Absolute, Reference, and Relative Dosimetry in Radiotherapy

Abstract

The correct estimation of the dose to be delivered to a patient is strongly dependent on a correct dosimetry procedure. To achieve this purpose, it must ensure that the measurement results represent the best possible value reported with its typical uncertainties, and the results must be comparable with other institutions. The International Metrological Network fundamentally seeks to standardize the processes and the methodologies among the various laboratories in the world. The concept and structure of the various levels of laboratories can be defined as primary or secondary standards laboratories. The absolute dosimetry refers to the measurement of a quantity with an instrument of the highest metrological quality, which allows its determination in accordance with its definition, usually carried out in Primary Laboratories. The main quantities of interest for the absolute dosimetry are exposure, air kerma, and absorbed dose to air and to water. This entire chain of measurements and formalism must consider the specific physical conditions of the interaction processes between the radiation beam with the detector in the measurement processes, aiming to ensure the least possible uncertainty in the dose delivered to the patient.

1. Introduction

A dosimetric procedure aims to estimate a quantity to guarantee the delivery of the correct prescribed dose to a patient or the dose resulting from a diagnostic procedure.

To achieve this purpose, one must ensure that:

• the measurement results represent the best possible value reported with its typical uncertainties, using the appropriate calibration coefficients and the correction factors necessary to adjust the measured value to the true value;

• the measurement results made by different institutions must be comparable when performed under similar reference conditions such as those established by international protocols, i.e., TRS#398-IAEA [1] TRS # 469 [2];

• the clinical results of different institutions can be comparable if the air Kerma or absorbed dose, in addition to the biological clinical parameters, is well known and fully described.

To fulfill those premises, the radiation detectors must be calibrated following a universal protocol agreed among the professional societies, and the quantities referenced to the standards at the BIPM as it was decided by the Metro Convention. The dissemination of these quantities until the final user is done through the calibration laboratory in each country either national or secondary following a logical chain of events as described in Figure 1.

Figure 1.

The main steps involved in the implementation of the quantities: (a) air kerma and (b) absorbed dose to water.

At this point, one must highlight the importance of a network called: International Metrological Network, which fundamentally seeks to standardize the processes and the methodologies among the various laboratories in the world. As a result, the measurement of the main quantities of interest in radiotherapy, radiology, and radioprotection such as air Kerma and absorbed dose to water allows the clinical results and the biological effects to be compared scientifically among different users, with an acceptable level of uncertainties for each area.

The two steps shown above in Figure 1 constitute a simplification of the various levels of complexity that represent the metrological chain, and the algorithms used now are best illustrated now in Figure 2.

Figure 2.

The international network of ionizing radiation metrology showing the traceability process between the primary standards coordinated by the BIPM followed by the network of the secondary laboratories traceable to the IAEA Laboratories, the BIPM or any other primary laboratory and the final user [1, 2].

2. Standards laboratories

The concept and structure of the various levels of laboratories can be defined as:

2.1 Primary standards dosimetry laboratory (PSDL)

Location where instruments with the highest metrological quality are used, the quantities are measured according to their definition, that is, in an absolute way. To reach this level, very sophisticated equipment, computer control systems, experimental arrangement, and very skilled staff are required, resulting in very small uncertainties, results impossible to be reproduced at the end user’s environment.

Those laboratories use free air chambers for air kerma standards in the low and medium energy X-ray beams; water or graphite calorimeters for absorbed dose standard to water or graphite; Fricke dosimeter is a standard for absorbed dose to water and ionization chambers with a well-known volume as standard for either air Kerma for gamma ray beams emitted by a collimated ⁶⁰Co or absorbed dose to graphite using a large variety of photons and electron beams.

To carry out periodical comparisons involving all National laboratories to ensure the appropriate metrological consistency within the metrological network in a decision agreed by tall country’s signatories of the Metro Convention, the BIPM was designated to carry out this task, as shown in Figure 3.

Figure 3.

Typical example of the result of one of the comparisons conducted by BIPM with several national laboratories for the quantity of absorbed dose to water using three different methods: Water calorimeter, graphite calorimeter, and the Fricke system [3].

2.2 Secondary standards dosimetry laboratory (SSDL)

Location where high-quality metrological instruments are used, though its calibration by one of the PSDL is required to assure that the users’ instruments are traceable to the national and international metrological network. In some situations, the IAEA- SSDL Laboratory provides periodical calibration to the members of the IAEA-SSDL network, and QA auditing is also conducted.

