Investigation of the Mass Attenuation Coefficients, Effective Atomic Numbers and Electron Densities for Compounds of Painkiller

In this study the effects of gamma radiations with compounds are an important subject in the field of medicine, radiation shielding and radiation physics. With technological advances the using of radiation has increased in the medicine in the last century. The mass absorpsion coefficient (µ/ρ) is the fundamental a quantity characterizing gamma ray and is of major importance in radiation shielding. In this study, the mass absorption coefficient of painkillers named Ketoprofen, Flurbiprofen, Etodolac, Ibuprofen, Meloxicam, Diclofenac and Aspirin were calculated at energy range from 4.65 keV to 59.543 keV using the WinXCom data programme. In addition total atomic (σ_ta), moleculer (σ_tm), electronic cross-section (σ_te), effective atomic number (Z_eff), effective electron density (N_eff) were calculated.

With the increasing use of radiation sources in areas related to human health such as nuclear medicine, radiotherapy and radiology, it was necessary to examine the parameters that are considerable in the interaction of photon with material. In radiation dose calculations, the effective atomic number information of the samples absorption of beam in the samples were required [1,2]. The mass absorption coefficient, which is a characteristic feature for materials is a very significant parameter in agriculture, pharmacy, radiation dosimetry, biology, nuclear and radiation physics [3]. The accurate reliable values of mass attenuation coefficients were required to provide essential data in varied fields such as nuclear diagnostics, radiation protection, nuclear medicine, radiation biophysics and etc. [4]. The effective atomic number physically enables the characteristic of the compound to be understandable with the help of a single atomic number [5]. µ/ρ was also used to calculate and control the material thickness because radiation can change the characteristics of material. Since this may cause various undesirable results, it was very important to examine the interaction of many materials, alloys and compounds with radiation and to know what changes they cause in the material [6]. In the literature, the effects of radiation material interactions at different energies on Z_eff and N_eff were studied. Z_eff were calculated in the energy range of 15.746-40.930 keV using the mixing rule depending on the Ni contribution in CuCoNi alloys, and it was stated that the Z_eff value increased with the increase in Ni ratio [7]. Z_eff and N_eff between at various energies of essential amino acids were calculated theoretically [8]. The Z_eff of composite materials at various energy ranges of 280 to 1115 keV were obtaned [9]. Experimental and theoretical µ/ρ values of vitamins in some photon energies were calculated [10]. The mass attenuation coefficient for compounds or compositions was calculated with the help of WinXCom program. WinXCom is a data programme base the "mixing rule". In this rule, the elements in the ingredient are considered independent from each other and their interaction with each other is neglected [11].

In this present work were calculated the mass attenuation coefficients for some painkiller compounds such as Ketoprofen (C₁₆H₁₄O₃), Flurbiprofen (C₁₅H₁₃FO₂), Etodolac (C₁₇H₂₁NO₃), Ibuprofen (C₁₃H₁₈O₂), Meloxicam (C₁₄H₁₃N₃O₄S₂), Diclofenac (C₁₄H₁₁C₁₂NO₂) and Aspirin (C₉H₈O₄) in the energy range from 4.65 keV to 59.543 keV using the WinXCom data. Z_eff and N_eff parameters were calculated with the help of the data obtained. It has been observed that N_eff and Z_eff values are interrelated and parallel to each other. The computational results of the pain relief compounds μ/ρ, Z_eff and N_eff presented in this study can be referenced as guiding in a variety of medical applications and fields. In the paper, calculated datas were published on the study of mass attenuation coefficient calculate on painkiller compounds in the photon energy 4.65 to 59.543 keV through which radiation interaction of the drug can be defined.

The substances used in around the world to address various pains are listed in table 1. Use of aspirin, ibuprofen were said to show beneficial synergistic effects by combatting pain at multiple sites of action [12]. Flurbiprofen was used in the treatment of pain or inflammation in humans. Flurbiprofen is indicated for the management of excimer laser photorefractive keratectomy, and ocular gingivitis. Recent reports suggest use of flurbiprofen in radioprotection, the inhibition of colon tumor, the protection of post irradiation myelosuppression and peridontal surgery [13]. Etodolac drug is an effective drug in the treatment of osteoarthritis, rheumatoid arthritis and spinal rheumatism.Since these painkillers was used for different purposes in the field of medicine [14]. It was considered necessary theoretically to examine their reactions to high energy rays.

The μ/ρ for a compound material is the total of the mass attenuation coefficients of every element according to "mixing rule" [15]. According to the WinXcom program, μ/ρ is calculated with the help of formula (1).

${\left(\frac{\mu }{\rho }\right)}_{\text{c}}={\displaystyle \sum }_{\text{i}}\omega \text{i }{\left(\frac{\mu }{\rho }\right)}_{\text{i}}\left(\text{1}\right)$

In equation (1), ω_i is fractional weight of the i atom.

Theoretical μ/ρ is calculated for compound materials using the WinXcom. Using the equation (2) σ_tm values ​​were calculated [16].

