

ORIGINAL ARTICLE 

Year : 2016  Volume
: 7
 Issue : 1  Page : 1826 

Mass attenuation coefficient and its photon interaction derivables of some skeletal muscle relaxants
HC Manjunatha
Department of Physics, Government College for Women, Kolar, Karnataka, India
Date of Web Publication  23Jun2016 
Correspondence Address: H C Manjunatha Department of Physics, Government College for Women, Kolar, Karnataka India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09730168.184608
Context: The study of photon interactions with biological materials is essential in radiation medicine and biology, nuclear technology and space research, since radioactive sources are used. Aims: A study of mass attenuation coefficient, effective atomic numbers (Z_{eff}) and electron density of some commonly used skeletal muscle relaxants. Materials and Methods: We have measured the mass attenuation some commonly used skeletal muscle relaxants such as tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide and mephenesin for various gamma sources of energy ranging from 84keV to 1330 keV (^{170}Tm, ^{57}Co, ^{141}Ce, ^{203}Hg, ^{51}Cr, ^{113}Sn, ^{22}Na, ^{137}Cs, ^{60}Co, ^{22}Na and ^{60}Co). The measured values agree with the theoretical values. The effective atomic numbers (Z_{eff}) and electron density (N_{e}) of commonly used skeletal muscle relaxants for total and coherent, incoherent, photoelectric absorption, pair production in atomic and nuclear field photon interaction have been computed in the wide region 1keV to 100GeV using an accurate database of photoninteraction cross sections and the WinXCom program. Results: The significant variation of Zeff and Nel is due to the variations in the dominance of different interaction process in different energy regions. A comparison is also made with the single values of the Zeff and Nel provided by the program XMuDat. We have also calculated CT numbers, kerma values relative to air and dose rate for relaxants which are also not remaining constant with energy. Conclusions: The computed data of mass attenuation coefficient, effective atomic numbers (Z_{eff}) and electron density and CT numbers in the low energy region helps in visualizing the image of the biological samples and precise accuracy in treating the inhomogenity of them in medical radiology. The calculated kerma values relative to air and dose rate for relaxants are useful in radiation medicine. Keywords: Computed tomography number, effective atomic number, electron density, relaxants
How to cite this article: Manjunatha H C. Mass attenuation coefficient and its photon interaction derivables of some skeletal muscle relaxants. J Radiat Cancer Res 2016;7:1826 
How to cite this URL: Manjunatha H C. Mass attenuation coefficient and its photon interaction derivables of some skeletal muscle relaxants. J Radiat Cancer Res [serial online] 2016 [cited 2018 Nov 22];7:1826. Available from: http://www.journalrcr.org/text.asp?2016/7/1/18/184608 
Introduction   
The study of photon interactions with biological materials is essential in radiation medicine and biology, nuclear technology, and space research since radioactive sources are used. Photons in the keV range are important in radiation biology as well as in medical diagnostics and therapy Hubbell.^{[1]} Photons in the MeV range finds importance in the field of radiography and medical imaging, and photons in the GeV range are of interest in astrophysics and cosmology.
Hine ^{[2]} stated that a single number cannot represent the Z_{eff} of a complex material. The parameter Z_{eff} is very useful in choosing a substitute composite material in place of an element for that energy depending on the requirement. The energy absorption in the given medium can be calculated by means of wellestablished formulae if certain constants such as Z_{eff} and N_{el} of the medium are known. Among the various parameters determining the constitutive structure of an unknown object or material, one should especially note the effective atomic number. In fact, this value can provide an initial estimation of the chemical composition of the material. A large Z_{eff} generally corresponds to inorganic compounds and metals, whereas a small Z_{eff}(≤10) is an indicator of organic substances. Several investigators have measured or calculated Z_{eff} for human tissue and other biological materials (Yang et al. 1 (1987), Rao et al. 1985).^{[3],[4],[5]} So far, to our knowledge, no study has been done for skeletal muscle relaxants (Biomedical compounds).
In this study, skeletal muscle relaxants such as tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide, and mephenesin have chosen, and its composition is given in [Table 1]. These agents are used as adjuvant to anesthesia to get the relaxation of skeletal muscle during the corrections of dislocations, surgery, radiotherapy, etc., and used as relieving painful muscle spasms because of various musculoskeletal and neuromuscular disorders. Hence, accurate calculation of photon mass attenuation coefficient, effective atomic number Z_{eff}, electron density N_{e}, and computed tomography (CT) numbers of above relaxants are important in medical diagnostics. The calculation of CT numbers of relaxants is important which gives the necessary information about relative electron density. Hence, the above parameters become a vital, interesting, and exciting field of research for characterization and visualization of matter (biological samples) in the medical field. The CT number outlines the inhomogeneities and also gives the direct information of the electron density from which accurate corrections can be made by suitable treatments. Even dose calculations are made based on the patientspecific information obtained from Xray CT.
