The empirical formula for calculating the incident air Kerma in intraoral radiographic imaging

Abstract

Objectives:

The aim of this paper is to determine the empirical formula for calculating the incident air kerma (Ki), used as a patient dose descriptor in the intraoral radiographic imaging.

Methods:

The data for the formula were collected during the regular annual inspection of intraoral dental X-ray units in 2018, 2019 and early 2020. The measurement data of 50 X-ray units were processed to develop the formula. Exposure factors for imaging molars of the upper jaw of an average patient in a clinical setting were used in the measurement. The formula validity was statistically evaluated using coefficient of correlation, standard error of the fitted function and the mean relative percentage deviation.

Results:

The measurement values of the radiation doses and calculated values obtained by using the final formula showed good agreement – the mean relative percentage deviation values less than ±15%.

Conclusions:

Although there are differences in X-ray units, voltages, manufacturers and device architectures (single-phase and high-frequency), the measurement data comply well with computed ones in all cases.

Introduction

It is well known that the medical exposure is the single largest category of population exposure to ionising radiation.¹ The frequency of dental X-ray procedures is high, but the effective dose per procedure is low. It has been reported that the frequency of dental radiographic procedures in the European Union is about 32% of all plain radiography procedures. Nevertheless, the low mean effective doses of these procedures make their contribution to the collective effective dose insignificant, typically only 2–4% of the total collective effective dose for the plain radiography.² According to 2012 data, more than 25% of all X-ray machines in the Republic of Serbia are intraoral dental X-ray units.³ There is a regular quality control by licensed out-of-hospital services.⁴ The majority of examinations were found to be periapical radiography (recordings spanning two to four teeth), while other bitewing, occlusal oblique lateral techniques were almost non-existent.⁵ Procedures are usually performed by X-ray technicians, although when there is the only one device in a practice, the procedure is usually performed by a dentist with insufficient radiation protection awareness. It has been shown that the patient dose recording could raise radiation protection awareness.

Because dose indices are unknown for many dental radiographic units in Serbia, we propose the empirical formula to calculate the incident air kerma (K_i) and kerma–area-product (KAP). This can provide an insight into the unmeasured doses and can be used to calculate the diagnostic reference level (DRL). The DRL has proven to be an effective tool for optimisation of the patient protection related to medical exposure of patients in diagnostic and interventional procedures.⁶ It can also be used to determine staff doses and to calculate protective barriers in the practice.

There are references of mathematical formulas for calculating incident air kerma (K_i) (or similar quantities) for conventional radiography X-ray units.^7–12 However, no data of the same formula for calculating the Ki of intraoral radiography could be found. Therefore, the aim of this paper is to determine an empirical formula for calculating the Ki in the intraoral radiography.

Methods and materials

The performance testing of dental X-ray units was performed by a calibrated multimeter (semiconductor detector) MPD Barracuda (RTI Electronics AB, Sweden). The multimeter is calibrated on an annual basis at Secundary Standard Dosimetry Laboratory (SSDL) INN Vinča Laboratory for Radiation Protection, Belgrade, Serbia. The measurement uncertainty of Barracuda MPD multimeter is ±7%. All performance testing measurements were repeated five times.

Exposure parameters of 50 intraoral X-ray units were collected during the regular annual inspections in 2018, 2019 and early 2020 in public and private facilities. Then, these parameters were used for measurements, in a clinical settings, as in the imaging molars of the upper jaw of an average patient. When measuring, the tip of the tube was placed on the detector.

The parameters checked, with tolerances, are given in the Table 1 and the list of examined intraoral dental X-ray devices with technical characteristics in the Table 2.¹³

Table 1.

Performance testing of the dental X-ray units

Parameter	Tolerancies
kVp reproducibility (%)	<±10
Timer accuracy (%)	<±10
Timer reproducibility (%)	<±10
Tube output reproducibility at FSD	<±10
Half-value layer (HVL)
For voltage <70 kV	≥1.5 mmAl
For voltage >70 kV	≥2.5 mmAl

Table 2.

