²³⁸U and ²³²Th concentrations measured in different medical drugs by using solid state nuclear track detectors and resulting radiation doses to the skin of patients

238 U and 232 Th concentrations measured in different medical drugs by using solid state nuclear track detectors and resulting radiation doses to the skin of patients 1 corresp first-author Corresponding author: E-mail address: misdaq@uca.ma (M.A.Misdaq) Corresponding author: E-mail address: misdaq@uca.ma (M.A.Misdaq) misdaq@uca.ma 1 2 Nuclear Physics and Techniques Laboratory, Faculty of Sciences Semlalia, BP.2390, University of Cadi Ayyad, Marrakech 40000, Morocco (URAC-15 Research Unit Associated to the CNRST, Rabat, Morocco). Nuclear Physics and Techniques Laboratory, Faculty of Sciences Semlalia, BP.2390, University of Cadi Ayyad, Marrakech 40000, Morocco (URAC-15 Research Unit Associated to the CNRST, Rabat, Morocco). Nuclear Medicine Service, Mohamed VI University Hospital Centre, Faculty of Medicine and Pharmacy, University of Cadi Ayyad, Marrakech 40000, Morocco Nuclear Medicine Service, Mohamed VI University Hospital Centre, Faculty of Medicine and Pharmacy, University of Cadi Ayyad, Marrakech 40000, Morocco Urban populations in Morocco receive free medical drugs as prescribed by doctors in district health centres. To explore the exposure pathway of 238 U and 232 Th and their decay products on the skin of patients, these radionuclides were measured in various medical drugs by using solid state nuclear track detectors (SSNTDs).The measured concentrations range of 238 U and 232 Th in the medical drug samples of interest vary from (4.3±0.3) mBq l -1 to (11.1±0.7) mBql -1 and (0.49±0.03) mBql -1 to (1.3±0.1) mBql -1 , respectively. A new dosimetric model, based on the concept of specific alpha-dose and alpha-particle residual energy, was developed for evaluating radiation doses to skin following the application of different medical drugs by patients. The maximum total equivalent effective dose to skin due to the 238 U and 232 Th series from cutaneous application of different medical drugs by patients was found to be 2.8 mSv y -1 cm -2 . Nuclear track detectors Medical drugs; 238 U and 232 Th concentrations Radiation dose assessment to skin 1 INTRODUCTION 1 The skin is the largest organ of the human body, with a total area of about 20 square feet. It protects individuals from microbes, helps regulate body temperature, and limits the sensation of touch, heat, and cold. The skin has three layers: (i) The epidermis, the outermost layer of skin which provides a waterproof barrier and creates the skin tone; (ii) the dermis, beneath the epidermis which contains tough connective tissue, hair follicles, and sweat glands, and (iii) the deeper subcutaneous tissue (hypodermis) which is made of fat and connective tissue. The critical cells in the skin are in the basal layer of the epidermis. There are considerable variations in the thickness of human epidermis with respect to body site [ 1 1 ]. On the face and trunk, the median thickness of the epidermis was 20-40 µm. In general, on the arms and legs it was 40-60 µm, although there were some considerably thicker areas on the hands and feet [ 1 1 ]. A more detailed evaluation of the hands showed fingertips to have the greatest thickness, greater than 160 µm [ 1 1 ]. The degree of undulation of the basal layer was found to increase with increasing epidermal thickness. Naturally occurring radionuclides of terrestrial origin are present in various degrees in all media of the environment and contribute significantly to external and internal doses of the population [ 2 2 ]. Among them, important radionuclides of interest belong to the 238 U and 232 Th series. These radionuclides emit alpha- and beta–particles, as well as gamma rays. The different forms of emitted radiation have different energies and penetrating power and, thus, have different effects on living beings. Once the radionuclides of the 238 U and 232 Th series are placed on the skin, they emit alpha-particles with a range of several tens of microns (between 20 µm and 100 µm). This is comparable with the depth of the basal layer of the epidermis. Due to their presence in soil and phosphate fertilizers, primordial radionuclides and their progeny are transferred via water from soil to plant flowers and medicinal plants to medical drugs. Thus, it is necessary to measure the radionuclide contents of medical drugs to assess the potential radiation doses, and if necessary, to take action to reduce the exposure of patients to radiation. 238 U and 232 Th concentrations have been measured in various medicinal plants by using solid state nuclear track detectors [ 3 3 ]. 238 U and 232 Th have also been analysed in aerial parts and roots of the Peperomia pellucida medicinal plant using alpha spectrometry after radiochemical separation by ionic exchange resins and measurement with a silicon surface-barrier detector [ 4 4 ]. However, this technique is both destructive (chemical agents are added to the material sample) and expensive. 238 U and 232 Th have been analyzed in different food samples using inductively coupled plasma mass spectrometry (ICP-MS), which is also destructive [ 5 5 ]. Committed effective doses due to the 238 U and 232 Th radioisotopes following the ingestion of various foodstuffs by individuals have been determined [ 6 6 ]. In previous works, we evaluated committed effective doses to skin due to only three alpha-emitting nuclei ( 238 U, 232 Th, and 222 Rn) from the application of Moroccan black soap [ 7 7 ] and olive oil [ 8 8 ] samples without taking into account the residual energies of the emitted alpha-particles. In the present work, CR-39 and LR-115 type II solid state nuclear track detectors (SSNTDs) were used for measuring 238 U and 232 Th alpha-activities per unit volume in different medical drugs. During the full course of medical drug application to different age groups of patients, the committed effective doses to the skin were evaluated due to alpha-particles emitted by the radio-nuclei of the 238 U and 232 Th series. 2 METHODS OF STUDY 1 2.1 Description of the medical drugs studied 2 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 Table 1 . 