2.1 Description of the medical drugs studied

Medical drugs are cutaneously prescribed by doctors for patients in dermatology, cardiology, gastro-enterology, anaesthesia-resuscitation, gynecology, pneumology, and rheumatology. The properties and dosages of the considered medical drugs are shown in Table 1.

2.2 Determination of ²³⁸U and ²³²Th alpha-activities per unit volume in medical drugs

The alpha-activities of ²³⁸U and ²³²Th were measured using the following types of solid state nuclear track detectors (SSNTDs):

- CR-39 discs, 2 cm in radius and 500 µm thick, manufactured by Pershore Mouldings Ltd, United Kingdom;

- LR-115 type II discs, 2 cm in radius, comprising 12 µm of cellulose nitrate on a 100 µm thick polyester base, manufactured by Kodak Pathé, France, and marketed by Dosirad, France.

The detectors were separately placed in close contact with different medical drugs in hermetically sealed (using glue and a cellophane tape) HDPE (high density polyethylene) cylindrical plastic containers for 30 days (Fig. 1). During this period of time, alpha-particles emitted by the nuclei of ²³⁸U, ²³²Th, and their daughters inside the medical drug samples exposed the SSNTD films. After irradiation, the exposed SSNTDs were etched in two NaOH solutions: one was 2.5 mol l^-1 at 60°C for 2 hours for the LR-115 II films and the other was 6.25 mol l^-1 at 70°C for 7 hours for the CR-39 detectors [9]. After chemical treatment, the track densities registered on the CR-39 and LR-115 II SSNTDs were determined by an ordinary microscope. Backgrounds on the CR-39 and LR-115 II SSNTDs were evaluated by placing these films in sealed plastic containers, containing ambient air, identical to those used for analysing the medical drug samples, for 30 days and counting the resulting track densities. This operation was repeated ten times, and it was found that the track densities registered on the CR-39 and LR-115 II detectors were identical within the statistical uncertainties. The reproducibility of the method was checked by analysing a set of ten samples of the same medical drug. Track density production rates registered on the CR-39 and LR-115 II detectors were evaluated for the P13 medical drug sample. Data obtained, for instance, for the P13 medical drug sample was: ${\rho }_G^{CR}$= (2.41±0.01) 10^-5 tracks cm^-2 s^-1 and ${\rho }_G^{LR}$= (9.25±0.05)10^-5 tracks cm^-2 s^-1, respectively. The relative uncertainty of the average track density rate determination is smaller than 1%.

Fig. 1.Full-screen View

Arrangement of a solid state nuclear track detector (SSNTD) on a medical drug material sample in a well-sealed plastic container with a radius of q=2 cm, depth of D=1 cm, and thickness of t=0.5 cm. Glue is put between the plastic cover and plastic container and both are covered by a cellophane tape with a 0.2 cm thickness.

There are three main factors which disturb the radioactive secular equilibrium between ²³⁸U and its progeny and between ²³²Th and its daughters: (a) the addition of any chemical compounds to the medical drug sample, (b) any escape of radon and thoron gases, and (c) the exposure time if it is shorter than 25 days. As the detection system used was well-sealed (i.e., there was no escape of radon and thoron) and the exposure time was 30 days, a radioactive secular equilibrium is established between ²³⁸U and each of its decay products and between ²³²Th and each of its daughters. For the experimental etching conditions, the residual thickness of the LR-115 type II detectors measured by means of a mechanical comparator is 5 µm. This thickness defines the lower (E_min= 1.6 MeV) and upper (E_max = 4.7 MeV) energy limits for the registration of tracks of alpha-particles in LR-115 type II films [10]. All alpha-particles emitted by the ²³⁸U and ²³²Th series that reach the LR-115 II detector at an angle smaller than its critical angle of etching, ${\theta }_c^{\text{'}}$, with a residual energy between 1.6 MeV and 4.7 MeV are registered as bright track-holes. The CR-39 detector is sensitive to all alpha-particles reaching its surface at an angle smaller than its critical angle of etching, ${\theta }_c$. The critical angles of etching, ${\theta }_c^{\text{'}}$ and ${\theta }_c$, were calculated using the method described in detail by Misdaq et al. [11].