List of examined intraoral dental X-ray devices and their basic technical characteristics

No	Model (Manufacturer)	Nominal X-ray tube potential (kV)	X-ray tube current (mA)	The source-skin distance (cm)	Total filtration (mm Al)
1.	CCX Digital (Trophy)	70	8	31	2.5
2.	RXDC (MYRAY)	60	7	20	2.0
3.	Elitys (Trophy)	60	7	20	1.5
4.	Expert DC (Gendex)	65	7	20	1.5
5.	Heliodent DS (Sirona)	60	3.5	20	1.5
6.	HeliodenVario (Sirona)	70	7	20	1.5
7.	Heliodent 70 (Siemens)	70	7	20	1.5
8.	Vario DG (Sirona)	70	3.5	20	1.5
9.	Dent (EiNiš)	50	10	10	1.5
10.	Minray (Soredex)	70	7	20	2
11.	Gnatus (Gnatus)	70	7	20	1.5
12.	CS 2100 (Carestream)	60	7	20	2
13.	Intra (Planmeca)	63	8	20	1.5
14.	Focus (Kavo)	70	7	20	2
15.	XDC (Fona)	70	7	20	1.5
16.	Xgenus (De Götzen)	70	8	20	1.5
17.	CS 2200 (Carestream)	70	7	20	2
18.	Endos DC (DentX)	65	5	20	2
19.	Endos AC (DentX)	70	8	20	2
20.	ANTHOS AC	70	7	20	1.5
21.	Leadex 70 (Ritter)	70	7	20	1.5

50 intraoral dental x-ray units in use in the public and private sector in Serbia.

It is worth to notice that all the devices given in the Table 2 have round collimators with a diameter of 6 cm, except Dent (EiNiš) which has a diameter of 5 cm. Also, in Serbia, the use of devices having a voltage of 50 kV (single-phase generator X-ray units (also Dent EiNiš)) is still permitted by law.^4,13

It should be emphasised that there are differences in X-ray units, voltages, manufacturers, device architectures (single-phase and high-frequency), but also in the image receptors (analogue: film (classes D and E) and digital: (CCD compound), CMOS (complementary metal oxide semiconductor) and PSP (phosphor storage plate)), which is also shown in Table 3.

Table 3.

Measurement results of X-ray tube voltage (kV) and time (s) compared to nominal values and measurement and calculated results of Ki (mGy and mR) of the 50 intraoral dental X-ray units in Serbia, with the displayed image receptors for each device separately

