Iranian Journal of Medical Physics ijmp.mums.ac.ir Telecobalt Machine Beam Intensity Modulation with Aluminium Compensating Filter Using Missing Tissue Approach Samuel Nii Adu Tagoe1* , Samuel Yeboah Mensah2 , John Justice Fletcher3 , Evans Sasu4 , 1. Department of Physics, School of Applied Physical Sciences, University of Cape Cost, Cape Coast, Ghana, National Centre for Radiotherapy and Nuclear Medicine, Korle Bu Teaching Hospital, Accra, Ghana 2. Department of Physics, School of Applied Physical Sciences, University of Cape Cost, Cape Coast, Ghana. 3. Department of Applied Physics, University for Development Studies, Navrongo Campus, Navrongo, Ghana 4. National Centre for Radiotherapy and Nuclear Medicine, Korle Bu Teaching Hospital, Accra, Ghana. A R T I C L E I N F O A B S T R A C T Article type: Introduction: The present study aimed to generate intensity-modulated beams with Aluminium Original Article compensating filters for a conventional telecobalt machine based on the outputs of a treatment planning system (TPS) performing forward planning and cannot simulate directly the compensating Article history: filter. Received: Jul 25, 2017 Materials and Methods: In order to achieve the beam intensity modulation during treatment planning Accepted: Aug 31, 2017 with the TPS, we used a bolus placed on the surface of a tissue-equivalent phantom. The treatment plans replicated on the telecobalt machine with the bolus were represented with compensating filters Keywords: placed at a certain distance from the phantom surface. An equation was proposed for the conversion of Compensating Filter the bolus thickness to the compensating filter thickness such that any point within the phantom would Bolus receive the planned dose. Correction factors were introduced into the proposed equation to account Regression for the influences of field size, treatment depth, and applied bolus thickness. The proposed equation Modulation was obtained based on the analyses of empirical data measured in a full scatter water phantom with and without the compensating filter. Results: According to the results, the dosimetric verification of the proposed approach outputs in a solid water phantom with calibrated Gafchromic EBT2 films were comparable to that of the TPS with deviation of ±4.73% (mean: 2.98±1.05%). Conclusion: As the findings of the present study indicated, the discrepancy between the measured doses and TPS-estimated doses was within the tolerance of ±5%, which is recommended for dose delivery in external beam radiotherapy. Therefore, the proposed approach is recommended for clinical application. ►Please cite this article as: Tagoe S, Mensah S, Fletcher J, Sasu E. Telecobalt Machine Beam Intensity Modulation with Aluminium Compensating Filter Using Missing Tissue Approach. Iran J Med Phys 2018; 15: 48-61. 10.22038/ijmp.2017.23548.1253. Introduction physics of the radiation interactions with a medium or Dose distribution within the irradiated region is matter [1, 2]. To enhance the efficiency of dose the most reliable and verifiable quantity linking the computation and speed up this process, specialized treatment parameters to observed therapeutic computers known as treatment planning systems outcomes for specific treatment technique in (TPSs) are used to simulate the treatment process for radiotherapy [1]. It is imperative to accurately know the realization of therapeutic intent prior to treatment the dose that would be deposited at any point within delivery. the patient undergoing external beam radiotherapy The process of simulating the treatment delivery (EBRT). It is also practically impossible to put process with a computer is referred to as treatment radiation detectors within the patient subjected to planning. Nonetheless, this process goes beyond the irradiation. sole treatment simulation and determines the dose The dose distributions within a patient are mostly distribution within the patient, which is usually calculated with the aid of dosimetric functions associated with treatment duration. Treatment determined in a full scatter water phantom and planning also involves all the steps needed for the mathematical algorithms that are aimed to explain the effective management of a patient. *Corresponding Author: Department of Physics, School of Applied Physical Sciences, University of Cape Cost, Cape Coast, Ghana, National Centre for Radiotherapy and Nuclear Medicine, Korle Bu Teaching Hospital, Accra, Ghana, Email: s.tagoe@kbth.gov.gh, Tel: +233244268061 Beam Intensity Modulation Using Missing Tissue Approach Samuel Nii Adu Tagoe et al. These steps include patient diagnoses to help the within the patient. These requirements are capital clinicians stage the disease and select the optimal intensive and may be costly for a developing country. treatment modalities, imaging to facilitate the effective However, this cost can be minimized by using localization of the intended target and the customized compensating filters fabricated from surrounding normal tissues, radiation dose locally available materials that can account for the optimization to facilitate the selection of irradiation effects of the patient's surface irregularities and tissue geometries maximizing doses to the intended target inhomogeneities [7, 8]. Moreover, the compensating volume and minimizing doses to the normal tissues, as filters can be utilized to address the issues associated well as treatment plan evaluation to assess the with multileaf collimator-based IMRT. These issues adequacies of the chosen irradiation geometries. include long beam on time [9], complexities of dose Therefore, TPSs are used as radiation dose verification during treatment delivery [10-12], and optimization tools for treatment delivery in EBRT. dosimetry requirements during commissioning [13]. Forward and inverse plannings are two variants of The use of bolus, wedge filters, or compensators treatment planning technique that can be performed can facilitate the correction of the increase in dose in a TPS. Forward planning is assigned to a condition inhomogeneity within an irradiated target volume when the planner selects beams and provides their caused by irregularities in the patient's surface orientations as well as weightings. In this kind of contour [14, 15]. Bolus, which is mostly made from planning, the TPS calculates the resultant dose tissue-equivalent materials, is placed on the skin of distribution within the irradiated region based on the the patient during the treatment delivery [14, 15]. An selected