Feasibility of tungsten functional paper in electron grid therapy: a Monte Carlo study

Double enhancement effect of a surface dose with tungsten rubber bolus in photon radiotherapy for keloids and superficial tumors

To clarify the dosimetric characteristics of a real-time variable shape rubber-containing tungsten (STR) bolus in a clinical plan and investigate the efficacy of the STR bolus in photon radiotherapy for keloids and other superficial tumors. A 5 mm gel bolus or 1 mm STR bolus was placed on a solid water phantom. Tangential irradiation was performed using a TomoTherapy Radixact-X9 and 6 MV X-ray flattening-filter-free beam, and the surface dose was measured with radiochromic film. Clinical-like plans (TomoDirect; TD and TomoHelical; TH) were applied with the same geometry and the dose distributions were measured. The increase in surface dose by the build-up effect and backscatter was 37.7% and 8.0% for the gel bolus, and 40.5% and 26.4% for the STR bolus, respectively. In the TD and TH plans, the increase in surface dose was 27.4% and 48.3% for the gel bolus, and 39.0% and 63.2% for the STR bolus. Similary, changes in the sagittal plane dose were - 3.9% and 6.1% for the gel bolus, and - 6.3% and 6.9% for the STR bolus. The STR bolus effectively increased the surface dose by the build-up effect and backscatter in photon radiotherapy for keloids and other superficial tumors.

Combining FLASH and spatially fractionated radiation therapy: The best of both worlds

FLASH radiotherapy (FLASH-RT) and spatially fractionated radiation therapy (SFRT) are two new therapeutical strategies that use non-standard dose delivery methods to reduce normal tissue toxicity and increase the therapeutic index. Although likely based on different mechanisms, both FLASH-RT and SFRT have shown to elicit radiobiological effects that significantly differ from those induced by conventional radiotherapy. With the therapeutic potential having been established separately for each technique, the combination of FLASH-RT and SFRT could therefore represent a winning alliance. In this review, we discuss the state of the art, advantages and current limitations, potential synergies, and where a combination of these two techniques could be implemented today or in the near future.

Estimating radiation exposure of the brain of a physician with a protective flap in interventional radiology: A phantom study

PURPOSE

The efficiency of protective equipment for the brain has not been verified at the left anterior oblique (LAO) position, which is commonly used in clinical procedures. The purpose of this study was to investigate radiation exposure of the brain in interventional radiology (IR) and the shielding ability of a new protective flap.

METHODS

We made a flap that combined a protective cap with a left lateral face shield. The flap was made of tungsten-containing rubber (TCR). An anthropomorphic head phantom was placed at the physician's position, and air kerma rates (μGy/min and μGy/15s) were measured by electronic dosimeter at three locations: the surface of the left side of the head, and the left and right temporal lobes with the protective cap and the flap in fluoroscopy and cine modes. The X-ray tube was at the lower left side of the physician, and its angles were LAO60 and LAO60CAU40. The tube voltage (95-125 kV), tube current (4.7-732 mA), and air kerma rate (27.8-1078 mGy/min) were automatically adjusted by the X-ray system. We obtained the cap and the flap shielding efficiencies.

RESULTS

In cine mode at LAO60CAU40, the shielding efficiencies on the surface of the left side of the head and left temporal lobe with the cap were 92.6% and 5.1%, respectively, and the corresponding shielding efficiencies with the flap were 92.5% and 86.1%, respectively. The flap can reduce radiation exposure of the brain more than the cap alone.

CONCLUSIONS

At the left anterior oblique in interventional radiology, the flap can reduce exposure to the brain.

Dosimetric characteristics of a thin bolus made of variable shape tungsten rubber for photon radiotherapy

