The International Commission on Radiological Protection (ICRP) recommends that Diagnostic Reference Levels (DRLs) should be used in the process of optimization in radiation diagnosis [ 1]. The first DRLs in Japan were published in June 2015 [ 2] and revised in 2020 [ 3]. DRL quantity in mammography are evaluated in terms of mean glandular dose (MGD). Since the MGD cannot be measured directly, it can be obtained by calculation. Equation (1) shows the equation [ 4,5,6] of Dance et al for obtaining the MGD.

where D is the MGD [mGy], K is the incident air kerma [mGy], g is the conversion factor to the MGD with 50% glandularity, c is the factor correct for the difference in composition of typical breasts from 50% glandularity, and s is the factor for the target and filter combination.

Besides Dance et al., the conversion factors to MGD were also reported by Wu et al. [ 7,8]. It was also reported by Sobol et al [ 9] that the conversion factor could be calculated using VBA (Visual Basic for Applications^TM) code. Software to estimate the MGD using this code has also been developed [ 10]. In recent years, however, the use of characteristic X-rays using Mo targets has been decreasing due to the widespread of digital equipment and improved image processing technology and is being replaced by W targets [ 11]. Therefore, the conversion factors of Wu et al. using Mo and Rh targets have become difficult to deal with. On the other hand, the equation of Dance et al. using the s-factor, which is the factor due to the combination of target and filter, has become popular. The conversion factor g in Equation. (1) is a value obtained from Monte Carlo simulations and is not reported from actual measurements. For actual measurements, ionization chamber dosimeters are often used, but it is difficult to insert an ionization chamber dosimeter into a PMMA phantom because of the physical size of the chamber itself. However, the nanoDot dosimeter, an optically stimulated luminescence (OSL) dosimeter that has been reported to be able to measure entrance surface dose (ESD) with an accuracy of about 15% [ 12] and backscatter factor [ 13], is It is very small (10 × 10 × 2 mm³ ), has a wide measurement range (10 µGy to 10 Gy) and energy range (5 keV to 20 MeV) [ 14], and has high detection sensitivity and almost no fading effects[ 15]. The nanoDot dosimeter, which is used in the diagnostic field, could also be used in the mammography field because of its features such as the ability to take multiple readings without erasing the element information.

In this study, we focused on the g-factor, which is a conversion factor to the MGD at 50% glandularity, and attempted to measure it using a nanoDot dosimeter to see if the nanoDot dosimeter can be used in mammography field.

In this study, the mammography system was a Sepio (Shimadzu Manufacturing corporation, Kyoto, Japan), the OSL dosimeter was a nanoDot dosimeter (Nagase Landauer Ltd, Ibaraki, Japan), the OSL dosimeter measurement system was a microStar (Nagase Landauer Ltd, Ibaraki, Japan), the phantom was a semicircular PMMA phantom (Φ16 cm, 1 cm thick). Measurement of half value layer (HVL) was a Radcal Accu Gold+ (Radical Corporation, California, USA), and the calibration of the nanoDot dosimeter was used an ionization chamber dosimeter of a model 9015 (10X5-6M) (Radical Corporation, California, USA).

The semi-circular PMMA phantom used in this study simulates the shape of a breast, and was processed so that nine nanoDot dosimeters could be inserted (Figure 1).

The HVL used in this study were 0.30 mm Al, 0.35 mm Al, and 0.40 mm Al. The target was Mo and the filter was Mo. To determine the exposure conditions that would result in the above HVLs, the HVLs were measured using an X-ray analyzer. The exposure conditions obtained from the results are shown inTable 1. For the films shown inTable 1, two polystyrene sheets were attached to the radiation inlet to adjust the HVL to 0.40 mmAl.

The arrangement of nanoDot dosimeters in the dosimetry is shown inFigure 2. 9 nanoDot dosimeters were inserted in a 1 cm thick PMMA phantom. The nanoDot dosimeters were inserted in the phantom and measured under the exposure conditions shown inTable 1, varying the depth every 1 cm from 0 cm to 6 cm. The nanoDot dosimeter was multiplied by the calibration constant of each element and air kerma, read five times each, and the average of the three readings, excluding the maximum and minimum values, was used as the measured value. The average value was calculated from the nine readings obtained and normalized by the value at 0 cm depth to obtain a relative value.

