

TECHNICAL NOTE 



Year : 2017  Volume
: 42
 Issue : 3  Page : 144150 

The impact of the grid size on tomotherapy for prostate cancer
Motohiro Kawashima^{1}, Hidemasa Kawamura^{2}, Masahiro Onishi^{2}, Yosuke Takakusagi^{3}, Noriyuki Okonogi^{4}, Atsushi Okazaki^{3}, Tetsuo Sekihara^{3}, Yoshitaka Ando^{3}, Takashi Nakano^{2}
^{1} Gunma University Heavy Ion Medical Center, Maebashi, Japan ^{2} Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi, Japan ^{3} Hidaka Hospital, Takasaki, Gunma, Japan ^{4} Department of Radiation Oncology, Gunma University Graduate School of Medicine, Maebashi; Hospital, National Institute of Radiological Sciences, National Institutes for Quantum and Radiological Science and Technology, Japan
Date of Submission  24Nov2016 
Date of Decision  19Jun2017 
Date of Acceptance  11Jul2017 
Date of Web Publication  13Sep2017 
Correspondence Address: Motohiro Kawashima Gunma University Heavy Ion Medical Center, Maebashi, Gunma Japan
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jmp.JMP_123_16
Abstract   
Discretization errors due to the digitization of computed tomography images and the calculation grid are a significant issue in radiation therapy. Such errors have been quantitatively reported for a fixed multifield intensitymodulated radiation therapy using traditional linear accelerators. The aim of this study is to quantify the influence of the calculation grid size on the dose distribution in TomoTherapy. This study used ten treatment plans for prostate cancer. The final dose calculation was performed with “fine” (2.73 mm) and “normal” (5.46 mm) grid sizes. The dose distributions were compared from different points of view: the dosevolume histogram (DVH) parameters for planning target volume (PTV) and organ at risk (OAR), the various indices, and dose differences. The DVH parameters were used Dmax, D2%, D2cc, Dmean, D95%, D98%, and Dmin for PTV and Dmax, D2%, and D2cc for OARs. The various indices used were homogeneity index and equivalent uniform dose for plan evaluation. Almost all of DVH parameters for the “fine” calculations tended to be higher than those for the “normal” calculations. The largest difference of DVH parameters for PTV was Dmax and that for OARs was rectal D2cc. The mean difference of Dmax was 3.5%, and the rectal D2cc was increased up to 6% at the maximum and 2.9% on average. The mean difference of D95% for PTV was the smallest among the differences of the other DVH parameters. For each index, whether there was a significant difference between the two grid sizes was determined through a paired ttest. There were significant differences for most of the indices. The dose difference between the “fine” and “normal” calculations was evaluated. Some points around highdose regions had differences exceeding 5% of the prescription dose. The influence of the calculation grid size in TomoTherapy is smaller than traditional linear accelerators. However, there was a significant difference. We recommend calculating the final dose using the “fine” grid size.
Keywords: Calculation grid size, dose distribution, TomoTherapy, treatment planning
How to cite this article: Kawashima M, Kawamura H, Onishi M, Takakusagi Y, Okonogi N, Okazaki A, Sekihara T, Ando Y, Nakano T. The impact of the grid size on tomotherapy for prostate cancer. J Med Phys 2017;42:14450 
How to cite this URL: Kawashima M, Kawamura H, Onishi M, Takakusagi Y, Okonogi N, Okazaki A, Sekihara T, Ando Y, Nakano T. The impact of the grid size on tomotherapy for prostate cancer. J Med Phys [serial online] 2017 [cited 2017 Nov 19];42:14450. Available from: http://www.jmp.org.in/text.asp?2017/42/3/144/214486 
Introduction   
Intensitymodulated radiation therapy (IMRT)^{[1]} and volumetricmodulated arc therapy ^{[2],[3]} are performed in many radiation treatment facilities. A specialized IMRT device called “helical TomoTherapy”^{[4],[5],[6]} has been developed in the early 1990s. The TomoTherapy HiArt system (Accuray Inc., Sunnyvale, CA, USA) combines delivery of intensitymodulated fanbeam rotational therapy with megavoltage computed tomography (CT) imaging capabilities. The nominal energy of the photon beam is 6 MV, there is no flattening filter, and the beam is cone shaped. The irradiation beam has a maximum lateral width of 40 cm at the isocenter plane, and this beam is shaped by an adjustable jaw and a binary multileaf collimator (MLC). The longitudinal field size after adjusting the jaw can be set to 1.0, 2.5, or 5.0 cm. The MLC consists of 64 binary leaves. A length of one binary leaf is 0.625 cm at the isocenter plane. The TomoTherapy treatment planning system (TPS), “TomoTherapy Planning Station,” determines the treatment plan parameters (e.g., the field width, pitch factor, and modulation factor) and optimizes the beam for irradiating the target while sparing normal tissue. A final dose calculation is performed after optimization. TomoTherapy uses a convolution/superposition algorithm to compute dose and utilizes a proprietary inverse planning optimization algorithm.^{[7],[8]} During the optimization and dose calculation, the grid size can be set to “fine,” “normal,” or “coarse.” The resolution of the fine grid size is down sampled (256 × 256) from CT images (512 × 512) in the axial plane. The resolutions of normal and coarse grid sizes are downsampled to half (128 × 128) and quarter (64 × 64) that of the fine resolution, respectively. The longitudinal resolution of all the grid sizes is the same as the slice thickness.