Materials and Methods   
Computation of effective atomic number
When a beam of photons passes through an absorber, the photons interact with the atoms and are either absorbed (photoelectric effect, pair and triplet production, and photonuclear) or scattered away from the beam (coherent and incoherent scattering). The intensity of the transmitted beam of photons is the sum of the crosssections, per atom for all the above processes. Hence, the total molecular cross section σ_{mol} is determined from the following equation using the values of the mass attenuation coefficient of relaxants using (µ/ρ)_{bio} obtained by running WinXCOM program (2004).
Where N is Avogadro number, n_{i} is the number of atoms of i^{th} element, and A_{i} is its atomic weight in a given molecule. The effective atomic cross section σ_{atm} are determined by:
Where f_{i} is the fractional abundance (µ/ρ)_{i} is mass attenuation coefficient of i^{th} element.
The effective electronic cross section σ_{ele} are determined by:
Where, and Z_{i} is the atomic number of i^{th} element in a molecule, respectively.
Then, effective atomic number is calculated using:
In the present work, we have generated mass attenuation coefficients and photon interaction cross sections in the energy range from 1 keV to 100 GeV using WinXCom.^{[6]} This program uses the same underlying crosssectional database as the wellknown tabulation of Hubbell and Seltzer.^{[7]} WinXCom makes it possible to export the crosssectional data to a predefined MS Excel template, a feature that greatly facilitates the subsequent graphical and numerical data analysis. XMuDat ^{[8]} is an alternative program for calculating photon interaction cross sections and absorption coefficients of elements, compounds, and mixtures in the energy range from 1 keV to 50 MeV. For a given compound, XMuDat also provides two single values for the effective atomic number and the electron density, respectively.
Calculation of electron density
The effective electron density, N_{el}, expressed in the number of electrons per unit mass is closely related to the effective atomic number. For a chemical element, the electron density is given by N_{el}= NZ/A. This expression can be generalized to a compound,
In the present work, we have calculated N_{el} using equation (7).
Calculation of computed tomography number
CT number is a normalized value of the calculated Xray absorption coefficient of a pixel (picture element) in a computed tomogram, expressed in Hounsfield units. We have also calculated CT number using following equation given by Thomas et al.^{[9]}
μ_{m} and μ_{w} are energy attenuation coefficient of given material and water, respectively.
Computation of kerma relative to air
Kinetic energy released per unit mass (kerma) is defined as the initial kinetic energy of all secondary charged particles liberated per unit mass at a point of interest by uncharged radiation.^{[10]} Let ψ (Jm ^{−2}) be the energy fluence of monoenergetic photons passing normally through an area A in an absorber. The energy transferred to charged particles in a volume over a short distance dx behind the area is then ψAμ_{en}dx. Since the mass in the volume with density ρ is ρA dx, the kerma is:
Therefore, kerma is the product of the energy fluence and the mass energyabsorption coefficient. Kerma of a biomolecule relative to air can be expressed as:
To compute kerma relative to air, the values of mass energyabsorption coefficient, μ_{en}/ρ, for air and biomolecule were calculated using the following equation:
where w_{i} and (μ_{en}/ρ)_{i} are the weight fraction and the mass energyabsorption coefficient of the i^{th} constituent element present in a molecule. For any chemical compound, w_{i} is given by:
The values of (μ_{en}/ρ)_{i} have been taken from the compilation of Hubbell and Seltzer.^{[7]}
Estimation of dose rate
The absorbed photon dose rate (dD/dt) at distance R from a point source of a biomolecule at various photon energies is estimated by the following relation:
where C = activity of source (Bq) E = energy per decay (MeV)
We have estimated photon absorbed dose rate of some commonly used gamma sources (Na21, Cs137, Mn52, Co60, and Na22) in skeletal muscle relaxants.
