

ORIGINAL ARTICLE 

Year : 2017  Volume
: 13
 Issue : 3  Page : 491497 

Small field depth dose profile of 6 MV photon beam in a simple airwater heterogeneity combination: A comparison between anisotropic analytical algorithm dose estimation with thermoluminescent dosimeter dose measurement
Abhijit Mandal^{1}, Chhape Ram^{1}, Ankur Mourya^{1}, Navin Singh^{2}
^{1} Department of Radiotherapy and Radiation Medicine, Institute of Medical Sciences, Banaras Hindu University, Varanasi, Uttar Pradesh, India ^{2} Department of Radiotherapy, King George Medical University, Lucknow, Uttar Pradesh, India
Date of Web Publication  31Aug2017 
Correspondence Address: Abhijit Mandal Department of Radiotherapy and Radiation Medicine, Institute of Medical Sciences, Banaras Hindu University, Varanasi, Uttar Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09731482.181187
Aim of Study: To establish trends of estimation error of dose calculation by anisotropic analytical algorithm (AAA) with respect to dose measured by thermoluminescent dosimeters (TLDs) in airwater heterogeneity for small field size photon. Materials and Methods: TLDs were irradiated along the central axis of the photon beam in four different solid water phantom geometries using three small field size single beams. The depth dose profiles were estimated using AAA calculation model for each field sizes. The estimated and measured depth dose profiles were compared. Results: The over estimation (OE) within air cavity were dependent on field size (f) and distance (x) from solid waterair interface and formulated as OE = − (0.63 f + 9.40) x^{2}+ (−2.73 f + 58.11) x + (0.06 f^{2} − 1.42 f + 15.67). In postcavity adjacent point and distal points from the interface have dependence on field size (f) and equations are OE = 0.42 f^{2} − 8.17 f + 71.63, OE = 0.84 f^{2} − 1.56 f + 17.57, respectively. Conclusion: The trend of estimation error of AAA dose calculation algorithm with respect to measured value have been formulated throughout the radiation path length along the central axis of 6 MV photon beam in airwater heterogeneity combination for small field size photon beam generated from a 6 MV linear accelerator. Keywords: Air tissue heterogeneity, anisotropic analytical algorithm, small field dose measurement
How to cite this article: Mandal A, Ram C, Mourya A, Singh N. Small field depth dose profile of 6 MV photon beam in a simple airwater heterogeneity combination: A comparison between anisotropic analytical algorithm dose estimation with thermoluminescent dosimeter dose measurement. J Can Res Ther 2017;13:4917 
How to cite this URL: Mandal A, Ram C, Mourya A, Singh N. Small field depth dose profile of 6 MV photon beam in a simple airwater heterogeneity combination: A comparison between anisotropic analytical algorithm dose estimation with thermoluminescent dosimeter dose measurement. J Can Res Ther [serial online] 2017 [cited 2020 May 27];13:4917. Available from: http://www.cancerjournal.net/text.asp?2017/13/3/491/181187 
> Introduction   
Medium heterogeneity is a very important issue in delivering the accurate dose since the early days of radiation oncology. To address this problem many approaches and calculation algorithms have been developed. Out of these, only limited algorithms have the capability of maintaining high accuracy in dose calculation considering the medium heterogeneity. The dose estimation disagreement due to medium heterogeneity shows extreme effect in the presence of air cavities in the path of the photon beam. The disagreement further increases for smaller field sizes if the width of the field becomes smaller than the lateral range of secondary electrons. In the modern era of radiation oncology practice, it is inevitable to use the smaller fields for routine circumstances. Thus, precise treatment techniques such as intensity modulated radiation therapy and stereotactic radiotherapy/surgery, and equipment such as cyber knife and tomotherapy frequently use smaller field size photon beam in the treatment of the patient.
The anisotropic analytical algorithm (AAA) is a very effective dose calculation algorithm, introduced in the year 2005 for the use of commercial treatment planning system (Eclipse™, Varian Medical System, Palo Alto, CA).^{[1],[2]} The AAA calculation model has passed through various experimental validation processes using recommended test cases and datasets. AAA is based on a convolutionsuperposition dose computation model that applies the Monte Carlo (MC)generated dose kernels for heterogeneous media dose estimation. Earlier studies showed a higher overestimation of the dose near airtissue interfaces by AAA algorithm.^{[3],[4],[5]} The overestimation (OE) of the dose near airtissue interfaces will lead to severe underdosing and may be concluded as treatment failure. Due to complexity of dose measurement in small field size near or within the air cavity, very few experimental studies are available. Literature survey showed no authentic documented formulation of estimation error of dose near airtissue interface and within the air cavity during irradiation of small field size photon beam.
