Research Article| Volume 98, P18-27, June 2022

# Dose area product primary standards established by graphite calorimetry at the LNE-LNHB for small radiation fields in radiotherapy

Open AccessPublished:April 27, 2022

## Highlights

• Lack of primary standards for small fields.
• Dose Area Product (DAP) is used to overcome the point dose traceability breakdown.
• Primary standards in terms of DAP are established down to 5 mm field size.
• Promising approach to surrogate the absorbed dose at a point in small fields.

## Abstract

### Purpose

To present primary standards establishment in terms of Dose Area Product (DAP) for small field sizes.

### Methods

A large section graphite calorimeter and two plane-parallel ionization chambers were designed and built in-house. These chambers were calibrated in a 6 MV FFF beam at the maximum dose rate of 1400 UM/min for fields defined by specifically designed circular collimators of 5, 7.5, 10, 13 and 15 mm diameter and jaws of 5, 7, 10, 13 and 15 mm side length on a Varian TrueBeam linac.

### Results

The two chambers show the same behaviour regardless of field shape and size. From 5 to 15 mm, calibration coefficients slightly increase with the field size with a magnitude of 1.8% and 1.1% respectively for the two chambers, and are independent of the field shape. This tendency was confirmed by Monte Carlo calculations. The average associated uncertainty of the calibration coefficients is around 0.6% at k=1.

### Conclusions

For the first time, primary standards in terms of DAP were established by graphite calorimetry for an extended range of small field sizes. These promising results open the door for an alternative approach in small fields dosimetry.

## 1. Introduction

Use of small fields is becoming standard in actual treatment modalities such as intensity-modulated radiotherapy (IMRT), volumetric-modulated arctherapy (VMAT) and stereotactic radiotherapy (SRT) thanks to the generalized availability of multileaf collimators (MLC). In particular, SRT is a widely used state-of-the-art technique combining high doses in small volumes accurately targeted, allowing a better sparing of surrounding healthy tissues. Initially developed to treat brain lesions [
• Leksell L.
The stereotaxic method and radiosurgery of the brain.
,
• Leksell L.
Cerebral radiosurgery. I. Gammathalanotomy in two cases of intractable pain.
], its use has been extended to all types of extra-cranial lesions (lung, liver, prostate, …) [
• Timmerman R.D.
• Hu C.
• Michalski J.M.
• Galvin J.
• Johnstone D.W.
• et al.
Long-term results of stereotactic body radiation therapy in medically inoperable stage I non-small cell lung cancer.
,
• Herfarth K.K.
• Debus J.
• Lohr F.
• Bahner M.L.
• Rhein B.
• Fritz P.
• et al.
Stereotactic single-dose radiation therapy of liver tumors: results of a phase I/II trial.
,
• Boike T.P.
• Lotan Y.
• Cho L.C.
• Brindle J.
• DeRose P.
• Xie X.-J.
• et al.
Phase I Dose-Escalation Study of Stereotactic Body Radiation Therapy for Low- and Intermediate-Risk Prostate Cancer.
] with irradiation fields as small as 4 mm. So far, primary standards for high-energy photons in radiotherapy are established in a 10 × 10 cm2 field size at 10 g cm−2 depth in terms of absorbed dose to water at a point, according to recommendations of international dosimetric protocols [

INTERNATIONAL ATOMIC ENERGY AGENCY, Absorbed Dose Determination in External Beam Radiotherapy: An International Code of Practice for Dosimetry Based on Standards of Absorbed Dose to Water. Technical Reports Series No 398, IAEA, Vienna 2000.