Macroscopically, the dose distribution is continuous in nature. However, the dose distribution calculated in the TPS is discretized. Therefore, the calculated dose distribution has inherent errors associated with discretization. The calculation grid size is one of the major determinants of the accuracy of the TPS.^{[9],[10],[11]} The effects of these errors have been quantitatively evaluated for a fixed multifield IMRT using traditional linear accelerators. TomoTherapy has a different irradiation method from fixed multifield IMRT. Therefore, the impact of the grid size on TomoTherapy may be different. In this study, a quantitative evaluation of the dose distribution influenced by the grid size was performed.
Materials and Methods   
Five patients each Stage II and Stage III prostate cancer cases were used for this study. Radiation oncologists created contours of planning target volume (PTV) and organ at risk (OAR; i.e., rectum and bladder) for all CT images.^{[12]} Okonogi et al. described how to contour delineation in the paper. One oncologist specializing in prostate cancer checked these contours. The CT images (3mm slices) were acquired using an Aquilion LB 16 (Toshiba Medical Systems, Otawara, Tochigi, Japan). Scanning was performed at the Xtube voltage of 120 kV, tube current of 150 mA, and helical pitch of 15 mm/rot. Treatment plans were designed using these images and contours in TomoTherapy Planning Station version 4.2.3 (Tomotherapy Incorporated, Madison, WI, USA) and were transferred to the treatment device in the network.
The prescription dose for the treatment plan was 78 Gy at 2 Gy/fraction. The treatment plan was optimized using dose constraints of the PTV and OAR. The dose constraints of the PTV stipulated that the dose prescription method was D95% (prescription dose covered 95% volume of PTV) and that the D2cc (the minimum dose to the highest irradiated 2cc volume) was no >105% of the prescription dose (D2cc <81.9 Gy). The dose constraints of OAR stipulated that D17% <65 Gy, D35% <40 Gy, and D60% <22 Gy (Dx% indicates the dose covering x% of the total volume) for the rectum and D25% <65 Gy and D50% <40 Gy for the bladder. The parameters in all treatment plans were set to same value. The field width, pitch, and modulation factor were set to 0.25, 0.287, and 2.0 in all treatment plans, respectively. The field width represents the longitudinal width of the jaw with a unit of mm/100. The pitch factor is the axial couch travel distance for one gantry rotation divided by the field width. The modulation factor is defined as the ratio of the maximum leaf open time to the average leaf open time. Here, this factor was set to ensure that maximum leaf open time was not more than twice the average leaf open time.
The grid size may be selected from among fine, normal, and coarse settings in the optimization and dose calculation. These grid sizes have an inverse relationship to the pixel size of the CT image, which is affected by the field of view (FOV). In this study, CT images were taken with a 700mm FOV. Therefore, the fine, normal, and coarse grid sizes were 2.73, 5.46, and 10.92 mm in the axial plane, respectively. Dosimetric validation tests described in task group 148, of the American Association of Physicists in Medicine, indicated that the normal grid should be used as the reference grid size.^{[13]} Therefore, because the course is less accurate than the normal, it was excluded from the comparison performed in this study.
The optimization of treatment plans was performed using the normal grid size in all treatment plans. Thereby, an MLC movement sequence was same for each patient. The final dose distributions were calculated using the normal and fine grid sizes after optimization.
The comparison of treatment plans calculated using the fine and normal grid sizes was performed using dosevolume histogram (DVH) dose parameters. Dmax, D2%, D2cc, Dmean, D95%, D98%, and Dmin were used to evaluate the dose coverage of PTV. Dmax, D2%, and D2cc for OARs (rectum and bladder) were used to evaluate dose differences. We also used the homogeneity index (HI)^{[14]} and equivalent uniform dose (EUD)^{[15]} as to evaluate the plan.