1 1 Medical drugs 1 1 Properties 1 1 Dosage 1 1 Medical speciality 1 1 P1 1 1 Used for surface anaesthesia (skin and mucosa) 1 1 1g maximum per 10cm 2 during 20 to 30 minutes 1 1 Anaesthesia 1 1 P2 1 1 Vascular protective and veinotonic 1 1 2 applications per day during 1 month 1 1 Cardiology 1 1 P3 1 1 Dermocorticoid 1 1 1 to 2 applications per day during 15 days 1 1 Dermatology 1 1 P4 1 1 Antibacterial agent 1 1 1 application per day during 7 to 15 days 1 1 Dermatology 1 1 P5 1 1 Antifungal agent 1 1 2 applications per day during 1 month 1 1 Dermatology 1 1 P6 1 1 Antiparasitic agent 1 1 2 applications per day during 8 days 1 1 Dermatology 1 1 P7 1 1 Used for antiseptic skin 1 1 1 application per day during 7 days 1 1 Dermatology 1 1 P8 1 1 Antiherpetic agent 1 1 5 applications per day during 5 to 10 days 1 1 Dermatology 1 1 P9 1 1 Used for antiacne treatment 1 1 1 to 2 applications per day during 3 months 1 1 Dermatology 1 1 P10 1 1 Used for antipruritic treatment 1 1 2 to 3 applications per day during 3 to 5 days 1 1 Dermatology 1 1 P11 1 1 Used for local treatment of skin ulcers 1 1 1 to 2 applications per day during 7 days 1 1 Dermatology 1 1 P12 1 1 Used for the treatment of hemorrhoids 1 1 2 to 3 applications per day during 7 days 1 1 Gastroenterology 1 1 P13 1 1 Estrogen agent 1 1 1 application per day 24 to 28 days per month during 5 years 1 1 Gynecology 1 1 P14 1 1 Progestin agent 1 1 1 application per day during 1 month 1 1 Gynecology 1 1 P15 1 1 Used in adjunctive therapy and as decongestant in respiratory diseases 1 1 2 applications per day during 3 days 1 1 Pneumology 1 1 P16 1 1 Non steroidal anti inflammatory 1 1 3 to 4 applications per day during 2 weeks 1 1 Rheumatology 1 1 P17 1 1 Used for the treatment of psoriasis 1 1 1 to 2 applications per day during 2 months 1 1 Dermatology 1 1 P18 1 1 Keratolytic agent 1 1 1 application per day during 3 month 1 1 Dermatology 1 1 P19 1 1 Used for the treatment of hyperpigmented lesions 1 1 2 applications per day during 3 month 1 1 Dermatology 1 1 P20 1 1 Used for rosacea treatment 1 1 2 applications per day during 3 to 4 months 1 1 Dermatology 1 1 P21 1 1 Used for local treatment of painful muscle contractures 1 1 2 applications per day during 2 weeks 1 1 Rheumatology 2.2 Determination of 238 U and 232 Th alpha-activities per unit volume in medical drugs 2 The alpha-activities of 238 U and 232 Th 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 Fig. 1 ). During this period of time, alpha-particles emitted by the nuclei of 238 U, 232 Th, 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 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: <math id="M1"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> = (2.41±0.01) 10 -5 tracks cm -2 s -1 and <math id="M2"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> = (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%. There are three main factors which disturb the radioactive secular equilibrium between 238 U and its progeny and between 232 Th 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 238 U and each of its decay products and between 232 Th 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 10 ]. All alpha-particles emitted by the 238 U and 232 Th series that reach the LR-115 II detector at an angle smaller than its critical angle of etching, <math id="M3"><mrow><msubsup><mi>θ</mi><mi>c</mi><mo>'</mo></msubsup></mrow></math> , 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, <math id="M4"><mrow><msub><mi>θ</mi><mi>c</mi></msub></mrow></math> . The critical angles of etching, <math id="M5"><mrow><msubsup><mi>θ</mi><mi>c</mi><mo>'</mo></msubsup></mrow></math> and <math id="M6"><mrow><msub><mi>θ</mi><mi>c</mi></msub></mrow></math> , were calculated using the method described in detail by Misdaq et al. [ 11 11 ]. The global track density rates (tracks cm -2 s -1 ), due to alpha-particles emitted by the 238 U and 232 Th series inside a material sample, registered on the CR-39 ( <math id="M7"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> ) and LR-115 II ( <math id="M8"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> ) detectors, after subtracting the corresponding backgrounds, are respectively given by [ 9 9 ]: <math display="block" id="M9"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mi>π</mi><msup><mi>q</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mtext> </mtext><msub><mi>S</mi><mi>d</mi></msub></mrow></mfrac><msub><mi>A</mi><mi>c</mi></msub><msub><mrow><mrow><mo>(</mo><mrow><mmultiscripts><mi>U</mi><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow><mrow/></msub><mrow><mo>[</mo><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mrow><msub><mi>k</mi><mi>j</mi></msub></mrow></mstyle><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup><msub><mi>R</mi><mi>j</mi></msub><mo>+</mo><mfrac><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mi>T</mi><mprescripts/><mi/><mn>232</mn></mmultiscripts><mi>h</mi></mrow><mo>)</mo></mrow></mrow><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mi>U</mi><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mrow><msubsup><mi>k</mi><mi>j</mi><mo>'</mo></msubsup></mrow></mstyle><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mi>C</mi><mi>R</mi></mrow></msubsup><msubsup><mi>R</mi><mi>j</mi><mo>'</mo></msubsup></mrow><mo>]</mo></mrow></mrow></math> and <math display="block" id="M10"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mi>π</mi><msup><mi>q</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mtext> </mtext><msubsup><mi>S</mi><mi>d</mi><mo>'</mo></msubsup></mrow></mfrac><msub><mi>A</mi><mi>c</mi></msub><msub><mrow><mrow><mo>(</mo><mrow><mmultiscripts><mi>U</mi><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow><mrow/></msub><mrow><mo>[</mo><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mrow><msub><mi>k</mi><mi>j</mi></msub></mrow></mstyle><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup><msub><mi>R</mi><mi>j</mi></msub><mo>+</mo><mfrac><mrow><msub><mi>A</mi><mi>C</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mrow><msubsup><mi>k</mi><mi>j</mi><mo>'</mo></msubsup></mrow></mstyle><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mi>L</mi><mi>R</mi></mrow></msubsup><msubsup><mi>R</mi><mi>j</mi><mo>'</mo></msubsup></mrow><mo>]</mo></mrow></mrow></math> where: <math id="M11"><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></math> , expressed in Bq cm -3 , is the activity per unit volume of 238 U inside a medical drug sample. <math id="M12"><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></math> , expressed in Bq cm -3 , is the activity per unit volume of 232 Th 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 <math id="M13"><mrow><msub><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow></msub></mrow></math> emitted by the nuclei of the 238 U and 232 Th series, respectively. k