,
• Almond P.R.
• Biggs P.J.
• Coursey B.M.
• Hanson W.F.
• Huq M.S.
• Nath R.
• et al.
AAPM’s TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams.
]. These protocols, published more than two decades ago and updated a few times to include new dosimeters, are used today in the absence of primary standards adapted to current clinical conditions.
Similarly, the emergence of specialized radiation delivery units (GammaKnife®, Tomotherapy®, Cyberknife®, and more recently MR-linacs, ZAP-X®) for which the conventional reference 10 × 10 cm2 field size and 100 cm source-to-surface distance (SSD) or source-to-detector (SDD) conditions are not applicable underlined the need of a new formalism for reference dosimetry of small fields [
• Alfonso R.
• Andreo P.
• Capote R.
• Huq M.S.
• Kilby W.
• Kjäll P.
• et al.
A new formalism for reference dosimetry of small and nonstandard fields.
]. Consequently, a joint IAEA-AAPM code of practice named TRS 483 was developed to standardize guidance for dosimetry of small static fields used in external beam radiotherapy [
• INTERNATIONAL ATOMIC ENERGY AGENCY
Dosimetry of Small Static Fields Used in External Beam Radiotheray : An International Code of Practice for Reference and Relative Dose Determination. Technical Reports Series No 483, IAEA.
]. Relative dosimetry in particular through field output factors (OF), which account for differences between reference and clinical field sizes conditions, is extensively discussed. Indeed, contrary to usual broad beams, OF cannot be accurately approximated as the ratio of detector readings and a field output correction factor depending on machine, beam quality, detector and field size-dependent perturbations has to be used [
• Benmakhlouf H.
• Sempau J.
• Andreo P.
Output correction factors for nine small field detectors in 6 MV radiation therapy photon beams: a PENELOPE Monte Carlo study.
,
• Francescon P.
• Cora S.
• Satariano N.
Calculation of k(Q(clin), Q(msr)) (f(clin), f(msr)) for several small detectors and for two linear accelerators using Monte Carlo simulations.
,
• Francescon P.
• Kilby W.
• Noll J.M.
• Masi L.
• Satariano N.
• Russo S.
Monte Carlo simulated corrections for beam commissioning measurements with circular and MLC shaped fields on the CyberKnife M6 System: a study including diode, microchamber, point scintillator, and synthetic microdiamond detectors.
,
• Bassinet C.
• Huet C.
• Derreumaux S.
• Brunet G.
• Chéa M.
• Baumann M.
• et al.
Small fields output factors measurements and correction factors determination for several detectors for a CyberKnife® and linear accelerators equipped with microMLC and circular cones.
]. In that way, IAEA TRS 483 provides an extensive set of correction factors for a set of detectors for Cyberknife®, Tomotherapy®, Gamma Knife®, and linac’s for with flattening filter (WFF) and flattening filter free (FFF) beams.
OF determination using these correction factors enables, in theory, to be free from the detector choice to be used for small fields measurement (as long as a correction factor is available). Nevertheless, the use of IAEA TRS 483 still raises a number of questions:
• -
A clear reduction in the dispersion of results obtained with different detectors has been shown by applying the IAEA TRS 483 correction factors [
• Huq M.S.
• Hwang M.-S.
• Teo T.P.
• Jang S.Y.
• Heron D.E.
• Lalonde R.J.
A dosimetric evaluation of the IAEA-AAPM TRS483 code of practice for dosimetry of small static fields used in conventional linac beams and comparison with IAEA TRS-398, AAPM TG51, and TG51 Addendum protocols.
,
• Dufreneix S.
• Bellec J.
• Josset S.
• Vieillevigne L.
Field output factors for small fields: A large multicentre study.
]. However, dispersions on the OF up to 5 % have been reported [
• Ghazal M.
• Westermark M.
• Kaveckyte V.
• Carlsson‐Tedgren Å.
• Benmakhlouf H.
6-MV small field output factors: intra-/intermachine comparison and implementation of TRS-483 using various detectors and several linear accelerators.
] and confirmed by a larger scale study [
• Dufreneix S.
• Bellec J.
• Josset S.
• Vieillevigne L.
Field output factors for small fields: A large multicentre study.
]. Therefore, the use of several detectors with their associated correction factors does not allow the determination of a unique OF. In all cases, IAEA TRS 483 and the recent AAPM TG 155 report [
• Das I.J.
• Francescon P.
• Moran J.M.
• Ahnesjö A.
• Cheng C.-W.
• et al.
Report of AAPM Task Group 155: Megavoltage photon beam dosimetry in small fields and non-equilibrium conditions.
] recommend using at least two detectors and comparing the results.
• -
IAEA TRS 483 correction factors were determined from data up to 2015. For PTW 60019 microdiamond detector, correction factors to be applied for fields smaller than 1 × 1 cm2 is still subject to debate in the medical physics community [
• Das I.J.
• Francescon P.
Comments on the TRS-483 protocol on small field dosimetry.
].
• -
New detectors for small fields measurements arrived on the market [
• Reggiori G.
• Mancosu P.
• Suchowerska N.
• Lobefalo F.
• Stravato A.
• Tomatis S.
• et al.
Characterization of a new unshielded diode for small field dosimetry under flattening filter free beams.
,
• Schönfeld A.-B.
• Poppinga D.
• Kranzer R.
• De Wilde R.L.
• Willborn K.
• Poppe B.
• et al.
Technical Note: Characterization of the new microSilicon diode detector.
,
• Galavis P.E.
• Hu L.
• Holmes S.
• Das I.J.
Characterization of the plastic scintillation detector Exradin W2 for small field dosimetry.
] and sometimes replace an existing model tabulated in the IAEA TRS 483. The use of these new detectors for OF is conditional on the knowledge of the associated correction factors. But as pointed out by the authors of the IAEA TRS 483, ‘users adopting new specific datasets appearing in the literature should be aware of the risks they assume’ [

Palmans H, Andreo P, Huq MS, Seuntjens J, Christaki KE, Meghzifene A. Reply to “Comments on the TRS-483 Protocol on Small field Dosimetry” [Med. Phys. 45(12), 5666–5668 (2018)]. Medical Physics 2018;45:5669–71. https://doi.org/10.1002/mp.13235.

]. The same issue appears for recent and future machines not tabulated in the code of practice.
The French primary dosimetry standards laboratory (PDSL) LNE-LNHB began to study the metrology in small beams with the construction of a new absorbed dose standard, the GR10 graphite calorimeter [
• Daures J.
• Ostrowsky A.
• Rapp B.
Small section graphite calorimeter (GR-10) at LNE-LNHB for measurements in small beams for IMRT.
], with a small sensitive element named core, such as Øcore = 6 mm. This 6 mm core diameter is small compared to the typical core diameter of a graphite calorimeter [
• Daures J.
• Ostrowsky A.
Test of the new GR9 graphite calorimeter Comparison with GR8.
,
• Picard S.
• Burns D.
• Roger P.
Construction of an absorbed-dose graphite calorimeter.
,
• Morishita Y.
• Kato M.
• Takata N.
• Kurosawa T.
• Tanaka T.
• Saito N.
A standard for absorbed dose rate to water in a 60Co field using a graphite calorimeter at the National Metrology Institute of Japan.
]. By calibrating a small volume ionization chamber Exradin A1SL, reference in terms of absorbed dose to water at a point in a 2 × 2 cm2 field has been established [

Delaunay F, De Carlan L, Daures J, Garcia T, Gouriou J, Le Roy M, et al. LNE-LNHB realisation of the unit of the absorbed dose to water under IMRT conditions. Conference on Advanced Metrology for Cancer Therapy (CAMCT 2011), Braunschweig, Germany: 2011.

