Monte Carlo uncertainty analysis of dose estimates in radiochromic film dosimetry with single-channel and multichannel algorithms

PurposeTo provide a multi-stage model to calculate uncertainty in radiochromic film dosimetry with Monte-Carlo techniques. This new approach is applied to single-channel and multichannel algorithms.Material and methodsTwo lots of Gafchromic EBT3 are exposed in two different Varian linacs. They are read with an EPSON V800 flatbed scanner. The Monte-Carlo techniques in uncertainty analysis provide a numerical representation of the probability density functions of the output magnitudes. From this numerical representation, traditional parameters of uncertainty analysis as the standard deviations and bias are calculated. Moreover, these numerical representations are used to investigate the shape of the probability density functions of the output magnitudes. Also, another calibration film is read in four EPSON scanners (two V800 and two 10000XL) and the uncertainty analysis is carried out with the four images.ResultsThe dose estimates of single-channel and multichannel algorithms show a Gaussian behavior and low bias. The multichannel algorithms lead to less uncertainty in the final dose estimates when the EPSON V800 is employed as reading device. In the case of the EPSON 10000XL, the single-channel algorithms provide less uncertainty in the dose estimates for doses higher than four Gy.ConclusionA multi-stage model has been presented. With the aid of this model and the use of the Monte-Carlo techniques, the uncertainty of dose estimates for single-channel and multichannel algorithms are estimated. The application of the model together with Monte-Carlo techniques leads to a complete characterization of the uncertainties in radiochromic film dosimetry.     

Polarized dosimetry method for Gafchromic EBT3

PurposeTo analyze the changes in the polarization state of the flatbed scanner light caused by the EBT3 films and to propose a new method for correcting the lateral effects.Methods and materialsThe polarization changes induced by radiochromic films are analyzed using linear polarizing film. Based on the results, the linear polarizing films are used in the scanning process of the EBT3 films. This method is tested against the conventional EBT3 dosimetry using a series of simple regular beams and 21 cases of IMRT.ResultsThe mean results are statically different from the conventional dosimetry with EBT3. Depending on the transmission axis of the polarizing sheet, the results are better or worse compared to conventional dosimetry EBT3 film. When the transmission axis of the polarizing sheet is parallel to the coating direction, the dosimetry results are better and its variability is smaller. However, when the polarizer transmission axis is perpendicular to the coating direction, results are worse as well as its variability.ConclusionUsing a polarized film with the polarization axis parallel to the coating direction of the radiochromic film, and preferably above it, significantly improves the dosimetry results and is an easy and inexpensive way to correct the lateral artifacts of the conventional EBT3 dosimetry.     

On the re-calibration process in radiochromic film dosimetry

PurposeThe accuracy and precision of the dose estimates obtained with radiochromic film dosimetry are investigated in a clinical environment. The improvement in the accuracy of dose estimates reached with corrective methods is analyzed. Two novel re-calibration algorithms for radiochromic film dosimetry are presented.MethodsTwo different EBT3 lots are evaluated in two different centres. They are calibrated in Varian linacs and read in two different EPSON scaners. Once the lots are calibrated, three films per lot are considered and divided into stripes that are exposed to known doses. Several dosimetry protocols usually employed in radiochromic film dosimetry are used to convert film responses to absorbed doses. These protocols are characterized by different choices of the film responses or different sensitometric curves. Finally, the accuracy and reproducibility of the dose estimates is investigated with and without the corrective methods.Results and ConclusionsThe variabilities that affect radiochromic film dosimetry, such as intra-lot variability, inter-scan variability, post-exposure time and film autodevelopment may give rise to inaccuracies in the dose estimates. However, the implementation of re-calibration methods leads to more accurate dose estimates. All the investigated protocols showed more accurate and reproducible results when the re-calibrated methods were employed. So, the novel re-calibration methods may be applied in order to improve the accuracy and reproducibility of radiochromic film dosimetry.     