No	Set X-ray tube Volt. (kV)	Measured X-ray tube Volt. (kV)	Set It (mAs)	Set t (s)	Meas. t (s)	Image recep.	Measur.Ki (mGy)	Calc. Ki (mGy)	Measur.Ki (mR)	Calc.Ki (mR)	Avr. RPDa (%)
17.	70	71.58 ± 0.03	4.41	0.63	0.63 ± 0.00	E film	5.70 ± 0.01	4.49	0.65 ± 0.01	0.50	23.67
8.	70	65.3 ± 0.2	3.5	0.5	0.5 ± 0.0	D film	4.39 ± 0.02	3.42	0.50 ± 0.02	0.39	21.10
16.	70	63.43 ± 0.09	4	0.8	0.83	E film	4.12 ± 0.02	3.95	0.47 ± 0.02	0.45	3.53
10.	70	69.58 ± 0.02	3.5	0.5	0.5 ± 0.0	D film	4.04 ± 0.01	3.42	0.46 ± 0.01	0.39	15.15
10.	70	70.36 ± 0.02	3.5	0.5	0.5 ± 0.0	E film	3.95 ± 0.01	3.42	0.45 ± 0.01	0.39	12.69
21.	70	69.46 ± 0.05	5.04	0.63	0.58 ± 0.05	E film	3.86 ± 0.05	5	0.44 ± 0.05	0.57	29.00
3.	60	60.8 ± 0.1	4.41	0.63	0.63 ± 0.00	D film	3.77 ± 0.02	3.6	0.43 ± 0.02	0.41	3.62
18.	70	69.9 ± 0.6	4	0.5	0.52 ± 0.03	E film	3.51 ± 0.03	3.95	0.40 ± 0.03	0.45	13.02
10.	70	69.0 ± 0.2	2.8	0.4	0.4 ± 0.0	E film	3.33 ± 0.01	2.81	0.38 ± 0.01	0.32	17.77
11.	70	65.9 ± 0.0	3.5	0.5	0.5 ± 0.0	E film	3.25 ± 0.01	3.42	0.37 ± 0.01	0.39	5.60
21.	70	67.4 ± 0.2	4	0.5	0.46 ± 0.09	E film	3.16 ± 0.05	3.95	0.36 ± 0.05	0.45	25.83
10.	70	71.5 ± 0.1	2.8	0.5	0.49 ± 0.02	E film	3.16 ± 0.05	2.81	0.36 ± 0.05	0.32	12.68
6.	70	66.5 ± 0.5	3.5	0.5	0.5 ± 0.0	CCD	3.07 ± 0.04	3.42	0.37 ± 0.04	0.39	7.25
6.	70	68.1 ± 0.2	3.5	0.5	0.5 ± 0.0	CCD	3.07 ± 0.05	3.42	0.36 ± 0.05	0.39	10.51
10.	70	72.5 ± 0.1	3.5	0.5	0.5 ± 0.0	PSP	3.07 ± 0.03	3.42	0.36 ± 0.03	0.39	10.39
6.	70	65.1 ± 0.5	3.5	0.5	0.5 ± 0.0	CCD	2.81 ± 0.05	3.42	0.32 ± 0.05	0.39	21.41
7.	70	68.6 ± 0.0	3.5	0.5	0.5 ± 0.0	CCD	2.72 ± 0.01	3.42	0.31 ± 0.01	0.39	25.09
7.	70	66.7 ± 0.02	3.5	0.5	0.5 ± 0.0	CCD	2.72 ± 0.02	3.42	0.35 ± 0.02	0.39	14.03
6.	70	66.6 ± 0.3	3.5	0.5	0.5 ± 0.0	CCD	2.72 ± 0.01	3.42	0.35 ± 0.01	0.39	13.02
18.	65	65.1 ± 0.4	2.5	0.48	0.48 ± 0.00	E film	2.46 ± 0.01	2.02	0.28 ± 0.01	0.23	16.50
4.	65	64.5 ± 0.6	2.24	0.32	0.32 ± 0.00	E film	2.46 ± 0.01	1.84	0.28 ± 0.01	0.21	25.53
4.	65	65.1 ± 0.0	2.24	0.32	0.32 ± 0.00	E film	2.46 ± 0.01	1.84	0.28 ± 0.01	0.21	25.02
4.	65	63.8 ± 0.2	2.24	0.32	0.32 ± 0.00	E film	2.46 ± 0.01	1.84	0.28 ± 0.01	0.21	24.42
16.	70	71.1 ± 0.1	2.8	0.35	0.32 ± 0.01	PSP	2.46 ± 0.01	2.81	0.28 ± 0.01	0.32	13.15
9.	50	45.7 ± 0.2	5	0.5	0.45 ± 0.08	D film	2.37 ± 0.01	2.1	0.27 ± 0.01	0.24	9.28
3.	70	71.8 ± 0.1	2.43	0.347	0.348 ± 0.002	CCD	2.37 ± 0.01	2.37	0.27 ± 0.01	0.27	2.73
16.	70	65.6 ± 0.3	2.56	0.32	0.32 ± 0.00	CCD	2.28 ± 0.03	2.54	0.26 ± 0.03	0.29	11.07
6.	70	64.6 ± 0.4	2.8	0.5	0.5 ± 0.0	CCD	2.19 ± 0.06	2.81	0.25 ± 0.06	0.32	26.98
11.	70	66.6 ± 0.3	2.24	0.32	0.32 ± 0.00	PSP	2.19 ± 0.04	2.19	0.25 ± 0.04	0.25	0.83
15.	70	70.2 ± 0.0	2.52	0.36	0.36 ± 0.00	PSP	2.02 ± 0.01	2.46	0.23 ± 0.01	0.28	21.13
10.	70	70.3 ± 0.0	1.75	0.25	0.25 ± 0.00	PSP	2.02 ± 0.01	1.75	0.23 ± 0.01	0.20	13.27
20.	70	70.4 ± 0.0	2	0.25	0.28 ± 0.04	CCD	1.93 ± 0.01	2.02	0.22 ± 0.01	0.23	2.43
8.	70	67.6 ± 0.1	2.24	0.64	0.62 ± 0.04	PSP	1.84 ± 0.02	2.19	0.21 ± 0.02	0.25	19.59
12.	60	62.5 ± 0.4	1.75	0.25	0.25 ± 0.00	E film	1.56 ± 0.03	1.35	0.18 ± 0.03	0.13	24.90
1.	70	70.1 ± 0.0	1.6	0.2	0.18 ± 0.02	CCD	1.56 ± 0.01	1.56	0.18 ± 0.01	0.18	1.78
10.	70	70.5 ± 0.0	1.4	0.2	0.2 ± 0.0	PSP	1.49 ± 0.00	1.4	0.17 ± 0.00	0.16	9.24
5.	60	61.8 ± 0.1	1.75	0.25	0.25 ± 0.00	E film	1.36 ± 0.02	1.31	0.16 ± 0.02	0.13	14.03
14.	70	70.0 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.32 ± 0.00	1.14	0.15 ± 0.00	0.13	14.01
14.	70	71 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.32 ± 0.01	1.14	0.15 ± 0.01	0.13	15.84
10.	70	70.3 ± 0.0	1.12	0.16	0.16 ± 0.00	PSP	1.32 ± 0.01	1.14	0.15 ± 0.01	0.13	14.50
2.	60	61.6 ± 0.2	1.4	0.2	0.2 ± 0.0	CCD	1.25 ± 0.02	1.13	0.14 ± 0.02	0.11	24.90
13.	63	60.2 ± 0.4	2	0.25	0.25 ± 0.00	PSP	1.23 ± 0.04	1.5	0.14 ± 0.04	0.23	56.45
4.	65	66.7 ± 0.1	1.12	0.16	0.16 ± 0.00	CCD	1.23 ± 0.03	0.88	0.14 ± 0.03	0.1046	23.35
4.	65	65.3 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.23 ± 0.03	0.88	0.14 ± 0.03	0.10	24.35
4.	65	64.1 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.23 ± 0.01	0.88	0.14 ± 0.01	0.10	23.31
14.	70	69.9 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.23 ± 0.01	1.14	0.14 ± 0.01	0.13	12.67
10.	70	70.6 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.23 ± 0.01	1.14	0.14 ± 0.01	0.13	12.04
8.	70	71.3 ± 0.0	1.12	0.16	0.16 ± 0.00	CCD	1.14 ± 0.01	1.14	0.13 ± 0.01	0.13	6.23
10.	70	69.8 ± 0.0	1.12	0.16	0.16 ± 0.00	PSP	1.14 ± 0.01	1.14	0.13 ± 0.01	0.13	4.87
10.	70	70.6 ± 0.0	0.7	0.1	0.1 ± 0.00	CCD	0.79 ± 0.00	0.7	0.09 ± 0.00	0.08	9.09

