Comparison of planned and measured rectal dose in-vivo during high dose rate Cobalt-60 brachytherapy of cervical cancer

Cobalt-60 (Co-60) is a relatively new source for the application of high-dose rate (HDR) brachytherapy. Radiation dose to the rectum is often a limiting factor in achieving the full prescribed dose to the target during brachytherapy of cervical cancer. The aim of this study was to measure radiation doses to the rectum in-vivo during HDR Co-60 brachytherapy. A total of eleven HDR brachytherapy treatments of cervical cancer were recruited in this study. A series of diodes incorporated in a rectal probe was inserted into the patient's rectum during each brachytherapy procedure. Real-time measured rectal doses were compared to calculated doses by the treatment planning system (TPS). The differences between calculated and measured dose ranged from 8.5% to 41.2%. This corresponds to absolute dose differences ranging from 0.3 Gy to 1.5 Gy. A linear relationship was observed between calculated and measured doses with linear regression R² value of 0.88, indicating close association between the measured and calculated doses. In general, absorbed doses for the rectum as calculated by TPS were observed to be higher than the doses measured using the diode probe. In-vivo dosimetry is an important quality assurance method for HDR brachytherapy of cervical cancer. It provides information that can contribute to the reduction of errors and discrepancies in dose delivery. Our study has shown that in-vivo dosimetry is feasible and can be performed to estimate the dose to the rectum during HDR brachytherapy using Co-60.     

End-to-end dosimetric audit: A novel procedure developed for Irish HDR brachytherapy centres

PurposeA dosimetric audit of Ir-192 high dose rate (HDR) brachytherapy remote after-loading units was carried out in 2019. All six brachytherapy departments on the island of Ireland participated in an end-to-end test and in a review of local HDR dosimetry procedures.Materials and methodsA 3D-printed customised phantom was created to position the following detectors at known distances from the HDR source: a Farmer ionization chamber, GafChromic film and thermoluminescent dosimeters (TLDs). Dedicated HDR applicator needles were used to position an Ir-192 source at 2 cm distance from these detectors. The end-to-end dosimetry audit pathway was performed at each host site and included the stages of imaging, applicator reconstruction, treatment planning and delivery. Deviations between planned and measured dose distributions were quantified using gamma analysis methods. Local procedures were also discussed between auditors and hosts.ResultsThe mean difference between Reference Air Kerma Rate (RAKR) measured during the audit and RAKR specified by the vendor source certificate was 1.3%. The results of end-to-end tests showed a mean difference between calculated and measured dose of 2.5% with TLDs and less than 0.5% with Farmer chamber measurements. GafChromic films showed a mean gamma passing rates of >95% for plastic and metal applicators with 2%/1 mm global tolerance criteria.ConclusionsThe results of this audit indicate dosimetric consistency between centres. The ‘end to end’ dosimetry audit methodology for HDR brachytherapy has been successfully implemented in a multicentre environment, which included different models of Ir-192 sources and different treatment planning systems.The ability to create a 3D-printed water-equivalent phantom customised to accurately position all three detector types simultaneously at controlled distances from the Ir-192 source under evaluation gives good reproducibility for end-to-end methodology.     

Dosimetric verification of a high dose rate brachytherapy treatment planning system in homogeneous and heterogeneous media

ObjectivesTo verify the dosimetric accuracy of treatment plans in high dose rate (HDR) brachytherapy by using Gafchromic EBT2 film and to demonstrate the adequacy of dose calculations of a commercial treatment planning system (TPS) in a heterogeneous medium.MethodsAbsorbed doses at chosen points in anatomically different tissue equivalent phantoms were measured using Gafchromic EBT2 film. In one case, tandem ovoid brachytherapy was performed in a homogeneous cervix phantom, whereas in the other, organ heterogeneities were introduced in a phantom to replicate the upper thorax for esophageal brachytherapy treatment. A commercially available TPS was used to perform treatment planning in each case and the EBT2 films were irradiated with the HDR Ir-192 brachytherapy source.ResultsFilm measurements in the cervix phantom were found to agree with the TPS calculated values within 3% in the clinically relevant volume. In the thorax phantom, the presence of surrounding heterogeneities was not seen to affect the dose distribution in the volume being treated, whereas, a little dose perturbation was observed at the lung surface. Doses to the spinal cord and to the sternum bone were overestimated and underestimated by 14.6% and 16.5% respectively by the TPS relative to the film measurements. At the trachea wall facing the esophagus, a dose reduction of 10% was noticed in the measurements.ConclusionsThe dose calculation accuracy of the TPS was confirmed in homogeneous medium, whereas, it was proved inadequate to produce correct dosimetric results in conditions of tissue heterogeneity.     