In this study, we aim to clarify the dosimetric characteristics of a real time variable shape rubber containing tungsten (STR) as a thin bolus in 6-MV photon radiotherapy. The percentage depth doses (PDDs) and lateral dose profiles (irradiation field = 10 × 10  cm²) in the water-equivalent phantom were measured and compared between no bolus, a commercial 5-mm gel bolus, and 0.5-, 1-, 2-, and 3-mm STR boluses. The characteristics of the PDDs were evaluated according to relative doses at 1 mm depth (D_1mm) and depth of maximum dose (d_max). To determine the distance of the shift caused by the STR bolus, the PDD value at a depth of 100 mm without a bolus was obtained. For each STR thickness, the difference between the depth corresponding to this PDD value and 100 mm was calculated. The penumbra size and width of the 50% dose were evaluated using lateral dose profiles. The D_1mm with no bolus, 5-mm gel bolus, and 0.5-, 1-, 2-, and 3-mm STR boluses were 47.6%, 91.5%, 78.2%, 86.6%, 89.3%, and 89.4%, respectively, and the respective d_max values were 15, 10, 13, 12, 11, and 10 mm. The shifting distance of the 0.5-, 1-, 2-, and 3-mm STR boluses were 2.7, 4.4, 4.8, and 4.9 mm, respectively. There were no differences for those in lateral dose profiles. The 1-mm-thick STR thin bolus shifted the depth dose profile by 4.4 mm and could be used as a customized bolus for photon radiotherapy.

Dosimetric evaluation of skin collimation with tungsten rubber for electron radiotherapy: A Monte Carlo study

PURPOSE

Skin collimation provides a sharp penumbra for electron beams, while the effect of bremsstrahlung from shielding materials is a concern. This phantom study was conducted to evaluate the safety and efficacy of a real-time variable shape rubber containing-tungsten (STR) that can be placed on a patient's skin.

METHODS

Electron beam profiles were acquired with the STR placed on a water-equivalent phantom and low melting-point alloy (LMA) placed at the applicator according to commonly used procedures (field sizes: 20- and 40-mm diameters). Depth and lateral dose profiles for 6- and 12-MeV electron beams were obtained by Monte Carlo (MC) simulations and were benchmarked against film measurements. The width of the off-axis distance between 80% and 20% doses (P80-20 ) and the maximum dose were obtained from the lateral dose profiles. Bremsstrahlung emission was analyzed by MC simulations at the depth of maximum dose (R100 ).

RESULTS

The depth dose profiles calculated by the MC simulations were consistently within 2% of the measurements. The P80-20 at R100 for 20- and 40-mm diameters were 4.0 mm vs. 7.6 mm (STR vs. LMA) and 4.5 mm vs. 9.2 mm, respectively, for the 6-MeV electron beam with 7.0-mm-thick STR, and 2.7 mm vs. 5.6 mm and 4.5 mm vs. 7.1 mm, respectively, for the 12-MeV electron beam with 12.0-mm-thick STR. A hotspot was not observed on the lateral dose profiles obtained with the STR at R100 . The bremsstrahlung emission under the region shielded by the STR was comparable to that obtained with the LMA, even though the STR was placed on the surface of the phantom.

CONCLUSIONS

Skin collimator with STR provided superior dosimetric characteristics and comparable bremsstrahlung emission to LMA collimator at the applicator. STR could be a new tool for the safe and efficient delivery of electron radiotherapy.

[Application of Real-time Variable Shape Tungsten Rubber for Nail Radiation Protection in the Total Skin Electron Beam (TSEB) Therapy]

PURPOSE

This study investigated whether real-time variable shape tungsten rubber (STR) could be applied for nail radiation protection in total skin electron beam (TSEB) therapy.

METHODS

Simulated finger phantoms were made from syringes filled with physiological saline of volumes 5, 10, 20, and 30 ml (inner diameters of 14.1, 17.0, 21.7, and 25.3 mm, respectively). Gafchromic film was applied to the phantom, and lead (thickness 1-3 mm) or STR (thickness 1-4 mm) with an area of 4´1.5 cm was used to cover the film. A 6 MeV electron beam with an 8 mm acrylic board was then used to irradiate the phantom. The source-surface distance (SSD) was 444 cm, the field size was 36´36 cm at SSD of 100 cm without an electron applicator, and the monitor unit was 2000 MU. The shielding rates were obtained from the dose profiles.

RESULTS

The mean values of the shielding rate values for all phantoms were 50.1, 97.6, and 98.7% for 1, 2, and 3 mm of lead, respectively, and -13.6, 53.9, 91.2, and 99.4% for 1, 2, 3, and 4 mm of STR, respectively.

CONCLUSION

STR with a thickness of 4 mm had the same shielding properties as lead with a thickness of 3 mm, which was an approximately 100% shielding rate. STR could therefore be used in TSEB therapy instead of lead.

