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,kQ,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 whichkQvalues can be derived either directly from calorimeter measurements, indirectly from comparison with other chambers or from Monte Carlo calculated overall chamber factors,fQ.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,fQ,and chamber perturbation correction factors,pQ,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 factorspQ.Based on this approach, average values of the beam quality independent part of the perturbation factors were derived to calculatekQvalues consistent with the data in the literature.Significance. The resulting data from this analysis are current best estimates ofkQvalues 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.

Experimental determination ofkQfactors for two types of ionization chambers in scanned proton beams.

Objective.Experimental determination of beam qualitykQfactors for two types of Farmer ionization chambers, NE2571 and IBA FC65-G, in a scanned proton beam for three nominal energies (140 MeV, 180 MeV and 220 MeV) based on water calorimetry.Approach.Beam quality correction factors were determined comparing the results obtained with water calorimetry and ionometry. Water calorimetry was performed to determine the absorbed dose at a depth of measurement in water of 5 g cm-2, limited by the extension of the calorimeter glass vessel used. For the ionometry, two chambers of each type were included in the study. The ionization chambers were calibrated in terms of absorbed dose to water in60Co at the Swedish Secondary Standard Dosimetry Laboratory, directly traceable to the BIPM, and were used according to the IAEA TRS-398 Code of Practice.Main results. ThekQvalues determined in the present work have been compared with the values tabulated in TRS-398 and its forthcoming update and also with those obtained in previous water calorimetric measurements and Monte Carlo calculations. All results were found to agree within the combined uncertainties of the different data.Significance. It is expected that the present work will serve as an experimental contribution tokQ-factors for the two chamber types and three scanned proton beam qualities used.

Cema-based formalism for the determination of absorbed dose for high-energy photon beams.

PURPOSE: Determination of absorbed dose is well established in many dosimetry protocols and considered to be highly reliable using ionization chambers under reference conditions. If dosimetry is performed under other conditions or using other detectors, however, open questions still remain. Such questions frequently refer to appropriate correction factors. A converted energy per mass (cema)-based approach to formulate such correction factors offers a good understanding of the specific response of a detector for dosimetry under various measuring conditions and thus an estimate of pros and cons of its application. METHODS: Determination of absorbed dose requires the knowledge of the beam quality correction factor kQ,Qo , where Q denotes the quality of a user beam and Qo is the quality of the radiation used for calibration. In modern Monte Carlo (MC)-based methods, kQ,Qo is directly derived from the MC-calculated dose conversion factor, which is the ratio between the absorbed dose at a point of interest in water and the mean absorbed dose in the sensitive volume of an ion chamber. In this work, absorbed dose is approximated by the fundamental quantity cema. This approximation allows the dose conversion factor to be substituted by the cema conversion factor. Subsequently, this factor is decomposed into a product of cema ratios. They are identified as the stopping power ratio water to the material in the sensitive detector volume, and as the correction factor for the fluence perturbation of the secondary charged particles in the detector cavity caused by the presence of the detector. This correction factor is further decomposed with respect to the perturbation caused by the detector cavity and that caused by external detector properties. The cema-based formalism was subsequently tested by MC calculations of the spectral fluence of the secondary charged particles (electrons and positrons) under various conditions. RESULTS: MC calculations demonstrate that considerable fluence perturbation may occur particularly under non-reference conditions. Cema-based correction factors to be applied in a 6-MV beam were obtained for a number of ionization chambers and for three solid-state detectors. Feasibility was shown at field sizes of 4 × 4 and 0.5 cm × 0.5 cm. Values of the cema ratios resulting from the decomposition of the dose conversion factor can be well correlated with detector response. Under the small field conditions, the internal fluence correction factor of ionization chambers is considerably dependent on volume averaging and thus on the shape and size of the cavity volume. CONCLUSIONS: The cema approach is particularly useful at non-reference conditions including when solid-state detectors are used. Perturbation correction factors can be expressed and evaluated by cema ratios in a comprehensive manner. The cema approach can serve to understand the specific response of a detector for dosimetry to be dependent on (a) radiation quality, (b) detector properties, and (c) electron fluence changes caused by the detector. This understanding may also help to decide which detector is best suited for a specific measurement situation.

Technical Note: SpekPy v2.0-a software toolkit for modeling x-ray tube spectra.