] and it has been shown that the calibration coefficient was relatively independent of the field size between 10 × 10 cm2 and 2 × 2 cm2. Below 2 × 2 cm2, the traceability of the measured dose to a national standard of absorbed dose to water at a point is no longer demonstrated, leading to an increased uncertainty of dose delivery. The technological limits of standards miniaturization having been reached, it was necessary to revisit the existing approach of dose at a point as the reference quantity for reference radiotherapy dosimetry. Quite easily measurable in homogeneous large field sizes and conceptually understandable from a macroscopic point of view, no solid state detectors small enough to make a true “point” measurement is today available.
The approach proposed by LNE-LNHB consists in performing an integrated measurement over an area larger than the irradiation field through another quantity: the Dose Area Product (DAP) [
• Djouguela A.
• Harder D.
• Kollhoff R.
• Rühmann A.
• Willborn K.C.
• Poppe B.
The dose-area product, a new parameter for the dosimetry of narrow photon beams.
]. While this concept has been investigated for output factor measurements [
• Djouguela A.
• Harder D.
• Kollhoff R.
• Rühmann A.
• Willborn K.C.
• Poppe B.
The dose-area product, a new parameter for the dosimetry of narrow photon beams.
,
• Hartmann G.H.
• Pena J.
• Roselló J.V.
• Russiello G.
• Gonzalez-Castaño D.M.
A new method for output factor determination in MLC shaped narrow beams.
,
• Fan J.
• Wang L.
• Jin L.
• Li J.
• Eldeeb A.
• et al.
Determination of output factors for stereotactic radiosurgery beams.
,
• Underwood T.S.A.
• Winter H.C.
• Hill M.A.
• Fenwick J.D.
Detector density and small field dosimetry: Integral versus point dose measurement schemes.
] as well as beam quality parameter [
• Niemelä J.
• Partanen M.
• Ojala J.
• Sipilä P.
• Björkqvist M.
• Kapanen M.
• et al.
Measurement and properties of the dose–area product ratio in external small-beam radiotherapy.
,
• Niemelä J.
• Partanen M.
• Ojala J.
• Kapanen M.
• Keyriläinen J.
Dose-area product ratio in external small-beam radiotherapy: beam shape, size and energy dependencies in clinical photon beams.
,
• Pimpinella M.
• Caporali C.
• Guerra A.S.
• Silvi L.
• De Coste V.
• Petrucci A.
• et al.
Feasibility of using a dose-area product ratio as beam quality specifier for photon beams with small field sizes.
], the major innovation introduced by LNE-LNHB is the DAP use as a reference quantity for small fields dosimetry.
This work was initiated by the construction of the GR11 graphite calorimeter with a 30 mm diameter core [
• Dufreneix S.
• Bordy J.-M.
• Daures J.
• Delaunay F.
• Ostrowsky A.
Construction of a large graphite calorimeter for measurements in small fields used in radiotherapy. 16th International Congress of Metrology.
]. The transfer of the primary standards in terms of DAP to the end user needs transfer dosimeters with the same sensitive area than the GR11 graphite calorimeter core. A previous work investigated DAP primary standards measurements for three circular fields with a first in-house designed plane-parallel ionization chamber [
• Dufreneix S.
• Ostrowsky A.
• Le Roy M.
• Sommier L.
• Gouriou J.
• Delaunay F.
• et al.
Using a dose-area product for absolute measurements in small fields: a feasibility study.
]. Some technical difficulties were encountered such as sealing defects of the chamber and the significant deformation of the collection volume due to water pressure. Those difficulties associated with the limited number of studied field sizes made a final conclusion difficult to reach.
This paper describes the validation of the Monte Carlo calculations required for the determination of the graphite to water dose conversion factor. Two identical new designed plane-parallel ionization chambers were built in-house. These ionization chambers, denoted DAP1 and DAP2, were used as reference detectors for DAP measurements and are compared. Finally, new DAP standards for a more extensive set of square and circular small fields up to 15 mm side length or diameter are presented.