The SSDL are recognized and accredited by the country’s metrological authority such as the National Laboratory, as it is responsible for disseminating the quantities to the final user in their country ensuring the proper metrological coherence among users with reference to their standards [1, 2]. Since it is possible to find more than one SSDL in one country, an internal network must be established, and periodic comparison must be carried out by the National Laboratory.

In this way, users of ionizing radiation sources will be tracked to the National and International Network with their intercomparable results.

Tips:

• It is not forbidden that the user calibrates their instruments in a PSDL outside the country instead of their SSDL. The drawback is the calibration cost in addition to transportation, insurance, customs clearance expenses, which makes this option too onerous and objectively unnecessary;

• Carrying out calibrations in the country’s laboratories reinforces the metrological consistency between users and the national laboratory.

2.3 Users level

Location where the calibration procedures of diagnostic and treatment machines are carried out under conditions such as those in which the instruments were calibrated. When using the formalism, for example, from the TRS#398 [1] or similar, it is essential that the measurement systems were calibrated in a laboratory traced to the metrological network.

In this situation, the instruments used can be classified as:

1. reference instrument (the one with the highest level of metrological quality in the institution);

2. field instrument (instrument used in daily routine that can be equal to the first one). This is recommended since some legislations require two sets, one of which could be the reference.

If the institution has only one treatment machine, it is recommended to leave a fixed dosimetry set on the control room bench with the cables passed through the wall of the treatment room, avoiding passing the cable under the door risking damaging it, and the other set as the institutional reference. If you have two treatment machines, leave each system fixed on each machine and as part of the periodic QA program, perform cross-calibration changing the electrometers and performing the measurements. If the values differ consistently by more than 1% between them, use another calibrated chamber on both machines.

The stability test of the dosimetry system shall be performed every three months with a source of ⁹⁰Sr or ¹³⁷Cs, as required by the regulatory authority. This test is accepted as a good indicator of the performance of the measurement set, which must include the leakage, repeatability, and linearity tests.

If the QA documentation demonstrates the stability of your system in other ways, it may also be accepted.

Since the numerical values of the uncertainties increase as we go down in the metrological chain, there is a demand for a high-quality measuring system, careful instrument handling procedures especially for the cables and connectors, instrument warm-up, proper documentation, and finally a consistency in positioning the experimental setup.

Measurement systems (ion chamber, electrometer, and cable) must be calibrated when purchased, unless they are calibrated by the manufacturer if it has an accredited laboratory, when they undergo any repairs, and every 2 years regardless of any problem. The calibration coefficient is given for the quantity of absorbed dose to water at the reference conditions. This coefficient is directly traceable to the national and international metrology network. It may be possible to calibrate the ion chamber separately from the electrometer and then use the chambers with different electrometers or vice versa.

3. Absolute, reference, and relative dosimetry

In general, there is a certain conceptual confusion not only by the users but also by the manufactures when using the concepts of absolute dosimetry, reference dosimetry, and relative dosimetry. Andreo et al. [3] very clearly discuss the differences between the three concepts so that they can be used properly.

3.1 Absolute dosimetry

It refers to the measurement of a quantity with an instrument of the highest metrological quality, which allows its determination in accordance with its definition. In general, it is carried out in Primary Laboratories.

For example, the quantity Exposure, X, as defined by ICRU 33 [4], is the result of the quotient of dQ and dm, where dQ is the absolute value of the charge produced by ions of the same sign in the mass of air, when electrons (négatron or positrons), released by photons in an air mass dm, are completely stopped in the air. The unit for the SI system is C/kg, but its special unit is the long-used Roentgen, equaling 2.58.10 C⁻⁴ C kg⁻¹.

Measures of the quantity Exposure, because of the air Kerma, are of great importance as they constitute the stakes of the metrological chain. They are directly related to the absorbed dose calibrations of the high energy photon and electron beams used in radiotherapy, radiobiology studies, and radioprotection measurements; the latter for the moment entirely dependent on the quantity air Kerma.

3.2 Formalism for the absolute determination of exposure, air kerma, and absorbed dose to water quantities from experimental measurements

3.2.1 Determination of the exposure

The determination of the exposure can be obtained through two methods, both with an ionization chamber:

Method 1. Free air chamber.