irradiation geometries. unfortunate consequence of using a bolus is the loss of On the other hand, in the -inverse planning, the skin sparing associated with megavoltage beams [14, planner selects the beams, provides their orientations, 15]. and indicates the desired dose distributions and Howbeit, moving the bolus from the patient constraints within the irradiated region. In this type, surface toward the teletherapy machine radiation the TPS applies the necessary beam weightings and source (specifically the block tray position) retains the modulations that will give rise to the desired dose compensation of the bolus, and also reestablishes the distributions within the patient. The lack of compromised skin sparing [14]. In this case, the bolus appropriate treatment equipment and/or paucity of can be composed of any non-tissue equivalent resources affect the ability to optimize the radiation material since it is no longer in contact with the dose to an irradiated target. patient. This bolus is referred to as a compensating During EBRT, the spatial distribution of radiation filter (or compensator). The compensating filters are dose within a patient is influenced by a lot of factors, usually placed at the distance of about 15-20 cm from such as surface topography at the point of beam the patient surface [14, 15]. entrance and tissue inhomogeneities within the A compensator used to account for a tissue deficit irradiated region [2]. These factors along with the on the patient surface is referred to as a missing tissue complex shape of an irradiated target volume (tumor) compensator [15]. The shape of the compensator call for the modulation of the beam fluence must be adjusted based on the position of the distribution across the individual radiation fields. This compensator relative to the representing bolus to modulation facilitates the optimization of the account for beam divergence and reduction in the radiation dose to the intended target volume while contributions of scattered photons to dose at any minimizing radiation dose to the neighboring normal point within the patients [15]. tissues. This has been culminated in the introduction Various approaches have been applied to of intensity-modulated radiotherapy (IMRT). determine the extent of tissue deficiencies along the The implementation of IMRT needs the fulfillment surfaces of the patients. Accordingly, various methods of basic requirements. One of these requirements is have been developed and evaluated to account for the the availability of a TPS with inverse or forward deficiencies with compensating filters [15, 16]. In this planning capabilities with direct optimization regard, wedge filters are used to compensate for algorithms [3-6] to assist the realization of the fluence missing tissues across sloping surfaces [15]. The distributions across beams based on predefined dose application of the wedge filters results in a distributions. The other requirement is the progressive decrease in the intensity across the beam accessibility to a conventional teletherapy machine in certain direction [15]. including multileaf collimators controlled with With this background in mind, the present study specialized computers and software to facilitate the aimed to investigate the production of intensity- movement of the leaves of the collimator system modulated beams with Aluminium compensating during the treatment delivery. filters in a conventional telecobalt machine based on The movements of the leaves of the collimator the outputs of a TPS performing forward planning system result in the modulation of intensity across without direct optimization algorithm, which cannot beams to achieve the desired dose distributions 49 Iran J Med Phys, Vol. 15, No. 1, January 2018 Samuel Nii Adu Tagoe et al. Beam Intensity Modulation Using Missing Tissue Approach directly simulate the presence of a compensating filter in the path of a beam. The TPS presumes the bolus as part of the patient body; therefore, no additional beam data are required. Bolus is traditionally used in the EBRT to even out the patient skin topography irregularities and increase skin dose [14]. The use of a bolus compromises the skin sparing of megavoltage beams [14]. Theory The intensity, I, of radiation with initial intensity, Io, transmitted through an absorber is defined by the Beer-Lambert's equation as [15, 17]: I = Ioe −μeffx (1) Figure 1. Schematic diagram of irradiation geometry for bolus and where μeff is effective linear attenuation coefficient compensating filter considering the departure from narrow beam geometry for irradiation geometries in EBRT. To characterize an absorber, it will be very Considering the irradiation geometries for the prudent to use the effective mass attenuation clinical implementation of a bolus and a compensating coefficient, μm , instead of effective linear filter (Figure 1), the transmitted radiation reaching eff attenuation coefficient of the absorber material. This the detector at a given depth within a phantom, is because Compton effect is the predominant considered to be water for each of the scenarios, is interaction process that occurs when a megavoltage given as the irradiation geometries with the beam for radiotherapy interacts with a material or compensating filter and bolus that are determined in medium [18]. The Compton effect is dependent on the the equations (2) and (3), respectively, as follows: adsorption coefficient as well as electron and physical I ln ( ) = −μeff . xc (2) I c densities of the absorber [18]. Therefore, expressing 0 c I the linear attenuation coefficient of the absorber Where ( ) is the transmission factor for the Io material in terms of mass attenuation coefficient c radiation as it traverses through the compensating makes it independent of absorber material density filter material, xc is the thickness of the compensating [18]. The effective mass attenuation coefficient of an filter material traversed by the radiation, and μeff is absorber with density of ρ relates to its effective linear c the effective linear attenuation coefficient of the attenuation coefficient as follows: μeff material the compensating filter is made of. μm = (4) eff ρ I ln ( ) = −μeff . f. xb (3) The substitution of equation (4) into equations (2) I0 bb I and (3) results in equations (5) and (6), respectively: where ( ) is the transmission factor for the I Io b ln ( ) = −μm . ρc. xc (5) I0 effc radiation as it traverses through the bolus material, xb c I is the thickness of bolus material traversed