PURPOSE: SpekPy is a free toolkit for modeling x-ray tube spectra with the Python programming language. In this article, the advances in version 2.0 (v2) of the software are described, including additional target materials and more accurate modeling of the heel effect. Use of the toolkit is also demonstrated. METHODS: The predictions of SpekPy are illustrated in comparison to experimentally determined spectra: three radiation quality reference (RQR) series tungsten spectra and one mammography spectrum with a molybdenum target. The capability of the software to correctly model changes in tube output with tube potential is also assessed, using the example of a GE RevolutionTM CT scanner (GE Healthcare, Waukesha, WI, USA) and specifications in the system's Technical Reference Manual. Furthermore, we note that there are several physics models available in SpekPy. These are compared on and off the central axis, to illustrate the differences. RESULTS: SpekPy agrees closely with the experimental spectra over a wide range of tube potentials, both visually and in terms of first and second half-value layers (HVLs) (within 2% here). The CT scanner spectrum output (normalized to 120 kV tube potential) agreed within 4% over the range of 70 to 140 kV. The default physics model (casim) is adequate in most situations. The advanced option (kqp) should be used if high accuracy is desired for modeling the anode heel effect, as it fully includes the effects of bremsstrahlung anisotropy. CONCLUSIONS: SpekPy v2 can reliably predict on- and off-axis spectra for tungsten and molybdenum targets. SpekPy's open-source MIT license allows users the freedom to incorporate this powerful toolkit into their own projects.

A model for the energy and angular distribution of x rays emitted from an x-ray tube. Part I. Bremsstrahlung production.

PURPOSE: To develop an analytical model for bremsstrahlung production in a thick x-ray target (i.e., the x-ray tube anode) that takes into account the intrinsic bremsstrahlung angular distribution. METHODS: X-ray spectrum models developed from theoretical principles have traditionally treated the angular distribution of the bremsstrahlung production as spherically uniform. This assumption stems from the rationale that electrons promptly attain a diffuse directional distribution in an x-ray target due to multiple scattering, thereby effectively masking the intrinsic bremsstrahlung angular distribution. In this work, a model that explicitly accounts for the angular distribution of the bremsstrahlung production is presented. The model combines Monte Carlo-calculated depth, energy, and angular distributions of electrons penetrating the x-ray target, and incorporates theoretical results for the differential bremsstrahlung cross section. The effects of using different simplified model assumptions for the electron penetration and the intrinsic bremsstrahlung angular distribution are analyzed for tungsten and molybdenum targets in the energy range 20-300 keV. RESULTS: Typical assumptions of previous models are shown to introduce errors in calculated spectra. Particularly, it is shown that predictions of fluence and air kerma free-in-air can be overestimated by 15-30% (2-3% in aluminum half-value layer thickness) for clinically relevant beam qualities. The present model is able to reproduce comprehensive Monte Carlo calculations of the bremsstrahlung production generally to within 1%. CONCLUSIONS: The bremsstrahlung model developed in this work is an improvement over previous models in that the main features of the electron penetration and the resulting bremsstrahlung are considered in detail. The model can be used for more accurate predictions of the energy and angular distribution of x rays emitted from an x-ray tube.

A model for the energy and angular distribution of x rays emitted from an x-ray tube. Part II. Validation of x-ray spectra from 20 to 300 kV.

PURPOSE: To present and validate a complete x-ray emission model (bremsstrahlung and characteristic x-ray emission) for the energy range 20-300 kV. METHODS: An analytical x-ray spectrum model that combines the bremsstrahlung emission model developed in Part I with a previously developed characteristic x-ray emission model is validated by comparison with Monte Carlo calculations, published measured spectra, and models developed by other authors. Furthermore, the assumptions and limitations of previous spectrum models are summarized, and their predictions are compared with results obtained by Monte Carlo simulations of x rays emitted from tungsten and molybdenum targets. RESULTS: The model is able to reproduce narrow-beam Monte Carlo calculations to within 0.5% in terms of the first and second aluminum half-value layer thickness (HVL). Compared with measured spectra, the difference in HVL is < 2% for typical diagnostic and therapeutic beam qualities available at primary standard laboratories. Compared with previous spectrum models, the present model performs especially well for low kilovoltage x-ray beams (below 50 kV), and is reliable for a wider range of take-off angles, that is, the angle between the target surface and the direction of emission. The difference in model and Monte Carlo predictions of the energy-fluence weighted air kerma (i.e., the photon energy absorption in air) is < 0.5% using the present model, while previous spectrum models can differ by more than 10%. CONCLUSIONS: The x-ray emission model developed in this work has been validated against Monte Carlo calculations and measured results. The model provides an efficient alternative to comprehensive Monte Carlo simulations and is an improvement over previous models. The model can be used to predict both central- and off-axis spectra, as well as off-axis effects such as the (anode) heel effect.