The HI is represented by the following equation:
where D2% and D98% are doses to 2% and 98% volumes of the PTV, respectively. HI becomes zero under ideal conditions. This index represents the uniformity of the dose in the PTV. We used the reference dose evaluation for highprecision treatment, as defined in the International Commission on Radiation Units and Measurements Report 83.^{[14]}
The EUD is defined by the following formula:
Where SF_{2} is the survival fraction at 2 Gy. We assumed the SF_{2} to be 0.5 in this study. N indicates the number of computational grid cells, and i is the index of the grid cell.
These indices were used to evaluate the treatment plan. We also performed a twotailed paired ttest to verify whether there was a significant difference between the calculations based on the fine and normal grids. The confidence interval was set to 95%.
We calculated the difference between the dose distributions calculated using fine and normal grid sizes at the isocenter plane. The difference between the dose distributions was obtained by subtracting the dose distribution calculated using the normal grid size from that calculated using the fine grid size. These calculations were performed using the MIM Maestro software package (MIM Software Inc., Cleveland, OH, USA). The result was illustrated by plotting a histogram of dose difference.
In addition, the calculated dose distributions were compared with EBT3 Gafchromic film measurement to evaluate the accuracy of the treatment plans.^{[16],[17]} The Gafchromic film dosimetry validated the prescribed dose delivery to within ±5% (one standard deviation). The gamma evaluation method was used to compare dose distributions with 3% dose difference and 3mm distancetoagreement criteria.^{[18]} The threshold was set to 30% in this study because the EBT3 has the larger uncertainty in the lowdose region. We compared the relative dose distributions normalized at the isocenter. These analyses were performed with the MapCHECK software package called SNC Patient version 6.1.1 (Sun Nuclear Corp., Melbourne, FL, USA). In addition, we verified whether similar DVH parameters for PTV could be obtained in three head and neck (HN) cases.
Results   
The calculated treatment plans were compared using the DVH [Figure 1]. The DVH calculated using the fine and normal grid sizes are represented by dotted and solid lines, respectively. In addition, we showed an expanded view of the highdose region. The maxima of the DVHs were larger in the plan calculated using the fine grid than in the plan calculated using the normal grid.  Figure 1: Cumulative dosevolume histograms of treatment plans calculated using the fine and normal grid sizes, illustrating the dose to the planning target volume, rectum and bladder and an expanded view of the highdose region. The two types of dosevolume histogram are generally similar in form
Click here to view 
The DVH parameters for the PTV and OAR are summarized in [Table 1] and [Table 2], respectively, for all cases. The average differences of Dmax, D2%, D2cc, Dmean, D95%, D98%, and Dmin for PTV were 3.5%, 1.9%, 1.6%, 0.6%, 0.4%, 0.9%, and 1.4% of prescription dose, respectively. The maximum differences of Dmax, D2%, D2cc, Dmean, D95%, D98%, and Dmin for PTV were 5.3%, 2.4%, 1.9%, 0.8%, 0.6%, 4.5%, and 4.2%. Overall, DVH parameters calculated with the fine grid size were greater than those calculated with the normal grid and were significantly different according to a twotailed paired ttest. The differences in D98% and Dmin were not statistically significant. The DVH parameters of the rectum and bladder had results similar to those of the PTV. The average of rectal D2cc was increased by 2.9%, and maximum differences were 6.0% for patient 3. All DVH parameters for OAR indicated statistically significant differences according to a twotailed paired ttest.
We present the indices for plan evaluation, HI and EUD, in [Table 3]. The D2% and D98% that was used to calculate HI increased when using the fine grid size. The mean HI obtained with the fine grid was 1.01 times greater than that obtained with the normal grid. The EUD calculated using the fine grid increased by approximately 0.5% of the prescription dose relative to that calculated using the normal grid size and exhibited a significant difference according to a twotailed paired ttest.  Table 3: Homogeneity index and equivalent uniform dose values for all cases
Click here to view 
The DVH has no information about location of the CT image. Therefore, we did not know where the dose difference indicated by DVH difference was on the CT images. The dose difference distribution was obtained by subtracting calculation with normal grid from that with the fine grid size. [Figure 2] shows the dose distribution of one patient calculated using the fine grid size. [Figure 3] shows the difference between the dose distributions calculated using the fine and normal grid sizes. The large difference evident in [Figure 3] was located at the steepdose gradients shown in [Figure 2]. There is difference of more than 5% between calculated dose using fine and normal grid.  Figure 2: Dose distribution calculated using the fine grid size. The isodose lines contours are defined according to the relative prescription dose
Click here to view 
 Figure 3: Difference between the dose distributions calculated using the fine and normal grid sizes. These differences were obtained by subtracting the dose distribution calculated using the normal grid size from that calculated using the fine grid size. The isodose contours are defined according to the relative prescription dose