Unlike wall chambers, free air chambers do not have walls, so the interaction process occurs within the air volume defined by the electric field defined between the guard ring and the collector plate inside the chamber, to obtain the electronic equilibrium. The thickness of the air layer varies depending on the energy fluence of the beam, and for this reason, two chambers with different volumes are used for energies up to 150 kVp and 300 kVp, respectively. A typical diagram of a free air chamber is illustrated in Figure 4.

Figure 4.

Typical diagram of a free air chamber where several important components can be identified, such as the diaphragm or frontal collimator with an area a, the collector electrode, and the guard plates when subjected to the same collector potential define the sensitive volume of the chamber.

This process is more largely described by [5], where the formalism for estimating the quantity air Kerma, including typical correction factors, is described in the Eq. (1):

$$K_{\mathit{air}}=\frac{Q_{\mathit{air}}}{\rho }\bullet V\bullet \frac{w}{e}\bullet \frac{1}{1-g}\bullet K_{\mathit{att}}\bullet K_{\mathit{sc}}\bullet k_e$$E1

Where:

$K_{\mathit{att}}$ = attenuation of the primary beam in air column between the diaphragm and the collector volume;

$K_{\mathit{sc}}$ = additional ionization collected caused by the scattering inside the chamber,

$k_e$= ionization lost by the shock of the electrons with the electrode;

$\frac{w}{e}$ = average energy needed to produce a pair of ions;

$g$ = the fraction of energy lost by the bremsstrahlung effect;

$\rho$ = air density under the measurement conditions, considering the air compressibility factor that corrects its deviation from the perfect gas law;

V = sensitive volume of the chamber in which charges are produced and collected;

$Q_{\mathit{air}}$ = is the charge produced in the air mass defined as the sensitive volume v of the chamber;

Method 2. Cavity chamber.

This method uses a cavity chamber, with a known volume, with the formalism proposed by [6] and extended by [7]. One must consider the cavity dimensions, the presence of the wall and a central electrode, in addition to the various correction factors empirically derived such as environmental quantities and measurement statistics. The characteristics of a chamber of this type used in several primary laboratories are described in Figure 5.

Figure 5.

Image represents the physical diagram, with the internal and external dimensions of the cylindrical chamber.

The final volume measured in the chamber described in Figure 5 is 1.076 ± 0.003 cm³, and the graphite caps are used to determine the wall attenuation using the extrapolation method. The graphite complements are added to the base of the chamber after the insertion of each cap to preserve the spatial conditions of scattering. Recently, the wall attenuation value was recalculated by [8] using the Monte Carlo technique, whose result, though slightly different than the experimental one, is more accurate and with less uncertainty.

The primary Standard shown in Figure 5 is a cylindrical graphite chamber built by the Austrian National Laboratory, with its volume defined by the same laboratory, constructed of ultra-pure graphite (99.99%) with an excellent insulating system to minimize the “leakage” and the polarization effects, guaranteeing an excellent long-term stability and a metrological quality compatible with similar standards, as reported by [9, 10, 11].

Its sensitive volume was estimated by the Ostereich Forschung Centrum and reported by [12] from the internal physical dimensions of the chamber, defined with an uncertainty of 0.1% after subtracting the electrode volume according to Figure 5, and including the additional sensitive volume in the electrode base.

Thus, according to the Bragg-Gray principle, the measure of ionization in the center of the chamber in its absence is defined by Eq. (2):

$$X=\frac{I}{\rho }\bullet V\bullet \mathit{sc},a\bullet {\left(\frac{\left({\mu }_{\mathit{en}}/{\rho }_{\mathit{air}}\right)}{\left({\mu }_{\mathit{en}}/\rho \right)}\right)}_C\bullet \mathrm{\Pi }{K}_j$$E2

Where:

$I$ = ionization current resulting from the collection of ions produced in the air within the chamber cavity, considering the attenuation of the air between the source and the chamber;

$V$ = sensitive volume of the chamber in which charges are produced and collected;

$\rho$ = density of the air under the measurement conditions, considering the air compressibility factor that corrects its deviation from the perfect gas law;

$\mathit{sc},a$ = the ratio of the restricted stopping power between graphite and air, calculated based on the Spencer-Attix theory [3] taking into account the average value of the energy in the electron spectrum generated by the Compton effect; considering as cutoff energy of 17.5 keV, the cavity size and the average excitation energy of 78 eV for carbon and 85.7 eV for air;