Integration of rotatable tandem applicator to conventional ovoid applicator toward complete framework of intensity modulated brachytherapy (IMBT) for cervical cancer

A new tandem applicator with tungsten shield for Ir-192 radiation source used in intra-cavitary brachytherapy (ICBT) enabled intensity modulated brachytherapy (IMBT) in cervical cancer treatment through fluence-modulation by rotating shield. Our previous work employed group-wise and element-wise sparsity constraints for plan optimization of tandem applicator to minimizes the number of activated angles and source dwell points for delivery efficiency. It, however, did not incorporate the ovoid applicators into the optimizing process, which is generally used to prevent cancer recurrence. To integrate ovoid applicators to the new tandem applicator, this work proposed a comprehensive framework that modifies 1) dose deposition matrix for inverse planning, and 2) plan optimizing algorithm. The dose deposition matrix was newly formulated by the Monte-Carlo simulated dose distribution for 10 positions of ovoid applicators, followed by combining those with tandem-associated dose deposition matrix. The plan optimizing algorithm decomposed entire elements into tandem and ovoid applicators, which were governed by different constraints adaptive to specified plan objectives. The integrated framework was compared against conventional ICBT, and IMBT with tandem only for three patients with asymmetric dose distributions. Integrated IMBT framework resulted in the most optimal plans. Including fluence-modulation by rotating-shield outperformed conventional ICBT in dose sparing to critical organs. Adopting ovoid applicators to the optimization yielded more conformal dose distribution around inferior, laterally expanded region of target volume. The resulting plans reduced D_5cc and D_2cc by 30.9% and 27.8% for critical organs over conventional ICBT, and by 20.6% and 21.5% for target volume over IMBT with tandem only.     

Radiation dose verification of an X-ray based blood irradiator using EBT3 radiochromic films calibrated using Gamma Knife machine

AimBlood irradiators (BI) initial acceptance testing and routine annual dosimetry checks require radiation dose measurements in order to comply with regulatory requirements.BackgroundTraditionally thermo-luminescence dosimeters (TLD) have been used to measure the dose. The EBT3 film is reported to be a better dosimeter for low energy X-rays than its predecessors EBT2 and EBT. To the best of our knowledge, the use of EBT3 films to perform dosimetry on X-ray based BI has not been reported yet.Materials and methodsWe performed routine radiation dosimetry checks using EBT3 films on a new X-ray based BI and compared the results with TLD dosimetry. Calibration films were irradiated with radiation beam from a Co-60 Gamma Knife (GK) radiosurgery machine and, alternatively, using an Ir-192 high dose rate (HDR) brachytherapy device. The films were calibrated to cover a wide dose range from 1 to 40 Gy. Such a wide dose range has not been reported yet in BI film dosimetry.ResultsWe obtained a relative difference of about 6.6% between doses measured using TLD and those measured using EBT3 films. Both irradiation methods using GK or HDR were found to be adequate for the calibration of the EBT3 Gafchromic films.ConclusionsWe recommend the use of EBT3 films in routine X-ray based BI dosimetry checks. The presented method takes advantage of available radiotherapy equipment that can be efficiently used for EBT3 films calibration. The method is fast, reproducible and saves valuable medical physicist's time.     

Evaluation of rectal dose discrepancies between planned and in vivo dosimetry using MOSkin detector and PTW 9112 semiconductor probe during 60Co HDR CT-based intracavitary cervix brachytherapy