Evaluation of a LED-based flatbed document scanner for radiochromic film dosimetry in transmission mode

Flatbed scanners are the most frequently used reading instrument for radiochromic film dosimetry because its low cost, high spatial resolution, among other advantages. These scanners use a fluorescent lamp and a CCD array as light source and detector, respectively. Recently, manufacturers of flatbed scanners replaced the fluorescent lamp by light emission diodes (LED) as a light source. The goal of this work is to evaluate the performance of a commercial flatbed scanner with LED based source light for radiochromic film dosimetry. Film read out consistency, response uniformity, film-scanner sensitivity, long term stability and total dose uncertainty was evaluated. In overall, the performance of the LED flatbed scanner is comparable to that of a cold cathode fluorescent lamp (CCFL). There are important spectral differences between LED and CCFL lamps that results in a higher sensitivity of the LED scanner in the green channel. Total dose uncertainty, film response reproducibility and long-term stability of LED scanner are slightly better than those of the CCFL. However, the LED based scanner has a strong non-uniform response, up to 9%, that must be adequately corrected for radiotherapy dosimetry QA. The differences in light emission spectra between LED and CCFL lamps and its potential impact on film-scanner sensitivity suggest that the design of a dedicated flat-bed scanner with LEDs may improve sensitivity and dose uncertainty in radiochromic film dosimetry.     

GafChromic® EBT3 films for patient specific IMRT QA using a multichannel approach

PurposeTo evaluate EBT3 for pre-treatment patient specific quality assurance (QA). The method we propose combines the experience gained in our center with the guidelines of the protocol proposed by Lewis et al. in 2012. To compare the multichannel approach with the single channel dosimetry.MethodsGafchromic® EBT3 films were irradiated both at linac and TomoTherapy and calibration curves were obtained. A series of irradiations with simple fields (uniform dose distributions on regular shaped targets) was performed. In a second stage, films were exposed to full clinical plans at linac (step and shoot IMRT and VMAT). At TomoTherapy dose maps were obtained for a clinical plan in three different coronal planes. Films were digitized using an Epson 10000XL scanner and FilmQA™ Pro software was employed for the analysis.ResultsThe measured calibration curves suggest that, at least for the two beams taken into account (6 MV linac and TomoTherapy), a single calibration can be successfully adopted for each film lot. The application of the multichannel optimization method strongly improves the results in terms of gamma passing rates of the comparison between measured and calculated maps.ConclusionsUp to now EBT films, although attractive, were not preferred for routine patient specific QA due to their complex and time consuming processing and to the challenging work of characterization. The application of the mentioned protocol, together with some additional precautions, and the adoption of the multichannel optimization dosimetry, make this detector a handy and reliable tool for patient specific QA.     

Characterisation of two new radiochromic gel dosimeters TruView™ and ClearView™ in combination with the vista™ optical CT scanner: A feasibility study

PurposeThis study aims at characterising the properties of TruView™ and ClearView™ two new gel dosimeters (Modus Medical Devices Inc.) and at studying the feasibility of relative dosimetry using these dosimeters and the Vista™ Optical CT scanner to accurately evaluate dose.MethodsIn this work, we investigated key dosimetric aspects (dose response, energy and dose rate dependence) and stability of these radiochromic gels initiated in preliminary works (Huet et al., 2017; Colnot et al., 2017) using spectrophotometric measurements. Moreover, by mean of optical CT scanning (Vista™), their performances to measure relative depth dose (PDD) and cross profiles were analysed.ResultsTruView™ and ClearView™ present a linear dose response up to 20 Gy and up to 80 Gy respectively, independent of both photon beam energy (4–18 MV) and dose rate (up to 9.9 Gy/min) (Huet et al., 2017; Colnot et al., 2017). ClearView™ response proves to be stable for a week post-irradiation and uniform within the batch whereas TruView™ presents an unstable but uniform response. Optical CT scanning generates errors due to stray light that need to be corrected in order to use these gels; ClearView™ scanning particularly requires important precautions. After corrections, those gels used in combination with the Vista™ scanner show promising spatial and dosimetric precision (dose difference <5%). Finally, TruView™ is reusable and presents excellent reproducible response (maximum 3% difference) and the ClearView™ dosimeter presents good spatial stability (0.5% difference after 6 days).ConclusionThis study provides important knowledge about two gel dosimeters presenting interesting dosimetric properties. A study is ongoing to benchmark those promising candidates for clinical dose verification.     