Depth-dose measurement corrections for the surface electronic brachytherapy beams of an Esteya®unit: a Monte Carlo study.

Three different correction factors for measurements with the parallel-plate ionization chamber PTW T34013 on the Esteya electronic brachytherapy unit have been investigated. This chamber type is recommended by AAPM TG-253 for depth-dose measurements in the 69.5 kV x-ray beam generated by the Esteya unit.Monte Carlo simulations using the PENELOPE-2018 system were performed to determine the absorbed dose deposited in water and in the chamber sensitive volume at different depths with a Type A uncertainty smaller than 0.1%. Chamber-to-chamber differences have been explored performing measurements using three different chambers. The range of conical applicators available, from 10 to 30 mm in diameter, has been explored.Using a depth-independent global chamber perturbation correction factor without a shift of the effective point of measurement yielded differences between the absorbed dose to water and the corrected absorbed dose in the sensitive volume of the chamber of up to 1% and 0.6% for the 10 mm and 30 mm applicators, respectively. Calculations using a depth-dependent perturbation factor, including or excluding a shift of the effective point of measurement, resulted in depth-dose differences of about ± 0.5% or less for both applicators. The smallest depth-dose differences were obtained when a shift of the effective point of measurement was implemented, being displaced 0.4 mm towards the center of the sensitive volume of the chamber. The correction factors were obtained with combined uncertainties of 0.4% (k = 2). Uncertainties due to chamber-to-chamber differences are found to be lower than 2%.The results emphasize the relevance of carrying out detailed Monte Carlo studies for each electronic brachytherapy device and ionization chamber used for its dosimetry.

Monte Carlo calculation of beam quality correction factors for PTW cylindrical ionization chambers in photon beams.

The beam quality correction factor k Q for megavoltage photon beams has been calculated for eight PTW (Freiburg, Germany) ionization chambers (Farmer chambers PTW30010, PTW30011, PTW30012, and PTW30013, Semiflex 3D chambers PTW31021, PTW31010, and PTW31013, and the PinPoint 3D chamber PTW31016). Simulations performed on the widely used NE-2571 ionization chamber have been used to benchmark the results. The Monte Carlo code PENELOPE/penEasy was used to calculate the absorbed dose to a point in water and the absorbed dose to the active air volume of the chambers for photon beams in the range 4 to 24 MV. Of the nine ionization chambers analysed, only five are included in the current version of the International Code of Practice for dosimetry based on standards of absorbed dose to water (IAEA TRS 398). The values reported in this work agree with those in the literature within the uncertainty estimates and are to be included in the average values of the data obtained by different working groups for the forthcoming update of TRS 398.

Data for the dosimetry of low- and medium-energy kV x rays.

Following the publication of the ICRU Report 90 (2016) on key data for measurement standards in radiation dosimetry, where ionometric air-kerma standards for kilovoltage (kV) x-ray beams are estimated to change by up to about 0.5%, an update of the backscatter factors and water/air ratios of mass energy-absorption coefficients in kV dosimetry protocols was deemed necessary for consistency through the entire dosimetry chain. In addition, numerical methods and Monte Carlo (MC) systems that did not exist at the time when air-kerma protocols were developed, are currently available. Calculations of the chamber-independent quantities required for the dosimetry of low- and medium-energy kV x rays were carried out using a consistent set of key data throughout the complete process. The quantities were based on MC calculations of a database for a dense grid of monoenergetic photons for different beam diameters and source-to-surface distances, followed by an averaging procedure to compute water/air energy-absorption coefficient ratios and backscatter factors for 342 experimental and calculated kV spectra. It was found that for a given HVL and field size the variation of backscatter factors for different kVs can be up to about 5%, a trend confirmed with independent calculations that shows the limitation of using only the HVL for the beam quality specification of kV x rays. Extensive tables as a function of beam quality in terms of kV and HVL were developed for configurations that might be encountered in clinical practice; the data are also available in the form of a GUI web app at http://52.233.195.208. Results were compared with data used at PTB for deriving low-energy [Formula: see text] ion chamber calibration coefficients, finding agreement within about [Formula: see text]0.5%, and with independent full MC kerma calculations that agreed within better than about 1%. Compared with the data in the AAPM TG-61 protocol (Ma et al 2001 Med. Phys. 28 868-93) there was in general good agreement for the ratios of mass energy-absorption coefficients, although differences of up to 1.5% resulted when both kV and HVL were taken into account; more significant discrepancies, within about 2%-6%, were obtained for backscatter factors, the present values being generally higher.

