Mass Stopping Power Ratio Research Articles

Current best estimates of beam quality correction factors for reference dosimetry of clinical proton beams

Objective. To review the currently available data on beam quality correction factors, for ionization chambers in clinical proton beams and derive their current best estimates for the updated recommendations of the IAEA TRS-398 Code of Practice. Approach. The reviewed data come from 20 publications from which values can be derived either directly from calorimeter measurements, indirectly from comparison with other chambers or from Monte Carlo calculated overall chamber factors, For cylindrical ionization chambers, a distinction is made between data obtained in the centre of a spread-out Bragg peak and those obtained in the plateau region of single-energy fields. For the latter, the effect of depth dose gradients has to be considered. To this end an empirical model for previously published displacement correction factors for single-layer scanned beams was established, while for unmodulated scattered beams experimental data were used. From all the data, chamber factors, and chamber perturbation correction factors, were then derived and analysed. Main results. The analysis showed that except for the beam quality dependence of the water-to-air mass stopping power ratio and, for cylindrical ionization chambers in unmodulated beams, of the displacement correction factor, there is no remaining beam quality dependence of the chamber perturbation correction factors Based on this approach, average values of the beam quality independent part of the perturbation factors were derived to calculate values consistent with the data in the literature. Significance. The resulting data from this analysis are current best estimates of values for modulated scattered beams and single-layer scanned beams used in proton therapy. Based on this, a single set of harmonized values is derived to be recommended in the update of IAEA TRS-398.

Validation of polylactic acid polymer as soft tissue substitutive in radiotherapy

We report the experimental study on the physical and radiation properties of polylactic acid polymer (PLA-C3H4O2) combined with Monte Carlo simulations for application in radiotherapy. The suitability of PLA for phantoms construction as a substitute for soft human tissue in MeV photon radiation dosimetry and therapy is discussed. The elemental composition and radiation properties are described as recommended by ICRU 44. In addition, Hounsfield unit (HU), mass attenuation coefficient, mass stopping power and tissue phantom ratio were determined. Previous works on this subject presented mainly the properties of the raw material formula, neglecting above all the effects of the printing matrix and commercial raw materials used for PLA's production. The present upon irradiation properties of polylactic acid polymer were contrasted to those known of solid water and attested the viability and performance of PLA to bio-mimic soft tissue. The experimental and simulated data demonstrate the adequacy of PLA to printed phantoms provided that the printer infills result in a density of 1.05–1.09 g/cm3.

Monte Carlo simulated beam quality and perturbation correction factors for ionization chambers in monoenergetic proton beams.

Beam quality correction factors provided in current codes of practice for proton beams are approximated using the water-to-air mass stopping power ratio and by assuming the proton beam quality related perturbation correction factors to be unity. The aim of this work is to use Monte Carlo simulations to calculate energy dependent beam quality and perturbation correction factors for a set of nine ionization chambers in proton beams. The Monte Carlo code EGSnrc was used to determine the ratio of the absorbed dose to water and the absorbed dose to the sensitive air volume of ionization chambers related to the reference photon beam quality (60 Co). For proton beams, the quantity was simulated with GATE/Geant4 for five monoenergetic beam energies between 70 MeV and 250MeV. The perturbation correction factors for the air cavity, chamber wall, chamber stem, central electrode, and displacement effect in proton radiation were investigated separately. Additionally, the correction factors of cylindrical chambers were investigated with and without consideration of the effective point of measurement. The perturbation factors were shown to deviate from unity for the investigated chambers, contradicting the assumptions made in dosimetry protocols. The beam quality correction factors for both plane-parallel and cylindrical chambers positioned with the effective point of measurement at the measurement depth were constant within 0.8%. An increase of the beam quality correction factors determined for cylindrical ionization chambers placed with their reference point at the measurement depth with decreasing energy is attributed to the displacement perturbation correction factors , which were up to 1.045±0.1% for the lowest energy and 1.005±0.1% for the highest energy investigated. Besides , the largest perturbation was found for the chamber wall where the smallest determined was 0.981±0.3%. Beam quality correction factors applied in dosimetry with cylindrical chambers in monoenergetic proton beams strongly depend on the positioning method used. We found perturbation correction factors different from unity. Consequently, the approximation of ionization chamber perturbations in proton beams by the respective water-to-air mass stopping power ratio shall be revised.