by the ln ( ) = −μm . ρb. f. xb (6) I0 effbb radiation, μeff is the effective linear attenuation b where μm and μ are the effective mass effc meffb coefficient of the compensating filter material, and f is attenuation coefficients (in cm2/g) of the a correction factor introduced to account for the compensating filter and bolus materials, respectively. effects of the position of the bolus relative to the Additionally, ρc and ρb are the densities (in g/cm3) of compensating filter. In this regard, f is the function of the compensating filter and bolus materials, field size, thickness of bolus material, source to respectively. absorber distance, and depth of measurement within The compensating filter was used to represent the the phantom. bolus such that the transmitted radiation at any depth Placing the absorber on the surface of the phantom within the phantom would be the same for the two would increase the transmitted radiation measured at irradiation geometries; therefore, the equations (5) any point within the phantom owing to increase in and (6) can be combined to give: scattered radiation contribution to dose at any point μm . ρc. xc = μm . ρb. f. xb (7) within the phantom (or patient), compared to the time effc effbRearranging equation (7) gives: the absorber is moved away from the surface of the μm .ρb.f.xeffb b phantom. xc = (8) μm .ρeffc c Since bolus are usually made of tissue-equivalent materials [2, 15], and the densities of those materials can be approximated to that of water (1.0 g/cm3), equation (8) can be written as: 50 Iran J Med Phys, Vol. 15, No. 1, January 2018 Beam Intensity Modulation Using Missing Tissue Approach Samuel Nii Adu Tagoe et al. k x = ( μ) fx (9) Commissioning c ρ bc All beam data were measured on the beam where kμ is the ratio of the effective mass central axis with 0.125 cc cylindrical ionization attenuation coefficient of bolus material to that of the chamber (TW31002-1505, PTW-Freiburg, Germany) compensating filter material. in a full scatter motorized water phantom, namely Using equations (1) and (4), it can be shown that Blue Phantom2 (IBA Dosimetry GmbH, Germany). the effective mass attenuation coefficient, μm , of an eff The ionization chamber was connected to a UNIDOS absorber material with density of ρ is given as: electrometer (10002-20204, PTW-Freiburg, −In(I⁄I ) Germany), which was set to measure the output of μ = 0m (10) eff ρx the teletherapy machine in terms of charges at 60- where x is the thickness of absorber traversed by sec intervals with a chamber bias voltage of +300 V. the radiation, and (I⁄ ) is the transmission offered by The teletherapy machine, which was used in this Io study and whose beam data were acquired, was an the absorber. Equinox 100 cobalt 60 teletherapy machine (Best From equation (10), it implies that: ρ x Theratronics, Canada). k c cμ = (11) ρ fx To measure the thickness ratio for the b b Since the density of the bolus material, ρb, is compensating filter, Aluminium plates with similar to that of water. Therefore, equation (11) thicknesses of 0-27.45 mm (increments of 3.05 mm) becomes: were successively mounted on a block tray and x kμ = ( c ) ρc (12) placed in the path of beams irradiated from the fxb telecobalt machine employing isocentric irradiation Based on equation (12), it is evident that the direct technique. Each beam had a field size of 10×10 cm2. k determination of ( μ) f in equation (9) is to measure The block tray was placed at the accessories holder ρc on the collimator system of the telecobalt machine. the dose with the compensating filter mounted on a For each thickness of Aluminium plate mounted tray within a beam irradiated from a teletherapy on the block tray, the transmitted output of the machine for appropriate field size and depth in a telecobalt machine was measured with the ionization tissue-equivalent phantom. The same measurement chamber placed at a depth of 5.0 cm within the was repeated without the compensating filter. In this phantom and electrometer reading that was process, the thickness of the phantom was adjusted to corrected for temperature and pressure influences. get the same dose as before. The ratio of The above measurements were repeated without the compensating filter thickness to that of the adjusted k Aluminium plates. The height of water within the thickness of the phantom gives ( μ) f. The ρ phantom was adjusted within 0-20 cm (increments c kμ of 2 cm) while keeping the detector at the same quantity ( ) f, can therefore be referred to as ρc depth and maintaining the isocentric irradiation thickness ratio or density thickness ratio. technique. The electrometer reading was obtained for each Materials and Methods adjusted height of water above the detector, and Prior to performing the experimental once again corrected for influencing factors (i.e., measurements, based on the AAPM TG 46 temperature and pressure). For each thickness of the recommendations [19], the quality assurance tests Aluminium plate, the adjusted height of water above were performed on the teletherapy machine, with the detector that would give the same corrected beam output of which was to be modulated with the electrometer reading as that of a measurement done proposed approach. These tests were administered with a particular thickness of Aluminium plate in the to ensure the accuracy and integrity of the measured path of the beam was determined. Subsequently, the beam data, which would be used for the correlation between the adjusted height of water commissioning. above the detector and the corresponding thickness In addition, constancy and stability checks were of Aluminium that would give the same beam output performed on the ionization chamber, which was was calculated. used for the beam data acquisitions to ensure the Additionally, the ratio of Aluminium thickness to reliability of the measured beam data. These checks the corresponding adjusted height of water above were based on the recommendations of the IEC the detector that would give the same beam output 60731 [20]. The following procedures were used for was determined for various adjusted heights of the effective commissioning of the Aluminium water above the detector. A graph of thickness ratio compensating filters for beam intensity modulation as a function of adjusted height of water above the based on the proposed approach. detector was plotted, and the correlation equation as well as the regression, R2, of the line of best fit was obtained. 