${\left(\frac{\left({\mu }_{\mathit{en}}/{\rho }_{\mathit{air}}\right)}{\left({\mu }_{\mathit{en}}/\rho \right)}\right)}_C$= the ratio of mass-energy absorption coefficients for air and graphite used from the work of Hubbel and Seltzer [13];

$\mathrm{\Pi }{K}_j$ = the product of several correction factors:

kl = leakage correction;

kh = correction for the presence of water vapor once exposure X is set to dry air;

kst = correction for scattering on the chamber stem;

krn = correction due to radial beam non-uniformity;

kan = correction due to axial beam non-uniformity;

kw = correction due to attenuation of the wall chamber;

kcep = origin of electron production;

kt,p = mass correction for reference temperature and pressure;

3.2.2 Determination of the air kerma (K_air)

The determination of the air kerma (K_air) from the measurements of the exposure X follows the formalism below:

$$K_{\mathit{air}}=\frac{X}{1-g}\bullet \frac{w}{e}$$E3

Where:

$X$ = the air exposure value (X) obtained in accordance with Eq. (2);

$g$ = the fraction of energy lost by the bremsstrahlung effect;

$\frac{w}{e}$ = average energy needed to produce a pair of ions.

3.2.3 Determination of the absorbed dose to air (D_air)

The determination of the absorbed dose to air (Dair), measured by a standard instrument, is defined as the energy delivered to a mass of air of the well-known sensitive volume of the ionization chamber, defined by the relation:

$$D_{\mathit{air}}=Q_{\mathit{air}}\bullet \frac{W_{\mathit{air}}/e}{m_{\mathit{air}}}$$E4

Where.

$Q_{\mathit{air}}$ = is the charge produced in the air mass defined as the sensitive volume v of the chamber;

$W_{\mathit{air}}/e$ = average energy needed to produce a pair of ions, its product being equal to the energy given to the air mass m_air of the reference sensitive volume;

$m_{\mathit{air}}$ = equal to the product of the air density ρ_air and the sensitive volume v.

This measurement may require the use of a set of factors necessary to correlate the reading of the measurement system with the final value of the quantity, such as absorbed dose. The measurements must be carried out under the well-standardized reference conditions, that is: radiation field of 10 x 10 cm² on the surface of the phantom, SSD (source surface distance) equal to 100 cm, with the center of the chamber positioned at 5 cm depth, reference temperature of 22°C (reference in Brazil), atmospheric pressure of 101.3 kPa, and relative humidity between 30 and 70% (Table 1).

Year	KLNMRI/KBIPM	uc	Reference
1986	1.0006	0.0026	de Almeida and Niatel [9]
1996	1.0004	0.0023	Allisy-Roberts et al. [14]
2005	1.0007	0.0022	Allisy-Roberts et al. [15]

Table 1.

Typical history of air kerma standard traceability between two laboratories LNMRI and BIPM.

uc = combined uncertainty.

3.2.4 Determination of the absorbed dose to water (D_w)

Method 1. Measurement performed using a graphite or water calorimeter.

A Calorimeter measures the quantity absorbed dose to water or to graphite according to its definition, that is, from the increase in temperature in the medium due to a process of radiation induction. This evaluation is done by thermistors installed in the calorimeter body filled with high-purity water, as reported by Malcolm [16]. The calorimeter, in this case, your heart (nucleus), is placed at the reference depth in a 30 cm x 30 cm x 30 cm phantom. The measured signal is generally very low, on the order of 1 mK for an absorbed dose of 2 Gy, and its reproducibility is an important factor. Due to its complexity, it is suitable for use not in clinical settings, but in National Metrology Laboratories or research (Figure 6).

Figure 6.

Shows a schematic diagram of the Domen-type water calorimeter, built jointly with the Canadian McGill University and reported by Rosado and de Almeida [17] to be operated with non-circulating water at 4.0°C.

An important parameter is the magnitude of the heat defect, that is, the fraction of energy that is not released in the form of heat, being material dependent, this effect being more significant in graphite.

The typical temperature fluctuation obtained when using a radiation source consists of three basic regions:

• the pre-trend that is prior to the irradiation, where fluctuation is stable,

• a constant and almost linear region, when the temperature rises; corresponds to the moment that the source enters the calorimeter being kept in a fixed position, this being the measurement point of the thermistors while the irradiation lasts;

• the post-trend, which is the region that exhibits the behavior of water temperature at time intervals after removal of the source from the calorimeter. The post-trend has a characteristic thermal profile and includes a relative region of low temperature rise that is governed by the increase in temperature gradient created in the water due to direct dose deposition in the water. This can be followed by a sudden increase in temperature due to the decay process of the effect source reaching the measurement point.