Therefore, in this study, an attempt has been made to establish and formulate the trend of dose estimation error in dose calculation using AAA algorithm with respect to measured values within the air cavity, near the airwater interfaces, and postair cavity for small field size 6 MV photon beam.
> Materials and Methods   
Phantom geometry
In this work, a solid water phantom (I'mRT Body Phantom, IBA Dosimetry) has been used, which has the facility to create different geometries using the various type of inserts supplied along with the phantom. The phantom dimension was 18 cm × 18 cm × 18 cm. Three different irradiation geometries were created by changing the position of an air cavity with dimensions 4 cm × 4 cm × 16 cm and one geometry was created without air cavity. The distance (d) of start of air cavity from the beam entry point in three geometries was 3 cm, 5 cm, and 9 cm, respectively.
Thermoluminescent dosimeter irradiation
The lithium fluoride thermoluminescent dosimeter (LiF TLD100) chips supplied by VICTOREEN were used in this study. The dimension of the chip used in this work was 1/8' × 1/8' × 0.035' (3.175 mm × 3.175 mm × 0.9 mm). The effective atomic number of LiF was 8.2.
To place the TLD in a straight line along the central axis, TLD chip trains were prepared by placing the TLD chips in aluminum foil. The TLD chips were placed in four solid water phantom geometries for irradiation as shown in [Figure 1]. As TLD chips have finite dimension, the center point is considered the measurement point for each TLD chip.  Figure 1: Schematic representation of thermoluminescent dosimeter irradiation set up
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In each geometry, three sets of TLD chip trains were irradiated by 6 MV photon beam (100 cm SSD) separately with the field sizes 1 cm × 1 cm, 2 cm × 2 cm and 3 cm × 3 cm by a 6 MV Linear Accelerator (UNIQUE™ Performance, Varian Medical System, Inc., Palo Alto, CA, USA).
Thermoluminescent output measurement
A standard annealing protocol for LiF TLD chips was carried out in a THERMOLYNE 47900 FURNACE oven. The preirradiation annealing protocol was 400°C for 1 h, followed by 100°C for 2 h and postirradiation annealing protocol was 100°C for 10 min. The thermoluminescent response was assessed after 24 h irradiation using a thermoluminescence reader (TL10091, NUCLEONIX, India). This reader was operated with a high voltage of −700 V. The temperature profile is used for LiF was as given in [Table 1].
Total area of the glow curve was taken as the reading of the measurements. The TL readouts of each TLD chip train were normalized with respect to the TL readout of the chip placed at 2 cm depth.
Calculation of modelbased depth dose profile
Computed tomography (CT) scans (2.5 mm slice thickness and 3 mm slice interval) of solid water phantom with three different irradiation geometry with air cavity and one without any air cavity were done using a 64 slice CT scanner (LightSpeed VCT, GE Health Care, USA) and imported to the ECLIPSE™ Treatment Planning System (Version 11.0.47) supplied by Varian Medical System, Inc., Palo Alto, CA, USA. Three single beam plans of field size 1 cm × 1 cm, 2 cm × 2 cm, and 3 cm × 3 cm were generated for each irradiation geometry using AAA calculation algorithm (Version 11.0.31). The depth dose profile was taken for each field sizes from the depth 2 cm to 16 cm along the central axis. The depth dose profile was normalized with respect to the dose received at 2 cm depth.
The estimation error of AAA dose calculation Algorithm was defined as:
The negative and positive estimation errors were considered as underestimation and OE by AAA calculation with respect to measured values.
> Results   
The AAA estimated and the measured central axis depth dose profiles (normalized with respect to the dose/TL readout at 2 cm) along with estimation error were plotted in [Figure 2].  Figure 2: The anisotropic analytical algorithm estimated and the measured central axis depth dose profiles along with estimation error
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The whole radiation path in the solid water phantom can be divided into three type of path length, the preair cavity path, within the air cavity path, and after air cavity path.