Evaluation of Gafchromic® EBT3 films characteristics in therapy photon,electron and proton beams

PurposeTo evaluate the uncertainties and characteristics of radiochromic film-based dosimetry system using the EBT3 model Gafchromic^® film in therapy photon, electron and proton beams.Material and methodsEBT3 films were read using an EPSON Expression 10000XL/PRO scanner. They were irradiated in five beams, an Elekta SL25 6 MV and 18 MV photon beam, an IBA 100 MeV 5 × 5 cm² proton beam delivered by pencil-beam scanning, a 60 MeV fixed proton beam and an Elekta SL25 6 MeV electron beam. Reference dosimetry was performed using a FC65-G chamber (Elekta beam), a PPC05 (IBA beam) and both Markus 1916 and PPC40 Roos ion-chambers (60 MeV proton beam). Calibration curves of the radiochromic film dosimetry system were acquired and compared within a dose range of 0.4–10 Gy. An uncertainty budget was estimated on films irradiated by Elekta SL25 by measuring intra-film and inter-film reproducibility and uniformity; scanner uniformity and reproducibility; room light and film reading delay influences.ResultsThe global uncertainty on acquired optical densities was within 0.55% and could be reduced to 0.1% by placing films consistently at the center of the scanner. For all beam types, the calibration curves are within uncertainties of measured dose and optical densities. The total uncertainties on calibration curve due to film reading and fitting were within 1.5% for photon and proton beams. For electrons, the uncertainty was within 2% for dose superior to 0.8 Gy.ConclusionsThe low combined uncertainty observed and low beam and energy-dependence make EBT3 suitable for dosimetry in various applications.     

Comparison of dose response functions for EBT3 model GafChromic™ film dosimetry system

ObjectiveDifferent dose response functions of EBT3 model GafChromic™ film dosimetry system have been compared in terms of sensitivity as well as uncertainty vs. error analysis. We also made an assessment of the necessity of scanning film pieces before and after irradiation.MethodsPieces of EBT3 film model were irradiated to different dose values in Solid Water (SW) phantom. Based on images scanned in both reflection and transmission mode before and after irradiation, twelve different response functions were calculated. For every response function, a reference radiochromic film dosimetry system was established by generating calibration curve and by performing the error vs. uncertainty analysis.ResultsResponse functions using pixel values from the green channel demonstrated the highest sensitivity in both transmission and reflection mode. All functions were successfully fitted with rational functional form, and provided an overall one-sigma uncertainty of better than 2% for doses above 2 Gy. Use of pre-scanned images to calculate response functions resulted in negligible improvement in dose measurement accuracy.ConclusionAlthough reflection scanning mode provides higher sensitivity and could lead to a more widespread use of radiochromic film dosimetry, it has fairly limited dose range and slightly increased uncertainty when compared to transmission scan based response functions. Double-scanning technique, either in transmission or reflection mode, shows negligible improvement in dose accuracy as well as a negligible increase in dose uncertainty. Normalized pixel value of the images scanned in transmission mode shows linear response in a dose range of up to 11 Gy.     

Design and clinical use of a rotational phantom for dosimetric verification of IMRT/VMAT treatments