The global track density rates (tracks cm^-2 s^-1), due to alpha-particles emitted by the ²³⁸U and ²³²Th series inside a material sample, registered on the CR-39 (${\rho }_G^{CR}$) and LR-115 II (${\rho }_G^{LR}$) detectors, after subtracting the corresponding backgrounds, are respectively given by [9]:

and

where: $A_c\left({}_{}{}^{238}\text{U}\right)$, expressed in Bq cm^-3, is the activity per unit volume of ²³⁸U inside a medical drug sample. $A_c\left({}_{}{}^{232}\text{Th}\right)$, expressed in Bq cm^-3, is the activity per unit volume of ²³²Th inside a medical drug sample. S_d and S_d^' are respectively the surface areas of the CR-39 and LR-115 II films. R_j and R_j^' are the ranges, in the medical drug sample, of an alpha-particle of index j and initial energy $E_{{\alpha }_j}$ emitted by the nuclei of the ²³⁸U and ²³²Th series, respectively. k_j and k'_j are respectively the branching ratios corresponding to the disintegration of the nuclei of the ²³⁸U and ²³²Th series. ${\epsilon }_j^{CR}$, ${\epsilon }_j^{\text{'}CR}$, ${\epsilon }_j^{LR}$ and ${\epsilon }_j^{\text{'}LR}$ are respectively the detection efficiencies of the CR-39 and LR-115 II detectors for the emitted alpha-particles [9].

Combining Eqs. (1) and (2), we obtain the following relationship between the track density rates and ²³²Th to ²³⁸U ratios:

The ²³⁸U alpha-activity per unit volume of a medical drug sample is given by (Eq. 2):

By measuring the ${\rho }_G^{CR}$ and ${\rho }_G^{LR}$ track density rates and calculating the ${\epsilon }_j^{CR}$, ${\epsilon }_j^{\text{'}CR}$, ${\epsilon }_j^{LR}$, and ${\epsilon }_j^{\text{'}LR}$ detection efficiencies [9] we evaluate the $\frac{A_c\left({}_{}{}^{232}\text{Th}\right)}{A_c\left({}_{}{}^{238}\text{U}\right)}$ ratio (Eq. (3)) and, consequently, the ²³⁸U and ²³²Th alpha-activities per unit volume in a given medical drug sample (Eq. (4)).

The ranges of the emitted alpha-particles in medical drugs and SSNTDs were calculated by using the TRIM (Transport of Ions in Materials) program [12].

2.3 A new dosimetric model for evaluating annual committed equivalent doses to skin due to alpha-particles emitted by the nuclei of the ²³⁸U and ²³²Th series from cutaneous application of medical drugs

The epidermis of the human skin is divided into several clearly defined zones [13]. Indeed, when a medical drug layer is placed on the skin of a patient, the nuclei of the ²³⁸U and ²³²Th series emit alpha-particles with a range of several tens of microns (20 to 100 µm) (Table 2). This is comparable with the depth of the basal layer of the epidermis, which is more sensitive (50 to 100 µm) [14].

An alpha-particle with an index of j and initial energy of $E_{{\alpha }_j}$ emitted from a nucleus localized on the point M inside the medical drug layer (Fig. 2) has a range:

Fig. 2.Full-screen View

Ranges of an alpha-particle inside the medical drug layer ($\overline{MI}= x_j$) and epidermis ($\overline{IF}=R_j^{skin}$). $E_{\alpha j}$ is the initial alpha-particle energy and $E_{\alpha j}^{Res}$ its residual energy on the point I. The medical drug layer has a depth of about 500 µm.

where $x_j$ ($x_j\le R_j$, $x_j$ is the range of the alpha-particle inside the medical drug layer) is the distance between the emission point and the skin surface (Fig. 2) and $R_j^{skin}$ is the range of the alpha-particle in skin.

The alpha-particle residual energy, $E_{{\alpha }_j}^{\mathrm{Re}s}$, which corresponds to the ($R_j$-$x_j$) range is determined by using the energy-range relation in the medical drug (Fig.3 (a)). By using the energy–range relation in skin, one can determine the range of the alpha-particle in skin, $R_j^{skin}$(Fig. 3(b)). For $x_j=R_j{}^{}$ and $E_{{\alpha }_j}^{\mathrm{Re}s}=0MeV$, there is no energy loss of alpha-particles in skin (case 1 of Fig. 2). For $x_j=0\mu m$ and $E_{{\alpha }_j}^{\mathrm{Re}s}=E_{{\alpha }_j}$, the energy loss of alpha-particles in the skin is at a maximum ($R_j^{skin}$ maximum) (case 3 of Fig. 2). For $x_j\prec R_j{}^{}$ and $E_{{\alpha }_j}^{\mathrm{Re}s}\prec E_{{\alpha }_j}$, the range of alpha-particle in the skin are lower than those corresponding to $x_j=0\mu m$ (case 2 of Fig. 2).