PENELOPE/PRIMO-calculated photon and electron spectra from clinical accelerators.

BACKGROUND: The availability of photon and electron spectra in digital form from current accelerators and Monte Carlo (MC) systems is scarce, and one of the packages widely used refers to linacs with a reduced clinical use nowadays. Such spectra are mainly intended for the MC calculation of detector-related quantities in conventional broad beams, where the use of detailed phase-space files (PSFs) is less critical than for MC-based treatment planning applications, but unlike PSFs, spectra can easily be transferred to other computer systems and users. METHODS: A set of spectra for a range of Varian linacs has been calculated using the PENELOPE/PRIMO MC system. They have been extracted from PSFs tallied for field sizes of 10 cm × 10 cm and 15 cm × 15 cm for photon and electron beams, respectively. The influence of the spectral bin width and of the beam central axis region used to extract the spectra have been analyzed. RESULTS: Spectra have been compared to those by other authors showing good agreement with those obtained using the, now superseded, EGS4/BEAM MC code, but significant differences with the most widely used photon data set. Other spectra, particularly for electron beams, have not been published previously for the machines simulated in this work. The influence of the bin width on the spectrum mean energy for 6 and 10 MV beams has been found to be negligible. The size of the region used to extract the spectra yields differences of up to 40% for the mean energies in 10 MV beams, but the maximum difference for TPR 20,10 values derived from depth-dose distributions does not exceed 2% relative to those obtained using the PSFs. This corresponds to kQ differences below 0.2% for a typical Farmer-type chamber, considered to be negligible for reference dosimetry. Different configurations for using electron spectra have been compared for 6 MeV beams, concluding that the geometry used for tallying the PSFs used to extract the spectra must be accounted for in subsequent calculations using the spectra as a source. CONCLUSIONS: An up-to-date set of consistent spectra for Varian accelerators suitable for the calculation of detector-related quantities in conventional broad beams has been developed and made available in digital form.

Fluence calculation methods in Monte Carlo dosimetry simulations.

Detailed information on the different methods used to compute charged-particle fluence spectra during a Monte Carlo (MC) calculation is scattered throughout the literature or discussed in internal reports. This work summarizes the most commonly used methods and introduces an alternative approach, makes comparisons between the different techniques, both from a theoretical ground and performing ad-hoc MC calculations, and discusses the advantages and constraints of each technique. It is concluded that methods based on the apportion of a track segment to the different energy bins of a linear or logarithmic grid are independent of the length of the track segment and the amount of energy loss between its extremes. This is the case for two of the methods presented, but not for a third one, the former group being considered to yield more accurate distributions in most cases. It is shown that the positron fluence contribution to the total restricted cema may amount up to several percent, and its omission lead to cema underestimates of that order. The influence of restricted radiative energy losses of electrons and positrons on fluence distribution and cema calculations are discussed on the grounds of the relative weight of restricted and unrestricted stopping powers, leading to expect a practically negligible influence on dosimetry calculations. The expectation is confirmed with MC calculations of a high-energy photon beam in gold, leading to the conclusion that restricted radiative energy losses can be disregarded for the most commonly used threshold energies for secondary charged particle production.

Dosimetry of small static fields used in external photon beam radiotherapy: Summary of TRS-483, the IAEA-AAPM international Code of Practice for reference and relative dose determination.