[Dosimetric Characteristics of a Real Time Shapeable Tungsten Containing Rubber with Electron Beams]

PURPOSE

This study investigated the dosimetric characteristics of electron beams shaped with a real-time shapeable tungsten-containing rubber (STR) collimator.

METHODS

Circular irradiation fields of 40 mm diameter were shaped using STR or low melting-point alloy (LMA) placed on the electron applicator. The STR heated with approximately 70-degree warm water was molded into the template bottom of the applicator. Percent depth doses (PDDs) and lateral dose profiles of 6 and 12 MeV electron beams were measured and compared between STR and LMA. For the PDDs, the depths of maximum dose (d_max), 90% dose (d₉₀), and 80% dose (d₈₀) were evaluated. For the lateral dose profiles, penumbra as the width of the off-axis distance from 80% to 20% doses and treatment diameter covering over 90% dose were evaluated at the surface, d_max, d₉₀, and d₈₀. The transmission of the STR was also investigated at thicknesses fit to electron applicator for 6 and 12 MeV electron beams.

RESULTS

The STR was softened with 70-degree warm water. Therefore, it was easy to mold it and attach the applicator. The PDDs and penumbras at the surface, d_max, d₉₀, and d₈₀ for the STR were almost equal to those for the LMA with 6 and 12 MeV electron beams. The treatment diameters covering over 90% dose for the irradiation fields with 40 mm diameter at d_max (LMA vs. STR) were 20.9 vs. 21.1 mm and 19.2 vs. 18.4 mm for 6 and 12 MeV electron beams, respectively. The transmission of the STR was almost same as that of LMA.

CONCLUSIONS

The dosimetric characteristics of the STR on the electron applicator were almost same as those of the LMA. The heated STR was shaped easily, flexibly, and immediately. The STR can be used as a substitute for LMA in electron radiotherapy.

One layer at a time: the use of 3D printing in the fabrication of cadmium-free electron field shaping devices

Introduction:

Electron blocks are typically composed of a low melting point alloy (LMPA), which is poured into an insert frame containing a manually placed Styrofoam aperture negative used to define the desired field shape. Current implementations of the block fabrication process involve numerous steps which are subjective and prone to user error. Occasionally, bowing of the sides of the insert frame is observed, resulting in premature frame decommissioning. Recent works have investigated the feasibility of utilising 3D printing technology to replace the conventional electron block fabrication workflow; however, these approaches involved long print times, were not compatible with commonly used cadmium-free LMPAs, and did not address the problem of insert frame bowing. In this work, we sought to develop a new 3D printing technique that would remedy these issues.

Materials and Methods:

Electron cutout negatives and alignment jigs were printed using Acrylonitrile Butadiene Styrene, which does not warp at the high temperatures associated with molten cadmium-free alloys. The accuracy of the field shape produced by electron blocks fabricated using the 3D printed negatives was assessed using Gafchromic film and beam profiler measurements. As a proof-of-concept, electron blocks with off-axis apertures, as well as complex multi-aperture blocks to be used for passive electron beam intensity modulation, were also created.

Results:

Film and profiler measurements of field size were in excellent agreement with the values calculated using the Eclipse treatment planning system, showing less than a 1% difference in line profile full-width at half-maximum. The multi-aperture electron blocks produced fields with intensity modulation ≤3.2% of the theoretically predicted value. Use of the 3D printed alignment jig – which has contours designed to match those of the insert frame – was found to reduce the amount of frame bowing by factors of 1.8 and 2.1 in the lateral and superior–inferior directions, respectively.

Conclusions:

The 3D printed ABS negatives generated with our technique maintain their spatial accuracy even at the higher temperatures associated with cadmium-free LMPA. The negatives typically take between 1 and 2 hours to print and have a material cost of approximately $2 per patient.

Feasibility of using tungsten functional paper as a thin bolus for electron beam radiotherapy