Fig. 3.Full-screen View

Alpha particle range-energy relation for a medical drug material sample (a) and skin (b).

Alpha-equivalent dose rates (Svs^-1) to the human skin due to a radionuclide of index of j belonging to the ²³⁸U series and a radionuclide of index of j’ belonging to the ²³²Th series from the application of medical drugs by patients are respectively given by:

and

where: $A_c^{skin}(j)(t)$ (Bq) is the alpha-activity, at time t, in skin due to a radionuclide of index j belonging to the ²³⁸U series. $A_c^{skin}(j\text{'})(t)$ (Bq) is the alpha-activity, at time t, in skin due to a radionuclide of index j’ belonging to the ²³²Th series. $D_{Sp}^{skin}(j)$ is the specific alpha-dose (Gy) deposited by 1Bq of a radionuclide of index j belonging to the ²³⁸U series in skin. $D_{Sp}^{skin}(j\text{'})$ is the specific alpha-dose (Gy) deposited by 1Bq of a radionuclide of index j’ belonging to the ²³²Th series in skin. W_R is the radiation weighting factor, which is equal to 20 for alpha-particles [13].

The $A_c^{skin}(j)(t)$ and $A_c^{skin}(j\text{'})(t)$ alpha-activities are respectively given by:

and

where $A_c^{sample}\left({}_{}{}^{238}\text{U}\right)$ (Bq cm^-3) is the alpha-activity due to ²³⁸U inside a medical drug sample. $A_c^{sample}\left({}_{}{}^{232}\text{Th}\right)$ (Bq cm^-3) is the alpha-activity due to ²³²Th inside a medical drug sample. λ_j is the radioactive decay constant of a radionuclide of index j belonging to the ²³⁸U series and λ_j’ is the radioactive decay constant of a radionuclide of index j’ belonging to the ²³²Th series. The term ½ means that only half of the emitted alpha-particles inside a medical drug sample may lose their energies inside the skin.

The $D_{Sp}^{skin}(j)$ and $D_{Sp}^{skin}(j\text{'})$ specific alpha-doses are respectively given by:

and

where: d_s is the density of skin (g cm^-3). $S_{skin}$ is the surface skin (cm²). k = 1.6.10^-13 (J MeV^-1) is a conversion factor. $R_j^{skin}$ is the range, in skin, of an alpha-particle of index j and a residual energy, $E_{{\alpha }_j}^{\mathrm{Re}s}$, belonging to the ²³⁸U series. $R_j^{skin}$ is the range, in skin, of an alpha-particle of index j and a residual energy, $E_{{\alpha }_{j\text{'}}}^{\mathrm{Re}s}$, belonging to the ²³²Th series (Fig. 3).

By integrating Eqs. 6 and 7, committed equivalent doses (Sv) to skin due to an alpha-particle of residual energy, $E_{{\alpha }_j}^{\mathrm{Re}s}$, emitted by a radionuclide of index j belonging to the ²³⁸U series and an alpha-particle of residual energy, $E_{\alpha j\text{'}}^{\mathrm{Re}s}$, emitted by a radionuclide of index j’ belonging to the ²³²Th series from the application of a medical drug sample are respectively given by:

and

where t_a is the application time.

Committed equivalent doses to the epidermis (EP) of the skin (Sv) due to all residual energies of an alpha-particle of index j and initial energy E_αj belonging to the ${}_{.}{}^{238}U$ series and an alpha-particle of index j’ and initial energy $E_{\alpha j^{\text{'}}}$ belonging to the ${}_{.}{}^{232}Th$ series are respectively given by:

and

Where Δ$E_{{\alpha }_j}^{\mathrm{Re}s}$ and Δ$E_{\alpha j\text{'}}^{\mathrm{Re}s}$ are the chosen steps.

Committed equivalent doses (Sv y^-1 cm^-2) to the skin surface of 1cm² of the epidermis during an exposure time is equal to 1 year due to the alpha-particles emitted by the ²³⁸U (eight alpha-emitting nuclei) and ²³²Th (seven alpha-emitting nuclei) series from the application of a medical drug sample by patients are respectively given by:

and 

3.1 ²³⁸U and ²³²Th alpha-activities per unit volume in medical drugs

The ²³⁸U (A_c (²³⁸U)) and ²³²Th (A_c (²³²Th)) alpha-activities per unit volume were measured in various medical drugs prescribed by doctors for different age groups of patients. Data obtained is shown in Table 3. Since the track detectors utilized were etched in two NaOH solutions at optimal conditions of etching, ensuring good sensitivities of the SSNTDs and a good reproducibility of the registered track density rates determined by means of the same optical microscope with a magnification of 40x, only the statistical uncertainty on track counting is predominant. From the statistical uncertainty on track counting, the uncertainty on track density production per unit time was determined, and then the uncertainty of the measured ²³⁸U and ²³²Th concentrations was determined, which gave values of about 8%. Natural uranium is formed by ²³⁸U, ²³⁵U, and ²³⁴U radioisotopes with isotopic abundances equal to 99.27%, 0.72%, and 0.0055%, respectively. So, the contribution of alpha-particles emitted by the ²³⁵U series to the global track densities registered on the SSNTDs utilized is negligible because they induce a relative uncertainty smaller than 1%, which is included in the uncertainty on the ²³⁸U and ²³²Th concentration determination (8 %). The data shown in Table 3 demonstrates that all medical drug samples studied contain more ²³⁸U than ²³²Th. This is probably due to the fact that raw materials used for the preparation of these medical drugs contain more ²³⁸U than ²³²Th. It is to be noted that the ²³⁸U contents of the P1, P3, P5, P9, P10, P12, P13, P17, P18, and P20 medical drugs are clearly higher than those of the P2, P4, P6, P7, P11, P14, and P21 medical drug samples (Table 3). We also noted that the ²³²Th contents of the P2, P6, P7, P11, P14, and P21 medical drug samples are clearly higher than those of the P1, P3, P9, P13, P17, and P18 samples (Table 3). The minimum detection activities (MDA) for ²³⁸U and ²³²Th were found to be equal to (0.81±0.05) mBql^-1 and (0.11±0.01) mBql^-1, respectively.

In order to validate this method, 10 medical drugs were analyzed using Isotope Dilution Mass Spectrometry (IDMS). Isotope Dilution Mass Spectrometry is based on the addition of a known amount of enriched isotope (called the spike) to a medical drug sample. After equilibrium of the spike with the natural isotope of the element in the sample, mass spectrometry is used to measure the altered isotopic ratio(s). Data obtained by the two methods, for the ²³⁸U and ²³²Th contents, are in good agreement with each other (Table 3).

3.2 Committed equivalent doses to skin due to the radionuclides of the ²³⁸U and ²³²Th series from the application of medical drugs by patients

Committed equivalent doses to the epidermis of skin due to the alpha-emitting nuclei of the ²³⁸U (H(U)(EP)) and ²³²Th (H(Th)(EP)) series from the application of medical drugs by different age groups of patients have been evaluated by means of Eqs. 16 and 17, and the results are shown in Tables 4, 5, 6 and 7. The statistical relative uncertainty of the committed dose determination is 9 %. It should be noted that H(U)(EP) and H(Th)(EP) increase with an increase in the application time of medical drugs by adults (Tables 1, 4, and 5).

It is to be noted from the data shown in Tables 4-7 that H(U)(EP) and H(Th)(EP) due to cutaneous application of the medical drug P1 are negligible compared to those due to the other medical drugs for adults and children. This is because the application time for medical drug P1, used for surface anaesthesia, is shorter than those for the other medical drugs (Table 1). It is to be noted from the results shown in Table 4 that committed equivalent doses to the epidermis of the skin due to alpha-particles emitted by ²¹⁴Po (H(²¹⁴Po)) and ²¹⁸Po (H(²¹⁸Po)) are negligible compared to those corresponding to the other alpha-emitters of the ²³⁸U series. This is because they have smaller half-lives, 1.6 10^-4 s and 3.05 min, respectively, than the other radionuclides. Also, one can note that committed equivalent doses to the epidermis due to ²¹²Po (H(²¹²Po)) and ²¹⁶Po (H(²¹⁶Po)) are negligible compared to those corresponding to the other alpha-emitters of the ²³²Th series (Table 5). This is due to the fact that these radionuclides possess smaller half-lives, 3.7 10^-7 s and 0.158 s, respectively, than the other alpha-emitters of the ²³²Th series. It is to be noted that total committed equivalent doses due to the ²³⁸U and ²³²Th series from cutaneous application of P1, P4, P5, P6, P10, and P11 medical drugs are higher for 5 year-old children than for the other age groups of patients (Tables 4-7). This is because 5 year-old children possess smaller skin surface area than the other age groups of patients [1]. The maximum total committed equivalent dose to skin due to the ²³⁸U and ²³²Th series was found to be equal to 2.8 mSv y^-1 cm^-2, obtained for women applying the P13 medical drug (Tables 4(a) and 5(a)), which is significantly smaller than the dose limit for members of the public, which is of 50 mSv y^-1 cm^-2 [1].