PurposeDose to the rectum during brachytherapy treatment may differ from an approved treatment plan which can be quantified with in vivo dosimetry (IVD). This study compares the planned with in vivo doses measured with MOSkin and PTW 9112 rectal probe in patients undergoing CT based HDR cervical brachytherapy with Co-60 source.MethodsDose measurement of a standard pear-shaped plan carried out in phantom to verify the MOSkin dose measurement accuracy. With MOSkin attached to the third diode, RP3 of the PTW 9112, both detectors were inserted into patients’ rectum. The RP3 and MOSkin measured doses in 18 sessions as well as the maximum measured doses from PTW 9112, RP_max in 48 sessions were compared to the planned doses.ResultsPercentage dose differences ΔD (%) in phantom study for two MOSkin found to be 2.22 ± 0.07% and 2.5 ± 0.07%. IVD of 18 sessions resulted in ΔD(%) of −16.3% to 14.9% with MOSkin and ΔD(%) of −35.7% to −2.1% with RP3. In 48 sessions, RP_max recorded ΔD(%) of −37.1% to 11.0%. MOSkin_measured doses were higher in 44.4% (8/18) sessions, while RP3_measured were lower than planned doses in all sessions. RP_max_measured were lower in 87.5% of applications (42/47).ConclusionsThe delivered doses proven to deviate from planned doses due to unavoidable shift between imaging and treatment as measured with MOSkin and PTW 9112 detectors. The integration of MOSkin on commercial PTW 9112 surface found to be feasible for rectal dose IVD during cervical HDR ICBT.     

Utilization of cone-beam CT for offline evaluation of target volume coverage during prostate image-guided radiotherapy based on bony anatomy alignment

AimTo assess target volume coverage during prostate image-guided radiotherapy based on bony anatomy alignment and to assess possibility of safety margin reduction.BackgroundImplementation of IGRT should influence safety margins. Utilization of cone-beam CT provides current 3D anatomic information directly in irradiation position. Such information enables reconstruction of the actual dose distribution.Materials and methodsSeventeen prostate patients were treated with daily bony anatomy image-guidance. Cone-beam CT (CBCT) scans were acquired once a week immediately after bony anatomy alignment. After the prostate, seminal vesicles, rectum and bladder were contoured, the delivered dose distribution was reconstructed. Target dose coverage was evaluated by the proportion of the CTV encompassed by the 95% isodose. Original plans employed a 1 cm safety margin. Alternative plans assuming a smaller 7 mm margin between CTV and PTV were evaluated in the same way. Rectal and bladder volumes were compared with the initial ones. Rectal and bladder volumes irradiated with doses higher than 75 Gy, 70 Gy, 60 Gy, 50 Gy and 40 Gy were analyzed.ResultsIn 12% of reconstructed plans the prostate coverage was not sufficient. The prostate underdosage was observed in 5 patients. Coverage of seminal vesicles was not satisfactory in 3% of plans. Most of the target underdosage corresponded to excessive rectal or bladder filling. Evaluation of alternative plans assuming a smaller 7 mm margin revealed 22% and 11% of plans where prostate and seminal vesicles coverage, respectively, was compromised. These were distributed over 8 and 7 patients, respectively.ConclusionSufficient dose coverage of target volumes was not achieved for all patients. Reducing of safety margin is not acceptable. Initial rectal and bladder volumes cannot be considered representative for subsequent treatment.     

In vivo dosimetry of the rectum in image-guided adaptive interstitial-intracavitary brachytherapy of cervix cancer – A feasibility study

Aim and backgroundTo investigate the feasibility of in vivo rectal dosimetry in image-guided adaptive brachytherapy of cervical cancer.Materials and methodsError of measurement of dose rate in a semiconductor diode probe was investigated depending on the distance and angle in water, and on temperature in a polymethyl methacrylate phantom using an Ir-192 source. Furthermore, the difference between the measured and calculated dose was analysed in the interstitial brachytherapy of 30 cervix cancer patients. The relationship between in vivo measured dose, calculated dose in the point of the diode, calculated maximal dose in the point of the diodes and calculated maximal dose of the rectum were examined.ResultsThe dosimeter measured with 85% accuracy at more than 5 cm from the source, but within a closer distance the accuracy decreased significantly. At 45–90° angle, the device measured with a 15% error. The error increased with the temperature, 22% at 35 °C. In 8 cases (26.7%) the maximal dose was measured in the correct diode. The device measured 73% of the calculated dose in the point of the diode. The maximum of the calculated doses of diodes was 60% of the calculated maximal dose. The in vivo measured dose was 35% of the calculated maximal dose.ConclusionsUnder treatment conditions, the semiconductor diode does not provide reliable measured data. The probe pushes the rectal wall closer to the high dose areas and underestimates the dose of it. Semiconductor probe is not recommended for in vivo dosimetry of the rectum in image-guided brachytherapy of cervical cancer.     