51 Iran J Med Phys, Vol. 15, No. 1, January 2018 Samuel Nii Adu Tagoe et al. Beam Intensity Modulation Using Missing Tissue Approach To study the influence of field size (or collimator without the plate in the path of the beam that would settings) on the thickness ratio, the above give the same corrected electrometer reading as that experimental procedures were repeated with a with the Aluminium plate in the path of the beam constant thickness of Aluminium plate mounted on was determined. the block tray and placed into the path of the beam; The depth of measurement with the Aluminium however, the field sizes were varied from 3×3 cm2 to plate in the path of the beam was subtracted from 35×35 cm2. A constant Aluminium plate thickness of the determined corresponding depth of 1.53 cm was used. For each field size setting, the measurement without the plate in the path of the obtained electrometer reading was corrected for beam to determine the related adjusted height of influencing factors (i.e., temperature and pressure). water above the detector. For each depth of For the measurements involved no Aluminium measurement, the ratio of the applied Aluminium plate in the path of the beam, the corrected plate thickness placed in the path of the beam during electrometer readings (beam outputs), obtained with the measurements to the corresponding adjusted the various adjusted heights of water above the height of water above the detector was obtained detector, were repeated for the various square field from the measurements without the compensating sizes. From the aforementioned measurements, we filter. determined the adjusted height of water above the Nevertheless, the height of water above the detector for a particular field size that would give the detector, adjusted to obtain the same beam output same corrected electrometer reading as that of a for both measurement scenarios, was calculated for measurement with the Aluminium plate in the path the various depth of measurements. The obtained of the beam using the same field size. ratios were normalized to that of the depth of For each field size, the ratio of the thickness of the measurement of 5.0 cm with the Aluminium plate in applied Aluminium plate placed in the path of the the path of the beam. The normalized ratios were beam during the measurements to the corresponding referred to as treatment depth correction factors. A adjusted height of water above the detector was graph of treatment depth correction factor was determined from the measurements involved no plotted against the depth of measurement with the compensating filter Nonetheless, the height of water Aluminium plate in the path of the beam (treatment above the detector, adjusted to obtain the same beam depth). Additionally, the correlation equation as well output for both measurement scenarios, was as the regression, R2, of the line of best fit was calculated for the various field sizes. calculated. The obtained ratios were normalized to that of In all the aforementioned measurements, it was the reference field size of 10×10 cm2. The normalized ensured that there was at least 10.0 cm of water ratios were referred to as field size correction below the detector to provide the needed factors. A graph of field size correction factor was backscattered radiation. The isocentric irradiation plotted against one side of a square field size technique was also maintained in all the (equivalent square field size). Furthermore, measurements by keeping the position of the correlation equation as well as regression, R2, of the detector constant and pumping water into the line of best fit were determined. phantom to obtain the desired depth of To study the impact of treatment depth on the measurement. The schematic diagram of the thickness ratio, the measurements with varying field experimental setup is illustrated in Figure 2. To sizes were repeated. However, the field size was kept ensure the reproducibility of the experimental constant at 10×10 cm2, and the depth of outcome, the density and mass attenuation measurement varied within 0.5-17.0 cm. For each coefficient of the Aluminium were empirically depth of measurement with the constant thickness of verified. Aluminium plate in the path of the beam, the output For the mass attenuation coefficient, the of the telecobalt machine was obtained and measurements were performed in air for field sizes corrected for influencing factors (i.e., temperature ranging within 3×3 cm2 to 30×30 cm2. The mass and pressure). attenuation coefficient for each field size was For the measurements without the Aluminium determined as the ratio of measured linear plate in the path of the beam and with the fixed field attenuation coefficient for that particular field size to size, the electrometer readings (telecobalt machine the density of Aluminium. The density of Aluminium outputs) obtained for measuring depths ranged was estimated by finding the weights of eight within 0.5-32.0 cm. The measured beam outputs different samples of Aluminium plates used for the (electrometer readings) for the various measuring study with a digital chemical balance (Mettler depths were corrected for variations in air density. Toledo™ ME-TE Precision Balance, Fisher scientific, From these measurements, for each depth of USA) and dividing the respective weights with their measurement with the Aluminium plate in the path corresponding volumes of Aluminium plates. of the beam, a corresponding depth of measurement 52 Iran J Med Phys, Vol. 15, No. 1, January 2018 Beam Intensity Modulation Using Missing Tissue Approach Samuel Nii Adu Tagoe et al. The volume of the plate was evaluated based on appropriate thickness ratio for a particular thickness its physical dimensions measured with an electronic of bolus applied within a grid (or along a ray line) digital caliper (Model # 50003, Chicago Brand under reference conditions (field size of 10×10 cm2 Industries, USA). Furthermore, the mean of the and treatment depth of 5 cm). This variable was determined densities was considered as the density represented by the correlation equation determined of the Aluminium used in this study. from the plot of thickness ratio against the adjusted height of water above the detector. The thicknesses of the compensating filter at various portions of the radiation field to be modulated were determined and recorded within the respective grids of the compensating filter sheet. Subsequently, the compensating filter sheet with the recorded thicknesses was pasted at the back of transparent Perspex block tray in use for the