Correction of stopping power and LET quenching for radiophotoluminescent glass dosimetry in a therapeutic proton beam

To measure the absorbed dose to water Dw in proton beams using a radiophotoluminescent glass dosimeter (RGD), a method with the correction for the change of the mass stopping power ratio (SPR) and the linear energy transfer (LET) dependence of radiophotoluminescent efficiency is proposed.The calibration coefficient in terms of Dw for RGDs (GD-302M, Asahi Techno Glass) was obtained using a 60Co γ-ray. The SPR of water to the RGD was calculated by Monte Carlo simulation, and was investigated experimentally using a 70 MeV proton beam. For clinical usage, the residual range Rres was used as a quality index to determine the correction factor for the beam quality and the LET quenching effect of the RGD . The proposed method was evaluated by measuring Dw at different depths in a 200 MeV proton beam.For both non-modulated and modulated proton beams, decreases rapidly where Rres is less than 4 cm. The difference in between a non-modulated and a modulated proton beam is less than 0.5% for the Rres range from 0 cm to 22 cm. decreases rapidly at a LET range from 1 to 2 keV µm−1. In the evaluation experiments, Dw using RGDs, showed good agreement with that obtained using an ionization chamber and the relative difference was within 3% where Rres was larger than 1 cm. The uncertainty budget for in a proton beam was estimated to investigate the potential of RGD postal dosimetry in proton therapy.These results demonstrate the feasibility of RGD dosimetry in a therapeutic proton beam and the general versatility of the proposed method. In conclusion, the proposed methodology for RGDs in proton dosimetry is applicable where Rres > 1 cm and the RGD is feasible as a postal audit dosimeter for proton therapy.

SU‐F‐T‐136: Breath Hold Lung Phantom Study in Using CT Density Versus Relative Stopping Power Ratio for Proton Pencil Beam Scanning System

Purpose:To evaluate mass density effects of CT conversion table and its variation in current treatment planning system of spot scanning proton beam using an IROC proton lung phantom for this study.Methods:A proton lung phantom study was acquired to Imaging and Radiation Oncology Core Houston (IROC) Quality Assurance Center. Inside the lung phantom, GAF Chromic films and couples of thermal luminescent dosimeter (TLD) capsules embedded in specified PTV and adjacent structures to monitor delivered dosage and 3D dose distribution profiles. Various material such as cork (Lung), blue water (heart), Techron HPV (ribs) and organic material of balsa wood and cork as dosimetry inserts within phantom of solid water (soft tissue). Relative stopping power (RLSP) values were provided. Our treatment planning system (TPS) doesn't require SP instead relative density was converted relative to water. However lung phantom was irradiated by planning with density override and the results were compared with IROC measurements. The second attempt was conducted without density override and compared with IROC's.Results:The higher passing rate of imaging and measurement results of the lung phantom irradiation met the criteria by IROC without density override. The film at coronal plane was found to be shift due to inclined cylinder insertion. The converted CT density worked as expected to correlate relative stopping power.Conclusion:The proton lung phantom provided by IROC is a useful tool to qualify our commissioned proton pencil beam delivery with TPS within reliable confidence. The relative mass stopping power ratios of materials were converted from the relative physical density relative to water and the results were satisfied.

SU‐F‐T‐175: Absorbed Dose Measurement Using Radiophotoluminescent Glass Dosimeter in Therapeutic Proton Beam

Purpose:To measure the absorbed dose to water Dw in therapeutic proton beam with radiophotoluminescent glass dosimeter (RGD), a methodology was proposed. In this methodology, the correction factor for the LET dependence of radiophotoluminescent (RPL) efficiency and the variation of mass stopping power ratio of water to RGD (SPRw, RGD) were adopted. The feasibility of proposed method was evaluated in this report.Methods:The calibration coefficient in terms of Dw for RGDs (GD‐302M, Asahi Techno Glass) was obtained using 60Co beam. The SPRw, RGD was calculated by Monte Carlo simulation toolkit Geant4. The LET dependence of RPL efficiency was investigated experimentally by using a 70 MeV proton beam at National Institute of Radiological Sciences. For clinical usage, the residual range Rres was used as a quality index to determine the correction factor for RPL efficiency. The proposed method was evaluated by measuring Dw at difference depth in the 200 MeV proton beam.Results:For both modulated and non‐modulated proton beam, the SPRw, RGD increases more than 3 % where Rres are less than 1 cm. RPL efficiency decreases with increasing LET and it reaches 0.6 at LET of 10 keV µm−1. Dw measured by RGD (Dw, RGD) shows good agreement with that measured by ionization chamber (Dw, IC) and the relative difference between Dw, RGD and Dw, IC are within 3 % where Rres is larger than 1 cm.Conclusion:In this work, a methodology for using RGD in proton dosimetry was proposed and the SPRw, RGD and the LET dependence of RPL efficiency in therapeutic proton beam was investigated. The results revealed that the proposed method is useful for RGD in the dosimetry of proton beams.