Containing 80% tungsten by weight, tungsten functional paper (TFP) is a radiation-shielding material that is lightweight, flexible, disposable, and easy to cut. Through experimental measurements and Monte Carlo simulations, we investigated the feasibility of using TFP as a bolus in electron beam radiotherapy. Commercial boluses of thickness 5 and 10 mm and from one to nine layers of TFPs (0.3-2.7 mm) were positioned on the surface of water-equivalent phantoms. The percentage depth dose curves and transverse dose profiles were measured using a 9-MeV electron beam from a clinical linear accelerator. Normalized to the value at the depth of maximum dose without bolus, the relative doses at the phantom surface for no bolus, 5-mm bolus, 10-mm bolus, 1 TFP, 3 TFPs, 6 TFPs, and 9 TFPs were 78%, 88%, 92%, 84%, 92%, 102%, and 112%, respectively; the therapeutic depths corresponding to a 90% dose level were 29.1 mm, 22.7 mm, 17.7 mm, 26.6 mm, 23.2 mm, 19.3 mm, and 15.8 mm, respectively. The TFP contributed to increased skin dose and provided dose uniformity within the target volume. However, it also resulted in increased lateral constriction and penumbra width. The results of Monte Carlo simulation produced similar trends as the experimental measurements. Our findings suggest that using TFP as a novel thin and flexible skin bolus for electron beam radiotherapy is feasible.

Reduction of Occupational Exposure Using a Novel Tungsten-Containing Rubber Shield in Interventional Radiology

This study investigates whether a novel tungsten-containing rubber shield could be used as substitute shielding material in interventional radiology to reduce the occupational exposure of operators to scattered radiation from a patient. The tungsten-containing rubber is a lead-free radiation-shielding material that contains as much as 90% tungsten powder by weight. Air kerma rates of scattered radiation from solid-plate phantoms, simulating a patient, were measured with a semiconductor dosimeter at the height of the operator's eye (1,600 mm from the floor), chest (1,300 mm), waist (1,000 mm), and knee (600 mm) with and without tungsten-containing rubber shielding (1-5 mm thickness). The tungsten-containing rubber and a commercial shielding material (RADPAD) were affixed onto the phantom on the operator's side, and reductions in air kerma rates were compared. Reduction rates for tungsten-containing rubber shielding with thicknesses of 1, 2, 3, 4, and 5 mm at each height level were as follows: 70.37 ± 0.40%, 72.17 ± 0.29%, 72.95 ± 0.31%, 72.58 ± 0.35%, and 73.63 ± 0.63% at eye level; 76.36 ± 0.19%, 77.13 ± 0.10%, 77.36 ± 0.14%, 77.62 ± 0.25%, and 77.66 ± 0.14% at chest level; 67.78 ± 0.31%, 68.12 ± 0.19%, 68.88 ± 0.28%, 68.97 ± 0.14%, and 68.85 ± 0.45% at waist level; and 0.14 ± 0.94%, 0.72 ± 0.56%, 1.08 ± 0.74%, 1.77 ± 0.80%, and 1.79 ± 1.82% at knee level, respectively. Reduction rates with RADPAD were 61.80 ± 0.67%, 60.33 ± 0.61%, 64.70 ± 0.25%, and 0.14 ± 0.66% at eye, chest, waist, and knee levels, respectively. The shielding ability of the 1 mm tungsten-containing rubber was superior to that of RADPAD. The tungsten-containing rubber could be employed to minimize an operator's radiation exposure instead of the commercial shielding material in interventional radiology.

Radiation dose reduction to the eye lens in head CT using tungsten functional paper and organ-based tube current modulation

PURPOSE

We investigated whether a tungsten functional paper (TFP) shield and/or organ-based tube current modulation (TCM) can reduce the dose to the eye lens.

MATERIALS AND METHODS

All scans were performed using our routine head examination protocol (spiral acquisition, 120 kVp, noise Index 3.5) with an anthropomorphic head phantom. The dose reduction rate was measured by the following methods with a scintillation fiber optic dosimeter: (a) without any dose reduction techniques (Original scan), (b) TFP shield, (c) TCM, and (d) TFP shield plus TCM. Image noise and CT number were obtained and compared between the three groups. In addition, image noise in method (d) was measured with varying distances between the TFP shield and eye lens.

RESULTS

The reduction rates using TFP shield, TCM, and TFP shield plus TCM compared with those for the Original scan were 17.8 %, 13.6 %, and 27.7 %, respectively. Image noise (mean ± standard deviation) in the anterior region for the Original scan, TFP shield, TCM, and TFP shield plus TCM were 4.1 ± 0.2, 4.6 ± 0.2, 4.4 ± 0.3, and 5.0 ± 0.2, while the CT numbers were 19.3 ± 0.8, 23.8 ± 0.8, 19.6 ± 0.8, and 24.1 ± 0.8, respectively. Increasing the distance between the TFP and the eye significantly decreased the CT number when using TFP shield plus TCM (p < .05).

