On the other hand, the concept of z-dependence of photon attenuation coefficient has been utilized in many applications of radiation studies. And it is very important to evaluate the amount of radiation especially in medical Physics (Shivalinge et al. (2004), Ingalagondi et al. (2017). Additionally, the mass attenuation coefficient provides a wide variety of information about fundamental properties of the matter in the atomic and molecular level. Accurate values of the photon mass attenuation coefficients are required to provide essential data in diverse fields such as nuclear diagnostics (computerized tomography), radiation protection, nuclear medicine, radiation dosimetry, gamma ray fluorescence studies, and radiation biophysics. The mass attenuation coefficients are also widely used in the calculation of the photon penetration and the energy deposition in biological shielding and other dosimetric materials.

The application of such effective atomic number can be described in two ways (i) the effective atomic number can be put into formulae and in this way a compound can be reduced to an ordinary element, if calculation of Z-dependent effects are to be carried out and (ii) the effective atomic number can be used to find compound with atomic composition like air or water, etc. Hence, a precise knowledge of effective atomic number plays a very important role in medical radiation dosimetry, radiation therapy etc. There are many researchers who performed research in determination of effective atomic numbers of composite materials ( Shivaramu et al. (2001),  Kıran and Venkata (1997), energies close to absorption edges of the elements (Mayneord (1937),  ( Shivaramu et al. (2001),  Kıran and Venkata (1997), Teli et al. (1996). In the recent years, several  theoretical experimental and investigations have been carried out to understand the nature of interaction of different biological molecules such as, amino acids, fatty acids, proteins, carbohydrates etc., but there are few reports in literature survey on the pharmaceutical active ingredients. Active Pharmaceutical Ingredient (API) is a substance used in a finished pharmaceutical product (FPP), intended to furnish pharmacological activity or to otherwise have direct effect in the diagnosis, cure, mitigation, treatment or prevention of disease, or to have direct effect in restoring, correcting or modifying physiological functions in human beings, the basic functioning product in the drug (Manjunath and Kerur (2015). But the drug which is available in the market is composition of active and inactive pharmaceutical gradients. The aim of this work is to calculate the total attenuation cross sections as well as the composition dependent quantities such as effective atomic number (Z_eff) and effective electron densities (N_e) of active pharmaceutical ingredients and to have a full understanding of the nature of interaction of active pharmaceutical ingredients (API) over some energy range.

 

2.    METHODOLOGY

A narrow beam of mono-energetic photons in the X-ray or gamma ray region is attenuated to an intensity I from an incident intensity I₀ in passing through a material thickness with mass per unit area x, according to the well established Beer-Lambert’s exponential law

 

                                                                                                                                                               Equation 1

 

               

 

 

                                                                                                                                                             Equation 2

 

in which   is the mass attenuation coefficient and can be obtained from the measured I, I₀ and x data. The photon mass attenuation coefficient for any chemical compounds or a mixture can be written as

 

                                                                                                                                                                                                Equation 3

 

Equation 2 is closely related to the total cross section per atom σ_tot according to the relation

 

                                                                                               Equation 4

 

in which N_A is Avogadro’s number and M is the atomic weight. The total cross section σ_tot in turn, can be written as the sum over contribution from the principal of interactions.

 

                                                                                                 Equation 5

 

in which σ_coh and σ_comt. are the coherent (Rayleigh) and incoherent (Compton) scattering cross section, respectively,  is the atomic photoelectric cross section, ᴋ is the positron electron pair-production (including triplet) cross section and σ_ph.n. is the photonuclear cross section.