Diamond detector in absorbed dose measurements in high-energy linear accelerator photon and electron beams.

Diamond detectors (DD) are preferred in small field dosimetry of radiation beams because of small dose profile penumbras, better spatial resolution, and tissue‐equivalent properties. We investigated a commercially available ‘microdiamond’ detector in realizing absorbed dose from first principles. A microdiamond detector, type TM 60019 with tandem electrometer is used to measure absorbed doses in water, nylon, and PMMA phantoms. With sensitive volume 0.004 mm3, radius 1.1 mm, thickness 1×10−3mm, the nominal response is 1 nC/Gy. It is assumed that the diamond detector could collect total electric charge (nC) developed during irradiation at 0 V bias. We found that dose rate effect is less than 0.7% for changing dose rate by 500 MU/min. The reproducibility in obtaining readings with diamond detector is found to be ±0.17% (1 SD) (n=11). The measured absorbed doses for 6 MV and 15 MV photons arrived at using mass energy absorption coefficients and stopping power ratios compared well with Nd, water calibrated ion chamber measured absorbed doses within 3% in water, PMMA, and nylon media. The calibration factor obtained for diamond detector confirmed response variation is due to sensitivity due to difference in manufacturing process. For electron beams, we had to apply ratio of electron densities of water to carbon. Our results qualify diamond dosimeter as a transfer standard, based on long‐term stability and reproducibility. Based on micro‐dimensions, we recommend these detectors for pretreatment dose verifications in small field irradiations like stereotactic treatments with image guidance.PACS number(s): 87.56.Da

Energy dependency of a water-equivalent fibre-coupled beryllium oxide (BeO) dosimetry system

Here we investigate the energy dependency of the radioluminescence (RL) and optically stimulated luminescence (OSL) of near water equivalent beryllium oxide (BeO) ceramics. The BeO ceramic is coupled to an optical fibre. We investigate the water equivalence of BeO ceramics by comparing the mass attenuation coefficients and mass stopping powers of BeO ceramic to those of water. We also compare the results to other common dosimeter materials; polyvinyl toluene (PVT) based plastic scintillators, lithium fluoride (LiF) and aluminium oxide (Al2O3:C). Results show that while PVT based plastic scintillators are the most water equivalent material investigated, the mass attenuation coefficients and mass stopping power ratios of BeO and water vary the least with energy. We also investigate the x-ray energy dependence of BeO ceramic for a range of energies produced by a superficial x-ray unit (SXR), an Iridium-192 source and a high energy linear accelerator. Results indicate a significant under response of the BeO ceramic RL and OSL signals for lower x-ray energies, up to 55% for the lower SXR beams. The RL signal from BeO ceramics shows a constant response for x-ray energies above a 50 kVp SXR beam.

The use of non-standard CT conversion ramps for Monte Carlo verification of 6 MV prostate IMRT plans