PurposeTo describe the design and clinical use of a rotational phantom for dosimetric verification of IMRT/VMAT treatment plans using radiochromic film.MethodsA solid water cylindrical phantom was designed with separable upper and lower halves and rests on plastic bearings allowing for 360° rotation about its central axis. The phantom accommodates a half sheet of radiochromic film, and by rotating the cylinder, the film can be placed in any plane between coronal and sagittal. Calculated dose planes coinciding with rotated film measurements are exported by rotating the CT image and dose distribution within the treatment planning system. The process is illustrated with 2 rotated film measurements of an SRS treatment plan involving 4 separate targets. Additionally, 276 patient specific QA measurements were obtained with the phantom and analyzed with a 2%/2 mm gamma criterion.ResultsThe average 2%/2 mm gamma passing rate for all 276 plans was 99.3%. Seventy-two of the 276 plans were measured with the plane of the film rotated between the coronal and sagittal planes and had an average passing rate of 99.4%.ConclusionsThe rotational phantom allows for accurate film measurements in any plane. With this technique, regions of a dose distribution which might otherwise require multiple sagittal or coronal measurements can be verified with as few as a single measurement. This increases efficiency and, in combination with the high spatial resolution inherent to film dosimetry, makes the rotational technique an attractive option for patient-specific QA.     

Calibration of MTT assay in proton beams using radiochromic films

PurposeThis study provides methodology of calibrating as well as controlling the output for an MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) colorimetric assay irradiated in a low energy proton beam using EBT3-model GAFCHROMIC^TM film, without correcting for quenching effect.MethodsA calibrated Markus ionization chamber was used to measure the depth dose and beam output for 26.5 MeV protons produced by a CS30 cyclotron. A time-controlled aluminum cylinder was added in front of the horizontal beam-exit serving as a radiation shutter. Following the TRS-398 reference dosimetry protocol for proton beams, the output was calibrated in water at a reference depth of 3 mm. EBT3 film was calibrated for doses up to 8 Gy at the same depth. To verify the dose distribution for each 96-well MTT assay plate, EBT3 film was placed at the reference depth during irradiation and cell doses were scaled by measured percent depth dose (PDD) data.ResultsThe radiochromic film dosimetry system in this study provides dose measurements with an uncertainty better than 3.3% for doses higher than 1 Gy. From a single exposure and utilizing the Gaussian shape of the beam, multiple dose points can be obtained within different wells of the same plate ranging from 6.9 Gy (sigma ∼4%) in the central well, and 2 Gy (sigma ∼8%) for wells positioned closer to the periphery.ConclusionsWe described a methodology for radiochromic film-based dose monitoring system, using low-energy protons, which can be used for the MTT assay in any proton beam, except within Bragg peak region.     

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.     

High throughput film dosimetry in homogeneous and heterogeneous media for a small animal irradiator

PurposeWe have established a high-throughput Gafchromic film dosimetry protocol for narrow kilovoltage beams in homogeneous and heterogeneous media for small-animal radiotherapy applications. The kV beam characterization is based on extensive Gafchromic film dosimetry data acquired in homogeneous and heterogeneous media. An empirical model is used for parameterization of depth and off-axis dependence of measured data.MethodsWe have modified previously published methods of film dosimetry to suit the specific tasks of the study. Unlike film protocols used in previous studies, our protocol employs simultaneous multi-channel scanning and analysis of up to nine Gafchromic films per scan. A scanner and background correction were implemented to improve accuracy of the measurements. Measurements were taken in homogeneous and inhomogeneous phantoms at 220 kVp and a field size of 5 × 5 mm². The results were compared against Monte Carlo simulations.ResultsDose differences caused by variations in background signal were effectively removed by the corrections applied. Measurements in homogeneous phantoms were used to empirically characterize beam data in homogeneous and heterogeneous media. Film measurements in inhomogeneous phantoms and their empirical parameterization differed by about 2%–3%. The model differed from MC by about 1% (water, lung) to 7% (bone). Good agreement was found for measured and modelled off-axis ratios.ConclusionsEBT2 films are a valuable tool for characterization of narrow kV beams, though care must be taken to eliminate disturbances caused by varying background signals. The usefulness of the empirical beam model in interpretation and parameterization of film data was demonstrated.     