## 2. Material and methods

### 2.1 Formalism

Establishment of primary standards for small fields in terms of Dose Area Product by graphite calorimetry is obtained by calibrating a plane-parallel reference ionization chamber in water from the integrated dose over the core area of the large section graphite calorimeter, at a source distance of 100 cm and 10 g cm−2 depth. The calibration coefficient NDAP,w (in Gy cm2 C-1) is expressed as:
$NDAP,w=DAPw/MonQw/Mon∗=Dcore/MonQw/Mon∗DwVcoreDcoreMCScoreki$
(1)

where:
• -
Dcore/Mon is the average absorbed dose in the core (sensitive part) of the large section calorimeter normalized to the monitor ionization chamber;
• -
Q*w/Mon is the charge measured by the reference ionization chamber corrected for polarization and recombination effects normalized to the monitor ionization chamber. The integration area being a critical quantity of the DAP, a 2D dose integral correction kint is introduced to take into account the difference in the deposited energy measured between the core and the collection area of the plane-parallel ionization chamber, related to their possible area differences (see Section 2.5.2). The corrected charge Q*w is then defined as: Q*w = Qw × ks × kpol × kint with Qw the charge measured by the reference ionization chamber in a 30 cm × 30 cm × 30 cm water-filled tank volume (denoted by water phantom afterwards) and corrected for influence quantities: temperature, pressure, humidity;
• -
[Dw(Vcore) / Dcore]MC is the graphite to water dose conversion factor calculated by Monte Carlo as the ratio of the average absorbed dose to water in a water volume similar in shape, dimensions and position to the graphite core volume Vcore and the average dose in the core Dcore;
• -
Score is the graphite core area (perpendicular to the beam direction);
• -
The impurity correction factor ki takes into account the effects on the absorbed dose to the core of all the impurities within the core that are different from graphite (thermistors, resin and kapton). This correction was considered here dosimetrically negligible because thermistors are located at the periphery of the core and are not in the direct beam. So it was taken equal to unity, with an uncertainty of 0.1%.
The exploitation of the DAP approach in a clinical situation for OF determination can be done in two ways:
• 1-
Convert DAP into point dose [
• Dufreneix S.
• Ostrowsky A.
• Rapp B.
• Daures J.
• Bordy J.M.
Accuracy of a dose-area product compared to an absorbed dose to water at a point in a 2 cm diameter field.
]. This could be done with films through a volume average correction factor [
• Kawachi T.
• Saitoh H.
• Inoue M.
• Katayose T.
• Myojoyama A.
• Hatano K.
Reference dosimetry condition and beam quality correction factor for CyberKnife beam.
] using a 2D dose map of the beam. The improvement of performances of film dosimetry [
• Chiu‐Tsao S.-T.
• Grams M.P.
• Lewis D.F.
• Soares C.G.
• Van Battum L.J.
• et al.
Report of AAPM Task Group 235 radiochromic film dosimetry: An update to TG-55.
] and dose distribution reconstruction from profiles measured with point dose detectors [
• de Chavez R.
• Jones C.E.
• Charles P.H.
Integral small field output factor measurements using a transmission ionisation chamber.
] is an active research field and the results obtained will benefit to this approach.
• 2-
The best and more direct option to exploit DAP primary standards would be to directly introduce DAP in Treatment Planning Systems (TPS). This would mean a formalism modification in TPS for OF input data, considering an integrated measurement instead of a point dose.

### 2.2 Methodology

This work was carried out in the 6 MV FFF beam of the Varian TrueBeam linear accelerator at the LNE-LNHB laboratory. The GR11 calorimeter inside its graphite phantom and the water phantom with the plane-parallel ionization chamber to be calibrated were on the treatment table with the original carbon couch replaced with a more rigid aluminum one. Measurements were made during four campaigns, with an irradiation time of 120 s and at the maximum dose rate of 1400 UM/min. The gantry was set at a 90 degree angle to exactly control the 10 cm reference depth of the plane-parallel chamber in the water phantom (4 mm PMMA entrance wall + 96 mm water), which is not possible at a 0 degree angle due to disturbances on the water surface. The calorimeter core center was positioned at a distance of 100 cm from the source, at a measurement depth of 10 g cm−2 in graphite, achieved by superimposing slices of the phantom at the front of the calorimeter.
The plane-parallel ionization chamber was positioned under the same reference conditions in the water phantom, considering its reference point at the center of the inner surface of the entrance window. An illustration is presented in Fig. 1. In order to investigate a potential dependence of the calibration coefficient with the field shape, two types of collimations were studied: square fields of 5; 7; 10; 13 and 15 mm side length defined with jaws, and circular fields of 5; 7.5; 10; 13 and 15 mm diameter defined with additional collimators. Uncertainties were estimated by using the Guide to the expression of Uncertainty in Measurements (GUM) report [
]. Unless otherwise stated, they are given for k=1 (one standard deviation).
Circular fields were defined using Tungsten collimators specifically designed for this work, which were fixed on the base plate of an electron applicator and was slid into an adjustable box using a system of six micrometric screws (see Fig. 2) to properly manage the critical alignment and centering of the collimator with the beam axis. In addition, a camera fixed on a goniometric support allowing movements along six axes was used. Positioning reproducibility of the collimator led to a charge measurement variation smaller than 0.1%.
Calorimetric and ionometric measurements were made successively by moving longitudinally the table without modifying the beam collimation. They were normalized to the monitor reading (see Eq.1), giving the link between the two measurements.
For circular fields, a machine field size larger than the largest circular collimators (15 mm diameter) needed to be defined and a square field size of 3 cm side length was realized with jaws. To improve the reliability of the monitoring system and in addition to the internal monitor ionization chamber, two external monitor ionization chambers Exradin A12S denoted ‘Mon1′ and ‘Mon2′ were set horizontally and tangentially to the irradiation field at the treatment head exit to be used as external monitor ionization chamber. Mon1 and Mon2 were located between the additional collimators and the output of the treatment head. All signals from the external monitors were corrected for influence quantities. Therefore, it was possible to normalize the measurements with respect to either the internal monitor, or Mon1 or Mon2.
For the square fields, it was not possible to use the external monitor ionization chambers without disturbing the beam, so only the internal monitor ionization chamber was used. For both cases, calorimetric measurements were systematically bracketed by ionometric measurements at the beginning and at the end of the day.