Monte Carlo (MC) dose calculation algorithms have been widely used to verify the accuracy of intensity-modulated radiotherapy (IMRT) dose distributions computed by conventional algorithms due to the ability to precisely account for the effects of tissue inhomogeneities and multileaf collimator characteristics. Both algorithms present, however, a particular difference in terms of dose calculation and report. Whereas dose from conventional methods is traditionally computed and reported as the water-equivalent dose (Dw), MC dose algorithms calculate and report dose to medium (Dm). In order to compare consistently both methods, the conversion of MC Dm into Dw is therefore necessary.This study aims to assess the effect of applying the conversion of MC-based Dm distributions to Dw for prostate IMRT plans generated for 6 MV photon beams. MC phantoms were created from the patient CT images using three different ramps to convert CT numbers into material and mass density: a conventional four material ramp (CTCREATE) and two simplified CT conversion ramps: (1) air and water with variable densities and (2) air and water with unit density. MC simulations were performed using the BEAMnrc code for the treatment head simulation and the DOSXYZnrc code for the patient dose calculation. The conversion of Dm to Dw by scaling with the stopping power ratios of water to medium was also performed in a post-MC calculation process.The comparison of MC dose distributions calculated in conventional and simplified (water with variable densities) phantoms showed that the effect of material composition on dose-volume histograms (DVH) was less than 1% for soft tissue and about 2.5% near and inside bone structures. The effect of material density on DVH was less than 1% for all tissues through the comparison of MC distributions performed in the two simplified phantoms considering water. Additionally, MC dose distributions were compared with the predictions from an Eclipse treatment planning system (TPS), which employed a pencil beam convolution (PBC) algorithm with Modified Batho Power Law heterogeneity correction. Eclipse PBC and MC calculations (conventional and simplified phantoms) agreed well (<1%) for soft tissues. For femoral heads, differences up to 3% were observed between the DVH for Eclipse PBC and MC calculated in conventional phantoms. The use of the CT conversion ramp of water with variable densities for MC simulations showed no dose discrepancies (0.5%) with the PBC algorithm. Moreover, converting Dm to Dw using mass stopping power ratios resulted in a significant shift (up to 6%) in the DVH for the femoral heads compared to the Eclipse PBC one.Our results show that, for prostate IMRT plans delivered with 6 MV photon beams, no conversion of MC dose from medium to water using stopping power ratio is needed. In contrast, MC dose calculations using water with variable density may be a simple way to solve the problem found using the dose conversion method based on the stopping power ratio.

SU-E-T-497: Study of Restricted Mass Stopping Power Ratio in Small Electron Tube Fields.

Electron tubes with small radii are useful to treat narrow regions which cannot accommodate normal electron applicators. In small electron fields, it is not trivial to estimate restricted mass stopping power ratio (MSR), which is needed to evaluate dose from ion chamber measurement. We studied MSRs in small electron tube fields using the Monte Carlo simulation. Electron tubes with radii, 3 and 2.5 cm, were used in this study. Nominal electron energies were 6 and 9 MeV. There were two types of tubes. One has a normal cut but the other has a 45-degree cut. For the normal cut tube, percent depth dose (PDD) in water was evaluated along the center of axis (CAX) of a beam. For the 45-degree cut tube, PDD was evaluated along the vertical line from the intersection of the CAX and the phantom surface with 45-degree gantry angle. The MSRs and mean electron energies were calculated using the Monte Carlo simulation. We found good agreement between the measured and calculated PDDs. The changes of mean energies from those in the 10×10 cm2 field at the depth of maximum dose (dmax) were very small for the normal cut electron tubes. For the 45-degree cut tubes, the changes of mean energies at dmax were less than 1 MeV. The MSRs in the normal cut tube fields were almost the same as those in the 10×10 cm2 field at the corresponding depths. The MSRs for the 45-degree cut tubes deviated from those in the 10×10 cm2 by about 1% (1.5 % at most). We evaluated the mean energies and MSRs in small electron tube fields. The deviations of them from the values in the 10×10 cm2 were small. The maximum difference of MSR was 1.5% in 45-degree cut tube fields. This work was supported by KAKENHI (23791449), Japan Society for the Promotion of Science, and Cancer Professional Training Plan, The Ministry of Education, Culture, Sports, Science and Technology, Japan.

TH-F-211-02: Evaluation of a Proton Pencil Beam Alogirithm for Dose Calculations in Heterogeneous Media

Purpose: To develop an improved nuclear halo dose model of a pencil beam algorithm (PBA) for dose calculation of proton beams in heterogeneous media. Methods: The proton PBA consisted of a central axis term and an off axis term. The central axis term was determined from a central axis depth dose of a proton beam in water and was scaled by the mass stopping power ratio to account for other materials. The off axis term was determined from Fermi‐Eyges scattering theory with material‐dependent scattering powers to calculate the spread of the proton beam in heterogeneous media. The nuclear halo dose arising from large angle and non‐elastic scatter was modeled using two terms: a Gaussian and a Cauchy‐Lorentz distribution. Depth‐dependent widths and amplitudes of each distribution were determined by fitting a simulated 1‐mm × 1‐mm pencil beam in water. The PBA was evaluated in approximately 30 test phantoms containing bone and/or air heterogeneities for 4 energies and 2 field sizes. Agreement between PBA and Monte Carlo simulations of the test conditions was quantified by computing the percentage of points within 2 percent dose difference or 1 mm distance to agreement. Results: With the improved nuclear halo model, PBA calculations showed better than of 97% of dose points within 2%/1 mm of MC distributions for all geometries examined. For phantoms containing laterally infinite heterogeneities, agreement between PBA and MC distributions was 100% at 2%/1mm. For phantoms containing laterally finite heterogeneities, agreement was at least 97%. The points failing were due to the central axis approximation of the PBA in regions not influenced by the nuclear halo model. Conclusions: The halo model developed in this work improves the agreement of the PBA with MC simulations in heterogeneous phantoms, particularly in low‐dose regions that can be important for scanned‐beam proton therapy. “This research was supported by contract W81XWH‐10‐1‐0005 awarded by The U.S. Army Research Acquisition Activity, 820 Chandler Street, Fort Detrick, MD 21702‐5014. This report does not necessarily reflect the position or policy of the Government, and no official endorsement should be inferred.”

