽ 65.7%). For the prescribed isodose level (87%), the percentage of the GTV encompassed (Vp) was 97.4% in the standard plan and 95.2% in the Monte Carlo plan. As previously noted, there was little change in the shape of the prescription isodose. Table 1 lists the differences in the dose parameters discussed above for each of the five patients’ modified GTVs. The average differences in the mean dose to GTV and D05 were 1.3% and 1.0%, respectively. Table 2 summarizes the average and associated standard deviations of D05, D95, Vp,
and the maximum dose (Dmax), for the modified GTV from the Monte Carlo and standard plans. The ratios of these parameters between the Monte Carlo and standard plans were calculated for each patient, to reduce the effect of individual anatomy. Average ratios of these dose indices were derived from the ratios for each patient and are listed in the last column of Table 2. Although the ratios of each dose parameter are close to unity, they are less than 1 for four of the five patients. This indicates that the dose to the hot spot, the target coverage and the maximum dose within the GTV are generally less than expected from the standard treatment plan. Critical structures. The critical normal structures in the head-and-neck region include spinal cord, brainstem, chiasm, lenses, retinas, and eyes. Because the lenses, retinas, and eyes are located partly in the buildup region, we cannot properly compare the Monte Carlo and standard plan predictions for these structures, as noted above. Therefore, we limit our discussion to the spinal cord, brainstem, and chiasm. Spinal cord. Figure 5 compares the DVHs for the three patients (#1, #4, and #5) for whom the cord were close
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Fig. 4. A comparison of the DVH for the modified GTV of patient #1 using the two dose-calculation methods: the Monte Carlo and the equivalent-pathlength methods. The solid line represents the Monte Carlo plan and the dashed line represents the standard plan.
enough to the GTV to be a concern. Because different extents of the spinal cord was outlined among these patients, the DVHs plot absolute rather than relative volumes. Figure 5 shows differences in details of the DVH, depending on the dose calculation technique. However, when comparing the dose parameters (such as the maximum dose, Dmax, and the dose to hottest 1 cc of volume, D1cc) quantitatively, the changes are found to be fairly small. For example, the largest absolute increase in D1cc was 4.7% of the dose to the 100% line (patient #1); the largest increase in Dmax was 6% (patient #5). This may attribute to fact that only part of the spinal cord is involved and it is either under the block (patient #7) or in only one of the treatment fields (AP field for patients #1 and #4). Table 2 lists the dose indices averaged among the five patients. Ratios were taken for each dose index and each patient to reduce the effect of patient-specific anatomy and the position of the critical structure in respect to the target. The average ratios were listed in the last column of Table 2. Although the ratios are approximately 10%, the absolute dose difference is small because the cord dose is only a small fraction of dose to the
GTV. Therefore, we do not expect the difference to be clinically significant. Brainstem. The DVHs of brainstem calculated by the two methods for each patient are almost identical. Hence, no graphical comparison is presented here. Because, in general, brainstem is well separated from any air cavities and is surrounded by soft tissue, it is anticipated that the tissue inhomogeneity effect is small and the two dose-calculation methods should give similar results for this structure. Table 2 lists the averaged dose indices for brainstem. The differences in the dose indices derived from two plans are negligible. Optic chiasm. The DVHs of optic chiasm for patient #1 are shown in Fig. 6. Most of the chiasm was located within the fields, but it is well separated from air cavities. However, a piece of the chiasm is at the edge of the two lateral fields, where there is loss of electronic equilibrium. For this reason, the Monte Carlo plan presents a notable drop in the shoulder of the DVH. The Monte Carlo calculated dose to the chiasm was slightly smaller than expected from the conventional treatment plan. However, the difference in the
Table 1. Differences between the standard plan and Monte Carlo plans for the important dose distribution parameters of the GTV Statistics
Dmax (%)
Dmean (%)
D95 (%)
D05 (%)
V95 (%)
Vp (%)
Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Average
2.3 ⫺2.7 2.4 0.6 1.3 0.8
2.4 0.4 0.8 1.8 1.3 1.3
1.5 1.6 1.2 1.7 1.5 1.5
2.3 ⫺0.9 0.7 2.0 0.9 1.0
35.5 2.8 3.7 32.4 6.8 16.3
2.3 3.7 0.7 1.4 3.3 2.2
The negative sign represents that the data of the Monte Carlo plan are larger than those of the standard plans.