### 2.3 Graphite calorimetry

The GR11 calorimeter is based on the same principle as the former generations of LNE-LNHB graphite calorimeters [
• Daures J.
• Ostrowsky A.
• Rapp B.
Small section graphite calorimeter (GR-10) at LNE-LNHB for measurements in small beams for IMRT.
,
• Daures J.
• Ostrowsky A.
New constant-temperature operating mode for graphite calorimeter at LNE-LNHB.
,
• Delaunay F.
• Gouriou J.
• Daures J.
• Le Roy M.
• Ostrowsky A.
• Rapp B.
• et al.
New standards of absorbed dose to water under reference conditions by graphite calorimetry for 60 Co and high-energy x-rays at LNE-LNHB.
]. It is made up of three concentric bodies: the core, the jacket and the shield, all embedded inside a fourth body, the block, of the same reference material. In order to minimize heat transfer phenomena between the bodies and its external environment and to ensure that the temperature increase measured is strictly proportional to the energy imparted into the medium, a good thermal insulation is ensured by vacuum gaps between the bodies. The core, the sensitive element, is a flat cylinder of 2.92 ± 0.01 mm thickness and 30.00 ± 0.01 mm diameter where the temperature rise induced by irradiation is measured by thermistors. Six thermistors are embedded in the core for the measurements, the thermal remote control and the electrical calibration. They are in the form of glass-coated beads of 0.35 mm diameter. More details about the large section calorimeter construction can be found in [
• Dufreneix S.
• Bordy J.-M.
• Daures J.
• Delaunay F.
• Ostrowsky A.
Construction of a large graphite calorimeter for measurements in small fields used in radiotherapy. 16th International Congress of Metrology.
] and radiographs are presented in Fig. 3.
The graphite calorimeter was operated in quasi-adiabatic mode. A feedback loop of the shield temperature to that of the core is set up allowing the temperature of all the bodies to grow continuously throughout irradiation and an electrical calibration is required in order to link the temperature rise to the absorbed dose Dcore [
• Renaud J.
• Palmans H.
• Sarfehnia A.
• Seuntjens J.
Absorbed dose calorimetry.
]. Temperature rise measurements were between 0.7 and 8.1 mK for the different field sizes considered, with a statistical uncertainty in the range of 0.01 to 0.12%, decreasing with the temperature rise magnitude. As an illustration, the temperature rise curves for the larger (15 mm) and the smaller (5 mm) circular field size diameters are reported in Fig. 4. Note that the DAP approach is based by definition on an integrated quantity and requires to have a well-defined sensitive volume in opposition to water calorimetry where it is only possible to carry out a point dose measurement.

### 2.4 DAP plane-parallel ionization chamber

The plane-parallel ionization chamber is a vented waterproof plane-parallel ionization chamber. The cylindrical cross-linked polystyrene body has an outer diameter of 100 mm with an internal cylindrical air cavity of 2 mm thick nominally. The entrance window has a thickness of 3.5 mm, made of 2.5 mm cross-linked polystyrene and 1 mm polarizing graphite electrode. The graphite-collecting electrode in front of the entrance window has a diameter of 29.5 mm. A 0.5 mm thick guard ring guards the sensitive volume. It leads to a collection area diameter, defined by the area of the collecting electrode plus half the gap between the collecting and guard electrode, of 30 mm. An operating voltage of + 200 V was used, in accordance with usual practice of 100 V per mm of air cavity to get an efficient ionization chamber regime.
The assembly accuracy of the two plane-parallel ionization chambers was checked by high-resolution X-ray tomography (XT H 320 large cabinet microfocus CT, Nikon Metrology CT) with voxels of 0.071 mm side length. The high-resolution was needed to distinguish slight radius variations for the 2D dose integral correction determination (see Section 2.5.2). A 2-views radiography can be found in Fig. 5. A slight deformation of the cover for the two chambers can be noticed due to a bending on the edges during the screws tightening, leading to a maximum additional air gap of 1 mm height (at the center) between the cover and the polarizing electrode. This defect has no impact because the average air gap remains constant over the 30 mm diameter collecting area and is located outside the collection volume.
The two plane-parallel ionization chambers were then evaluated in a 6 MV FFF 10 × 10 cm2 beam in terms of long-term stability under irradiation (3 h time span), noise contribution to signal, polarity and recombination correction factors.