Dosimetric characteristics of an unshielded p-type Si diode: linearity, photon energy dependence and spatial resolution

The unshielded Si diode PTW 60012, used for accurate measurements of the transversal dose profiles of narrow photon beams, has been investigated with regard to its linearity, photon energy dependence and spatial resolution. The diode shows a slight supralinearity, i.e. increase of the response with pulse dose, by 3% over the pulse dose range 0.1 to 0.8mGy. In p-type silicon, supralinearity results from the increased chance for radiation-induced electrons to escape recombination when the pulse dose increases. Over the energy range from 6 to 15 MV, the response decreases by about 4%. This small variation of the response results from partial compensation between the influences of the secondary electron energy on the mass stopping power ratio silicon/water and on electron backscattering from the silicon chip. The lateral response function of the examined diode has a full half width of 1.3mm. Dose profiles of 5mm half-width can still be recorded with negligible error.

Clinical comparison of head and neck and prostate IMRT plans using absorbed dose to medium and absorbed dose to water

Conventional photon radiation therapy dose-calculation algorithms typically compute and report the absorbed dose to water (Dw). Monte Carlo (MC) dose-calculation algorithms, however, generally compute and report the absorbed dose to the material (Dm). As MC-calculation algorithms are being introduced into routine clinical usage, the question as to whether there is a clinically significant difference between Dw and Dm remains. The goal of the current study is to assess the differences between dose–volume indices for Dm and Dw MC-calculated IMRT plans. Ten head-and-neck (H&N) and ten prostate cancer patients were selected for this study. MC calculations were performed using an EGS4-based system. Converting Dm to Dw for MC-based calculations was accomplished as a post-MC calculation process. Dw and Dm results for target and critical structures were evaluated using the dose–volume-based indices. For H&N IMRT plans, systematic differences between dose–volume indices computed with Dw and Dm were up to 2.9% for the PTV prescription dose (D98), up to 5.8% for maximum (D2) dose to the PTV and up to 2.7% for the critical structure dose indices. For prostate IMRT plans, the systematic differences between Dw- and Dm-based computed indices were up to 3.5% for the prescription dose (D98) to the PTVs, up to 2.0% for the maximum (D2) dose to the PTVs and up to 8% for the femoral heads due to their higher water/bone mass stopping power ratio. This study showed that converting Dm to Dw in MC-calculated IMRT treatment plans introduces a systematic error in target and critical structure DVHs. In some cases, this systematic error may reach up to 5.8% for H&N and 8.0% for prostate cases when the hard-bone-containing structures such as femoral heads are present. Ignoring differences between Dm and Dw will result in systematic dose errors ranging from 0% to 8%.

Proton stopping powers averaged over beam energy spectra

Stopping powers averaged over the proton energy spectra at various depths inwater and a tissue-like material were calculated for proton beams with initialenergies between 50 and 250 MeV. The analysis was made for proton beams with aspread-out Bragg peak (SOBP) to assess in particular the variations of stoppingpower with depth in the SOBP plateau region. Nuclear interactions were accountedfor in determination of the proton energy spectra. In modulated beams, stoppingpower varies considerably with depth along the plateau region of the spread-outpeak. Moreover, stopping powers at the same water depth may differ from eachother by up to 20% if referring to modulated or non-modulated beams.Calculations of water-air mass stopping power ratios were also performed, withand without the inclusion of nuclear interactions, for modulated and non-modulated beams. The stopping power ratios do not depend significantly on protonenergy, and this makes the effect of accounting for nuclear interactions inproton fluence calculation negligible. For the same reason the stopping powerratios for modulated beams do not appreciably differ from those referred to non-modulated beams with the same Emax at the same depth in water. Thepresent results also show that the dependence of stopping power on energy spreadand spatial divergence for proton beams is not negligible in some conditions.Some conclusions are drawn on the possibility of using the residual range as adescriptor of the proton beam quality for different experimental beamconditions.