Measurement and comparison with theoretical values
The narrow geometry experimental setup is as shown in [Figure 1]. We have used a NaI(Tl) crystal detector (5.8 cm ^{2}× 5.8 cm ^{2}) mounted on a photomultiplier tube housed in a lead chamber and a sophisticated PCbased MCA for a detection purpose, gamma sources such as ^{170} Tm (84 keV),^{57} Co (122 keV),^{141} Ce (145 keV),^{203} Hg (279 keV),^{51} Cr (320 keV)^{113} Sn (392 keV,^{22} Na (511 keV),^{137} Cs (662 keV),^{60} Co (1170 keV),^{22} Na (1274 keV), and ^{60} Co (1330 keV). The sample was directly attached to the opening of the lead shield where source is placed. The integral intensities, I_{0} and I of the beam before and after passing through the sample are measured for sufficient time (μ/ρ) is then estimated using the relation.  Figure 1: Schematic diagram of the experimental setup (S  Source position, T  Target sample, L  Lead shielding, D  Detector, PM  Photomultiplier)
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Where, t and ρ are the thickness and density of the sample, respectively.
Results and Discussions   
The measured (μ/ρ) is compared with theoretical values, and it is given in [Table 2] and [Table 3]. The measured values agree with the theoretical values. The values of these parameters have been found to change with energy and interaction of gamma with the medium.  Table 2: Comparison of measured mass attenuation coefficients with theoretical values
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 Table 3: Comparison of measured mass attenuation coefficients with theoretical values
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Effective atomic number, electron density and ct number
The Z_{eff} and N_{e} and CT numbers of skeletal muscle relaxants tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide, and mephenesin are computed in the energy region 1 keV–100 GeV. It is found that Z_{eff} and N_{e} of relaxants vary with energy and composition of them. This variation is shown in the [Figure 2],[Figure 3],[Figure 4],[Figure 5],[Figure 6],[Figure 7],[Figure 8],[Figure 9],[Figure 10],[Figure 11],[Figure 12],[Figure 13] for total and all partial photon interaction (coherent, incoherent, photoelectric absorption, and pair production in atomic and nuclear field).  Figure 2: Variation of Z_{eff} with photon energy E in MeV for total photon interaction (with coherent). (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 3: Variation of Z_{eff} with Photon energy E in MeV for photoelectric absorption. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 4: Variation of Z_{eff} with Photon energy E in MeV for incoherent. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 5: Variation of Z_{eff} with Photon energy E in MeV for coherent. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride (5) tubocurarine chloride
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 Figure 6: Variation of Z_{eff} with Photon energy E in MeV for pair production in the electric field. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 7: Variation of Z_{eff} with photon energy E in MeV for pair production in the nuclear field. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 8: Variation of N_{e} with photon energy E in MeV for total photon interaction (with coherent). (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 9: Variation of Ne with photon energy E in MeV for photoelectric absorption. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 10: Variation of N_{e} with photon energy E in MeV for incoherent scattering. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 11: Variation of N_{e} with photon energy E in MeV for coherent scattering. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 12: Variation of N_{e} with photon energy E in MeV for pair production in the electric field. (1) Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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 Figure 13: Variation of N_{e} with photon energy E in MeV for pair production in the nuclear field. (1)Gallamine triethiodide, (2) mephenesin, (3) pancuronium bromide, (4) suxamethonium chloride, (5) tubocurarine chloride
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Total photon interaction
The variation of Z_{eff} with photon energy for total photon interactions is as shown in [Figure 1] and this variation is because of dominance of different photon interactions with skeletal muscle relaxants. In lower energy region, photoelectric interaction dominates, hence Z_{eff} varies similar to photon interaction. Except mephenesin, all other relaxants Z_{eff} increases and becomes maximum and decreases sharply in the energy region 0.002–025 MeV. These variations are due to the presence of halogens (Cl, Br and I) in their composition and these elemental cross sections vary larger in the energy region 0.002–025 MeV. The Z_{eff} and found to remain constant up to 10 MeV, which shows that scattering (coherent and incoherent) processes increases. From 10 MeV to 100 MeV, there is a regular increase in the Z_{eff} with photon energy. This is due to the increase in incoherent and pair production processes. From 100 MeV onward Z_{eff} remains constant which is due to dominance in pair production processes. The Z_{eff} values of relaxants vary from the element with lowest Z to the highest Z present in their composition.