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Table 2. Summary of the dose distributions averaged over 5 patients for the Monte Carlo and standard plans
GTV
Spinal cord Brainstem Chiasm
D05 (%) D95 (%) Vp Dmax (%) D1cc Dmax (%) D05 (%) Dmax (%) D05 (%) Dmax (%)
Monte Carlo
Standard
Ratio*
106.0 ⫾ 6.9 90.0 ⫾ 3.9 91.4 ⫾ 8.5 111.1 ⫾ 8.6 19.6 ⫾ 11.9 41.7 ⫾ 13.5 63.8 ⫾ 30.7 73.6 ⫾ 30.9 79.6 ⫾ 27.4 84.5 ⫾ 28.2
107.0 ⫾ 5.6 91.3 ⫾ 3.9 93.5 ⫾ 7.4 112.0 ⫾ 7.1 18.1 ⫾ 12.8 40.1 ⫾ 11.2 64.3 ⫾ 30.8 74.1 ⫾ 31.9 79.2 ⫾ 30.0 85.0 ⫾ 31.0
0.990 ⫾ 0.013 0.985 ⫾ 0.002 0.977 ⫾ 0.012 0.992 ⫾ 0.021 1.14 ⫾ 0.14 1.03 ⫾ 0.11 0.99 ⫾ 0.01 0.99 ⫾ 0.04 1.02 ⫾ 0.08 1.01 ⫾ 0.06
* Monte Carlo/Standard. D05 ⫽ Dose encompassing 5% of volume. D1cc ⫽ Dose encompassing 1 cc of volume. D95 ⫽ Dose encompassing 95% of volume. Vp ⫽ Percent volume receiving at least the prescribed percent dose.
dose indices, such as D05 and Dmax, are negligible given the fact that uncertainty in dose calculation is 1.5%. For four patients, the chiasm was close enough to the PTV to be a concern. Two of the patients have almost identical DHVs between the Monte Carlo and the standard plans. The largest change (an increase) was seen for patient #4, for whom the chiasm is bisected by one field edge and is about 2 cm outside the edge of the other. For this patient, the absolute increase in D05 is about 4.5% and is 3.6% for Dmax. DISCUSSION As most head-and-neck cancers originate from the mucosa of the upper aerodigestive tract, these tumors are either in contact with or surround air cavities. The competing effects of increased transmission, decreased photon scatter, and the loss of electronic equilibrium in an air cavity determine the overall dose distribution. Modern treatment planning systems are able to account for the change of primary transmission in heterogeneous media with relatively simple algorithms, but most cannot account for loss of electronic equilibrium near tissue-air interfaces. We performed Monte Carlo calculations to assess the accuracy of dose distributions calculated by standard methods in the presence of typical head-andneck tissue inhomogeneities. The presence of bony structures mainly reduces the transmission of the primary beam. The increased scatter by high-density material (bone) for 6-MV photons is insignificant (34). The effect of electronic disequilibrium and variation of photon scatter near air-tissue interfaces depends strongly on cavity volume, field size, and beam energy (5). As normal anatomic air cavities in the head and neck region have dimensions less than 3 cm in diameter (5), and the treatment field sizes are often greater than 6 ⫻ 6 cm2, electronic equilibrium is retained for intermediate photon energies, such as 6 MV. If patients have large surgical cavities (patients #1 and #4),
tissue surrounding the cavity is considered to be at risk and is included in the GTV or CTV. For our patients, GTV was expanded to PTV by 1 cm in most directions, providing a larger volume of irradiated soft tissue surrounding the cavity. Therefore, even for simple field arrangements, the most heavily-weighted fields fully enclose the cavity, preventing large underdose for tissue surrounding and protruding into the cavity. We find that, although tissue inhomogeneities in head and neck alter features of the dose distribution, when the effect of inhomogeneity is assessed by Monte Carlo dose calculation, the target coverage and normal organ doses do not differ greatly from the predictions of the equivalent pathlength corrected pencil-beam method. As shown in Table 1, Monte Carlo and standard calculations of the average maximum and mean doses to the GTV beyond the buildup region differ, on average, by less than 2%. The average volume of GTV encompassed by the prescribed isodose level is lower by Monte Carlo calculation, but only by approximately 