Characterization of commercial MOSFET detectors and their feasibility for in-vivo HDR brachytherapy

AimThe present study was to investigate the use of MOSFET as an vivo dosimeter for the application of Ir-192 HDR brachytherapy treatments.Material and methodsMOSFET was characterized for dose linearity in the range of 50–1000 cGy, depth dose dependence from 2 to 7 cm, angular dependence. Signal fading was checked for two weeks.Result and discussionDose linearity was found to be within 2% in the dose range (50–1000 cGy). The response varied within 8.07% for detector-source distance of 2–7 cm. The response of MOSFET with the epoxy side facing the source (0 degree) is the highest and the lowest response was observed at 90 and 270 degrees. Signal was stable during the study period.ConclusionThe detector showed high dose linearity and insignificant fading. But due to angular and depth dependence, care should be taken and corrections must be applied for clinical dosimetry.     

A phantom study on bladder and rectum dose measurements in brachytherapy of cervix cancer using FBX aqueous chemical dosimeter

The ferrous sulphate-benzoic acid-xylenol orange (FBX) chemical dosimeter, due to its aqueous form can measure average volume doses and hence may overcome the limitations of point dosimetry. The present study was undertaken to validate the use of FBX dosimeter for rectum and bladder dose measurement during intracavitary brachytherapy (ICBT) and transperineal interstitial brachytherapy (TIB). We filled cylindrical polypropylene tubes (PT) and Foley balloons (FB) with FBX solution and used them as substitutes for rectum and bladder dose measurements respectively. A water phantom was fabricated with provision to place the Fletcher-type ICBT and MUPIT template applicators, and FBX filled PT and FB within the phantom. The phantom was then CT scanned for treatment planning and subsequent irradiation. Our results show that the average difference between DVH derived dose value and FBX measured dose is 3.5% (PT) and 13.7% (FB) for ICBT, and 9% (PT) and 9.9% (FB) for TIB. We believe that the FBX system should be able to provide accuracy and precision sufficient for routine quality assurance purposes. The advantage of the FBX system is its water equivalent composition, average volume dose measuring capability, and energy and temperature independent response as compared to TLD or semiconductor dosimeters. However, detailed studies will be needed with regards to its safety before actual in-vivo dose measurements are possible with the FBX dosimeter.     

Optimization of catheter’s implementation in the mold,in the case of vaginal HDR brachytherapy treatment

BackgroundThe purpose of this study was to evaluate and compare results obtained in high dose rate (HDR) brachytherapy treatment of vaginal cancer. Different catheters distributions inside the custom mold were explored. The difference between those distributions is the position of the posterior catheter located near the rectum in the actual custom mold applicator used in different hospitals, each one having a catheter displacement of 0.5 which is equal to the length of a step position. The best catheters distribution offering an optimal dose distribution: better coverage of the clinical target volume (CTV), while reducing the dose received by organs at risk (OARs), were discussed.Materials and methodsA group of 60 patients treated with HDR brachytherapy, alone or in combination with external radiotherapy, was investigated. A custom mold is normally used for HDR brachytherapy vaginal cancer treatment. Three different geometrical positions of the catheters (G1, G2 and G3) and, consequently, 3 different dosimetries were simulated out for each patient on the CT images, using the Oncentra planning system. The coverage of the CTV was studied.ResultsThe average volume treated was 30.46 cc (min = 9.8 cc, max = 70.86 cc). The total prescribed dose, including external and internal radiotherapy, was 80 Gy. We evaluated conformity index (CI), dose homogeneity index (DHI) and conformality index (COIN) indices for the three implantation geometries to reach the same coverage criteria of the CTV. The D2cc parameter allowed the evaluation of the dose received by the OARs. For the rectum, a dose reduction of 9.67% (range 0.29–32.86) was obtained with the second geometry of implantation compared to 10.14% (range 1.43–28.33) with the third geometry. For the bladder, the second geometry of implantation showed a better preservation for this organ [15.93% (range 0.86–58.71) vs. 8.35% (range 0.33–30.43) with the third geometry]. The sigmoid was more protected using the second plan of implantation as well [6.33% (range 0.14–40.71) for the second implantation compared to 5.95% (range 0.33–36) for the third implantation].ConclusionsG2 and G3 catheters’ distribution, having catheter position farther from the mold wall and so from the vaginal wall compared to the catheter position applied showed a better protection for the OARs while giving the same prescribed dose for the CTV.     