^aRelative percent difference.

The results of the performance testing were statistically analysed and shown in Table 3.⁴

The information on Ki, together with the beam area, can be used to calculate KAP and to determine diagnostic reference levels (DRL).^6,14 Furthermore, the effective dose can be estimated based on KAP and coefficients from references.¹⁵

The results of the QC measurements showed¹²:

1. The nominal tube voltage was accurate within 5%, except for two measured X-ray units.

2. The measured time was accurate within 5%, except for two measured X-ray units.

3. The largest deviation from the mean K_i was 6%.

The Table 3 shows that the measured K_i is strongly influenced by the time/current product and voltage of the device. Following the results from the Table 3 and the mathematical model used by Kothan et al⁸ (the equation in this case referred to classical radiography), an empirical formula of K_i in milliroentgen (mR) can be set:

$${\displaystyle K_i\left(mR\right)=k\times \frac{U^n\times I\times t}{d^2}}$$ (1)

where U is X-ray peak tube voltage, I is the current, t is the exposure time, d the source-chamber distance and n the constant value. All the source-chamber distances are normalised to 20 cm using the quadratic law. The value of the constant k is taken to be one. One of the reasons for this is the impossibility of changing the voltage value on the measured intraoral dental X-ray units.

The coefficient n of Eq. (1) was estimated by the multiple nonlinear regression method using measured values of radiation doses at set points values V and Ixt. The MATLAB 2013a (MathWorks) was used for surface fitting (non-linear regression method) of the Eq. (1). MATLAB is a high-performance language for technical computing. It integrates computation, visualisation and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.¹⁶

The Eq. (1) validity was statistically evaluated using a coefficient of correlation (R), standard error (SE) of the fitted function and the mean relative percentage deviation (MRPD).^17,18 These parameters are defined by the following equations:

$${\displaystyle R^2=1-\sum _1^N\frac{{\left(y_i-f_i\right)}^2}{{\left(y_i-y_{av}\right)}^2}}$$ (2)

$${\displaystyle SE=\sqrt{\frac{\sum _1^N{\left(y_i-f_i\right)}^2}{N}}}$$ (3)

$${\displaystyle MRPD=\frac{100}{N}\sum _{i=1}^N|\frac{y_i-f_i}{y_i}|}$$ (4)

where y_i is experimental data, f_i is fitted data, y_av is the average of experimental data and N is the number of data points.