j and k' j are respectively the branching ratios corresponding to the disintegration of the nuclei of the 238 U and 232 Th series. <math id="M14"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> , <math id="M15"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> , <math id="M16"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> and <math id="M17"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> are respectively the detection efficiencies of the CR-39 and LR-115 II detectors for the emitted alpha-particles [ 9 9 ]. Combining Eqs. (1) and (2), we obtain the following relationship between the track density rates and 232 Th to 238 U ratios: <math display="block" id="M18"><mrow><mfrac><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mfrac><mrow><msubsup><mi>S</mi><mi>d</mi><mo>'</mo></msubsup></mrow><mrow><msub><mi>S</mi><mi>d</mi></msub></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mrow><msub><mi>k</mi><mi>j</mi></msub><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup><msub><mi>R</mi><mi>j</mi></msub><mo>−</mo><mfrac><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mrow><msub><mi>k</mi><mi>j</mi></msub><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></mstyle><msub><mi>R</mi><mi>j</mi></msub></mrow></mstyle></mrow><mrow><mfrac><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mrow><msubsup><mi>k</mi><mi>j</mi><mo>'</mo></msubsup><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>C</mi><mi>R</mi></mrow></msubsup><msubsup><mi>R</mi><mi>j</mi><mo>'</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>S</mi><mi>d</mi><mo>'</mo></msubsup></mrow><mrow><msub><mi>S</mi><mi>d</mi></msub></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mrow><msubsup><mi>k</mi><mi>j</mi><mo>'</mo></msubsup><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>L</mi><mi>R</mi></mrow></msubsup><msubsup><mi>R</mi><mi>j</mi><mo>'</mo></msubsup></mrow></mstyle></mrow></mstyle></mrow></mfrac></mrow></math> The 238 U alpha-activity per unit volume of a medical drug sample is given by (Eq. 2): <math display="block" id="M19"><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mn>2</mn><mtext> </mtext><msubsup><mi>S</mi><mi>d</mi><mo>'</mo></msubsup><mtext> </mtext><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow><mrow><mi>π</mi><mtext> </mtext><msup><mi>q</mi><mn>2</mn></msup><mrow><mo>[</mo><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mrow><msub><mi>k</mi><mi>j</mi></msub><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup><msub><mi>R</mi><mi>j</mi></msub><mo>+</mo><mfrac><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mrow><msubsup><mi>k</mi><mi>j</mi><mo>'</mo></msubsup></mrow></mstyle><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>L</mi><mi>R</mi></mrow></msubsup><msubsup><mi>R</mi><mi>j</mi><mo>'</mo></msubsup></mrow></mstyle></mrow><mo>]</mo></mrow></mrow></mfrac></mrow></math> By measuring the <math id="M20"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> and <math id="M21"><mrow><msubsup><mi>ρ</mi><mi>G</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> track density rates and calculating the <math id="M22"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> , <math id="M23"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>C</mi><mi>R</mi></mrow></msubsup></mrow></math> , <math id="M24"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> , and <math id="M25"><mrow><msubsup><mi>ε</mi><mi>j</mi><mrow><mo>'</mo><mtext> </mtext><mi>L</mi><mi>R</mi></mrow></msubsup></mrow></math> detection efficiencies [ 9 9 ] we evaluate the <math id="M26"><mrow><mfrac><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow><mrow><msub><mi>A</mi><mi>c</mi></msub><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math> ratio (Eq. (3)) and, consequently, the 238 U and 232 Th 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 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 238 U and 232 Th series from cutaneous application of medical drugs 2 The epidermis of the human skin is divided into several clearly defined zones [ 13 13 ]. Indeed, when a medical drug layer is placed on the skin of a patient, the nuclei of the 238 U and 232 Th series emit alpha-particles with a range of several tens of microns (20 to 100 µm) ( Table 2 Table 2 ). This is comparable with the depth of the basal layer of the epidermis, which is more sensitive (50 to 100 µm) [ 14 14 ]. 1 1 Nuclide 1 1 E αj (MeV) 1 1 k j 1 1 R j (μm) 1 1 (a) Uranium family 1 1   1 1   1 1   1 1 238 U 1 1 4.19 1 1 1 1 1 25.64 1 1 230 Th 1 1 4.62 1 1 1 1 1 29.52 1 1 234 U 1 1 4.77 1 1 1 1 1 30.93 1 1 226 Ra 1 1 4.78 1 1 1 1 1 31.03 1 1 210 Po 1 1 5.3 1 1 1 1 1 36.16 1 1 222 Rn 1 1 5.49 1 1 1 1 1 38.13 1 1 218 Po 1 1 6.00 1 1 1 1 1 43.64 1 1 214 Po 1 1 7.68 1 1 1 1 1 64.19 1 1 Nuclide 1 1 Eα j’ (MeV) 1 1 <math id="M27"><mrow><mi>k</mi><msub><mo>'</mo><mi>j</mi></msub></mrow></math> 1 1 R j’ (μm) 1 1 (b) Thorium family 1 1   1 1   1 1   1 1 232 Th 1 1 4.01 1 1 1 1 1 24.09 1 1 228 Th 1 1 5.42 1 1 1 1 1 37.39 1 1 224 Ra 1 1 5.71 1 1 1 1 1 40.46 1 1 212 Bi 1 1 6.05 1 1 0.36 1 1 44.19 1 1 220 Rn 1 1 6.29 1 1 1 1 1 46.93 1 1 216 Po 1 1 6.78 1 1 1 1 1 52.73 1 1 212 Po 1 1 8.78 1 1 0.64 1 1 79.62 An alpha-particle with an index of j and initial energy of <math id="M28"><mrow><msub><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow></msub></mrow></math> emitted from a nucleus localized on the point M inside the medical drug layer ( Fig. 2 Fig. 2 ) has a range: <math display="block" id="M33"><mrow><mover accent="true"><mrow><mi>M</mi><mi>F</mi></mrow><mo stretchy="true">¯</mo></mover><mo>=</mo><msub><mi>x</mi><mi>j</mi></msub><mo>+</mo><msubsup><mstyle mathsize="140%" displaystyle="true"><mi>R</mi></mstyle><mi>j</mi><mrow><mo>s</mo><mo>k</mo><mo>i</mo><mo>n</mo></mrow></msubsup></mrow></math> where <math id="M34"><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow></math> ( <math id="M35"><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>≤</mo><msub><mi>R</mi><mi>j</mi></msub></mrow></math> , <math id="M36"><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow></math> 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 Fig. 2 ) and <math id="M37"><mrow><msubsup><mi>R</mi><mi>j</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow></math> is the range of the alpha-particle in skin. The alpha-particle residual energy, <math id="M38"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> , which corresponds to the ( <math id="M39"><mrow><msub><mi>R</mi><mi>j</mi></msub></mrow></math> - <math