CONCLUSION

TFP shield plus TCM reduced the dose to the eye lens in head CT while maintaining image quality with an air gap between the TFP and skin surface.

Estimation of radiation shielding ability in electron therapy and brachytherapy with real time variable shape tungsten rubber

PURPOSE

To clarify the physical characteristics of a newly developed real time variable shape rubber containing tungsten (STR) with changes in heat and estimate its shielding abilities against electron beams and γ-rays from ¹⁹²Ir.

METHODS

Dynamic mechanical analysis for the STR (density = 7.3 g/cm³) was conducted at a frequency of 1.0 Hz in the temperature range of -60 °C to 60 °C. We evaluated tanδ, defined as the ratio (E″/E') between the storage modulus (E') and loss modulus (E″). The transmission rates were measured against 6- and 12-MeV electron beams and the percentage depth dose and lateral dose profile were compared with low-melting alloy (LMA). For the shielding rate of ¹⁹²Ir against γ-rays, measurement data and Monte Carlo simulation data were obtained with STR thickness ranging from 1.0 mm to 16.0 mm.

RESULTS

At 36 °C, the tanδ value was 0.520, while at 60 °C, this value was 1.016. For 6- and 12-MeV electron beams, the transmission rates decreased with increasing STR thickness and reached plateaus at approximately 1.0% and 4.0% with STR thickness of >7.0 and >12.0 mm, respectively. The dose distributions were almost equal to those for LMA. Against γ-rays, the thickness of STR that obtained a 50% attenuation rate for ¹⁹²Ir was 5.804 mm. The Monte Carlo calculation results were 2.6% higher on average than the measurement results.

CONCLUSION

The STR can be changed shape in real time at 60 °C and maintains its shape at body temperatures. It has adequate shielding abilities against megavoltage electron beams and γ-rays from ¹⁹²Ir.

Reduction of Operator Hand Exposure in Interventional Radiology With a Novel Finger Sack Using Tungsten-containing Rubber

The purpose of this study was to evaluate the x-ray shielding ability of a novel tungsten-particle-containing rubber-based finger sack for use in interventional radiology. Shielding rates for the air kerma (mGy m) were measured using a semiconductor dosimeter with and without the finger sack and commercial lead gloves, at a 20 cm distance from the field of view. A C-arm digital angiography system was used with x-ray tube voltages of 60, 80, 100, and 120 kVp. In addition, the 70 μm dose equivalent to the operator's finger was measured using fluorescent glass dosimeters with and without the finger sack during interventional radiology examinations. The x-ray shielding rates for 60, 80, 100, and 120 kV x rays were 98.0 ± 0.03%, 94.8 ± 0.05%, 92.3 ± 0.12%, and 90.1 ± 0.03%, respectively, with the finger sack and 69.8 ± 0.39%, 61.0 ± 0.53%, 52.3 ± 0.52%, and 47.0 ± 0.69% with the lead gloves. The x-ray shielding rates for the fluoroscopy and cine mode with the finger sack were 91.3 ± 0.21% and 56.5 ± 0.58%, respectively, while with the lead gloves they were 96.5 ± 0.04% and 67.6 ± 0.33%. The 70 μm dose equivalent for the operator's finger exposure dose was reduced by approximately 39.4% using the finger sack. The finger shields were more user friendly, had excellent radiation shielding ability against x rays, and should reduce finger exposure in interventional radiology.

A novel radiation-shielding undergarment using tungsten functional paper for patients with permanent prostate brachytherapy

Tungsten functional paper (TFP) is a paper-based radiation-shielding material, which is lead-free and easy to cut. We developed a radiation protection undergarment using TFP for prostate cancer patients treated with permanent 125I seed implantation (PSI). The aim of this study was to evaluate the shielding ability of the undergarment with respect to household contacts and members of the public. Between October 2016 and April 2017, a total of 10 prostate cancer patients treated with PSI were enrolled in this prospective study. The external radiation exposure from each patient 1 day after PSI was measured with and without the undergarment. Measurements were performed using a survey meter at 100 cm from the surface of the patient's body. The exposure rates were measured from five directions: anterior, anteriorly oblique, lateral, posteriorly oblique, and posterior. The measured radiation exposure rates without the undergarment, expressed as mean ± standard deviation, from the anterior, anteriorly oblique, lateral, posteriorly oblique, and posterior directions were 1.28 ± 0.43 μSv/h, 0.70 ± 0.34 μSv/h, 0.21 ± 0.062 μSv/h, 0.65 ± 0.33 μSv/h and 1.24 ± 0.41 μSv/h, respectively. The undergarment was found to have (mean ± standard deviation) shielding abilities of 88.7 ± 5.8%, 44.0 ± 42.1%, 50.6 ± 15.9%, 72.9 ± 27.0% and 90.4 ± 10.7% from the anterior, anteriorly oblique, lateral, posteriorly oblique, and posterior directions, respectively. In conclusion, this shielding undergarment is a useful device that has the potential to reduce radiation exposure for the general public and the patient's family.