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The histogram represents the dose difference between distributions calculated with fine and normal grid sizes [Figure 4]. We found that the dose distributions were consistent overall. The mean dose difference was 0.03% of the prescribed dose, and the variation was 0.56%. The results for the fine grid size dose were slightly higher than for the normal.  Figure 4: Frequency histogram of the difference between the doses calculated using the fine and normal distributions. The height corresponds to the ratio of the number of voxels. The horizontal axis represents the relative prescription dose. The bin width is 0.01%
Click here to view 
The calculation accuracy was evaluated by performing film measurements. We compared calculations with measurements through gamma analysis that acceptance criteria were 3%/3 mm. The pass rates, which were derived from comparisons of calculations and film measurement, were approximately the same. We generated a histogram of the percentage dose difference between each calculation and the EBT3 measurement, as shown in [Figure 5]a and [Figure 5]b. The [Figure 5]a and [Figure 5]b show the dose differences between the calculations with normal and fine grid sizes, respectively, and the measurements. The [Figure 5]a has a wider distribution than the [Figure 5]b. The calculations that used the fine grid size were found to be more consistent than for those that used the normal grid size.  Figure 5: Histogram of the difference between the dose measurement and calculation. The height corresponds to the grid number. The bin width is 1%. The (a and b) figures represent the difference between the measurement and the calculations calculation with the normal and fine grid sizes, respectively
Click here to view 
The comparison of DVH parameters between prostate and HN cases is summarized in [Table 4]. The treatment plans for HN require stronger modulation than those for the prostate due to the proximity of critical structures, the spinal cord, and parotid glands. However, the variation of DVH parameters excluding Dmax for PTV in HN case was not so different from one in prostate. In contrast, the difference between the Dmax calculated with normal and fine grid for HN cases was much larger than that for prostate cases.  Table 4: Comparison of dosevolume histogram parameters between prostate and head and neck cases
Click here to view 
Discussion   
We assessed the treatment plans from several perspectives to quantify the influence of the calculation grid size on the dose distribution in TomoTherapy. The differences in the various DVH parameters and dose indices of the calculation using fine and normal grid sizes were statistically significant. Moreover, we compared film's measurements with calculated dose distribution using each grid size. Since fine grid size is more consistent with real film measurements, it is better to generate radiation treatment plan using fine grid size instead of normal grid size. On the other hand, the dose distribution obtained using the normal grid size is very useful in the clinic because it can be generated in a short time. The time required to calculate the final dose with the fine grid size is approximately four times that for the normal grid size. For example, the average computational times for the normal and fine grid sizes were 1.5 and 5.6 min, respectively, in this work. However, if the normal organ dose is barely tolerable in the treatment plan with the normal grid size, there is a high probability that the actual irradiation dose exceeds the tolerance dose. This is particularly important for serious toxicity of serial organs. On this basis, if time permits, we recommend performing calculations using the fine grid size for improved accuracy.
A previous study for traditional linear accelerator has reported similar conclusions.^{[11]} Chung et al. found that the overall dose distribution was shifted to higher values when the grid size is increased, and the D95% obtained using a 4mm grid size was 2.6% greater than that obtained using a 2mm grid size. Although the fine and normal grid sizes are 2.73 mm and 5.46 mm, respectively, there is a 0.4% and 0.2% prescription difference between the D95% values obtained using the different grid sizes for prostate and HN cases, respectively. We considered that this difference emerges from irradiation method. The influence of the DVH parameters in TomoTherapy is smaller those that in fixedfield IMRT.
TomoTherapy Planning Station calculates the dose distributions using the average CT values of pixels in the grid.^{[19]} The current study verified the dose calculation at the pelvic region. There were no large differences among the CT values in this region. However, treatment plans for the lung region, for which there are large differences among the CT values, may exhibit a greater dose calculation error. Because there is a possibility that the influence of the grid size may differ in lung cases, future studies may be needed to verify these results.
Conclusions   
The calculation grid size is one of the major determinants of the accuracy of the TPS. The selection of grid size is very important for reducing generation times of treatment plans, too.
The overall dose distribution was almost identical regardless of the grid size, and the variations of DVH parameters for TomoTherapy were smaller than those fixed for multifield IMRT. However, the D2% of the PTV and D2cc of the OAR, which are often used for treatment plan evaluation, were significantly changed by the grid size. TomoTherapy, a specialized IMRT device, is a highprecision treatment machine.
Therefore, we recommend that the “fine” calculation grid size be used for dose computation, at least.
Acknowledgments
We thank Mikio Irie, Shinichi Ueki, and Takuya Suda for helping with film measurements and chamber to verify the treatment plans. We also acknowledge support regarding the TomoTherapy software operations from the Department of Applications in Hitachi Medico Corporation.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2], [Table 3], [Table 4]