In this study, no specific trend in dose estimation error could be observed in spite of variation of air cavity starting depths (3 cm, 5 cm, and 9 cm) from the beam entry surface in all three with air cavity phantom. The observed estimation errors were independent of depth of solid waterair interface depth.
Very good agreements were observed in AAA estimation of normalized relative dose with normalized measured values in all the three field sizes in solid water phantom without air cavity. The estimation errors ranged from −5.28% to 3.48% with a mean value of −0.47% and a median value of −2.8%. This observation validates the dose calculation by AAA algorithm and TLD measurement technique satisfactorily.
In the rest of three geometries, the precavity depth dose profiles showed good agreement between the AAA dose estimation with air cavity, measurements with cavity, AAA estimation without air cavity, and measurements without air cavity. The AAA estimation with air cavity with respect to the measurements with air cavity ranged from −3.48% to 9.46% with a mean value of 0.66% and a median value of 0.0%. AAA calculation algorithm was able to estimate the dose in preair cavity region satisfactorily.
However, within the air cavity, AAA dose calculation algorithm highly overestimated the dose in all geometries and field sizes. As the distance of the points from the solid waterair interface was increased, the OE values also increased. The average OE values decrease with the increase of field size for each experimental point of consideration [Table 2].  Table 2: Overestimation of anisotropic analytical algorithm calculation model with respect to measured values within cavity
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The highest value of OE was observed to be 117.82% (for field size 1 cm × 1 cm and point of measurement 3.84 cm distal from solid waterair interface). The lowest value of OE was observed 1.27% (for field size 3 cm × 3 cm and point of measurement was 0.16 cm away from solid waterair interface).
In addition, in the post air cavity path length, it was noted that the AAA calculation model again overestimates the dose much more than the measured values. The OE in the point of measurement, adjacent to the airsolid water interface (0.16 cm from the airsolid interface) was sufficiently high [Table 3].  Table 3: Overestimation of anisotropic analytical algorithm calculation model with respect to measured values at postcavity point at 0.16 cm from the airsolid water interface
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The OE reduces to a constant value at the points ≥1 cm from the airsolid interface for a constant field size [Table 4]. This study also shows that OE values for adjacent point and point's ≥1 cm from the airsolid interface were decreased with the increase of field size.  Table 4: Average overestimation of anisotropic analytical algorithm calculation model with respect to measured values at postcavity point's ≥1.0 cm from the airsolid water interface
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The OE values at the adjacent point were highest for field size 1 cm × 1 cm (71.17%) and lowest for field size 3 cm × 3 cm (23.58%). Similarly, the average OE values at the points ≥1 cm from the airsolid interface were highest for field size 1 cm × 1 cm (16.10%) and lowest for field size 3 cm × 3 cm (10.36%).
Formulation of trends of estimation error
This study showed specific trends of AAA calculated estimation error in dose within the air cavity and postair cavity path length. Within the air cavity, very high OE was observed. The OE values varied with the depth from the airsolid water interface and the field size. The average OE value of each respective depth was plotted against the depth from the airsolid water interface for each field size [Figure 3].
The equation of best fit of each plot was determined as [Table 5].  Table 5: Best fit equations of overestimation values of anisotropic analytical algorithm within air cavity
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From equations 1, 2, and 3 [Table 5] a basic equation of over estimation:
may be formulated, where a, b, and c are coefficients and depend on field size. After plotting the a, b, and c against field size in cm^{2} [Figure 4], the best fit equation for a, b, and c was determined as shown in [Table 6].
The final equation of OE may be represented as:
Postair cavity OE at a point 0.16 cm from the airsolid interface also showed field size dependence [Figure 5].  Figure 5: Formulation of overestimation postair cavity at 0.15 cm distance from airwater interface
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The best fit equation of OE may be derived as:
with a regression coefficient R^{2} = 1.
Postair cavity OE at points situated ≥1 cm from the airsolid interface were independent of distance from airsolid water interface and were field size dependent [Figure 6]. The best fit equation of OE may be derived as:  Figure 6: Formulation of overestimation postair cavity beyond 1.0 cm distance from airwater interface
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with a regression coefficient R^{2} = 1.