Monte Carlo Study of Radiation Dose Enhancement by Gadolinium in Megavoltage and High Dose Rate Radiotherapy

MRI is often used in tumor localization for radiotherapy treatment planning, with gadolinium (Gd)-containing materials often introduced as a contrast agent. Motexafin gadolinium is a novel radiosensitizer currently being studied in clinical trials. The nanoparticle technologies can target tumors with high concentration of high-Z materials. This Monte Carlo study is the first detailed quantitative investigation of high-Z material Gd-induced dose enhancement in megavoltage external beam photon therapy. BEAMnrc, a radiotherapy Monte Carlo simulation package, was used to calculate dose enhancement as a function of Gd concentration. Published phase space files for the TrueBeam flattening filter free (FFF) and conventional flattened 6MV photon beams were used. High dose rate (HDR) brachytherapy with Ir-192 source was also investigated as a reference. The energy spectra difference caused a dose enhancement difference between the two beams. Since the Ir-192 photons have lower energy yet, the photoelectric effect in the presence of Gd leads to even higher dose enhancement in HDR. At depth of 1.8 cm, the percent mean dose enhancement for the FFF beam was 0.38±0.12, 1.39±0.21, 2.51±0.34, 3.59±0.26, and 4.59±0.34 for Gd concentrations of 1, 5, 10, 15, and 20 mg/mL, respectively. The corresponding values for the flattened beam were 0.09±0.14, 0.50±0.28, 1.19±0.29, 1.68±0.39, and 2.34±0.24. For Ir-192 with direct contact, the enhanced were 0.50±0.14, 2.79±0.17, 5.49±0.12, 8.19±0.14, and 10.80±0.13. Gd-containing materials used in MRI as contrast agents can also potentially serve as radiosensitizers in radiotherapy. This study demonstrates that Gd can be used to enhance radiation dose in target volumes not only in HDR brachytherapy, but also in 6 MV FFF external beam radiotherapy, but higher than the currently used clinical concentration (>5 mg/mL) would be needed.     

Dosimetric evaluation of image based brachytherapy using tandem ovoid and tandem ring applicators

Aim

The aim of the study is to evaluate the differences in dosimetry between tandem-ovoid and tandem-ring gynaecologic brachytherapy applicators in image based brachytherapy.

A dosimetry method in the transverse plane of HDR Ir-192 brachytherapy source using gafchromic EBT2 film

Radiochromic film dosimetry is increasingly used in brachytherapy applications for its higher resolution ability as compared to other experimental methods. The present study was aimed to assess the accuracy and suitability of use of the improved radiochromic film model, Gafchromic EBT2, to evaluate the dose distribution in the transverse plane of microselectron HDR ¹⁹²Ir source.A specially designed and locally fabricated Polymethyl methacrylate (PMMA) phantom was used in this work for the experimental measurement of dose distribution around the source in its transverse plane. The AAPM TG-43U1 recommended radial dose function, g (r), and dose rate constant, Λ, for the source were measured using Gafchromic EBT2 film and thermoluminescent dosimeters (TLD). The EBT2 film measured dosimetric quantities were validated against their values obtained from the TLD measurements and previously published values for the same source available in literature.The dose rate constant and radial dose function for microselectron HDR ¹⁹²Ir source obtained from Gafchromic EBT2 film measurements are in agreement with their TLD measured results within 3.9% and 2.8% respectively. They also agree within the accepted range of uncertainty with their experimental and Monte Carlo calculated results reported in literature.This work demonstrates the suitability of using Gafchromic EBT2 film dosimetry in characterization of dose distribution in the transverse plane of HDR Ir-192 source. This is a more efficient method than TLD dosimetry at discrete and distant positions. Relative to TLD dosimetry, it is found to be better reproducible, easy to use and a less expensive method of dosimetry.     

Fetal dose measurements and shielding efficiency assessment in a custom setup of 192Ir brachytherapy for a pregnant woman with breast cancer