Using a model of heat conduction in water, the onset time of this sudden temperature rise can be accurately predicted as a function of the distance between the measurement point and the source.

Specifically, for a standard of absorbed dose to water such as the calorimeter, the dose D_w at a point in the water at a given distance (r) from the thermistor corresponds to the measured temperature increase at that point (ΔT) being quantified through the relationship:

$$D_w=∆T_w\bullet \mathit{cw}\bullet \mathit{kt}\bullet \mathit{kc}\bullet \mathit{kv}\bullet \mathit{kdd}\bullet \mathit{k\rho }\bullet \mathit{kHD}$$E5

where:

$∆T_w\bullet$= increase in the temperature;

cw = specific heat of the water;

kt = transient effect on the thermistor response due to dose deposition;

kc = conductive transfer of heat due to the excess of heat from the glass components and temperature gradients;

kv = conductive transfer of heat when water temperature is different from 4°C;

kp = disturbance caused in the radiation field due to the presence of the heart (core) of the calorimeter and thermistors, calculated by Monte Carlo simulation;

kdd = refers to the non-uniformity of radiation the beam;

kρ = variation in the density of water due to the presence of the calorimeter;

kHD = the heat defect, that is, the difference between the absorbed energy and the energy that appears as heat due to chemical reactions induced by radiation.

One of the advantages of the water calorimeter is that the quantity of absorbed dose to water is being measured directly in water, while in the case of using graphite, a graphite to water conversion factor is necessary.

Method 2. Measurement performed on the graphite phantom using a known volume ionization chamber.

In general, the measurement of the absorbed dose to water D_w [1] is carried out under the same reference conditions as mentioned before, as illustrated in Figure 7.

Figure 7.

Parallel plates graphite ionization chamber (1.8 gm/cm³) with 2.8 mm wall thickness, inner diameter of 45 mm, outer diameter of 50.5 mm, used by the BIPM and reported by Boutillon and Niatel [18].

The reference conditions include radiation field of 10 x 10 cm² in the plane of the phantom surface, SSD = 100 cm, with the center of the chamber positioned at 5 g/cm² depth in graphite, reference air temperature of 22°C, atmospheric pressure of 101.3 kPa, and humidity between 30 and 70%, according to the formalism:

$$D_w=\frac{I}{\rho }\bullet v\bullet \frac{W_{\mathit{air}}}{e}\bullet {\left(\frac{{\mu }_{\mathit{en}}}{\rho }\right)}_{w,c}\bullet \mathit{sc},a\bullet \mathrm{\Pi }{k}_j$$E6

where:

I = current reading corrected for the reference conditions of T and P;

$\rho$ = air density;

$v$ = sensitive volume of the cavity;

$\frac{W_{\mathit{air}}}{e}$ = average energy needed to produce a pair of ions, its product being equal to the energy ceded to the air mass m_air from the reference sensitive volume;

${\left(\frac{{\mu }_{\mathit{en}}}{\rho }\right)}_{w,c}$ = ratio between the mass-energy absorption coefficients for water and graphite. Proposed by Hubbel and Seltzer [15];

$\mathit{sc},a$ = ratio of the restricted stopping power between graphite and air, calculated based on the Spencer-Attix theory taking into account the average value of the energy in the electron spectrum generated by the effect;

$\mathrm{\Pi }{k}_j$ = the product of several correction factors:

kh = correction for the reference humidity;

ks = loss by ionic recombination;

km = radial non-uniformity of the beam in the chamber plane;

(d/do) = deviation correction between nominal and actual distance;

f = graphite to water conversion factor.

Fricke dosimetry consists of measuring the conversion, due to the ionizing radiation, of the ferrous ions present in the solution, into ferric ions through spectrophotometry. The Fricke dosimeter consists of a 96% water solution, therefore its attenuation to radiation is very similar to that of water and can be used in the dose range of 5 Gy–400 Gy with dose rates of up to 106 Gy/s.