Dosimetric feasibility of using tungsten-based functional paper for flexible chest wall protectors in intraoperative electron radiotherapy for breast cancer

Intraoperative electron radiotherapy (IOERT), which is an accelerated partial breast irradiation method, has been used for early-stage breast cancer treatment. In IOERT, a protective disk is inserted behind the target volume to minimize the dose received by normal tissues. However, to use such a disk, the surgical incision must be larger than the field size because the disk is manufactured from stiff and unyielding materials. In this study, the applicability of newly developed tungsten-based functional paper (TFP) was assessed as an alternative to the existing protective disk. The radiation-shielding performance of the TFP was verified through experimental measurements and Monte Carlo simulations. Percentage depth dose curves and lateral dose profiles with and without TFPs were measured and simulated on a dedicated IOERT accelerator. The number of piled-up TFPs was changed from 1 to 40. In the experimental measurements, the relative doses at the exit plane of the TFPs for 9 MeV were 42.7%, 9.2%, 0.2%, and 0.1% with 10, 20, 30, and 40 TFPs, respectively, whereas those for 12 MeV were 63.6%, 27.1%, 8.6%, and 0.2% with 10, 20, 30, and 40 TFPs, respectively. Slight dose enhancements caused by backscatter radiation from the TFPs were observed at the entrance plane of the TFPs at both beam energies. The results of the Monte Carlo simulation indicated the same tendency as the experimental measurements. Based on the experimental and simulated results, the radiation-shielding performances of 30 TFPs for 9 MeV and 40 TFPs for 12 MeV were confirmed to be acceptable and close to those of the existing protective disk. The findings of this study suggest the feasibility of using TFPs as flexible chest wall protectors in IOERT for breast cancer treatment.

Grid Block Design Based on Monte Carlo Simulated Dosimetry, the Linear Quadratic and Hug-Kellerer Radiobiological Models

Purpose

The clinical efficacy of Grid therapy has been examined by several investigators. In this project, the hole diameter and hole spacing in Grid blocks were examined to determine the optimum parameters that give a therapeutic advantage.

Methods

The evaluations were performed using Monte Carlo (MC) simulation and commonly used radiobiological models. The Geant4 MC code was used to simulate the dose distributions for 25 different Grid blocks with different hole diameters and center-to-center spacing. The therapeutic parameters of these blocks, namely, the therapeutic ratio (TR) and geometrical sparing factor (GSF) were calculated using two different radiobiological models, including the linear quadratic and Hug-Kellerer models. In addition, the ratio of the open to blocked area (ROTBA) is also used as a geometrical parameter for each block design. Comparisons of the TR, GSF, and ROTBA for all of the blocks were used to derive the parameters for an optimum Grid block with the maximum TR, minimum GSF, and optimal ROTBA. A sample of the optimum Grid block was fabricated at our institution. Dosimetric characteristics of this Grid block were measured using an ionization chamber in water phantom, Gafchromic film, and thermoluminescent dosimeters in Solid Water™ phantom materials.

Results

The results of these investigations indicated that Grid blocks with hole diameters between 1.00 and 1.25 cm and spacing of 1.7 or 1.8 cm have optimal therapeutic parameters (TR > 1.3 and GSF~0.90). The measured dosimetric characteristics of the optimum Grid blocks including dose profiles, percentage depth dose, dose output factor (cGy/MU), and valley-to-peak ratio were in good agreement (±5%) with the simulated data.

Conclusion

In summary, using MC-based dosimetry, two radiobiological models, and previously published clinical data, we have introduced a method to design a Grid block with optimum therapeutic response. The simulated data were reproduced by experimental data.