PURPOSE: A joint IAEA/AAPM international working group has developed a Code of Practice (CoP) for the dosimetry of small static fields used in external megavoltage photon beam radiotherapy, published by the IAEA as TRS-483. This summary paper introduces and outlines the main aspects of the CoP. METHODS: IAEA TRS-483 is a condensation of the wide range of different approaches that have been described in the literature for the reference dosimetry of radiotherapy machines with nominal accelerating potential up to 10 MV that cannot establish the conventional 10 cm × 10 cm reference field, and for the determination of field output factors for relative dosimetry in small static photon fields. The formalism used is based on that developed by Alfonso et al. [Med Phys. 2008;35:5179-5186] for this modality. RESULTS: Three introductory sections describe the rationale and context of the CoP, the clinical use of small photon fields, and the physics of small-field dosimetry. In the fourth section, definitions of terms that are specific to the CoP (as compared to previous CoPs for broad-beam reference dosimetry, such as IAEA TRS-398 and AAPM TG-51) are given; this section includes a list of the symbols and equivalences between IAEA and AAPM nomenclature to facilitate the practical implementation of the CoP by end users of IAEA TRS-398 and AAPM TG-51. The fifth section summarizes the equations and procedures that are recommended in the CoP and the sixth section provides an overview of the methods used to derive the data provided in IAEA TRS-483. CONCLUSIONS: This is the first time an international Code of Practice for the dosimetry of small photon fields based on comprehensive data and correction factors has been published. This joint IAEA/AAPM CoP will ensure consistent reference dosimetry traceable to the international System of Units and enable common and internationally harmonized procedures to be followed by radiotherapy centers worldwide for the dosimetry of small static megavoltage photon fields.

Comment on 'Origins of the changing detector response in small megavoltage photon radiation fields'.

A clarification is made with regard to the erroneous statement that assigns an incorrect conclusion to a paper by Andreo and Benmakhlouf (2017 Phys. Med. Biol. 62 1518-32) and in relation to other comments on that work. It is also argued that the Monte Carlo calculations made by the authors are based on physically incorrect input data for the fictitious materials used in their simulations, as density-effect corrections and stopping powers must correspond to the specific properties assigned to the fictitious material. Hence, their conclusions remain to be demonstrated using reliable input datasets.

Optimized I-values for use with the Bragg additivity rule and their impact on proton stopping power and range uncertainty.

Novel imaging modalities can improve the estimation of patient elemental compositions for particle treatment planning. The mean excitation energy (I-value) is a main contributor to the proton range uncertainty. To minimize their impact on beam range errors and quantify their uncertainties, the currently used I-values proposed in 1982 are revisited. The study aims at proposing a new set of optimized elemental I-values for use with the Bragg additivity rule (BAR) and establishing uncertainties on the optimized I-values and the BAR. We optimize elemental I-values for the use in compounds based on measured material I-values. We gain a new set of elemental I-values and corresponding uncertainties, based on the experimental uncertainties and our uncertainty model. We evaluate uncertainties on I-values and relative stopping powers (RSP) of 70 human tissues, taking into account statistical correlations between tissues and water. The effect of new I-values on proton beam ranges is quantified using Monte Carlo simulations. Our elemental I-values describe measured material I-values with higher accuracy than ICRU-recommended I-values (RMSE: 6.17% (ICRU), 5.19% (this work)). Our uncertainty model estimates an uncertainty component from the BAR to 4.42%. Using our elemental I-values, we calculate the I-value of water as 78.73 ± 2.89 eV, being consistent with ICRU 90 (78 ± 2 eV). We observe uncertainties on tissue I-values between 1.82-3.38 eV, and RSP uncertainties between 0.002%-0.44%. With transport simulations of a proton beam in human tissues, we observe range uncertainties between 0.31% and 0.47%, as compared to current estimates of 1.5%. We propose a set of elemental I-values well suited for human tissues in combination with the BAR. Our model establishes uncertainties on elemental I-values and the BAR, enabling to quantify uncertainties on tissue I-values, RSP as well as particle range. This work is particularly relevant for Monte Carlo simulations where the interaction probabilities are reconstructed from elemental compositions.

Monte Carlo simulations in radiotherapy dosimetry.

BACKGROUND: The use of the Monte Carlo (MC) method in radiotherapy dosimetry has increased almost exponentially in the last decades. Its widespread use in the field has converted this computer simulation technique in a common tool for reference and treatment planning dosimetry calculations. METHODS: This work reviews the different MC calculations made on dosimetric quantities, like stopping-power ratios and perturbation correction factors required for reference ionization chamber dosimetry, as well as the fully realistic MC simulations currently available on clinical accelerators, detectors and patient treatment planning. CONCLUSIONS: Issues are raised that include the necessity for consistency in the data throughout the entire dosimetry chain in reference dosimetry, and how Bragg-Gray theory breaks down for small photon fields. Both aspects are less critical for MC treatment planning applications, but there are important constraints like tissue characterization and its patient-to-patient variability, which together with the conversion between dose-to-water and dose-to-tissue, are analysed in detail. Although these constraints are common to all methods and algorithms used in different types of treatment planning systems, they make uncertainties involved in MC treatment planning to still remain "uncertain".