Gafchromic film dosimetry: Four years experience using FilmQA Pro software and Epson flatbed scanners

Purposes: To assess performance of FilmQA Pro software for pre-treatment patient-specific quality assurance (QA), using radiochromic films and two commercial flatbed scanners. To evaluate a novel multichannel approach compared to the classical red channel evaluation.Material and methodsPatient films (mostly EBT2 films, one box of EBT3) were digitalized using successively two flatbed scanners: the A4-size Epson V750 and the A3-size Epson 10000XL. Prior to patient dose verification, basic characteristics of films and scanners were investigated. Patient films were analyzed using FilmQA Pro software, which enables to use the signal from all three colour channels (Red, Green, Blue).ResultsCompared to the red channel evaluation, multichannel evaluation presents better passing rates with regard to local gamma index. As expected, we obtained better results using A3-size scanner compared to A4-size scanner, especially when considering large region of interest. An observation of great interest was made for both scanners: after intensive use, a tilting in the blue transmittance profiles appeared in the lamp direction, making multichannel analysis unsuitable for accurate dose evaluation.     

A protocol for absolute dose verification of SBRT/SRS treatment plans using Gafchromic™ EBT-XD films

PurposeTo provide a practical protocol for absolute dose verification of stereotactic body radiotherapy (SBRT) and stereotactic radiosurgery (SRS) treatment plans, based on our clinical experience. It aims to be a concise summary of the main aspects to be considered when establishing an accurate film dosimetry system.MethodsProcedures for film calibration and conversion to dose are described for a dosimetry system composed of Gafchromic™ EBT-XD films and a flatbed document scanner. Factors that affect the film-scanner response are also reviewed and accounted for. The accuracy of the proposed methodology was assessed by taking a set of strips irradiated to known doses and its applicability is illustrated for ten SBRT/SRS treatment plans. The film response was converted to dose using red and triple channel dosimetry. The agreement between the planned and measured dose distributions was evaluated using global gamma analysis with criteria of 3%/2mm 10% threshold (TH), 2%/2mm 10% TH, and 2%/2mm 20% TH.ResultsThe differences between the expected and determined doses from the strips analysis were 0.9 ± 0.6% for the red channel and 1.1 ± 0.7% for the triple channel method. Regarding the SBRT/SRS plans verification, the mean gamma passing rates were 99.5 ± 1.0% vs 99.6 ± 1.0% (3%/2mm 10% TH), 96.9 ± 3.5% vs 99.1 ± 1.3% (2%/2mm 10% TH) and 98.4 ± 1.8% vs 98.8 ± 1.5% (2%/2mm 20% TH) for red and triple channel dosimetry, respectively.ConclusionsThe proposed protocol allows for accurate absolute dose verification of SBRT/SRS treatment plans, applying both single and triple channel methods. It may work as a guide for users that intend to implement a film dosimetry system.     

Film-based delivery quality assurance for robotic radiosurgery: Commissioning and validation

PurposeRobotic radiosurgery demands comprehensive delivery quality assurance (DQA), but guidelines for commissioning of the DQA method is missing. We investigated the stability and sensitivity of our film-based DQA method with various test scenarios and routine patient plans. We also investigated the applicability of tight distance-to-agreement (DTA) Gamma-Index criteria.Methods and materialWe used radiochromic films with multichannel film dosimetry and re-calibration and our analysis was performed in four steps: 1) Film-to-plan registration, 2) Standard Gamma-Index criteria evaluation (local-pixel-dose-difference ≤2%, distance-to-agreement ≤2 mm, pass-rate ≥90%), 3) Dose distribution shift until maximum pass-rate (Max_γ) was found (shift acceptance <1 mm), and 4) Final evaluation with tight DTA criteria (≤1 mm). Test scenarios consisted of purposefully introduced phantom misalignments, dose miscalibrations, and undelivered MU. Initial method evaluation was done on 30 clinical plans.ResultsOur method showed similar sensitivity compared to the standard End-2-End-Test and incorporated an estimate of global system offsets in the analysis. The simulated errors (phantom shifts, global robot misalignment, undelivered MU) were detected by our method while standard Gamma-Index criteria often did not reveal these deviations. Dose miscalibration was not detected by film alone, hence simultaneous ion-chamber measurement for film calibration is strongly recommended. 83% of the clinical patient plans were within our tight DTA tolerances.ConclusionOur presented methods provide additional measurements and quality references for film-based DQA enabling more sensitive error detection. We provided various test scenarios for commissioning of robotic radiosurgery DQA and demonstrated the necessity to use tight DTA criteria.     