From the obtained relative values, a PDD CURVE (percentage depth dose curve) was created and an approximate equation was obtained. Equation (2) shows the formula for calculating X_g [ 16,17].

where X_g is the ratio of the dose at depth z to the dose at the incident surface in the breast model [ 16] at thickness τ, xg(z) is the ratio of the dose at depth z to the dose at the incident surface, and τ is the PMMA thickness.

From the obtained X_g, the g-factor (conversion factor) in the actual measurement was calculated. Equation (3) shows the formula for calculating the g-factor in the actual measurement.

where 0.00090 is the value to convert 0.79 mrad / R of the f-factor of the breast to mGy / mGy [ 16,17].

Note that all nanoDot dosimeters used were calibrated for use as air kerma by each tube voltage (HVL) under the exposure conditions inTable 1. For the calibration method, 10 nanoDot dosimeters were simultaneously exposed to the ionization chamber dosimeter. Three exposures were performed at each tube voltage (0.3, 0.35, and 0.4 mmAl in HVL), and the average value was used as the calibration constant for each element.

The PDD curve for a HVL of 0.3 mmAl is shown inFigure 3. The dose decreased exponentially with depth. Approximate equations and coefficients of determination for each HVL are also shown. The coefficients of determination of the approximate equations for each HVL are above 0.99, indicating that the equations are reflected.Table 2 shows the g-factors for each PMMA thickness at the HVL= 0.30 mm Al, 0.35 mm Al, and 0.40 mm Al in Figures 4, 5, and 6, respectively.

For all HVLs, the measured g-factors are in close agreement with those of Dance et al. However, as the PMMA thickness increased, the measured g-factor tended to be larger than that of Dance et al. However, the difference was smaller at 0.40 mm Al.

In Japan, DRL was first introduced in 2015 [ 2] and revised in 2020 [ 3], with DRL quantities and DRL values published for CT, general radiography, mammography, dental radiography, interventional radiography (IVR), diagnostic fluoroscopy, and nuclear medicine. The DRL quantity for mammography is the MGD. In the evaluation, the average dose to the breast is evaluated because of the higher risk of the mammary gland, rather than the dose at the incident surface, which is the maximum dose as in general radiography. For this purpose, a factor to convert into the MGD is needed. Currently, the g-factor of Dance et al. is used [ 4,5,6].

MGD conversion factors other than those of Dance et al. include a backscattering-factor or multiply by an appropriate backscatter factor [ 18], as reported by Stanton et al. However, the g-factor of Dance et al. does not take this backscatter factor into account. For the calculation of MGD, the incident dose in air without backscatter is measured using a Sharrow-type ionization chamber dosimeter and multiplied by the MGD conversion factor [ 19]. This is true for DRL measurements as well, but only for instrumental qualty control, and the backscatter factor is considered necessary in consideration of actual patient exposure. Therefore, we focused on the nanoDot dosimeter, which can be used without any problem in terms of direction dependence, except for scattering in the 90° direction [ 20], and has an uncertainty of about 10 % [ 21]. There is also a report of measuring backscatter factor using the nanoDot dosimeter [ 13], so we used it in this study.

The results show that for thicker PMMA phantoms, the measured g-factor is larger than the existing g-factor of Dance et al. In the measured values, the dose ratio decreased exponentially with depth, suggesting that the difference between the nanoDot dosimeter, which includes a certain amount of backscatter factor, and the existing g-factor, which does not account for backscattere, increased with depth.Table 3 shows the backscatter factors for mammography recommended by European protocols in the HVLs used in this study. It can be seen that there is a backscatter of up to 10% at 0.45 mm Al in the HVL[ 22]. It should also be noted that the results indicate that thicker phantom thicknesses may lead to underestimation of the MGD. The fact that the difference between the present study and existing values was smaller for the 0.4 mmAl HVL than for the other HVLs may be due to the presence or absence of a compression plate, since the 0.4 mmAl was measured without a compression plate to make the beam quality concerned, while the compression plate was attached for the other HVLs.

The measured g-factors values using the nanoDot dosimeter tended to be larger as the PMMA thickness increased, which was attributed to the effect of backscatter factor. However, the measured results of the nanoDot dosimeter were in close agreement with the g-factor of Dance et al. even after taking uncertainties into account. Therefore, it can be said that nanoDot dosimeters used in the diagnostic field can also be used in the mammography field.