**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**.

#### **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;

#### **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].*

• 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:


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.

#### *Absolute, Reference, and Relative Dosimetry in Radiotherapy DOI: http://dx.doi.org/10.5772/intechopen.101806*

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<sup>4</sup> C kg<sup>1</sup> .

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**.

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):

$$K\_{air} = \frac{Q\_{air}}{\rho} \bullet V \bullet \frac{w}{e} \bullet \frac{1}{1-g} \bullet K\_{att} \bullet K\_{sc} \bullet k\_e \tag{1}$$

Where:

*Katt* = attenuation of the primary beam in air column between the diaphragm and the collector volume;

*Ksc* = additional ionization collected caused by the scattering inside the chamber,

*ke*= ionization lost by the shock of the electrons with the electrode;

*w <sup>e</sup>* = average energy needed to produce a pair of ions;

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

*ρ* = 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;

*Qair* = 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

#### **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.*

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**.

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 longterm stability and a metrological quality compatible with similar standards, as reported by [9–11].

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):

$$X = \frac{I}{\rho} \bullet V \bullet \mathfrak{sc}, a \bullet \left(\frac{(\mu\_{en}/\rho\_{air})}{(\mu\_{en}/\rho)}\right)\_{\mathbb{C}} \bullet \Pi K\_j \tag{2}$$

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;

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

*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;

*μen=ρair* ð Þ ð Þ *μen=ρ C* = the ratio of mass-energy absorption coefficients for air and graphite used from the work of Hubbel and Seltzer [13];

Π*K <sup>j</sup>* = 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;

**Figure 5.**

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

### *3.2.2 Determination of the air kerma (Kair)*

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

$$K\_{air} = \frac{X}{1-\text{g}} \bullet \frac{w}{e} \tag{3}$$

Where:

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

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

*w <sup>e</sup>* = average energy needed to produce a pair of ions.