telecobalt machine. This was performed in such a way that a beam central axis inscribed on the surface of the block tray matched with that of the compensating filter sheet. The block tray was similar to the one used during the commissioning process. The samples of Aluminium plates used for the commissioning had dimensions of 1×1 cm2 with different thicknesses. Figure 2. Schematic diagram of experimental setup These samples were stacked together on the block tray to obtain the stipulated thicknesses of Compensating filter construction Aluminium within the various grids. The Aluminium In constructing the compensating filter, the length plates or blocks were held in place with an adhesive and width were tapered to account for beam (or bonding agent). divergence. To achieve this aim, a compensating filter sheet with grid lines having grid area of 1×1 Treatment planning cm2 and two perpendicular lines, running through Treatment simulations were performed with the central part to represent the major axes of a Prowess Panther TPS, version 4.6 (Prowess Inc., beam, was designed to record the applied bolus USA). A phantom with the dimensions of 30×30×20 thicknesses along the patient surface. The grid part cm3 with radiological properties similar to an acrylic covered an area of about 2×2 cm2 at the isocentre of slab phantom (used to verify treatment plans) was the telecobalt machine. created with the TPS using a slice thickness of 5 mm. The thickness of the compensating filter along the After the outline of the phantom were delineated on direction of beam propagation was also tapered to each slice with the auto-contouring tool, multiple account for the reduction of scattered radiation plans were generated for the phantom using the plan contribution to radiation dose at any point within the manager tool. Each plan had a single anterior beam patient for using the compensating filter as a employing source to axis distance treatment replacement for bolus during the treatment planning technique. process. After the calculation of the bolus thickness, Nevertheless, the field size and treatment depth xb, within each grid and using equation (9), the (i.e., dose prescription depth) for the various plans thickness, xc , of a compensating filter along the grid were different. The plans were named as plan 1, plan was determined using the following equation: 2, plan 3, plan 4, and plan 5. The field sizes of 10×10, xc = Tt f 2b rfdxb (13) 15×6, 25×15, 25×25, and 23×4 cm and treatment Where fd is the treatment depth correction factor depths of 5, 7, 10, 15, and 2 cm were used for plans 1, applicable to a specified treatment depth. This value 2, 3, 4, and 5 to deliver prescribed doses of 100, 150, was generally represented by the correlation 200, 250, and 250 cGy at the isocenter, respectively. equation obtained from the plot of depth correction During the treatment planning processes with the factor against treatment depth for the compensating TPS, beam intensity modulation was achieved by filter material under consideration. The fr is the field placing the bolus shaped in form of step wedges on size correction factor applicable to a particular field the surface of the phantom at the point of beam size (equivalent square field). This value was entrance. It was ensured in each case that the area represented generally by the correlation equation covered by the bolus extended about 2 cm beyond determined from the plot of field size correction the radiation field limits (field edges), indicated on factor against field size for the compensating filter the surface of the phantom. Prior to the creation of material under consideration. Furthermore, T is the the bolus, the Hounsfield unit (HU) of the bolus tb 53 Iran J Med Phys, Vol. 15, No. 1, January 2018 Samuel Nii Adu Tagoe et al. Beam Intensity Modulation Using Missing Tissue Approach material was set to that of water (HU=0), which was tools of the TPS. Subsequently, these measurements the default for the TPS. were converted to compensating filter thicknesses The axial view of the bolus per case scenario is using equation (13) to facilitate the construction of depicted in the planning windows shown in Figure 3. the compensating filter for each plan. For each of the plans, the beam central axis was The various treatment plans, replicated on the made central to the phantom, and the beam was telecobalt machine with the replacement of bolus by incident normally to the surface of the phantom. appropriate Aluminium compensating filters. These Dose calculation points were then placed at the filters were constructed based on the developed and isocenter along the beam major axis in the direction proposed approach and placed in the path of the of the steps of the step wedge. Starting from the beam. The off-axis doses were measured with beam isocenter, the calculation points were placed at calibrated Gafchromic EBT2 film samples (Lot #: 2 cm apart from each other on either side of the 08221302, Ashland Inc., USA). The Gafchromic EBT2 beam central axis as shown in Figure 3A and 3B, film was calibrated against a 0.6 cc cylindrical respectively. ionization chamber (TW 30013, PTW Freiburg, The step wedges were created such that the Germany) having traceability to a secondary middle of the steps were closely in line with the standard laboratory, based on the International calculation points placed along the beam major axis Atomic Energy Agency technical report series 398 at the isocenter. Two types of step wedges were protocol [21]. created; accordingly, the bolus and the step wedges The optical densities of exposed films were read were referred to as scenarios case 1 and 2, with ImageJ analyzing software (National Institutes respectively. Various plans were repeated with each of Health, USA). Afterwards, the obtained optical type of step wedge of the bolus on the phantom. Dose densities were converted to doses using the distributions within the phantom were calculated sensitometric curve of the film determined during with various prescribed doses and irradiation the calibration process. The exposed films were geometries in the TPS; furthermore, the scanned with a flatbed scanner (ScanMaker® corresponding treatment times were recorded for 9800XL plus, Microtek, USA), and the images were the various plans. saved in Tagged Image File Format (TIFF) prior to In addition, the off-axis dose profiles along the performing the analysis in the ImageJ software. isocenter in the direction of the step wedge together During the dose measurements, the films were with their corresponding off-axis distances from the sandwiched between the piles of the acrylic slabs beam central axis were recorded. Bolus thicknesses forming the phantom (T2967, PTW Freiburg, along the surface of the phantom were determined Germany) at the required treatment depth and held for the various grids with the aid of available in place by gravity on the treatment couch of the graduated patient origin indicators and measuring telecobalt machine. 