id="M40"><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow></math> ) range is determined by using the energy-range relation in the medical drug ( Fig.3 (a) Fig.3 (a) ). By using the energy–range relation in skin, one can determine the range of the alpha-particle in skin, <math id="M41"><mrow><msubsup><mi>R</mi><mi>j</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow></math> ( Fig. 3(b) Fig. 3(b) ). For <math id="M42"><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>=</mo><msub><mi>R</mi><mi>j</mi></msub><msup><mrow/><mrow/></msup></mrow></math> and <math id="M43"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup><mo>=</mo><mn>0</mn><mtext> </mtext><mi>M</mi><mi>e</mi><mi>V</mi></mrow></math> , there is no energy loss of alpha-particles in skin (case 1 of Fig. 2 Fig. 2 ). For <math id="M44"><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>=</mo><mn>0</mn><mtext> </mtext><mi>μ</mi><mi>m</mi></mrow></math> and <math id="M45"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup><mo>=</mo><msub><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow></msub></mrow></math> , the energy loss of alpha-particles in the skin is at a maximum ( <math id="M46"><mrow><msubsup><mi>R</mi><mi>j</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow></math> maximum) (case 3 of Fig. 2 Fig. 2 ). For <math id="M47"><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>≺</mo><msub><mi>R</mi><mi>j</mi></msub><msup><mrow/><mrow/></msup></mrow></math> and <math id="M48"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup><mo>≺</mo><msub><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow></msub></mrow></math> , the range of alpha-particle in the skin are lower than those corresponding to <math id="M49"><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>=</mo><mn>0</mn><mtext> </mtext><mi>μ</mi><mi>m</mi></mrow></math> (case 2 of Fig. 2 Fig. 2 ). Alpha-equivalent dose rates (Svs -1 ) to the human skin due to a radionuclide of index of j belonging to the 238 U series and a radionuclide of index of j’ belonging to the 232 Th series from the application of medical drugs by patients are respectively given by: <math display="block" id="M50"><mrow><msub><mrow><mover><mi>H</mi><mo>•</mo></mover></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mi>A</mi><mi>C</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow><mtext> </mtext><msub><mi>W</mi><mi>R</mi></msub></mrow></math> and <math display="block" id="M51"><mrow><msub><mrow><mover><mi>H</mi><mo>•</mo></mover></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msub><mrow><mo>(</mo><mrow><mi>j</mi><mo>'</mo></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mi>A</mi><mi>C</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mi>j</mi><mo>'</mo></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mi>j</mi><mo>'</mo></mrow><mo>)</mo></mrow><mtext> </mtext><msub><mi>W</mi><mi>R</mi></msub></mrow></math> where: <math id="M52"><mrow><mtext> </mtext><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext></mrow></math> (Bq) is the alpha-activity, at time t, in skin due to a radionuclide of index j belonging to the 238 U series. <math id="M53"><mrow><mtext> </mtext><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo>'</mo><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext></mrow></math> (Bq) is the alpha-activity, at time t, in skin due to a radionuclide of index j’ belonging to the 232 Th series. <math id="M54"><mrow><mtext> </mtext><msubsup><mi>D</mi><mrow><mi>S</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo></mrow></math> is the specific alpha-dose (Gy) deposited by 1Bq of a radionuclide of index j belonging to the 238 U series in skin. <math id="M55"><mrow><mtext> </mtext><msubsup><mi>D</mi><mrow><mi>S</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo>'</mo><mo stretchy="false">)</mo></mrow></math> is the specific alpha-dose (Gy) deposited by 1Bq of a radionuclide of index j’ belonging to the 232 Th series in skin. W R is the radiation weighting factor, which is equal to 20 for alpha-particles [ 13 13 ]. The <math id="M56"><mrow><mtext> </mtext><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext></mrow></math> and <math id="M57"><mrow><mtext> </mtext><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo>'</mo><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext></mrow></math> alpha-activities are respectively given by: <math display="block" id="M58"><mrow><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mi>j</mi></msub><mi>t</mi></mrow></msup><msup><mrow><mo>×</mo><mtext>1cm</mtext></mrow><mn>3</mn></msup></mrow></math> and <math display="block" id="M59"><mrow><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mi>j</mi><mo>'</mo></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mrow><mi>j</mi><mo>'</mo></mrow></msub><mi>t</mi></mrow></msup><msup><mrow><mo>×</mo><mtext>1cm</mtext></mrow><mn>3</mn></msup></mrow></math> where <math id="M60"><mrow><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></math> (Bq cm -3 ) is the alpha-activity due to 238 U inside a medical drug sample. <math id="M61"><mrow><msubsup><mi>A</mi><mi>c</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow></mrow></math> (Bq cm -3 ) is the alpha-activity due to 232 Th inside a medical drug sample. λ j is the radioactive decay constant of a radionuclide of index j belonging to the 238 U series and λ j’ is the radioactive decay constant of a radionuclide of index j’ belonging to the 232 Th 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 <math id="M62"><mrow><mtext> </mtext><msubsup><mi>D</mi><mrow><mi>S</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo stretchy="false">)</mo></mrow></math> and <math id="M63"><mrow><mtext> </mtext><msubsup><mi>D</mi><mrow><mi>S</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>j</mi><mo>'</mo><mo stretchy="false">)</mo></mrow></math> specific alpha-doses are respectively given by: <math display="block" id="M64"><mrow><msubsup><mtext>D</mtext><mrow><mtext>sp</mtext></mrow><mrow><mtext>Skin</mtext></mrow></msubsup><mrow><mo>(</mo><mtext>j</mtext><mo>)</mo></mrow><mo>=</mo><mtext>k</mtext><mfrac><mrow><msub><mtext>k</mtext><mtext>j</mtext></msub></mrow><mrow><msub><mtext>d</mtext><mrow><mtext>Skin</mtext></mrow></msub><msub><mtext>S</mtext><mrow><mtext>Skin</mtext></mrow></msub></mrow></mfrac><mfrac><mrow><msubsup><mtext>E</mtext><mrow><mtext>αj</mtext></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow><mrow><msubsup><mtext>R</mtext><mtext>j</mtext><mrow><mtext>Skin</mtext></mrow></msubsup></mrow></mfrac></mrow></math> and <math display="block" id="M65"><mrow><msubsup><mtext>D</mtext><mrow><mtext>sp</mtext></mrow><mrow><mtext>Skin</mtext></mrow></msubsup><mrow><mo>(</mo><msup><mi>j</mi><mo>′</mo></msup><mo>)</mo></mrow><mo>=</mo><mtext>k</mtext><mfrac><mrow><msub><mi>k</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub></mrow><mrow><msub><mtext>d</mtext><mrow><mtext>Skin</mtext></mrow></msub><msub><mtext>S</mtext><mrow><mtext>Skin</mtext></mrow></msub></mrow></mfrac><mfrac><mrow><msubsup><mtext>E</mtext><mrow><mi>α</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow><mrow><msubsup><mi>R</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow><mrow><mtext>Skin</mtext></mrow></msubsup></mrow></mfrac></mrow></math> where: d s is the density of skin (g cm -3 ). <math id="M66"><mrow><msub><mi>S</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></math> is the surface skin (cm 2 ). k = 1.6.10 -13 (J MeV -1 ) is a conversion factor. <math id="M67"><mrow><msubsup><mi>R</mi><mi>j</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow></math> is the range, in skin, of an alpha-particle of index j and a residual energy, <math id="M68"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> , belonging to the 238 U series. <math id="M69"><mrow><msubsup><mi>R</mi><mi>j</mi><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow></math> is the range, in skin, of an alpha-particle of index j and a residual energy, <math id="M70"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mrow><mi>j</mi><mo>'</mo></mrow></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> , belonging to the 232 Th series ( Fig. 3 Fig. 3 ). By integrating Eqs. 6 and 7, committed equivalent doses (Sv) to skin due to an alpha-particle of residual energy, <math id="M71"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> , emitted by a radionuclide of index j belonging to the 238 U series and an alpha-particle of residual energy, <math id="M72"><mrow><msubsup><mi>E</mi><mrow><mi>α</mi><mi>j</mi><mo>'</mo></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> , emitted by a radionuclide of index j’ belonging to the 232 Th series from the application of a medical drug sample are respectively given by: <math display="block" id="M73"><mrow><msub><mrow><mover><mi>H</mi><mrow/></mover></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><msup><mrow><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></mrow><mrow/></msup><msub><mi>W</mi><mi>R</mi></msub></mrow><mrow><mn>2</mn><msub><mi>λ</mi><mi>J</mi></msub></mrow></mfrac><msubsup><mi>A</mi><mi>C</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>238</mn></mmultiscripts></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mi>J</mi></msub><msub><mstyle mathsize="140%" displaystyle="true"><mi>t</mi></mstyle><mi>a</mi></msub></mrow></msup></mrow><mo>)</mo></mrow></mrow></math> and <math display="block" id="M74"><mrow><msub><mrow><mover><mi>H</mi><mrow/></mover></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msub><mrow><mo>(</mo><mrow><mi>j</mi><mo>'</mo></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mi>p</mi></mrow><mrow><mi>s</mi><mi>k</mi><mi>i</mi><mi>n</mi></mrow></msubsup><msup><mrow><mrow><mo>(</mo><mrow><mi>j</mi><mo>'</mo></mrow><mo>)</mo></mrow></mrow><mrow/></msup><msub><mi>W</mi><mi>R</mi></msub></mrow><mrow><mn>2</mn><msub><mi>λ</mi><mrow><mi>j</mi><mo>'</mo></mrow></msub></mrow></mfrac><msubsup><mi>A</mi><mi>C</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mrow><mi>j</mi><mo>'</mo></mrow></msub><msub><mstyle mathsize="140%" displaystyle="true"><mi>t</mi></mstyle><mi>a</mi></msub></mrow></msup></mrow><mo>)</mo></mrow></mrow></math> 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 <math id="M75"><mrow><mmultiscripts><mi>U</mi><mprescripts/><mo>.</mo><mrow><mn>238</mn></mrow></mmultiscripts></mrow></math> series and an alpha-particle of index j’ and initial energy <math id="M76"><mrow><msub><mi>E</mi><mrow><mi>α</mi><msup><mi>j</mi><mo>'</mo></msup></mrow></msub></mrow></math> belonging to the <math id="M77"><mrow><mmultiscripts><mi>T</mi><mprescripts/><mo>.</mo><mrow><mn>232</mn></mrow></mmultiscripts><mi>h</mi></mrow></math> series are respectively given by: <math display="block" id="M78"><mrow><mtext>H</mtext><mrow><mo>(</mo><mtext>j</mtext><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mi>E</mi><mi>P</mi></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msub><mrow><mtext>k k</mtext></mrow><mrow><mtext>j </mtext></mrow></msub><msubsup><mtext>A</mtext><mtext>C</mtext><mrow><mtext>Sample</mtext></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>U</mtext><mprescripts/><mo>.</mo><mrow><mn>238</mn></mrow></mmultiscripts></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mtext>e</mtext><mrow><mo>−</mo><msub><mtext>λ</mtext><mtext>j</mtext></msub><msub><mtext>t</mtext><mi>a</mi></msub></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn><msub><mrow><mtext> λ</mtext></mrow><mrow><mtext>j </mtext></mrow></msub><msub><mtext>d</mtext><mrow><mtext>skin</mtext></mrow></msub><msub><mtext>S</mtext><mrow><mtext>Skin</mtext></mrow></msub><msubsup><mtext>E</mtext><mrow><msub><mtext>α</mtext><mtext>j</mtext></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow></mfrac><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∫</mo></mstyle><mn>0</mn><mrow><msub><mtext>E</mtext><mrow><msub><mtext>α</mtext><mtext>j</mtext></msub></mrow></msub></mrow></munderover><mfrac><mrow><msubsup><mtext>E</mtext><mrow><msub><mtext>α</mtext><mtext>j</mtext></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow><mrow><msubsup><mtext>R</mtext><mtext>j</mtext><mrow><mtext>Skin</mtext></mrow></msubsup><mrow><mo>(</mo><mrow><msubsup><mtext>E</mtext><mrow><msub><mtext>α</mtext><mtext>j</mtext></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></mfrac><msubsup><mrow><mtext>dE</mtext></mrow><mrow><msub><mtext>α</mtext><mtext>j</mtext></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow></math> and <math