### 2.5 Monte Carlo calculations

A few phase-spaces files (PSF) from different Monte Carlo codes are freely available within the medical physics community [
• Capote R.
• Jeraj R.
• Ma C.M.
• Rogers D.W.O.
• Sempau J.
• et al.
Phase-space database for external beam radiotherapy, Summary report of a consultants’ meeting.
]. They are then used as input data for simulations and calculations of dosimetric quantities. However, these PSF’s have limited size, and assume that all machines are strictly equivalent. It has been shown that this last assumption has some limits, especially for small field sizes less than 1 × 1 cm2 related to spot size shifts and the occlusion effect [
• Ghazal M.
• Westermark M.
• Kaveckyte V.
• Carlsson‐Tedgren Å.
• Benmakhlouf H.
6-MV small field output factors: intra-/intermachine comparison and implementation of TRS-483 using various detectors and several linear accelerators.
,
• Czarnecki D.
• Wulff J.
• Zink K.
The influence of linac spot size on scatter factors.
,
• Wang L.L.W.
• Leszczynski K.
Estimation of the focal spot size and shape for a medical linear accelerator by Monte Carlo simulation.
,
• Scott A.J.D.
• Nahum A.E.
• Fenwick J.D.
Monte Carlo modeling of small photon fields: quantifying the impact of focal spot size on source occlusion and output factors, and exploring miniphantom design for small-field measurements.
].
To overcome this limitation, it was decided to create our own full Monte Carlo 6 MV FFF beam source for the Varian TrueBeam head using the EGSnrc code (2019a version) [
• Kawrakow I.
• Mainegra-Hing E.
• Rogers D.W.O.
• Tessier F.
• Walters B.R.B.
The EGSnrc Code System: Monte Carlo simulation of electron and photon transport.
]. With a good knowledge of the TrueBeam head components with data provided by Varian, we were able to accurately model our TrueBeam machine. The linac model was compiled as a shared library to be used as a full beam source in a specific BEAMnrc simulation (ISOURC = 23). A model by field size and field shape was created, representing a total of ten configurations (five for square and five for circular fields).
At least five different sets of measurements, moving the jaws from either the smallest or the largest field size to the field size of interest were performed with a PTW 60019 Microdiamond detector to take into account the jaws reproducibility. The different experimental PDD and profiles were averaged to get a more reliable reference data set. Then, the hysteresis of jaws is taken into account and minimized. For Monte Carlo simulation, the DOSXYZnrc and DOSRZnrc user codes were used for absorbed dose calculations in the water phantom for respectively square and circular fields. The dose was obtained by scoring the energy deposited in scoring volume dimensions equivalent to the microdiamond detector volume (diameter: 2.2 mm) [
• Marinelli M.
• Prestopino G.
• Verona C.
• Verona-Rinati G.
Experimental determination of the PTW 60019 microDiamond dosimeter active area and volume.
], with a statistical uncertainty better than 0.4% on central axis.
The validation of each configuration was performed by comparing experimental and calculated percentage depth-doses (PDD) and inline/crossline profiles in the water phantom with a strict 0.5%/0.5 mm global gamma-index analysis, regarding the metrological expectations. A very good agreement was found for all configurations, with a gamma passing rate higher than 85%.

#### 2.5.1 Graphite to water dose conversion factor $DwVcoreDcoreMC$

As part of primary standards establishment by graphite calorimetry, the graphite to water dose conversion factor [Dw(Vcore)/Dcore]MC is of critical importance in the determination of the absorbed dose area product to water. The DOSRZnrc user code was used to calculate Dw(Vcore) and Dcore of Eq. (1). Dcore was calculated in the large section graphite calorimeter core, modelled in details inside its graphite phantom, placed with its reference point at the reference depth of 10 g cm−2 at a source distance of 100 cm. The Dw term was obtained by scoring the energy deposited in a volume of the same dimensions as the core (15.00 mm radius and 2.92 mm thickness) located at 10 cm depth in the water phantom (4 mm PMMA entrance wall + 96 mm water).
Material cross-section files were generated using the PEGS4 program taken into account the density correction files distributed with the EGSnrc distribution. In particular, the crystalline density of graphite (2.265 g cm−3) to determine the density effect correction, as well as the updated average excitation potentials of graphite and water (I = 81 eV and 78 eV respectively) from ICRU 90 recommendations for stopping-power ratio calculations [

ICRU 90 -Small Field Dosimetry. J Internat Comm Radiat Units Measur; 2014;14:31–53. https://doi.org/10.1093/jicru/ndx012.

] were taken into account. The density of water was set at 0.998 g cm−3 (corresponding to a temperature of 20 °C), in accordance with the updated water-density file distributed with the EGSnrc distribution. The different densities of graphite in the calorimeter and its phantom were all considered by specifically adapting their values in the original density correction file and by regenerating a new cross sections file. In order to take into account a recommendation issued in 2017 by the CCRI (Consultative Committee for Ionizing Radiation) concerning the adoption of re-normalized cross sections for the photoelectric effect, the photon cross section table ‘mcdf-xcom’ was used during the dosimetric calculations. The photon and electron cutoff energies (PCUT and ECUT, respectively) have been taken equal to 1 keV (PCUT = 0.001 MeV and ECUT = 0.512 MeV) to account for the integration of a large fraction of scattered radiation. No variance reduction techniques were applied in the dosimetric calculations. The number of histories was adapted to get a statistical uncertainty around 0.1% for each Dcore and Dw parameter while a type-B uncertainty of 0.55% was considered [
• Pimpinella M.
• Caporali C.
• Guerra A.S.
• Silvi L.
• De Coste V.
• Petrucci A.
• et al.
Feasibility of using a dose-area product ratio as beam quality specifier for photon beams with small field sizes.
], related to the large out-scattered part predominant in the DAP approach for which the uncertainty of cross sections tables at low energies is more important. The other transport parameters related to the simulation of the absorbed dose calculations are reported in Table 1.
Table 1Modified Monte Carlo transport parameters for graphite to water dose conversion factor calculation. Those not mentioned have been taken equal to their default value.
ParameterValue
Global ECUT (MeV)0.512
Global PCUT (MeV)0.001
Brem cross sectionsNIST
Bound Compton scatteringOn
Pair angular samplingKM
Rayleigh scatteringOn
Electron Impact IonizationOn
Photon cross sectionsmcdf-xcom