2%. The average decrease in the dose encompassing the hottest 5% and 95% of the GTV is only 1.0% and 1.5%, respectively. Our results indicate that the dose coverage of the target predicted by the approximate inhomogeneity correction method implemented in our treatment planning system (equivalent pathlength corrected pencil beam) is very similar to that obtained by Monte Carlo calculation. The electron transport accounted for in the Monte Carlo calculation has small influence on the dose distribution in the target for 6-MV photons. Hence, the loss of electronic equilibrium does not have a severe effect on the coverage of targets near normal, or even surgically-enlarged nasopharyngeal, air cavities. Although the Monte Carlo results may slightly overestimate the dose at the surface of a cavity build-up region due to the 3 mm3 voxel size, we believe that this is sufficiently fine resolution to detect significant underdoses. Our results agree with the mea-
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Fig. 5. A comparison of the DVH of the spinal cord for patients #1, #4, and #5.
surement results obtained in a cubic air cavity in solid water phantom by Kan et al. (5). For the critical structures, the dose difference between the two calculation methods varies with the location of the structure relative to the air cavities and field edges. If the structure lies within the fields and well separated from air cavities (e.g., brainstem), the difference in the dose distribution is small and may be attributed to statistical variation in the Monte Carlo calculations. If the structure is at a beam edge and is surrounded by soft tissue or is adjacent to air cavities, the dose
calculated by Monte Carlo is slightly higher than obtained by conventional calculation. We expect that the observed differences are clinically insignificant. Although electron contamination was not included in the current version of the Monte Carlo dose calculation, our conclusions are not altered, as neither the modified GTV nor the critical structures analyzed include volumes within Dmax of the skin. Nonetheless, it would be useful to modify the Monte Carlo code to include an accurate assessment of the dose in the buildup region.
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Fig. 6. A comparison of the DVH for the chiasm of patient #1.
CONCLUSION We compared the dose distributions for 5 patients with head-and-neck cancer calculated by the Monte Carlo method and by a measurement-based pencil-beam algorithm. We assessed the accuracy of the latter for conformal, CT-based treatment plans in the presence of tissue inhomogeneities in the head and neck, especially air cavities. A variety of conformal static field arrangements with 6-MV photons were used. For all patients studied, the Monte Carlo calculations showed a slight decrease in the target coverage (about 1–2%) in terms of Vp from that of the standard calculations based on the pencil-beam algorithm. Dose distributions of individual fields were altered to different extents, depending on the size and
location of the air cavities relative to the beam geometry, including field size and beam orientation. However, upon combining the multiple fields employed in the treatment plan, the overall dose distribution showed only small differences. For the cord, the Monte Carlo calculation indicates that the dose to the hottest 1 cc is generally increased by a small fraction. For the brainstem and the optic chiasm, the differences are minimal. Our results indicate that conformal 6-MV photon treatment plans for head-and-neck tumors, designed with a pathlengthcorrected, measurement-based pencil-beam algorithm, give adequate target coverage and sparing of normal organs at risk, even in the presence of large surgical air cavities.
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