${\sigma }_{\text{tm}}=\frac{1}{{\text{N}}_{\text{A}}}{\left(\frac{\mu }{\rho }\right)}_{\text{C}}{\displaystyle \sum }_{\text{i}}{\text{n}}_{\text{i }}{\text{A}}_{\text{i}}\left(\text{2}\right)$

A_i is the atomic weight, n_i is the number of atoms, N_A is Avogadro's number.

σ_ta is calculated using the following Equation (3) [16].

${\sigma }_{\text{ta}}=\frac{{\sigma }_{\text{tm}}}{{{\displaystyle \sum }}^{\text{}}{\text{n}}_{\text{i}}}\left(\text{3}\right)$

In formula (3), σ_ta is the total atomic cross section, σ_tm is the total molecular cross section, ni is the total number of atoms. The unit of σ_ta is cm²/atom.

The electronic cross section was obtaned by using the mass attenuation coefficient of each element in the samples. σ_te was calculated using Formula (4) [16].

${\sigma }_{\text{te}}=\frac{1}{{\text{N}}_{\text{A}}}{\displaystyle \sum }_{\text{i}}{\text{f}}_{\text{i}}\frac{{\text{A}}_{\text{i}}}{{\text{Z}}_{\text{i}}}{\left(\frac{\mu }{\rho }\right)}_{\text{i}};{\text{ f}}_i=\left(\frac{{\text{n}}_{\text{i}}}{{{\displaystyle \sum }}_{\text{i}}{\text{n}}_{\text{i}}}\right)\left(\text{4}\right)$

Z_i atomic weight and f_i is abundance fraction.

${\text{Z}}_{\text{eff}}=\frac{{\sigma }_{\text{ta}}}{{\sigma }_{\text{te}}}\left(\text{5}\right)$

N_eff was calculated using the following formula (6) [17].

WinXCom program determines the μ/ρ of the compounds consisting of more than single element for any sample, taking into account "mixture rule" while calculating the mass absorption coefficients. According to the this rule, μ/ρ of the compound is the sum of the mass absorption coefficients of each element [18]. μ/ρ, Z_eff and N_eff values ​​calculated at the specified energies of the compounds are given in tables 2-4.

As can be seen from the table 2, with increasing energy a decrease is observed in the µ/ρ values and accordingly the Z_eff values. The highest mass absorption coefficient of 134.8 belongs to the compound C₁₄H₁₁C₁₂NO₂ called Diclofenac at 4.65 keV energy. The mass attenuation coefficient value of C₁₄H₁₁C₁₂NO₂ compound named Diclofenac was found as 0.248 at the highest energy calculated at 59.543 keV. It can be seen from Table 2 that the lowest mass attenuation coefficient of the calculated energy ranges belongs to the C₁₃H₁₈O₂ compound.

It seems obvious that the total moleculer cross-section values decrease with increasing photon energies as shown in the figure 1. It can be seen from figure 1 that the lowest total moleculer cross-section value of the calculated energy ranges belongs to the İbuprofen C₁₃H₁₈O₂ compound.

Figure 1: Total moleculer cross-section for painkiller compounds at different photon energies.

Figure 2: Effective atomic number for painkiller compounds at different photon energies.

It is clearly seen that the mass attenuation coefficient depends on the photon energy and on the chemical structure of the compounds. The µ/ρ values decrease with increasing photon energies as shown in the table 1. With the presence of Cl in the compound, Diclofenac (C₁₄H₁₁C₁₂NO₂) compound has the largest Z_eff value. Simultaneously while the effective atomic number for the C₁₄H₁₁C₁₂NO₂ compound increased, a parallel increase was observed in the effective electron density. Although there is not much change in low energies in compounds with multiple elements, a decrease in the effective atomic numbers has been observed due to the increase in energy. Ibuprofen (C₁₃H₁₈O₂) is a pain reliever with the lowest mass attenuation coefficient in the energies studied. In general, as the number of quantity elements forming the compound increases, μ/ρ and Z_eff values increase.

The effective electron dentisity value of C₁₄H₁₁C₁₂NO₂ compound named Diclofenac was found as 3.900 at the highest energy calculated at 59.543 keV. It can be seen from table 4 that the lowest effective electron dentisity value of the calculated energy ranges belongs to the C₁₃H₁₈O₂ compound.

In this study, µ/ρ at various energies were calculated for some compounds belonging to painkillers. By using µ/ρ values, σ_tm, σ_ta, σ_te, Z_eff, N_eff values ​​were calculated. Absorption of the photon at various energies occurs depending on the properties of the material under study. Therefore, beam permeability data at different energies provide information about the absorption and shielding properties of the material. Radiation absorption properties at low energies give better results for pain relief compounds. As can be seen from the results of the calculations, the radiation energy and the mass absorption coefficient vary, and it is understood that the materials cause changes in the attenuation parameters of the material withal increasing radiation. The data obtained from this study is important in terms of guiding researchers working in this field. The data obtained in the light of these values ​​will be used in various fields and it is thought to be suitable for use as shielding material in order to protect from radiation in low and medium energy beams.

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