#### 2.5.2 2D dose integral correction $kint$

In the DAP approach, it is necessary to ensure that the charge collection of the plane-parallel ionization chamber is representative of the energy deposited in the calorimeter core. Therefore, the sensitive area of the primary and transfer dosimeters must be as close as possible. Although they were designed to be the same, the manufacturing process introduces slight differences due to machining tolerances. A correction factor called 2D dose integral correction kint is therefore introduced to account for this effect.
The correction factor kint is defined as:
$kint=∫∫ScoregdS∫∫SDAPgdS$
(2)

where g is the 2D dose distribution in water at the reference depth of 10 cm and a source distance of 100 cm, and Score and SDAP are respectively the area of the core and of the effective collection area of the plane-parallel ionization chamber. The diameter of the core can be determined using a mechanical caliper. For the plane-parallel ionization chamber collection diameter, the determination was more challenging and was measured by X-ray tomography.
This quantity kint was calculated with the DOSRZnrc user code by scoring the average absorbed dose into two water volumes of surface Score and SDAP, and 2.91 mm thickness (corresponding to the core thickness). Then the quantity kint is given by the ratio:
$kint=DcoreScoreDDAPSDAP$
(3)

The same parameters as reported in Table 1 were used for this Monte Carlo calculation. A type B uncertainty of 0.05% coming from tomographic radius determination was added.

#### 2.5.3 Monte Carlo modeling of DAP plane-parallel ionization chamber

To confirm experimental findings, Monte Carlo simulations were further carried out with the aim of calculating the dose ratio Dw/Dcav of the plane-parallel ionization chamber. Dcav was obtained by recording the energy deposited in the air cavity of the ionization chamber, modeled in an ideal case without the cover bending, using the DOSRZnrc user code. A half-symmetrical cut view of the modeled ionization chamber is shown in Fig. 6 with the sensitive air cavity highlighted in red. The ionization chamber was placed with its reference point located on the inner surface of the entrance window at 10 cm depth in the water phantom. The dose in water Dw was recorded in the same region, replacing all the components of the ionization chamber with water. Transport parameters from Table 1 were used.
Water-to-air stopping power ratios were also calculated for all field sizes using the SPRRZnrc user code, in a volume equivalent to the air cavity of the ionization chamber.

## 3. Results and discussion

### 3.1 DAP plane-parallel ionization chamber performances as a reference detector

The dosimetric performance evaluation of the two plane-parallel ionization chambers are presented in Table 2. Additionally, the recombination correction factors are given for the 5 mm and 15 mm diameter field size.
Table 2Characterization measurements of the two DAP plane-parallel ionization chambers performed for a 6 MV FFF beam quality and a 10 × 10 cm2 field. The recombination correction factors are for the 5 and 15 mm diameter field size.
Stability under irradiation (%)Noise contribution to signal (%)kpolks (5 mm)ks (15 mm)
DAP10.040.0060.9992(0)1.0016(5)1.0034(6)
DAP20.050.0080.9991(1)1.0014(5)1.0034(5)
It was found that the plane-parallel ionization chambers showed an excellent signal stability with deviations less than 0.05% after 3 h of consecutive measurements and a negligible noise contribution to the measured signal, revealing the good sealing of the chamber and the no deformation of the sensitive volume contrary to the previous version [
• Dufreneix S.
• Ostrowsky A.
• Le Roy M.
• Sommier L.
• Gouriou J.
• Delaunay F.
• et al.
Using a dose-area product for absolute measurements in small fields: a feasibility study.
]. The polarity correction factor is very close to unity, showing the high quality of the two detectors, and is in accordance with the reference-class ionization chamber specifications for megavoltage photon-beam dosimetry recommended in TG-51 Addendum [
• McEwen M.
• DeWerd L.
• Ibbott G.
• Followill D.
• Rogers D.W.O.
• Seltzer S.
• et al.
Addendum to the AAPMˈs TG-51 protocol for clinical reference dosimetry of high-energy photon beams: TG-51 photon addendum.
]. Also, the recombination correction factor increases with field size, related to the larger part of the plane-parallel ionization chamber irradiated and subjected to the general recombination regime.

### 3.2 Calibration coefficients NDAP,w

Calibration coefficients for the two plane-parallel ionization chambers measured for a 6 MV FFF beam quality are plotted in Fig. 7 for the two collimating systems. Additionally, the values are summarized in Table 3. Calibration coefficients are independent of the beam shape but increase slightly with the field area (maximum variation of 1.1% for DAP1 and 1.8% for DAP2 from 19.6 mm2 to 225 mm2), following a linear trend. The slopes of the two plane-parallel ionization chambers are however different, preventing the application of a single field size correction factor. Uncertainties are around 0.6% for circular fields and a little bit larger for square fields due to the use of the internal monitor chamber. Whatever the field shape, uncertainties are larger for the smaller field sizes, due to lower temperature rises of the calorimeter core. With a coverage factor of k=2, all calibration coefficients of each chamber are in agreement.
Table 3Calibration coefficients NDAP,w for the two DAP plane-parallel ionization chambers in circular and square fields and a 6 MV FFF beam quality.
6 MV FFF – Circular fields
Ionization ChamberDAP1DAP2
Area (mm2)Field size diameter (mm)NDAP,w