The physics of small megavoltage photon beam dosimetry.

The increased interest during recent years in the use of small megavoltage photon beams in advanced radiotherapy techniques has led to the development of dosimetry recommendations by different national and international organizations. Their requirement of data suitable for the different clinical options available, regarding treatment units and dosimetry equipment, has generated a considerable amount of research by the scientific community during the last decade. The multiple publications in the field have led not only to the availability of new invaluable data, but have also contributed substantially to an improved understanding of the physics of their dosimetry. This work provides an overview of the most important aspects that govern the physics of small megavoltage photon beam dosimetry.

Collision-kerma conversion between dose-to-tissue and dose-to-water by photon energy-fluence corrections in low-energy brachytherapy.

The AAPM TG-43 brachytherapy dosimetry formalism, introduced in 1995, has become a standard for brachytherapy dosimetry worldwide; it implicitly assumes that charged-particle equilibrium (CPE) exists for the determination of absorbed dose to water at different locations, except in the vicinity of the source capsule. Subsequent dosimetry developments, based on Monte Carlo calculations or analytical solutions of transport equations, do not rely on the CPE assumption and determine directly the dose to different tissues. At the time of relating dose to tissue and dose to water, or vice versa, it is usually assumed that the photon fluence in water and in tissues are practically identical, so that the absorbed dose in the two media can be related by their ratio of mass energy-absorption coefficients. In this work, an efficient way to correlate absorbed dose to water and absorbed dose to tissue in brachytherapy calculations at clinically relevant distances for low-energy photon emitting seeds is proposed. A correction is introduced that is based on the ratio of the water-to-tissue photon energy-fluences. State-of-the art Monte Carlo calculations are used to score photon fluence differential in energy in water and in various human tissues (muscle, adipose and bone), which in all cases include a realistic modelling of low-energy brachytherapy sources in order to benchmark the formalism proposed. The energy-fluence based corrections given in this work are able to correlate absorbed dose to tissue and absorbed dose to water with an accuracy better than 0.5% in the most critical cases (e.g. bone tissue).

Role of the density, density effect and mean excitation energy in solid-state detectors for small photon fields.

A number of recent publications on small photon beam dosimetry aim at contributing to the understanding of the response of solid-state detectors in small fields. Some of them assign the difference in response to the mass density, or to the electron density, of the sensitive detector material relative to that of water. This work analyses the role of the mass and electron density ([Formula: see text]), density effect (δ) and mean excitation energy (I-value) of some detector materials in a 6 MV photon beam of 0.5 cm radius, its rationale being that the response of a detector depends critically on the stopping-power ratio detector-to-water. The influence on the detector response of volume scaling by electron density, and of electron single and multiple scattering, is also investigated. Detector materials are water, diamond and silicon, and additional materials are included for consistency in the analysis. A detailed analysis on the ([Formula: see text]) dependence of stopping-power ratios shows that the density effect δ depends both on the electron density and on the I-value of the medium, but not on the mass density ρ alone as is usually assumed. This leads to a double dependence of stopping-power ratios on the I-value and questions the adequacy of a 'density perturbation factor' or of common interpretations of detector response in terms of ρ alone. Differences in response can be described in terms of the variation of stopping power ratios detector-to-water, mainly due to different I-values and to a lesser extent to different values of electron density. It is found that at low energies the trend of Monte Carlo-calculated electron fluence spectra inside the detector materials depends solely on their I-values. No dependence on mass density or density effect alone is observed at any energy. The trend of restricted-cema ratios to water (as a substitute of absorbed dose ratios) follows that of stopping-power ratios at 1 MeV, the most probable energy of differential restricted-cema distributions in this study. It is concluded that the combined effect of the I-value and the dependence of δ on [Formula: see text] governs the restricted-cema values, and that neither ρ or a [Formula: see text] alone explain the different response of diverse detector materials. The results show that, for the small non-scaled and scaled volumes in this work, [Formula: see text] is practically constant and that in both cases the contribution of electron scattering to the restricted-cema values is about 2%.