The quantity determined by the Fricke chemical dosimetry system is the absorbed dose to the Fricke solution (D_F), as defined in Eq. (7) and described in the literature by [19, 20].

$$G\left({\mathit{Fe}}^{3+}\right)=\frac{∆\mathit{OD}}{D_F.L.\rho .\epsilon }$$E7

Where:

$∆\mathit{OD}$ = difference between the absorbance of the irradiated solution and the control solution, corrected for the temperature during irradiation and reading measured at 304 nm;

G(Fe⁺³) = chemical yield of the reaction for the gamma radiation beam;

L = optical pathlength of the cuvette, where the solution is placed during the readings by the spectrophotometer;

$\rho$ = density of the Fricke solution;

_ε = molar absorptivity coefficient or molar extinction coefficient;

To determine the quantity of interest, D_w in water, it is necessary to use the correction factors defined in Eq. (8), as proposed by [21] and expanded by [19]:

$$D_w=D_F\bullet f_{w,F}·P_{\mathit{\text{wall}}}\bullet f_{\mathit{avg}}$$E8

Where:

$D_F$ = absorbed dose to the Fricke solution;

$f_{w,F}$= factor that converts the absorbed dose to the Fricke solution to the absorbed dose to water.

$P_{\mathit{\text{wall}}}$= factor that corrects disturbances caused by the PMMA walls of the holders containing the solution.

$f_{\mathit{avg}}$ = factor that corrects the inhomogeneity of the dose deposited in the Fricke solution along the radial and the vertical axis.

This method requires laboratories with several parameters under control such as temperature, dust, cleaning, laminar flow hoods, Milli Q water production, glassware, quartz cuvettes, high-resolution double-beam spectrophotometer with filters for your QA, and high-purity chemicals. For this reason, its use is restricted to laboratories and not to be used at clinical environments.

4. Reference dosimetry

It refers to the measurement of the absorbed dose in water with an ionization chamber in the beam of the user’s Institution. The reference conditions used in the calibration laboratory must reproduced, and the influence quantities (T, P, U) are measured at the time of data acquisition and correction accordingly.

Step 1: Calibration of a user’s chamber at the level of the National Laboratory or of an SSDL according to interface [3].

$${\mathit{ND}}_{w,Q}=\frac{{}^{\mathit{lab}}{D}_{w,Q}}{{}^{\mathit{lab}}{M}_{w,Q}}$$E9

where:

${\mathit{ND}}_{w,Q}$ = calibration coefficient provided by SSDL or PSDL to the user;

${}^{\mathit{lab}}{D}_{w,Q}$ = absorbed dose to water determined in the SSDL by the standard instrument under reference conditions, that is, SSD = 100 cm, radiation field 10 × 10 cm² and the chamber centered at a depth of 5 cm in water;

${}^{\mathit{lab}}{D}_{w,Q}$ = reading of the user’s chamber called reference chamber, performed on the same beam and under the same conditions as in the SSDL or PSDL.

Step 2. With the calibration coefficient ${\mathit{ND}}_{w,Q.}$

These measurements are performed at the user’s institution with its reference chamber to obtain the absorbed dose to water with a beam of the same quality as the SSDL under the reference conditions: SSD =100 cm, radiation field 10 x 10 ^cm2 and depth of 5 cm in water according to the Eq. (10):

$${}^u{D}_{w,Q}={}^u{M}_{w,Q}\bullet N_{D,w,Q}$$E10

where:

${}^u{D}_{w,Q}$ = dose measured in the user’s beam under reference conditions;

${}^u{M}_{w,Q}$ = average reading of the reference chamber in the user’s beam;

$N_{D,w,Q}$ = calibration coefficient provided to the user for a given beam quality by the Calibration Laboratory, in general gamma rays of ⁶⁰Co.

As the calibration coefficient is normally defined for a ⁶⁰Co gamma ray beam, if the user has a different beam (e.g., photons with 6, 10, 15 MV) a Kq factor well described by Andreo et al. [6] should be used to adjust the detector’s response to this new beam quality according to the Eq. (11):

$${}^u{D}_{w,Q}={}^u{M}_{w,Q}\bullet N_{D,w,Q}\bullet k_Q$$E11

where:

${}^u{D}_{w,Q}$ = dose measured in the user’s beam under reference conditions;

${}^u{M}_{w,Q}$ = average reading of the reference chamber in the user’s beam;

$N_{D,w,Q}$ = calibration coefficient provided to the user for a given beam quality by the Calibration Laboratory, in general gamma rays of ⁶⁰Co.