Results and discussion

Experimental data obtained by measurement (Table 3) and data from reference show that the final measured dose is certainly influenced by the age and architecture of the dental device, the choice of image receptors and the operator’s training and knowledge of the device. ^19–22 In the case of films, it depends on whether development is done manually or automatically. The data from reference indicate that, depending on the architecture of a device, the exposure time can vary up to five times resulting in final dose variations (Table 3).^{19–21,23,24} The choice of image receptors can reduce the dose up to nine times (comparison of D film as image receptors (analog) and PSP and CCD receptors (digital).^{19–21,23,24} Table 3 also shows the differences in doses up to four times in the case of devices that use the same image receptors and have a similar device architecture (CCD, 70 kV, 20 cm tube). The final result is also affected by the age of the device and insufficient operator training. Finally, it should be mentioned that the dose may be affected by irregular maintenance. The influence of difference in the shape of the collimator on the dose is not discussed in this paper though it exists, but all investigated units had cylindrical collimator.²²

The experimental data on K_i were analyzed by the multiple nonlinear regression model based on the actual levels of the exposure conditions (V and Ixt), whereas Eq. (1) was used to fit the radiation dose data. The goal of the multiple nonlinear regression model is to model a non-linear relationship (Eq. 1) between the independent (K_i) and dependent (U and Ixt) variables. Figure 1 shows the surface fitting of the Eq. (1) and the residual plot. The Eq. (1) describes the dependence of K_i on U, Ixt and d, but not on the architecture of the unit. Based on the results of the measured K_i for devices of different architecture, the coefficient n in Eq. (1) was determined by fitting. This gave a universal formula of K_i for devices of different architecture.

Figure 1.

The 3D plots for measured radiation doses (K_i) as a function of the X-ray peak tube voltage (V) and the exposure current and time product, (Ixt), visual representation in support of an empirical formula (1); surface fitting (a) and residual plot (b).

The mathematical model describing relationship between the radiation dose, X-ray peak tube voltage (V) and the exposure current/time product (Ixt) is presented by Eq. (5). Value of the coefficient n is given in Eq. (5). The values of R = 0.897 and SE = 0.003 show that the model of Eq. (5) fitted the measurement data very well. The effect of the X-ray peak tube voltage and the exposure current/time product on radiation dose is shown in Figure 1. With the increase in the exposure current/time product, the radiation doses increase linearly (Figure 1). Radiation doses increase with increasing the U^2.5.

$${\displaystyle K_i=\frac{U^{2.5}\times I\times t}{400}}$$ (5)

For easier insight and comparison of the obtained results, the Table 3 shows calculated K_i (mGy, mR) values (columns 9 and 11) and measured K_i (mGy, mR) values.

The accuracy of the models of Eq. (5) was estimated by calculating the MRPD. Measurement values of the radiation doses and calculated values obtained by using Eq. (5) showed good agreement, as illustrated in Figure 2. The MRPD between calculated and measured values was less than 15% indicating validity of Eq. (5).

Figure 2.

Diagnostic plots of measurement and calculated values of radiation doses (R).

The obtained formula for empirical calculation of incident kerma in air shows good matches with measured values in all X-ray units, whose deviations of measured nominal voltage does not exceed the value more than 10%. On the other hand, if deviations were higher than 10% calculated doses did not match the measured ones.

Conclusion

The empirical formula found in this work to calculate K_i shows good matches with the measured values and can be used in practice. It can help dentists to determine Ki of the procedure, if devices does not estimate it. The Ki deviation can mean wrong mode of operation, that is, poorly set parameter. Also, if the K_i is known, typical value could be set in order to compare to DRL and optimize the practice. It can also be used in other aspects of radiological protection, that is, dose calculation of occupationally exposed persons who are close to the patient during imaging. This can facilitate the calculation of protective barriers.