display="block" id="M79"><mrow><mi>H</mi><mrow><mo>(</mo><msup><mi>j</mi><mo>′</mo></msup><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mi>E</mi><mi>P</mi></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>k</mi><msub><mi>k</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub><msubsup><mi>A</mi><mtext>C</mtext><mrow><mtext>Sample</mtext></mrow></msubsup><mrow><mo>(</mo><mrow><mmultiscripts><mtext>Th</mtext><mprescripts/><mi/><mn>232</mn></mmultiscripts></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub><msub><mi>t</mi><mtext>a</mtext></msub></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn><msub><mrow><mi>λ</mi></mrow><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub><msub><mi>d</mi><mrow><mtext>skin</mtext></mrow></msub><msub><mrow><mi>S</mi></mrow><mrow><mtext>Skin</mtext></mrow></msub><msubsup><mrow><mi>E</mi></mrow><mrow><msub><mi>α</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow></mfrac><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∫</mo></mstyle><mn>0</mn><mrow><msub><mi>E</mi><mrow><msub><mi>α</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub></mrow></msub></mrow></munderover><mfrac><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow><mrow><msubsup><mi>R</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow><mrow><mtext>Skin</mtext></mrow></msubsup><mrow><mo>(</mo><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></mfrac><msubsup><mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><msub><mi>α</mi><mrow><msup><mi>j</mi><mo>′</mo></msup></mrow></msub></mrow><mrow><mtext>Res</mtext></mrow></msubsup></mrow></math> Where Δ <math id="M80"><mrow><msubsup><mi>E</mi><mrow><msub><mi>α</mi><mi>j</mi></msub></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> and Δ <math id="M81"><mrow><msubsup><mi>E</mi><mrow><mi>α</mi><mi>j</mi><mo>'</mo></mrow><mrow><mi>Re</mi><mi>s</mi></mrow></msubsup></mrow></math> are the chosen steps. Committed equivalent doses (Sv y -1 cm -2 ) to the skin surface of 1cm 2 of the epidermis during an exposure time is equal to 1 year due to the alpha-particles emitted by the 238 U (eight alpha-emitting nuclei) and 232 Th (seven alpha-emitting nuclei) series from the application of a medical drug sample by patients are respectively given by: <math display="block" id="M82"><mrow><mtext> H</mtext><mrow><mo>(</mo><mtext>U</mtext><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mtext>EP</mtext></mrow><mo>)</mo></mrow><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mtext>j</mtext><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mtext>H</mtext><mrow><mo>(</mo><mtext>j</mtext><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mtext>Tot</mtext></mrow><mo>)</mo></mrow></mrow></math> and  <math display="block" id="M83"><mrow><mtext>H</mtext><mrow><mo>(</mo><mrow><mtext>Th</mtext></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mtext>EP</mtext></mrow><mo>)</mo></mrow><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><msup><mi>j</mi><mo>′</mo></msup><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mtext>H</mtext><mrow><mo>(</mo><msup><mi>j</mi><mo>′</mo></msup><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mtext>Tot</mtext></mrow><mo>)</mo></mrow></mrow></math> 3 RESULTS AND DISCUSSION 1 3.1 238 U and 232 Th alpha-activities per unit volume in medical drugs 2 The 238 U (A c ( 238 U)) and 232 Th (A c ( 232 Th)) 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 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 238 U and 232 Th concentrations was determined, which gave values of about 8%. Natural uranium is formed by 238 U, 235 U, and 234 U radioisotopes with isotopic abundances equal to 99.27%, 0.72%, and 0.0055%, respectively. So, the contribution of alpha-particles emitted by the 235 U 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 238 U and 232 Th concentration determination (8 %). The data shown in Table 3 Table 3 demonstrates that all medical drug samples studied contain more 238 U than 232 Th. This is probably due to the fact that raw materials used for the preparation of these medical drugs contain more 238 U than 232 Th. It is to be noted that the 238 U 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 Table 3 ). We also noted that the 232 Th 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 Table 3 ). The minimum detection activities (MDA) for 238 U and 232 Th were found to be equal to (0.81±0.05) mBql -1 and (0.11±0.01) mBql -1 , respectively. 1 1 Medical drug samples 1 1 <math id="M84"><mrow><msubsup><mi>ρ</mi><mtext>G</mtext><mrow><mtext>LR</mtext></mrow></msubsup></mrow></math> (10 -5 tr cm -2 s -1 ) 1 1 <math id="M85"><mrow><msubsup><mi>ρ</mi><mtext>G</mtext><mrow><mtext>CR</mtext></mrow></msubsup></mrow></math> (10 -5 tr cm -2 s -1 ) 4 1 This method 2 1 IDMS 1 1   1 1   1 1   1 1 C ( 238 U)(ppm) 1 1 C ( 232 Th)(ppm) 1 1 A c ( 238 U)(mBq/l) 1 1 A c ( 232 Th)(mBq/l) 1 1 C ( 238 U)(ppm) 1 1 C ( 232 Th)(ppm) 1 1 P1 1 1 2.29±0.16 1 1 8.74±0.61 1 1 0.74±0.05 1 1 0.28±0.02 1 1 9.1±0.6 1 1 1.15±0.07 1 1   1 1   1 1 P2 1 1 1.08±0.09 1 1 4.13±0.33 1 1 0.35±0.02 1 1 0.15±0.01 1 1 4.3±0.3 1 1 0.62±0.04 1 1 0.36±0.01 1 1 0.14±0.01 1 1 P3 1 1 2.33±0.20 1 1 8.89±0.8 1 1 0.76±0.05 1 1 0.28±0.02 1 1 9.3±0.7 1 1 1.16±0.07 1 1   1 1   1 1 P4 1 1 1.85±0.13 1 1 7.05±0.49 1 1 0.61±0.04 1 1 0.21±0.01 1 1 7.5±0.5 1 1 0.86±0.05 1 1 0.60±0.03 1 1 0.20±0.01 1 1 P5 1 1 2.48±0.2 1 1 9.36±0.75 1 1 0.81±0.06 1 1 0.23±0.01 1 1 9.9±0.7 1 1 0.95±0.06 1 1 0.82±0.04 1 1 0.24±0.01 1 1 P6 1 1 1.29±0.10 1 1 4.93±0.37 1 1 0.42±0.03 1 1 0.17±0.01 1 1 5.2±0.3 1 1 0.70±0.05 1 1   1 1   1 1 P7 1 1 1.41±0.11 1 1 5.39±0.44 1 1 0.45±0.03 1 1 0.19±0.01 1 1 5.5±0.4 1 1 0.78±0.06 1 1   1 1   1 1 P8 1 1 2.02±0.14 1 1 7.69±0.54 1 1 0.67±0.05 1 1 0.21±0.01 1 1 8.2±0.5 1 1 0.86±0.06 1 1 0.66±0.04 1 1 0.20±0.01 1 1 P9 1 1 2.24±0.18 1 1 8.54±0.71 1 1 0.73±0.05 1 1 0.26±0.02 1 1 9.0±0.7 1 1 1.07±0.07 1 1 0.74±0.04 1 1 0.25±0.01 1 1 P10 1 1 2.50±0.19 1 1 9.51±0.78 1 1 0.83±0.06 1 1 0.24±0.01 1 1 10.2±0.8 1 1 0.98±0.07 1 1 0.82±0.04 1 1 0.25±0.01 1 1 P11 1 1 1.69±0.12 1 1 6.42±0.45 1 1 0.56±0.04 1 1 0.15±0.01 1 1 6.9±0.4 1 1 0.62±0.04 1 1   1 1   1 1 P12 1 1 2.17±0.17 1 1 8.27±0.66 1 1 0.71±0.05 1 1 0.24±0.01 1 1 8.7±0.6 1 1 0.98±0.07 1 1   1 1   1 1 P13 1 1 2.42±0.21 1 1 9.24±0.76 1 1 0.78±0.06 1 1 0.30±0.02 1 1 9.6±0.7 1 1 1.23±0.07 1 1 0.79±0.05 1 1 0.32±0.01 1 1 P14 1 1 1.68±0.12 1 1 6.37±0.45 1 1 0.57±0.04 1 1 0.120±0.006 1 1 7.0±0.5 1 1 0.49±0.03 1 1 0.58±0.03 1 1 0.125±0.004 1 1 P15 1 1 2.07±0.15 1 1 7.88±0.63 1 1 0.68±0.05 1 1 0.21±0.01 1 1 8.4±0.6 1 1 0.86±0.06 1 1 0.67±0.04 1 1 0.20±0.01 1 1 P16 1 1 1.95±0.13 1 1 7.42±0.61 1 1 0.64±0.04 1 1 0.19±0.01 1 1 7.9±0.6 1 1 0.78±0.05 1 1   1 1   1 1 P17 1 1 2.53±0.18 1 1 9.64±0.67 1 1 0.84±0.06 1 1 0.28±0.02 1 1 10.2±0.7 1 1 1.15±0.07 1 1   1 1   1 1 P18 1 1 2.58±0.23 1 1 9.85±0.89 1 1 0.85±0.06 1 1 0.32±0.02 1 1 10.3±0.8 1 1 1.3±0.1 1 1   1 1   1 1 P19 1 1 2.05±0.14 1 1 7.80±0.55 1 1 0.68±0.05 1 1 0.20±0.01 1 1 8.4±0.5 1 1 0.82±0.05 1 1   1 1   1 1 P20 1 1 2.71±0.18 1 1 10.30±0.52 1 1 0.90±0.06 1 1 0.24±0.01 1 1 11.1±0.8 1 1 0.98±0.06 1 1 0.92±0.04 1 1 0.26±0.01 1 1 P21 1 1 1.22±0.10 1 1 4.66±0.37 1 1 0.39±0.03 1 1 0.16±0.01 1 1 4.8±0.3 1 1 0.66±0.04 1 1   1 1   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 238 U and 232 Th contents, are in good agreement with each other ( Table 3 Table 3 ). 