$k_Q$ = factor that adjusts the value measured in the quality of the user’s beam defined from the relationship between the readings taken on the water phantom, with a 10 x 10 cm² radiation field size defined at 20 cm and measured at 10 cm in depth in the same geometry, that is, according to the definition of the TPR_20,10 as shown in Figure 8.

Figure 8.

Geometry that should be used for measurement of the quality of the Q beam, to obtain the $k_Q$ factor from the TPR_20,10 ratio, for a source chamber distance (SCD) of 100 cm, 10 x 10 cm² field and measurements at depths of 10 and 20 g/cm² of water as recommended by the TRS#398 [1].

The numerical value of this factor varies with the type of materials used in the chambers, whose beam quality is expressed by the TPR_20,10 ratio, which empirically represents the variation in the interaction and absorption behavior of each of the materials due to the different cross sections. Typical behavior of Kq values as a function of the beam quality, defined by the TPR_20,10, is shown in Figure 9.

Figure 9.

Typical behavior of Kq values as a function of the beam quality, defined by the TPR_20,10.

The graph clearly shows a dependence of the Kq value with the type of the chamber, in this case for photons of different energies, using Farmer-type cylindrical chambers from various manufacturers, built with different materials. TRS#398 [1].

The measurement system that best suits this application at the user level is the ionization chamber, in which case there is no need to know its volume as the calibration coefficient considers the chamber’s response and not its real volume.

The TPR_20,10 can also be estimated from the Percentage Depth Dose measurements using the empirical relationship, according to Eq. (12):

$${\mathit{TPR}}_{20,10}=1.2661\bullet {\mathit{PDD}}_{20.10}-0.0595$$E12

where,

${\mathit{TPR}}_{20,10}$= ratio of ionization measurements at 20 cm and 10 cm depth in water for a constant source to chamber distance and with a 10 x 10 cm field at the plane of the detector.

${\mathit{PDD}}_{20.10}$ = ratio between the values measured at 20 and 10 cm depth for a 10 x 10 cm² field at a source camera distance of 100 cm.

5. Relative dosimetry

In the clinical environment various measurements are performed under non-reference conditions where the calibration coefficient does not need to be used. These measurements are called relative, such as: dosimetry of other radiation fields (values compared with the reference field, output factors), wedge filter factor (ratio between readings performed with and without filter on the same geometry), measurements of depth dose (normalized to the values obtained at the maximum dose point for that specific radiation field and type of beam).

In these cases, there is a variety of detectors that can be used without compromising on having their values related to the true value of the quantity.

For example: diodes, TLDs, micro-cameras, detector array, alanine, film, MOSFET among others, all of them with their well-defined and different characteristics, such as (sensitivity, short term repeatability, long-term stability, angular, dose rate and energy dependence, detector size, leakage, signal fading) among others must be considered.

6. Key points

Check and consider, if applicable, the following:

• energy dependence with depth of water.

• Dose rate dependence, especially on FFF (flattening filter-free) beams.

• Directional dependence due to the detector geometry and volume.

• Signal-to-noise ratio as a function of field size, detector shape and size, and signal sensitivity.

• Permanent defects caused by dose storage

• volume that results in loss of spatial resolution.

Special cases where the reference conditions are not able to follow TRS#398 [1] recommendations are called non-reference conditions. Small fields used in radiosurgery show a more complex spectrum and require ionization chambers with other dimensions, additional geometric conditions, and specific formalism.

In this case, the TRS# 483 [20] should be used as a reference, the most suitable one at this time, where a relatively small variety of detectors are used, generally limited by the field size and the loss of lateral electronic balance.

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7. Conclusion

This entire chain of measurements and formalism must take into account the specific physical conditions of the interaction processes between the radiation beam with the detector in the measurement processes, aiming to ensure the least possible uncertainty in the dose delivered to the patient.

The different levels of complexity and duties of the metrological stakeholders are a result of the complexity of the experimental arrangements, the quality of the measurement systems, the degree of control over the environmental conditions and the high cost, which makes it not compatible with the clinical environment.

However, the metrological consistency between the different levels guarantees a level of final uncertainty of the dose delivered to the patient compatible with the recommendations of international organizations.

Therefore, if we keep the instruments (electrometer + cable + camera) accompanied by a quality assurance program, with its periodic calibrations and care to maintain its functional integrity, the final quality of the measurements will always be in accordance with the concept of the best practice.

Conflict of interest

The authors declare no conflict of interest.