x108 (Gy cm2 C-1)
uc (%)NDAP,w

x108 (Gy cm2 C-1)
uc (%)
19.651.6410.621.7160.63
44.27.51.6430.611.7190.62
78.5101.6500.611.7240.62
132.7131.6550.611.7260.62
176.7151.6570.611.7300.62
6 MV FFF – Square fields
Ionization ChamberDAP1DAP2
Area (mm2)Field size side length (mm)NDAP,w

x108 (Gy cm2 C-1)
uc (%)NDAP,w

x108 (Gy cm2 C-1)
uc (%)
2551.6460.691.7190.70
4971.6480.641.7200.65
100101.6570.641.7290.65
169131.6620.641.7310.65
225151.6710.641.7350.64
As an illustration, all the parameters necessary to determine the DAP to water calibration coefficient NDAP,w and the associated uncertainties for the 5 mm diameter field size are given in Table 4 for the DAP1 plane-parallel ionization chamber.
Table 4Example of DAP1 calibration coefficient determination for the 5 mm diameter field size.
Valueu (%)
(Dcore/Mon / Qw/Mon) (Gy C-1)2.343 1070.20
kpol0.99850.03
ks1.00160.05
kint1.00030.06
[Dw (Vcore) / Dcore]MC0.99080.57
Score (cm2)7.07000.04
ki1.00000.10
NDAP,w (Gy cm2 C-1)1.641 1080.62
It can be seen that the major uncertainty source of the calibration coefficient comes from the graphite to water dose conversion calculated by Monte Carlo. This parameter is constant within uncertainties lying between 0.9887 and 0.9922 for all the configurations (u = 0.57%). The 2D dose integral correction kint, is expected to increase with the field size due simply to a larger difference in the energy deposited in the tail region if the collecting area diameters of the DAP chambers are different from the 30 mm diameter calorimeter core. Those corrections are however very small for the two plane-parallel ionization chambers, in the range [1.0003 to 1.0005] and [1.0007 to 1.0009] for the DAP1 and DAP2 plane-parallel ionization chambers respectively, as the diameters are very close (DAP1: 14.956 mm and DAP2: 14.911 mm).

### 3.3 Comparison of calculated dose ratios and measured calibration coefficients NDAP,w

Calculated dose ratios Dw/Dcav are presented in Fig. 8, with a type-B uncertainty of 0.55%. The same trend can be observed on the calibration coefficient variation with field size.
Reference ionization chamber dosimetry is based on the cavity theory, providing a relation between the absorbed dose in the air volume of the cavity Dcav and the absorbed dose in the homogeneous water medium replacing the chamber, Dw.
In order to take into account the fluence perturbation induced by the presence of the chamber (air-filled volume, walls, effect of electrodes, electronics,…) and to correct for any departure from perfect Bragg-Gray conditions, a global correction factor pch is introduced, product of small and independent correction factors. Thus, for an air-filled ionization chamber, one writes:
$Dw=Dcavsw,airpch$
(4)

where sw,air is the water-to-air stopping-power ratio. The dose ratios Dw/Dcav increase is thus related to 1- sw,air increase, 2- pch increase, or 3- both. Results showed that sw,air are constant within the statistical uncertainties given by Monte Carlo of about 0.2%. Dose ratios (and in extension calibration coefficients) increase with the field size is then explained solely by the fluence perturbation factor pch which is related to the design geometry of the ionization chamber and the materials used to build it [
• Bouchard H.
• Kamio Y.
• Palmans H.
• Seuntjens J.
• Duane S.
Detector dose response in megavoltage small photon beams. II. Pencil beam perturbation effects.
,
• Fenwick J.D.
• Georgiou G.
• Rowbottom C.G.
• Underwood T.S.A.
• Kumar S.
• Nahum A.E.
Origins of the changing detector response in small megavoltage photon radiation fields.
,
• Andreo P.
• Benmakhlouf H.
Role of the density, density effect and mean excitation energy in solid-state detectors for small photon fields.
,
• Benmakhlouf H.
• Andreo P.
Spectral distribution of particle fluence in small field detectors and its implication on small field dosimetry.
].
To compare the magnitude of the increase, the relative calculated dose ratios and experimental calibration coefficients are normalized to the largest field size for each beam shape, corresponding to a 15 mm field size. Results are shown in Fig. 9. It can be noticed that the calculated and measured results show similar trends within the uncertainties.

## 4. Conclusion

Primary standards in small fields by graphite calorimetry in terms of Dose Area Product have been established at the LNE-LNHB for a 6 MV FFF beam for circular and square field sizes from 5 mm to 15 mm (side length and diameter). For the two plane-parallel ionization chambers DAP1 and DAP2, calibration coefficients slightly increase with the field size and are independent of the field shape. This latter property allows these primary standards to be used independently with stereotactic cones or MLC/jaws. The next step following the establishment of these new primary standards will be to promote and investigate conjointly with TPS manufacturers the possibility to implement Dose Area Product directly in their code. In parallel, a work on the use in clinical conditions of DAP through the point dose conversion will be carried out.

## Funding sources

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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