Gas-to-Wall Absorbed Dose Conversion Factors from 25 to 250 MeV Neutron Energy

Gas-to-wall absorbed dose conversion factors rm.g were calculated with Bragg_Gray cavity theory for the 25 to 250 MeV neutron energy range. Calculations of rm.g were made for propane-based tissue-equivalent gas and walls of C, O, Mg, Al, Si, Fe, Zr, AlN, Al2O3, Zr, ZrO2, and A-150 plastic. Charged particle production in the wall materials was calculated with nuclear model codes. Mass stopping powers were taken from recent tabulations. Above 70 MeV neutron energy the rm.g values were found to be nearly constant and to approach the wall-to-gas mass stopping power ratio of minimum ionising particles. Slight energy dependencies were found in rm.g below 70 MeV. Uncertainties in rm.g are estimated to be less than five per cent below 100 MeV neutron energy and are primarily from the uncertainties of the stopping power data.

Proposed semi-analytical formulae for the determination of [formula omitted] and P repl for electron beams as used in radiotherapy

To convert an ionization measurement to absorbed dose, the TG-21, the IAEA, and the TG-25 protocols for the calibration of high energy electron therapy machines demand an accurate knowledge of the mean restricted collision mass stopping power ratio, ( L ϱ ) air med , and the electron fluence correction factor, P repl. This paper presents a semi-analytical expression to calculate ( L ϱ ) air med at depths in the range of 0 to 30 g/cm 2 and for any energy in the range of 4–60 MeV, for water, polystyrene, and acrylic relative to air, and another expression to calculate P repl for any cylindrical ionization chamber with an inner diameter in the range of 3 to 7 mm. The published values for ( L ϱ ) air med were fitted to a single analytical expression with 10 coefficients using a nonlinear least square routine. Another expression with 4 coefficients was used to fit the electron fluence correction factor, P repl, for cylindrical ionization chambers, as a function of chamber diameter and the mean electron energy at depth of measurement. In the electron energy range of 4–60 MeV, and for all published depths, the calculated ( L ϱ ) air med values agree with the published values within ±1% in 99% of the cases. The calculated P repl values agree with the tabulated values within ±1% in all of the cases. The proposed equations now allow one to use a computer to calculate the values of ( L ϱ ) air med and P repl accurately, doing away with the time-consuming procedure of interpolating between values from tables during the routine calibration of high energy electron therapy machines.

Beiträge zur praktischen Dosimetrie hochenergetischer Photonenstrahlung

The determination of the absorbed dose with ionisation chambers is mainly influenced by the energy dependence of the mass stopping power ratio of the phantom material water to the material air of the probe volume. Also the material and dimensions of the ionisation chamber, represented by the pertubation factor, give energy dependent corrections. For a set of standard ionisation chambers this dependence will be presented up to an energy of 45 MV.

Semianalytical expressions for and Prepl for electron beams

The tables of the mean restricted collision mass stopping power ratios for water, polystyrene and acrylic relative to air given in the AAPM TG‐21 protocol have been fitted to an expression with 20 coefficients using the depth in the phantom and the mean incident electron energy as two independent variables. Using these expressions, the calculated values agree with the tabulated values within +0.5% in 85% of the cases and within ±1.0% in 95% of the cases. For each of the four cylindrical chamber inner diameters, given in the protocol, the electron fluence correction Prepl has been fitted to an expression with four coefficients using the mean electron energy at depth z as an independent variable.

Energy determination for electron beam calibration

Presents the results of independent energy determinations, one by ion-chamber measurements in a water phantom, one by film analysis in a lucite phantom, and one by the ion-chamber response ratio described by the authors. The energy differences are insignificant with regard to the corresponding mass stopping power ratios needed for calibration. The greatest variation exists for 6 MeV electrons, mainly a result of the steep slope on the descending portion of the ionisation-depth curve. Even in the worse-case situation, however, the differences in the stopping power values (L/ rho ) are less than 1%.

An Additional Note on Effective Mass Stopping Power Ratio in High-Energy Photon and Electron Dosimetry

An Additional Note on Effective Mass Stopping Power Ratio in High-Energy Photon and Electron Dosimetry