> Discussion   
The therapeutic success in radiotherapy treatment technique can only be realized if one can accurately estimate the dose in the treated volume. The estimation of dose is quite simple for irradiation in a homogeneous medium. However, in practical clinical situations, when the heterogeneous medium gets involved, the dose estimation process is very complex, and it is very tough to maintain the level of accuracy. Lots of efforts have been made to understand the dose calculation in heterogeneous medium. AAPM report number 85, addressed the issue of tissue heterogeneity corrections for megavoltage photon beams very elaborately.^{[6]} This report also discussed the various categories of approaches considering the local energy deposition (no electron transport), nonlocal energy deposition (electron transport), and dimensions of sampling. Das et al.^{[7]} elaborately discussed the problem, present knowledge and future direction in small field dose measurement. The AAA algorithm is a superposition – convolutionbased dose calculation model and where threedimensional density CT information for the transport of both scattered photons and electrons were taken account applying complex methodology. After the inception in the radiation oncology, AAA algorithm was tested extensively by the medical physics community,^{[8],[9],[10]} and often found to be an effective calculation model for most of the clinical situations.
Several studies have been conducted to define the error in dose estimation by various commonly used dose calculation algorithms in heterogeneous medium. The researchers mainly focused on the dose estimation near the interface or within the heterogeneity region.
These studies were carried out to estimate the accuracy of dose calculation algorithm varies in photon energy (Co6015 MV), field sizes (2 cm × 2 cm to 10 cm × 10 cm), type of heterogeneity of medium (air to bone), sizes, and shapes (layer, channel, cubic cavity, and triangle) of heterogeneity using simulation data^{[11],[12],[13],[14],[15],[16]} (TPS or MC) or measured data.^{[5],[17],[18],[19],[20],[21],[22],[23]} Most of the work considered the waterair heterogeneity combination phantom to demonstrate the results effectively.^{[5],[11],[12],[13],[14],[17],[18],[19],[20],[21],[22],[23]} Various clinical situations such as larynx,^{[18],[19]} nasopharyngeal region,^{[5],[12]} endorectal balloon cavity,^{[12]} large frontal air sinus in acromegaly patients,^{[11]} involves the presence of air cavity in treatment region.
Considering a clinical situation larynx, NiroomandRad et al.^{[18]} discussed the effect of air cavity on radiation dose distribution to the larynx using Co60, 6 MV, and 10 MV photon beams of 7 cm × 7 cm parallel opposed fields. This study demonstrated that the variation at the tissueair interface is more significant for lower energies (8% [60Co], 7.3% [6 MV]). This variation is about 4.3% for 10 MV photon beam. Ostwald et al.^{[19]} taken measurement in an anatomic larynx phantom and stated severe mucosal underdosing, some surface positions receive <80% of the prescribed dose.
The presence of air cavity in the radiation path length causes severe perturbation in dose deposition within and around the air cavity and leads to inaccuracy of dose calculation in routinely used algorithms. Most of the studies indicate that all the works stated the results in terms of dose reduction or as error of estimation in percentage, but none have established any specific trends or dependence on variables of the estimation error of a particular dose calculation algorithm.
The researchers discussed results of errors in dose estimation by any calculation algorithm near the interface and within the air cavity, it increases with (1) higher energy of photon, (2) smaller field sizes, and (3) large size air cavity.
The results of present work are in good agreement with the results of other reported literature. In this study, the equations of estimation error of AAA dose calculation algorithm within the air cavity, adjacent point of airsolid water interface, and beyond air cavity points (distance ≥1 cm away from airsolid water interface) were formulated for small field size 6 MV photon beam. The trend of equation shows that the estimation error in the air cavity region depends on field sizes and the depth from solid waterair interface. Similarly, the results also demonstrate that the estimation error at adjacent point of airsolid water interface and postair cavity points (≥1 cm away from airsolid water interface) are dependent on the field size of the beam.
The limitations of the present work are (1) the energy dependence was not investigated, only 6 MV photon beam was used, (2) TLD chips have finite size, but the center point was considered as point of measurement, (3) very thin aluminum foil were used to prepare the TLD chip train and to align the chip train along the central axis of the beam, the aluminum foil may contribute a little effect in dose measurement.
It may be concluded that AAA dose calculation algorithm is not able to calculate dose accurately in the air cavity and beyond it. Therefore, it is necessary to make certain modifications in the algorithm. The methodology described in the present work may also be used to validate other commonly used dose calculation algorithm in heterogeneous medium.
Acknowledgment
Authors are thankful to Dr. L. M. Aggarwal for his kind support in preparing manuscript.
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], [Figure 6]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]