3.2 Committed equivalent doses to skin due to the radionuclides of the 238 U and 232 Th series from the application of medical drugs by patients 2 Committed equivalent doses to the epidermis of skin due to the alpha-emitting nuclei of the 238 U (H(U)(EP)) and 232 Th (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 Tables 4 , 5 5 , 6 6 and 7 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 Tables 1 , 4 4 , and 5 5 ). 1 1 Medicaldrugsamples 1 1 H ( 238 U)(10 -8 Sv y -1 cm -2 ) 1 1 H( 230 Th)(10 -8 Sv y -1 cm -2 ) 1 1 H( 234 U)(10 -8 Sv y -1 cm -2 ) 1 1 H ( 226 Ra)(10 -8 Sv y -1 cm -2 ) 1 1 H ( 210 Po)(10 -8 Sv y -1 cm -2 ) 1 1 H ( 222 Rn)(10 -8 Sv y -1 cm -2 ) 1 1 H ( 218 Po)(10 -9 Sv y -1 cm -2 ) 1 1 H ( 214 Po)(10 -12 Sv y -1 cm -2 ) 1 1 H(U)(EP)(µSv y -1 cm -2 ) 1 1 (a) 1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1 P1 1 1 1.97 1 1 2.2 1 1 2.79 1 1 2.23 1 1 2.43 1 1 2.49 1 1 3.96 1 1 4.20 1 1 0.14±0.01 1 1 P2 1 1 1347 1 1 1471 1 1 1513 1 1 1516 1 1 1567 1 1 314 1 1 1.88 1 1 2 1 1 77±6 1 1 P3 1 1 1461 1 1 1596 1 1 1641 1 1 1644 1 1 1747 1 1 638 1 1 4.07 1 1 4.32 1 1 76±6 1 1 P4 1 1 1172 1 1 1280 1 1 1317 1 1 1319 1 1 1402 1 1 512 1 1 3.3 1 1 3.5 1 1 70±6 1 1 P5 1 1 3113 1 1 3400 1 1 3497 1 1 3503 1 1 3620 1 1 724 1 1 4.34 1 1 4.59 1 1 179±16 1 1 P6 1 1 431 1 1 471 1 1 484 1 1 485 1 1 522 1 1 289 1 1 2.25 1 1 2.4 1 1 27±2 1 1 P7 1 1 404 1 1 441 1 1 453 1 1 454 1 1 490 1 1 290 1 1 2.41 1 1 2.56 1 1 25±1 1 1 P8 1 1 858 1 1 937 1 1 964 1 1 966 1 1 1036 1 1 503 1 1 3.59 1 1 3.80 1 1 57±4 1 1 P9 1 1 8421 1 1 9196 1 1 9459 1 1 9476 1 1 8782 1 1 656 1 1 3.91 1 1 4.14 1 1 460±41 1 1 P10 1 1 532 1 1 581 1 1 598 1 1 599 1 1 648 1 1 444 1 1 4.45 1 1 4.71 1 1 34±3 1 1 P11 1 1 502 1 1 549 1 1 564 1 1 565 1 1 610 1 1 361 1 1 3 1 1 3.2 1 1 32±3 1 1 P12 1 1 637 1 1 695 1 1 715 1 1 717 1 1 773 1 1 458 1 1 3.8 1 1 4 1 1 40±3 1 1 P13 1 1 33608 1 1 36702 1 1 37751 1 1 37813 1 1 23428 1 1 701 1 1 4.2 1 1 4.4 1 1 1700±153 1 1 P14 1 1 2191 1 1 2393 1 1 2461 1 1 2466 1 1 2548 1 1 510 1 1 3 1 1 3.23 1 1 126±11 1 1 P15 1 1 2610 1 1 2850 1 1 2930 1 1 2940 1 1 3200 1 1 652 1 1 3.64 1 1 3.85 1 1 170±15 1 1 P16 1 1 1230 1 1 1343 1 1 1381 1 1 1384 1 1 1471 1 1 537 1 1 3.43 1 1 3.63 1 1 73±6 1 1 P17 1 1 6389 1 1 6977 1 1 7177 1 1 7189 1 1 7032 1 1 747 1 1 4.45 1 1 4.72 1 1 355±31 1 1 P18 1 1 9687 1 1 10578 1 1 10881 1 1 10900 1 1 10102 1 1 757 1 1 4.50 1 1 4.77 1 1 529±47 1 1 P19 1 1 7839 1 1 8561 1 1 8806 1 1 8821 1 1 8175 1 1 611 1 1 3.64 1 1 3.86 1 1 428±38 1 1 P20 1 1 13840 1 1 15115 1 1 15547 1 1 15574 1 1 13690 1 1 809 1 1 4.82 1 1 5.11 1 1 895±80 1 1 P21 1 1 750 1 1 819 1 1 842 1 1 844 1 1 897 1 1 327 1 1 2.1 1 1 2.2 1 1 45±4 1 1 (b) 1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1 P1 1 1 1.72 1 1 1.92 1 1 2.44 1 1 1.94 1 1 2.12 1 1 2.18 1 1 3.46 1 1 3.67 1 1 0.12±0.01 1 1 P2 1 1 1177 1 1 1285 1 1 1322 1 1 1324 1 1 1368 1 1 274 1 1 1.64 1 1 1.74 1 1 68±6 1 1 P3 1 1 1461 1 1 1394 1 1 1434 1 1 1437 1 1 1527 1 1 557 1 1 3.56 1 1 3.70 1 1 76±6 1 1 P4 1 1 1024 1 1 1119 1 1 1150 1 1 1152 1 1 1225 1 1 447 1 1 2.82 1 1 3.02 1 1 61±5 1 1 P5 1 1 2720 1 1 2970 1 1 3055 1 1 3061 1 1 3163 1 1 633 1 1 3.79 1 1 4.017 1 1 156±14 1 1 P6 1 1 377 1 1 411 1 1 423 1 1 424 1 1 465 1 1 252 1 1 1.96 1 1 2.08 1 1 23±2 1 1 P7 1 1 353 1 1 385 1 1 396 1 1 397 1 1 428 1 1 254 1 1 2.11 1 1 2.23 1 1 22±2 1 1 P8 1 1 750 1 1 819 1 1 842 1 1 844 1 1 905 1 1 440 1 1 3.14 1 1 3.32 1 1 46±4 1 1 P9 1 1 7357 1 1 8034 1 1 8264 1 1 8279 1 1 8672 1 1 573 1 1 3.42 1 1 3.62 1 1 402±36 1 1 P10 1 1 465 1 1 507 1 1 522 1 1 523 1 1 566 1 1 388 1 1 3.88 1 1 4.12 1 1 30±2 1 1 P11 1 1 439 1 1 479 1 1 493 1 1 494 1 1 533 1 1 316 1 1 2.62 1 1 2.78 1 1 28±2 1 1 P12 1 1 556 1 1 607 1 1 624 1 1 626 1 1 675 1 1 400 1 1 3.32 1 1 3.52 1 1 35±2 1 1 P13 1 1 29363 1 1 32066 1 1 32982 1 1 33036 1 1 20468 1 1 613 1 1 3.66 1 1 3.87 1 1 1485±133 1 1 P14 1 1 1914 1 1 2091 1 1 2150 1 1 2154 1 1 2226 1 1 455 1 1 2.67 1 1 2.82 1 1 110±9 1 1 P15 1 1 2280 1 1 2490 1 1 2560 1 1 2570 1 1 2790 1 1 540 1 1 3.18 1 1 3.37 1 1 150±9 1 1 P16 1 1 1074 1 1 1174 1 1 1207 1 1 1209 1 1 1285 1 1 469 1 1 3 1 1 3.17 1 1 64±5 1 1 P17 1 1 5582 1 1 6096 1 1 6270 1 1 6281 1 1 6143 1 1 652 1 1 3.89 1 1 4.12 1 1 31±2 1 1 P18 1 1 8463 1 1 9242 1 1 9506 1 1 9523 1 1 8826 1 1 659 1 1 3.93 1 1 4.16 1 1 462±41 1 1 P19 1 1 6849 1 1 7480 1 1 7693 1 1 7707 1 1 7143 1 1 534 1 1 3.18 1 1 3.37 1 1 374±33 1 1 P20 1 1 12092 1 1 13206 1 1 13583 1 1 13607 1 1 11961 1 1 707 1 1 4.21 1 1 4.46 1 1 789±71 1 1 P21 1 1 655 1 1 716 1 1 736 1 1 738 1 1 784 1 1 286 1 1 1.83 1 1 1.94 1 1 39±3 1 1 Medical drug samples 1 1 H ( 232 Th)(10 -8 Sv y -1 cm -2 ) 1 1 H( 228 Th)(10 -8 Sv y -1 cm -2 ) 1 1 H( 224 Ra)(10 -8 Sv y -1 cm -2 ) 1 1 H ( 212 Bi)(10 -9 Sv y -1 cm -2 ) 1 1 H ( 220 Rn)(10 -9 Sv y -1 cm -2 ) 1 1 H ( 216 Po)(10 -12 Sv y -1 cm -2 ) 1 1 H ( 212 Po)(10 -18 Sv y -1 cm -2 ) 1 1 H(Th)(EP)(µSv y -1 cm -2 ) 1 1 (a) 1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1 P1 1 1 1.89 1 1 2.47 1 1 2.58 1 1 8.26 1 1 1.24 1 1 3.77 1 1 6.85 1 1 0.080±0.006 1 1 P2 1 1 1294 1 1 1664 1 1 1755 1 1 13.5 1 1 0.6 1 1 1.78 1 1 3.25 1 1 47±4 1 1 P3 1 1 1403 1 1 1818 1 1 1908 1 1 29.3 1 1 1.27 1 1 3.9 1 1 7.04 1 1 45±4 1 1 P4 1 1 1125 1 1 1458 1 1 1531 1 1 23.5 1 1 1.02 1 1 3.11 1 1 5.65 1 1 41±3 1 1 P5 1 1 2989 1 1 3845 1 1 4056 1 1 31.2 1 1 1.35 1 1 4.13 1 1 7.50 1 1 109±9 1 1 P6 1 1 414 1 1 538 1 1 563 1 1 16.2 1 1 0.7 1 1 2.14 1 1 3.89 1 1 15±1 1 1 P7 1 1 388 1 1 505 1 1 528 1 1 17.4 1 1 0.8 1 1 2.3 1 1 4.17 1 1 14±1 1 1 P8 1 1 824 1 1 1071 1 1 1122 1 1 25.8 1 1 1.12 1 1 3.4 1 1 6.2 1 1 30±2 1 1 P9 1 1 8086 1 1 10099 1 1 10847 1 1 28.1 1 1 1.22 1 1 3.72 1 1 6.76 1 1 291±26 1 1 P10 1 1 511 1 1 665 1 1 696 1 1 32 1 1 1.4 1 1 4.2 1 1 7.69 1 1 19±1 1 1 P11 1 1 482 1 1 628 1 1 657 1 1 21.6 1 1 0.9 1 1 2.85 1 1 5.19 1 1 18±1 1 1 P12 1 1 611 1 1 795 1 1 832 1 1 27.4 1 1 1.2 1 1 3.6 1 1 6.57 1 1 22±2 1 1 P13 1 1 32273 1 1 35850 1 1 41847 1 1 30 1 1 1.3 1 1 4 1 1 7.23 1 1 1100±9 1 1 P14 1 1 2104 1 1 2706 1 1 2855 1 1 22 1 1 0.9 1 1 2.9 1 1 5.28 1 1 77±6 1 1 P15 1 1 251 1 1 3270 1 1 3420 1 1 26 1 1 1.1 1 1 3.5 1 1 6.30 1 1 9.0±0.8 1 1 P16 1 1 1181 1 1 1530 1 1 1606 1 1 24.7 1 1 1.07 1 1 3.26 1 1 5.92 1 1 43±3 1 1 P17 1 1 6135 1 1 7775 1 1 8288 1 1 32 1 1 1.4 1 1 4.2 1 1 7.70 1 1 22±1 1 1 P18 1 1 9302 