54 Iran J Med Phys, Vol. 15, No. 1, January 2018 Beam Intensity Modulation Using Missing Tissue Approach Samuel Nii Adu Tagoe et al. Figure 3. Planning window of treatment planning system showing plans for dosimetry verification, A: bolus shape for case 1, B: bolus shape for case 2 Results Figure 4 presents the variation of compensating filter (or Aluminium plate) thickness as a function of the adjusted height of water above the detector. The correlation equation as well as the regression, R2, of the line of best fit is displayed above the curve in Figure 4. Figure 5. Graph of thickness ratio against adjusted height of water above chamber or simulated bolus thickness Figure 6 presents a graph of field size correction factor as a function of one side of a square field size. The correlation equation and the regression, 𝑅2, of the line of best fit are depicted above the curve in Figure 6. Figure 4. Variation of compensating filter thickness as a function of adjusted height of water above detector A graph representing the ratio of compensating filter thickness to adjusted height of water above the detector (thickness ratio) against adjusted height of water above the detector is depicted in Figure 5. In addition, the correlation equation and regression, R2, of the line of best fit are illustrated below the curve in Figure 5. Figure 6. Graph of field size correction factor as a function of field size A graph illustrating the treatment depth correction factor as a function of the depth of 55 Iran J Med Phys, Vol. 15, No. 1, January 2018 Samuel Nii Adu Tagoe et al. Beam Intensity Modulation Using Missing Tissue Approach measurement within the water phantom is demonstrated in Figure 7. Furthermore, above the curve in Figure 7 are displayed the correlation equation and the regression, 𝑅2, of the line of best fit. Figure 8. Variation of mass attenuation coefficient with field size the various calculation points, which are expressed Figure 7. Graph treatment depth correction factor as a function of treatment depth as percentage differences of the respective measured doses. The variation of mass attenuation coefficient In this regard, the deviations ranged within -1.3 measured in air for the Aluminium used in this study to 3.98% (mean: 2.55±1.02%) and -4.39 to 4.72% with one side of a square field size is displayed in (mean: 3.35±0.94%) for cases 1 and 2, respectively. Figure 8. The correlation equation and the The omissions in Table 1 indicate places where the regression, 𝑅2, of the line of best are shown above calculation points fall outside the steps of the step the curve in Figure 8. wedge bolus generated with the TPS. Table 1 presents the measured doses at various calculation points with the Gafchromic films for the Based on the graphical manipulations and curve compensating filter and the treatment plans fitting analyses performed on the experimental data, replicated on the teletherapy machine for various the various terms in equation (13), proposed for treatment plans and case scenarios. The calculated converting the applied bolus thickness to Aluminium doses represent the doses estimated by the TPS with compensating filter thickness, are given as follows: bolus on the surface of the phantom at point of beam entrance. Table 1 also illustrates the deviations between the calculated and the measured doses for 𝑇𝑡 = (−2 × 10 −7)𝑡 5𝑏 + (1 × 10 −5)𝑡 4𝑏 − (0.0002)𝑡 3 + (0.0017)𝑡 2𝑏 𝑏 + (0.0022)𝑡𝑏 + 0.2539 (14) 𝑏 𝑓𝑟 = (−6 × 10 −8)𝑟6 + (7 × 10−6)𝑟5 − (0.0003)𝑟4 + (0.0063)𝑟3 − (0.0702)𝑟2 + (0.3378 )𝑟 + 0.6123 (15) and 𝑓 −6 5 5𝑑 = (1 × 10 )𝑑 − (5 × 10 )𝑑 4 + (0.0013)𝑑3 − (0.0176)𝑑2 + (0.1116)𝑑 + 0.7521 (16) where 𝑡𝑏 , 𝑟 and 𝑑 are applied bolus thickness within a grid of the compensating filter sheet, equivalent square field size and treatment depth, respectively. 56 Iran J Med Phys, Vol. 15, No. 1, January 2018 Beam Intensity Modulation Using Missing Tissue Approach Samuel Nii Adu Tagoe et al. Table 1. Comparison of doses for case 1 and case 2 Plan Calc. Pt Calculated dose with Measured doses (cGy) Deviation between doses TPS (cGy) (%) Case 1 Case 2 Case 1 Case 2 Case 1 Case 2 1 1 100.00 100.00 101.21 101.52 1.20 1.50 2 98.38 85.08 101.27 88.51 2.85 3.88 3 92.06 80.29 94.89 83.62 2.98 3.98 4 86.56 69.38 90.12 72.23 3.95 3.95 5 82.54 66.79 85.86 69.03 3.87 3.24 2 1 150.00 150.00 153.17 153.66 2.07 2.38 2 148.15 125.75 151.87 130.51 2.45 3.65 3 146.37 123.47 150.73 128.43 2.89 3.86 4 129.54 99.70 133.88 103.31 3.24 3.49 5 126.30 98.48 131.08 103.28 3.65 4.65 6 159.70 94.90 166.08 98.69 3.84 3.84 7 121.30 94.80 125.73 99.10 3.52 4.34 3 1 200.00 200.00 202.55 200.16 1.26 0.08 2 198.17 169.79 202.86 175.62 2.31 3.32 3 196.67 170.48 200.42 175.68 1.87 2.96 4 175.36 140.83 177.63 144.99 1.28 2.87 5 174.27 139.99 179.00 145.28 2.64 3.64 6 220.14 140.00 226.95 144.45 3.00 3.08 7 173.48 138.45 179.88 144.60 3.56 4.25 8 214.61 136.12 221.00 141.64 2.89 3.90 9 167.95 117.51 169.65 120.75 1.00 2.68 10 206.83 110.05 212.99 114.42 2.89 3.82 11 208.25 110.82 216.63 115.25 3.87 3.84 12 130.61 107.56 131.64 109.51 0.78 1.78 13 123.53 58.01 124.97 55.57 1.15 -4.39 4 1 250.00 250.00 254.27 255.57 1.68 2.18 2 248.60 213.25 255.95 219.33 2.87 2.77 3 246.85 214.02 252.82 219.42 2.36 2.46 4 222.63 176.95 227.13 182.67 1.98 3.13 5 220.48 176.70 228.62 183.18 3.56 3.54 6 277.75 175.81 288.84 183.02 3.84 3.94 7 219.26 173.65 224.88 178.10 2.50 2.50 8 270.00 171.55 281.07 178.59 3.94 3.94 9 212.27 148.02 217.47 155.32 2.39 4.70 10 259.69 138.92 263.27 144.56 1.36 3.90 11 263.04 139.88 266.23 144.50 1.20 3.20 12 167.20 135.44 168.18 139.03 0.58 2.58 13 158.14 122.27 162.95 127.30 2.95 3.95 5 1 250.00 250.00 254.01 254.01 1.58 1.58 2 247.82 227.48 255.48 236.17 3.00 3.68 3 247.62 226.01 254.44 219.68 2.68 -2.88 4 225.60 195.12 224.59 203.21 -0.45 3.98 5 224.56 194.58 233.16 204.22 3.69 4.72 6 266.20 194.76 277.23 202.88 3.98 4.00 7 221.67 192.11 228.15 199.78 2.84 3.84 8 261.36 192.08 269.36 197.35 2.97 2.67 9 185.29 171.04 192.35 179.32 3.67 4.62 10 251.41 140.66 258.60 144.68 2.78 2.78 11 - 161.59 - 155.26 - -4.08 12 