PurposeTo assess the radiation dose to the fetus of a pregnant patient undergoing high-dose-rate (HDR) ¹⁹²Ir interstitial breast brachytherapy, and to design a new patient setup and lead shielding technique that minimizes the fetal dose.MethodsRadiochromic films were placed between the slices of an anthropomorphic phantom modeling the patient. The pregnant woman was seated in a chair with the breast over a table and inside a leaded box. Dose variation as a function of distance from the implant volume as well as dose homogeneity within a representative slice of the fetal position was evaluated without and with shielding.ResultsWith shielding, the peripheral dose after a complete treatment ranged from 50 cGy at 5 cm from the caudal edge of the breast to <0.1 cGy at 30 cm. The shielding reduces absorbed dose by a factor of two near the breast and more than an order of magnitude beyond 20 cm. The dose is heterogeneous within a given axial plane, with variations from the central region within 50%. Interstitial HDR ¹⁹²Ir brachytherapy with breast shielding can be more advantageous than external-beam radiotherapy (EBRT) from a radiation protection point of view, as long as the distance to the uterine fundus is higher than about 10 cm. Furthermore, the weight of the shielding here proposed is notably lower than that needed in EBRT.ConclusionsShielded breast brachytherapy may benefit pregnant patients needing localized radiotherapy, especially during the early gestational ages when the fetus is more sensitive to ionizing radiation.     

Calibration of 192Ir high dose rate brachytherapy source using different calibration procedures

Aim

To calibrate Ir-192 high dose rate (HDR) brachytherapy source using different calibration methods and to determine the accuracy and suitability of each method for routine calibrations.

Background

The source calibration is an essential part of the quality assurance programme for dosimetry of brachytherapy sources. The clinical use of brachytherapy source requires an independent measurement of the air kerma strength according to the recommendations of medical physics societies.

Materials and methods

The Ir-192 HDR brachytherapy source from Gammamed plus machine (Varian Medical Systems, Palo Alto, CA) was calibrated using three different procedures, one using the well-type ionization chamber, second by the in-air calibration method and third using solid water phantoms. The reference air kerma rate (RAKR) of the source was determined using Deutsche Gesellschaft fur Medizinische Physik (DGMP) recommendations.

Results

The RAKR determined using different calibration methods are in good agreement with the manufacturer stated value. The mean percentage variations of 0.21, −0.94, −0.62 and 0.58 in RAKR values with respect to the manufacturer quoted values were observed with the well-type chamber, in-air calibration, cylindrical phantom and slab phantom measurements, respectively.

Conclusion

Measurements with a well-type chamber are relatively simple to perform. For in-air measurements, the indigenously designed calibration jig provides an accurate positioning of the source and chamber with minimum scatter contribution. The slab phantom system has an advantage that no additional phantom and chamber are required other than those used for external beam therapy dosimetry. All the methods of calibration discussed in this study are effective to be used for routine calibration purposes.     

Application of Monte Carlo calculations for validation of a treatment planning system in high dose rate brachytherapy

AimThe accuracy of treatment planning systems is of vital importance in treatment outcomes in brachytherapy. In the current study the accuracy of dose calculations of a high dose rate (HDR) brachytherapy treatment planning system (TPS) was validated using the Monte Carlo method.Materials and methodsThree ⁶⁰Co sources of the GZP6 afterloading brachytherapy system were modelled using MCNP4C Monte Carlo (MC) code. The dose distribution around all the sources was calculated by MC and a dedicated treatment planning system. The results of both methods were compared.ResultsThere was good agreement (<2%) between TPS and MC calculated dose distributions except at a point near the sources (<1 cm) and beyond the tip of the sources.ConclusionsOur study confirmed the accuracy of TPS calculated dose distributions for clinical use in HDR brachytherapy.     

Using matrix summation method for three dimensional dose calculation in brachytherapy

AimThe purpose of this study is to calculate radiation dose around a brachytherapy source in a water phantom for different seed locations or rotation the sources by the matrix summation method.BackgroundMonte Carlo based codes like MCNP are widely used for performing radiation transport calculations and dose evaluation in brachytherapy. But for complicated situations, like using more than one source, moving or rotating the source, the routine Monte Carlo method for dose calculation needs a long time running.Materials and methodsThe MCNPX code has been used to calculate radiation dose around a ¹⁹²Ir brachytherapy source and saved in a 3D matrix. Then, we used this matrix to evaluate the absorbed dose in any point due to some sources or a source which shifted or rotated in some places by the matrix summation method.ResultsThree dimensional (3D) dose results and isodose curves were presented for ¹⁹²Ir source in a water cube phantom shifted for 10 steps and rotated for 45 and 90° based on the matrix summation method. Also, we applied this method for some arrays of sources.ConclusionThe matrix summation method can be used for 3D dose calculations for any brachytherapy source which has moved or rotated. This simple method is very fast compared to routine Monte Carlo based methods. In addition, it can be applied for dose optimization study.