1 1 11617 1 1 12509 1 1 32 1 1 1.4 1 1 4.3 1 1 7.78 1 1 334±30 1 1 P19 1 1 7528 1 1 9402 1 1 10123 1 1 26.2 1 1 1.14 1 1 3.5 1 1 6.30 1 1 271±24 1 1 P20 1 1 13291 1 1 16359 1 1 17794 1 1 34.7 1 1 1.5 1 1 4.6 1 1 8.34 1 1 474±42 1 1 P21 1 1 720 1 1 933 1 1 980 1 1 15 1 1 0.7 1 1 2 1 1 3.61 1 1 26±2 1 1 (b) 1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1   1 1 P1 1 1 1.66 1 1 2.16 1 1 2.26 1 1 7.22 1 1 1.08 1 1 3.3 1 1 5.99 1 1 0.070±0.006 1 1 P2 1 1 1130 1 1 1453 1 1 1534 1 1 11.8 1 1 0.5 1 1 1.56 1 1 2.84 1 1 41±3 1 1 P3 1 1 1226 1 1 1588 1 1 1667 1 1 25.6 1 1 1.11 1 1 3.39 1 1 6.15 1 1 45±3 1 1 P4 1 1 983 1 1 1274 1 1 1337 1 1 20.5 1 1 0.89 1 1 2.72 1 1 4.96 1 1 36±3 1 1 P5 1 1 2612 1 1 3359 1 1 3544 1 1 27.3 1 1 1.18 1 1 3.61 1 1 6.55 1 1 95±8 1 1 P6 1 1 361 1 1 470 1 1 492 1 1 14.2 1 1 0.6 1 1 1.87 1 1 3.40 1 1 13±1 1 1 P7 1 1 339 1 1 441 1 1 461 1 1 15.2 1 1 0.66 1 1 2 1 1 4.17 1 1 12±1 1 1 P8 1 1 720 1 1 935 1 1 980 1 1 22.5 1 1 1 1 1 2.98 1 1 5.42 1 1 26±2 1 1 P9 1 1 7065 1 1 8823 1 1 9500 1 1 24.6 1 1 1.07 1 1 3.25 1 1 5.91 1 1 254±22 1 1 P10 1 1 446 1 1 581 1 1 608 1 1 27.9 1 1 1.21 1 1 3.7 1 1 6.72 1 1 16±1 1 1 P11 1 1 421 1 1 548 1 1 574 1 1 18.9 1 1 0.82 1 1 2.5 1 1 4.53 1 1 15±1 1 1 P12 1 1 534 1 1 695 1 1 727 1 1 23.9 1 1 1.04 1 1 3.2 1 1 5.74 1 1 20±1 1 1 P13 1 1 28196 1 1 31321 1 1 36561 1 1 26.3 1 1 1.14 1 1 3.5 1 1 6.32 1 1 961±84 1 1 P14 1 1 1838 1 1 2364 1 1 2494 1 1 19.2 1 1 0.8 1 1 2.5 1 1 4.61 1 1 67±6 1 1 P15 1 1 2190 1 1 2860 1 1 2980 1 1 25.1 1 1 1 1 1 3 1 1 5.50 1 1 81±7 1 1 P16 1 1 1032 1 1 1337 1 1 1403 1 1 21.5 1 1 0.9 1 1 2.8 1 1 5.18 1 1 38±3 1 1 P17 1 1 5360 1 1 6793 1 1 7241 1 1 28 1 1 1.2 1 1 3.7 1 1 6.67 1 1 194±17 1 1 P18 1 1 8127 1 1 10149 1 1 10929 1 1 28.3 1 1 1.22 1 1 3.74 1 1 6.80 1 1 292±26 1 1 P19 1 1 6577 1 1 8214 1 1 8845 1 1 23 1 1 1 1 1 3 1 1 5.50 1 1 236±21 1 1 P20 1 1 11612 1 1 14292 1 1 15546 1 1 30.3 1 1 1.31 1 1 4.01 1 1 7.28 1 1 414±37 1 1 P21 1 1 629 1 1 815 1 1 856 1 1 13.1 1 1 0.6 1 1 1.7 1 1 3.16 1 1 23±2 1 1 Medical drug samples 4 1 Annual committed equivalent doses (µSv y -1 cm -2 ) 1 1   2 1 15 years (Female) 2 1 15 years (Male) 1 1   1 1 H(U)(EP) 1 1 H(Th)(EP) 1 1 H(U)(EP) 1 1 H(Th)(EP) 1 1 P1 1 1 0.16±0.01 1 1 0.0085±0.0007 1 1 0.152±0.01 1 1 0.0081±0.0007 1 1 P4 1 1 76±6 1 1 44±3 1 1 73±6 1 1 42±3 1 1 P5 1 1 191±17 1 1 117±10 1 1 183±16 1 1 112±10 1 1 P6 1 1 29±2 1 1 16±1 1 1 28±2 1 1 16±1 1 1 P9 1 1 493±44 1 1 311±27 1 1 471±42 1 1 230±20 1 1 P10 1 1 37±3 1 1 20±1 1 1 35±3 1 1 19±1 1 1 P11 1 1 34±3 1 1 19±1 1 1 33±2 1 1 18±1 1 1 Medical drug samples 4 1 Annual committed equivalent doses (µSv y -1 cm -2 ) 1 1   2 1 10 years 2 1 5 years 1 1   1 1 H(U)(EP) 1 1 H(Th)(EP) 1 1 H(U)(EP) 1 1 H(Th)(EP) 1 1 P1 1 1 0.22±0.01 1 1 0.012±0.001 1 1 0.32±0.02 1 1 0.017±0.001 1 1 P4 1 1 105±9 1 1 61±5 1 1 151±13 1 1 88±7 1 1 P5 1 1 270±24 1 1 161±14 1 1 380±34 1 1 232±20 1 1 P6 1 1 40±3 1 1 23±2 1 1 58±5 1 1 32±3 1 1 P10 1 1 51±4 1 1 28±2 1 1 73±6 1 1 40±3 1 1 P11 1 1 47±4 1 1 26±2 1 1 68±6 1 1 38±3 It is to be noted from the data shown in Tables 4 Tables 4 - 7 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 Table 1 ). It is to be noted from the results shown in Table 4 Table 4 that committed equivalent doses to the epidermis of the skin due to alpha-particles emitted by 214 Po (H( 214 Po)) and 218 Po (H( 218 Po)) are negligible compared to those corresponding to the other alpha-emitters of the 238 U 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 212 Po (H( 212 Po)) and 216 Po (H( 216 Po)) are negligible compared to those corresponding to the other alpha-emitters of the 232 Th series ( Table 5 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 232 Th series. It is to be noted that total committed equivalent doses due to the 238 U and 232 Th 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 Tables 4 - 7 7 ). This is because 5 year-old children possess smaller skin surface area than the other age groups of patients [ 1 1 ]. The maximum total committed equivalent dose to skin due to the 238 U and 232 Th 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) Tables 4(a) and 5(a) 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 1 ]. 4 CONCLUSION 1 In this study, it has been shown that the use of CR-39 and LR-115 type II solid state nuclear track detectors (SSNTDs) allows for the evaluation of 238 U and 232 Th alpha-activities per unit volume in various medical drug samples. A new dosimetric model was developed for evaluating radiation doses to skin due to the alpha-emitting nuclei of the 238 U and 232 Th series from the application of medical drugs by patients. The committed equivalent doses to the epidermis of the skin due to the alpha-emitting nuclei of the 238 U and 232 Th series increase with the application time of medical drugs. It has been shown that only nine alpha-emitting nuclei belonging to the 238 U and 232 Th series significantly contribute to the global radiation dose to the epidermis of skin from the application of medical drugs by patients. It has also been shown that the committed effective dose due to the 238 U and 232 Th series increases when the skin surface area of the patients decreases. Thus, there is no radiation risk to the epidermis from cutaneous application of the studied medical drugs by patients. The SSNTD’s method used has the advantage of being inexpensive, accurate, sensitive, and does not require the use of standard sources for its calibration. It is a useful tool for measuring 238 U and 232 Th concentrations in medical drugs, as well as essential oils extracted from aromatic and medicinal plants. References International Commission on Radiological Protection . Recommendations of the International Commission on Radiological Protection . ICRP Publication 60 , 1990 . Recommendations of the International Commission on Radiological Protection United Nations Scientific Committee on the Effects of Atomic Radiation . Sources and effects of ionising radiation . Report to the General Assembly , New York , United Nations , 2000 . Sources and effects of ionising radiation Misdaq M A , Ait Nouh F , Bourzik W . The influence of the soil and plant natures and pollution on the radon and thoron alpha-activities inside various herbal infusions by using solid state nuclear track detectors . 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(Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2016 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-016-0045-2 http://dx.doi.org/10.1007/s41365-016-0045-2 . 2016 Nuclear Science and Techniques 03 27