An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®

PurposeA method of calibrating radiochromic films for Gamma Knife^® (GK) dosimetry was developed. The applicability and accuracy of the new method were examined.MethodsThe dose distribution for a sixteen millimeter single-shot from a GK was built using a reference film that was calibrated using the conventional multi-film calibration (MFC) method. Another film, the test film, from a different set of films was irradiated under the same conditions as the reference film. The calibration curve for the second set of films was obtained by assigning the dose distribution of the reference film to the optical density of the test film, point by point. To assess the accuracy of this single-film calibration (SFC) method, differences between gamma index pass rates (GIPRs) were calculated.ResultsThe SFC curves were successfully obtained with estimated errors of 1.46%. GIPRs obtained with the SFC method for films irradiated using a single-shot showed differences less than one percentage point when dose difference criterion (ΔD) was 2% and the distance to agreement criterion (Δd) was 1 mm. The GIPRs of the SFC method when the films were irradiated following a virtual target treatment plan were consistent with the GIPRs of the MFC method, with differences of less than 0.2 percentage points for ΔD = 1% and Δd = 1 mm.ConclusionThe accuracy of the SFC method is comparable to that of conventional multi-film calibration method for GK film dosimetry.     

Prevention of Transfusion-Associated Graft-versus-Host Disease by Irradiation: Technical Aspect of a New Ferrous Sulphate Dosimetric System

Irradiation of whole blood and blood components before transfusion is currently the only accepted method to prevent Transfusion-Associated Graft-Versus-Host-Disease (TA-GVHD). However, choosing the appropriate technique to determine the dosimetric parameters associated with blood irradiation remains an issue. We propose a dosimetric system based on the standard Fricke Xylenol Gel (FXG) dosimeter and an appropriate phantom. The modified dosimeter was previously calibrated using a ⁶⁰Co teletherapy unit and its validation was accomplished with a ¹³⁷Cs blood irradiator. An ionization chamber, standard FXG, radiochromic film and thermoluminescent dosimeters (TLDs) were used as reference dosimeters to determine the dose response and dose rate of the ⁶⁰Co unit. The dose distributions in a blood irradiator were determined with the modified FXG, the radiochromic film, and measurements by TLD dosimeters. A linear response for absorbed doses up to 54 Gy was obtained with our system. Additionally, the dose rate uncertainties carried out with gel dosimetry were lower than 5% and differences lower than 4% were noted when the absorbed dose responses were compared with ionization chamber, film and TLDs.     

Use of a control film piece in radiochromic film dosimetry

PurposeRadiochromic films change their color upon irradiation due to polymerization of the sensitive component embedded within the sensitive layer. However, agents, other than monitored radiation, can lead to a change in the color of the sensitive layer (temperature, humidity, UV light) that can be considered as a background signal and can be removed from the actual measurement by using a control film piece. In this work, we investigate the impact of the use of control film pieces on both accuracy and uncertainty of dose measured using radiochromic film based reference dosimetry protocol.MethodsWe irradiated “control” film pieces (EBT3 GafChromic^TM film model) to known doses in a range of 0.05–1 Gy, and five film pieces of the same size to 2, 5, 10, 15 and 20 Gy, considered to be “unknown” doses. Depending on a dose range, two approaches to incorporating control film piece were investigated: signal and dose corrected method.ResultsFor dose values greater than 10 Gy, the increase in accuracy of 3% led to uncertainty loss of 5% by using dose corrected approach. At lower doses and signals of the order of 5%, we observed an increase in accuracy of 10% with a loss of uncertainty lower than 1% by using the corrected signal approach.ConclusionsIncorporation of the signal registered by the control film piece into dose measurement analysis should be a judgment call of the user based on a tradeoff between deemed accuracy and acceptable uncertainty for a given dose measurement.