174.62 157.61 172.38 161.42 -1.30 2.36 13 - 116.81 - 121.49 - 3.85 Calc. Pt: measured doses at various calculation points, TPS: treatment planning system 57 Iran J Med Phys, Vol. 15, No. 1, January 2018 Samuel Nii Adu Tagoe et al. Beam Intensity Modulation Using Missing Tissue Approach Discussion appropriate correction factor to be incorporated for The Aluminium used in this study had a any field size, and specify the proper correction measured density of 2.70±0.03 g/cm3. Furthermore, factor for any treatment depth, respectively. for the field sizes ranged from 3×3 cm2 to 30×30 cm2, Furthermore, the respective regression values and the in air mass attenuation coefficients were were closely approaching or equal to unity for the found to range within 0.05163-0.06000 cm2/g lines of best fits as shown in figures 5, 6 and 7. This (mean: 0.058074±0.002937 cm2/g). The value of signifies that these correlation equations can be used mass attenuation coefficient generally decreased to predict with great accuracy the thickness ratio, with increasing field size due to the enhancement of field size correction factor, and treatment depth scattered radiation contribution to dose at the beam correction factor based on their respective central axis along with field size. correlated treatment parameters. The scattered radiation comes from the jaws of The depth of measurement within the water the collimator system and the radiation source phantom is synonymous to treatment depth with encapsulation itself. As field size increases, the regards to a patient. Using the expression for a surface area of a particular jaw exposed to the correlation equation would facilitate the radiation elevates, which results in the production of determination of a required factor from any related more scattered radiation. The correlation between treatment parameter, and also help in generalizing the mass attenuation coefficient and field size can be the proposed equation. To simplify the expressed with a second degree polynomial. The computational process for converting a bolus measured density and the value of the mean mass thickness to compensating filter thickness, lookup attenuation coefficient of Aluminium for various field tables may be generated for the required factors. sizes compared favourably well with those stated in However, in the present study, Microsoft the literature [22]. spreadsheet (Microsoft Inc., USA) was applied for The aforementioned radiological properties (i.e., performing various calculations. density and mass attenuation coefficient) affect The measurements with and without the radiation scattering and absorption characteristics of compensating filter demonstrated that the the compensating filter material. Therefore, these introduced correction factors for the stipulated properties would have influence on the proposed treatment parameters could be expressed as fifth equation for converting an applied bolus thickness to degree polynomial equations in terms of treatment a compensating filter thickness. The constants within depth and applied bolus thickness, respectively, and the various polynomial equations expressing the a sixth degree polynomial in terms of field size by correction factors would be dependent on the using the graphical considerations and curve fitting radiological properties. analyses of the empirical data. Consequently, it is necessary to verify and The high degree of the polynomial equations validate the density and mass attenuation coefficient necessitates to be cautious about not using treatment of the material chosen for the construction of the parameters beyond the limits applied for the compensating filter prior to the implementation of empirical determination of the correction factors and the proposed approach. It can also be inferred that thickness ratio. Accordingly, lack of attention to this the various correction factors introduced would be issue will constitute uncertainties in a determined dependent on beam energy (quality). Since the dose within the patient. Consequently, it is prudent correction factors are related to scattered radiation, to include all ranges of bolus thickness, field size, and anything that affects the scattering would influence treatment depths as likely to be used for clinical the correction factors. As a result, the correction applications during the commissioning process. factors would be dependent on the collimator system For the field size correction factor, a correlation design of a teletherapy machine. was established for square field sizes. Field size The measurements with the adjusted heights of correction factors may be determined for other non- water above the detector were used to simulate or square field sizes through the concept of equivalent mimic the bolus in the path of beams. Since bolus is square field size [23-37]. The one side of a square composed of tissue-equivalent materials, it was very field size used for the plot corresponds to an convenient to use water to represent the bolus. equivalent square field size. Therefore, the Moreover, representing the bolus with water made it determination of the equivalent square field size for very easy to change the thickness of the bolus during a particular non-square field size and substitution of the measurements. this value into the correlation equation gives the The correlation equations (or coefficients) of the required field size correction factor that needs to be curves, depicted in figures 5, 6 and 7, were used to applied to account for the influence of field size on express and determine the thickness ratio needed to the thickness ratio. convert the bolus thickness to compensating filter All the measurements were performed with thickness for any applied bolus thickness, obtain the isocentric (source to axis distance) irradiation 58 Iran J Med Phys, Vol. 15, No. 1, January 2018 Beam Intensity Modulation Using Missing Tissue Approach Samuel Nii Adu Tagoe et al. technique since it is the therapeutic method of choice made it impossible to simulate situations requiring that is frequently used in the radiotherapy high levels of compensation, which are frequently department where the study is being conducted. The encountered in IMRT. majority of the doses that were measured during the In addition, the use of abutting fields were replication of treatment plans on the telecobalt problematic when there was overlap of fields since machine were higher than those calculated with the the TPS did not allow for entering bolus for TPS. This shows that