The effective (average) atomic cross section (σ_a) can be easily determined from the following expression,

 

                                                                                 Equation 6

 

Similarly, effective electronic cross section (σ_e) for the individual element is given by the following relation,

 

                                                                                Equation 7

 

Where, f_i and Z_i are fractional abundance and atomic number respectively of constituent element i. Now the effective atomic number can be written as

 

                                                                                                         Equation 8

 

The effective electron density (N_el) which is the number of electrons per unit mass can be derived by using the Equation 3 and (7),

 

 

 

 

                                                                                                                                                                                                           Equation 9                                                                          

 

The mass attenuation coefficient values can be found in the tabulation by Hubbell and Seltzer (Hubbell and Seltzer (1995). The effective atomic numbers for mixture or composite materials were determined by the formula Jackson and Hawkes (1981). A convenient alternative to manual calculations, using tabulated data, is to generate data as needed, using a computer. For this, Berger and Hubbell (1987) developed a computer program, XCOM, for calculating cross sections and attenuation coefficients for any elements, compounds or mixtures at energies from 1 keV to 100 GeV. The program has since undergone a number of updates and now available in window version. Recently, this well-known and much used program has been developed to the Windows platform (Gerward et al. (2001), Gerward et al. (2004), Manjunath and Kerur (2015) and the Windows version is being called WinXCom Manjunath and Kerur (2015), Kadir Günoğlu (2018).

 

3.    RESULTS AND DISCUSSION

In this work, the variation of effective atomic number, effective electron density and mass attenuation coefficient with photon energy 1keV to 100 GeV for seven active pharmaceutical ingredients were studied and the details of the drugs are tabulated in the Table 1. The results obtained clearly support the remarks made by Hine (1952) that the effective atomic number varies with energy. The chemical compositions of the seven API drugs are organic elements only but the ratio of content is different. Except in Alprazolam which contains Carbon, Hydrogen, Chlorine, and Nitrogen other drugs contain basic organic elements (C, H, O), since Alprazolam is grouped in the steroidal class of drug and others are Non steroidal class o drug/Non-Steroidal Anti Inflammatory Class of drug Manjunath and Kerur (2015). The Z_eff values of seven organic materials composed of H, C, N, and O were calculated according to the Equation 1. The obtained results of effective atomic number and total mass attenuation coefficient and are shown in Figure 1, Figure 2, Figure 3.

Figure 1 Variation of effective atomic number Zeff of API’s in drugs with energies for total photon interaction

 

 

The interpretations of variations are being due to photoelectric effect which varies as Z_4-5 and less but significantly due to coherent scattering which varies as Z_2-3. In the intermediate energy region, where incoherent scattering is dominating process, the mass attenuation coefficient is found to be constant and is due to Z-dependence of incoherent scattering and significant role played by pair production. Singh (2014) also found the negligible variation between 165 keV and  7 MeV for biological materials. In the high energy region, significant variation in the mass attenuation coefficient is due to the Z_2-3 dependence of pair production.

The variation of effective atomic number with photon energy for total photon interactions (Figure 3) which involves a dominating interactions viz., photoelectric, coherent and incoherent processes. The variation of effective atomic number (Z_eff) with energy is almost similar in case of Amiodar, Femotidine, Nimesulide and Diclofenac Sodium drugs except in the case of Ciprofloxacin and Amiodarone. The discrimination among the effective atomic numbers for the opted API drugs is due to near absorption edges. There were no edge effect observed in Ciprofloxacin drug while two Amiodarone has Iodine K, L₁, L₂, L₃ and M₁ absorption edges at 34.5, 5.15, 4.76, 4.48 and 1.09 keV respectively. Up to 16-22 keV onwards there is a sharp decrease in effective atomic number and decrease in Z_eff with energy up to 150 keV, showing that contribution of scattering processes increases which decreases Z_eff. From 155 keV to 3.5 MeV, Z_eff is almost independent of energy. This may be due to the dominant of incoherent scattering in this region. From 3.5 MeV to 410 MeV, there is regular increase in Z_eff with photon energy. Hence it is observed that the variation of Z_eff also depends on the relative proportion and the range of atomic numbers of the elements of which API drug is composed (Fig. 1). The Amiodarone has large range of atomic numbers (Z’s) from Hydrogen (1) to Iodine (53) than any other API drugs to which the variation in its Z_eff with energy is significant in comparison to any other API’s. Variation of Zeff with photon energy for photo electric absorption is shown in the Figure 2 which indicates that composition is also very important as explained above. There is a sudden jump observed in all the cases except in Ciprofloxacin. It has a least range of atomic numbers from 1 (H) to 9(Fluorine) and hence no absorption edge effect is exist. Diclofenac sodium takes an immediate jump in Zeff at 1.07 keV and 2.82 keV, which are the K absorption edge energies of Sodium (Na) and Chlorine (Cl) respectively. Up to 1 MeV increases sharply and then onwards remains a constant and this is due the fact that photoelectric is the predominant processes in the low energy region (<1MeV) and is for low Z materials. The Figure 2 also confirms that the variation of Z_eff in pharmaceutical drugs probably due to more number of elements in Amiodarone and also the API’s having edge effect because Ciprofloxacin has no edges in it. Hence in all other active pharmaceutical ingredients, the variation of Z_eff is almost independent of energy. This is because of the fact that these API’s consist of elements which are same in the number and are of close to the atomic number.