the proposed approach individual radiation field. The constant thickness of generally undercompensates the beam output. This Aluminium plate used in the measurements to assess could be attributed to the challenges encountered the field size and treatment depth correction factors with the fabrication of the compensating filter to was chosen such that there were always significant obtain the required thickness, which resulted from scattered radiation in the forward direction and low the method used in constructing the filter. Regarding noise to signal ratios. This was done to facilitate the this, other methods may be used for the construction variation of field size or treatment depth whilst of the compensating filter once the shape of the filter keeping the other treatment parameters constant. is determined based on the proposed approach. Nevertheless, there is ongoing research to assess the In the present study, similar approach was used influence of varying the constant thickness of the with a constant thickness ratio for a particular beam Aluminium plate used in the determination of the energy. Furthermore, the effects of field size, field size and treatment depth correction factors. bolus/compensating thickness, and treatment depth were ignored, which resulted in encouraging results Conclusion (measured doses after transmitting through the In the present study, we outlined the procedures compensator showed discrepancies within ±5% from of determining the shape of a compensating filter what was expected) for missing tissue compensation made of Aluminium and constructing the [15]. The application of the proposed approach led to compensating filter for a conventional telecobalt dose discrepancies of ± 4.73% from what was machine to produce a desired dose distribution expected. This value is within the recommended within a patient based on the output of a TPS dose tolerance of ±5% required for dose delivery in performing forward planning, which cannot directly EBRT [38]. simulate the compensating filter. The outputs of the Ignoring the inherent uncertainties associated proposed approach compared favorably well to with film dosimetry [39, 40] supports the assertion those of the TPS based on the dose verification that apart from the separation between the patient measurements performed with samples of calibrated surface and compensating filter, other treatment films in a solid water phantom for various irradiation parameters have marginal influence on the required geometries. thickness ratio for a particular beam energy [15, 41]. The discrepancies in the measured doses, Nonetheless, the dose verification procedure needs compared to those of the TPS, were within ±4.73% to be repeated with other two-dimensional array (mean of 2.98±1.05%). This signifies that the detectors based on ionization chamber or diode. proposed approach can be recommended for clinical In other studies investigating compensating application. Therefore, the use of the proposed filters, some of the researchers incorporated the approach could facilitate the generation of intensity- effects of off-axis distance in their respective modulated beam with limited resources using the approaches for the determination of the missing tissue approach rendering encouraging compensating filter thickness. This was due to the results. fact that most of their beam data were acquired on The proposed approach might be suitable for the beam central axis and compensation needed to beam intensity modulations where the possibility of be done at other parts of the radiation field other realizing the beam intensity map is not available. than on the beam central axis [42, 43]. It is also This approach can be used for missing tissue expected that if the effects of the off-axis distance are compensation in the treatment of head and neck also considered in the proposed approach, there will cancers, tangential breast irradiation, and total body be much improvement in the output of the proposed irradiation with photon beams. It can also be used to approach. account for tissue heterogeneities, especially in the Nevertheless, there were some challenges with treatment of lung cancers. Generally, the proposed the proposed approach. In this regard, the approach can be used to enhance the conformity determination of the applied bolus thicknesses for index of dose coverage in EBRT. beams with oblique incidence relative to the surface of the phantom were quiet challenging and Acknowledgement cumbersome. Moreover, there was limitation with The completion of this study could not have been the thickness of the bolus that could be applied since possible without the involvement and assistance of it should not have been more than 14 cm. This issue co-workers at the National Centre for Radiotherapy, 59 Iran J Med Phys, Vol. 15, No. 1, January 2018 Samuel Nii Adu Tagoe et al. Beam Intensity Modulation Using Missing Tissue Approach Korle Bu Teaching Hospital, Accra, Ghana, whose 10. George R, Keall PJ, Kini VR, et al. Quantifying the names may not all be enumerated. Their effect of intrafraction motion during breast IMRT contributions are sincerely appreciated and planning and dose delivery. Med Phys 2003; 30: gratefully acknowledged. However, I would like to 552–62. DOI: 10.1118/1.1543151. 11. Buckey CR, Stathakis S, Papanikolaou N. The inter- express my deep appreciation and indebtedness and intrafraction reproducibilities of three common particularly to Professor A. W. K. Kyere and C. IMRT delivery techniques. Med. Phys. 2010; 37( 9): Schandorf, Dr. Joel Yarney and S. Y. Opoku, and my 4854 - 60. DOI: 10.1118/1.3476413. PhD advisory team assigned by the University of 12. Chang SX, Cullip TJ, Deschesne KM. Intensity Cape Coast, Ghana, for their endless support as well modulation delivery techniques: “Step & shoot” MLC as kind and understanding spirit during the research auto sequence versus the use of a modulator. Med period. Phys. 2000 May; 27(5): 948–59. DOI: I would also like to express my gratitude to the 10.1118/1.598989. manager of the Sweden Ghana Medical Centre, Accra, 13. Sharma SD. Challenges of small photon field dosimetry are still challenging. Journal of medical Ghana, for letting me have access to their three- physics/Association of Medical Physicists of India. dimensional motorized water phantom (Blue 2014 Jul;39(3):131-2. DOI: 10.4103/0971- Phantom2) for the beam data acquisition. 6203.138998. . Another thanks goes to all relatives, friends, and 14. 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