Figure 2 Variation of effective atomic number Zeff of API’s in drugs with energies for total photon interaction

 

The electron density of the selected API’s in drug samples are found to be varying from 2.96 x 10²³ to10.14x10²³ electrons/g but in the case of Amiodarone it is from 4.85x10²³ to 31.42x10²³ electron/g. Hence electron density is closely related to the effective atomic number and depends on the photon energy and chemical content of the API’s in drug samples.

Figure 3 Variation of mass attenuation coefficient with energy for API in drugs

 

In Figure 3 the results of the total mass attenuation coefficients of active pharmaceutical ingredients against the photon energy is presented. In these cases no absorption edge is found in the ciprofloxacin drug. In the case of  Nimesulide, Femotidine, Amiodar, there are two values for mass attenuation coefficients at 2.50 keV due to K-absorption edge. The value 2.17x10² cm²/g, 2.21x10²cm²/g and 2.26x10² cm²/g respectively are valid immediately below the absorption edge and 6.57x10²cm²/g, 4.34x10²cm²/g and 5.13x10² cm²/g respectively are valid immediately above the absorption edge. Alprazolam at 2.89 keV have the values of mass attenuation coefficients 1.43x10²cm²/g and 3.12x10²cm²/g below and above the chlorine K absorption edges respectively. Diclofenac sodium has two K-absorption edges at 1.07 keV for Sodium and 2.89 keV for chlorine. The values of mass attenuation coefficients varies between 2.10x10² cm²/g and 1.65x10² cm²/g immediately below the sodium and chlorine K absorption edge and 2.39 x10²cm²/g and 3.92 x10² cm²/g immediately above the Sodium and Chlorine K-absorption edges. The interesting property of API drug in which we opted is the Amiodarone which has K, L₁, L₂, L₃ and M₁ absorption edges at 34.3, 6.17, 5.85, 4.56 and 1.09 keV. The values of mass attenuation coefficient for these edges are 2.83x10²cm²/g, 3.03x10²cm²/g, 2.74x10²cm²/g, 1.20 x10²cm²/g and 4.39 x10³ cm²/g respectively below the absorption edges and 17.35cm²/g, 5.58x10⁺² cm2/g, 7.56x10⁺² cm2/g, 4.94x10⁺² cm2/g and 5.42x10⁺³ cm2/g above the absorption edges. The above discussion and graph of mass attenuation coefficient vs. energy shows that there are three processes photoelectric absorption, Compton scattering and pair production which are dominant in the interaction with API in the drug materials. Results of (Kaginelli et al. (2009), Manjunath and Kerur (2015) that the theoretical/calculated values have been obtained without considering the edge effects since the effective atomic numbers are under/over estimated when any elements falls below the absorption edge.

 

Table 1 Some of the common active pharmaceutical ingredients used in the drugs
S/No	API Name	Chemical Composition
1	Nimesulide	C13H12N2O5S
2	Alprazolam	C17H13ClN4
3	Amiodar	C22H28FN3O6S
4	Amiodarone	C25H29I2NO3
5	Ciprofloxacin	C17H18FN3O3
6	Diclofenac sodium	C22H19Cl2N2NaO4
7	Femotidine	C8H15N7O2S3

                    

4.    CONCLUSION

The unique number named in the composite materials as effective number and it may plays an important role in pharmacology or pharmaceutical industry by means of determining the quality and quantity of the drug materials in which one can also identify the active and inactive ingredients added during the manufacturing /formulation processes of different firms.

 

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