Photoelectric absorption
The variation of Z_{eff} with photon energy for photoelectric absorption interaction is as shown in [Figure 2] and this indicates that Z_{eff} increases up to 0.040 MeV for all relaxants except for mephenesin which is independent of photon energy. In case of Gallamine triethiodide, there is a sudden increase in Z_{eff} at 0.033169 MeV which is the K absorption edge of iodine and it remains constant with photon energy. In pancuronium bromide, sudden increase in Z_{eff} is found at 0.01347 MeV which is the K absorption edge of bromine, and it remains constant with photon energy. The Z_{eff} of suxamethonium chloride and tubocurarine chloride increases at 0.002822 MeV because chlorine (K absorption edge of Cl is 2.8224 keV). Thereafter, it becomes constant with increase in photon energy. This is due to the dominance in photoelectric processes in low energy region, i.e., <1 MeV and for the substances of higher atomic number (Z) than for low Z substances.{Figure 2}
Incoherent scattering
The variation of Z_{eff} with photon energy for incoherent scattering is as shown in [Figure 3] and it indicates that Z_{eff} increases from 0.001 MeV to 0.10 MeV shows that it depend on energy. This variation is because of the proportion and the range of atomic numbers of the elements present in relaxants. Above 0.10 MeV Z_{eff} remains constant and independent of energy for all relaxants.{Figure 3}
Coherent scattering
The variation of Z_{eff} with photon energy for coherent scattering is as shown in [Figure 4] and it indicates that Z_{eff} increases for mephenesin up to 0.03 MeV and remains constant. All other relaxants show increment in Z_{eff} from 0.001 MeV to 0.40 MeV. Thereafter, remains constant, i.e. independent of energy. The values of Z_{eff} for gallamine triethiodide, pancuronium bromide, suxamethonium chloride, and tubocurarine chloride have comparatively higher. This is due to the presence of halogens (42.70% of I in gallamine triethiodide, 21.81% of Br in pancuronium bromide, 17.84% of Cl in suxamethonium chloride, and 09.87% of Cl in tubocurarine chloride).{Figure 4}
Pair production in electric field
The variation of Z_{eff} with photon energy for pair production in electric field is as shown in [Figure 5]. It shows that Z_{eff} is constant with increase in photon energy from 3 MeV to 30 MeV, i.e., independent of energy. It slightly decreases from 30 MeV to 1000 MeV and thereafter remains constant for all relaxants. Here also, in case of gallamine triethiodide and pancuronium bromide, Z_{eff} values are slightly more compared to the other relaxants. This is due to the large range of atomic number of constituent elements in them.{Figure 5}
Pair production in nuclear field
The variation of Z_{eff} with photon energy for pair production in the nuclear field is as shown in [Figure 6] and it shows that Z_{eff} slightly decreases with increase in photon energy from 1.25 MeV onward and found to remain constant thereafter. This is because pair production in nuclear field is Z ^{2} dependent. In case gallamine triethiodide and pancuronium bromide, the variation of Z_{eff} values is more compared to the other relaxants. This is due to the large range of atomic number of constituent elements in them.{Figure 6}
The variation of N_{e} with photon energy of all relaxants for total and partial photon interaction processes are similar to that of Z_{eff}, which can be explained on the similar manner. The variation is as shown in [Figure 7],[Figure 8],[Figure 9],[Figure 10],[Figure 11],[Figure 12]. The values of Z_{eff} and N_{e} are used for planning and treatment in radiotherapy.{Figure 7},{Figure 8},{Figure 9},{Figure 10},{Figure 11},{Figure 12}
Usually, above relaxants may be administered to the patient before treatment. Hence, while treating tissue inhomogeneity of the patient, the contribution of CT numbers of relaxants has to be considered though the values are very small. The CT numbers for total photon interaction is given in [Table 4]. The CT numbers for coherent, incoherent, and photoelectric absorption region and total photon interaction helps in visualizing the image of the biological samples and precise accuracy in treating the inhomogeneity of them in medical radiology.
Comparison with XMuDat
For a given compound, the XMuDat program provides two single values, (Z_{eff})_{XMuDat} program, and (N_{el})_{XMuDat} for the effective atomic number and the electron density, respectively. The comparison of computed max (Z_{eff})_{win}, min (Z_{eff})_{win}, max (N_{el})_{win}, and min (N_{el})_{win} with XMuDat program is given in [Table 5] and [Table 6]. Where, max (Z_{eff})_{win}, min (Z_{eff})_{win}, max (N_{el})_{win}, and min (N_{el})_{win}, are the maximum and minimum values of the atomic number and the electron density obtained in our calculations using WinXCom in the energy range from 1 keV to 100 GeV. It is not clear from the documentation of the software how XMuDat actually calculates the effective atomic number and the electron density. However, it is obvious from the data that in [Table 5] and [Table 6], (Z_{eff})_{XMuDat} and (N_{el})_{XMuDat} are not related by equation (7), since for each compound (Z_{eff})_{XMuDat} is close to max (Z_{eff})_{win}, whereas 0 (N_{el})_{XMuDat} is in perfect agreement with min (N_{el})_{win}., As discussed above, max (Z_{eff})_{win} occurs in the lowenergy region, where photoelectric absorption is the main interaction process, and min (N_{el})_{win} occurs at intermediate energies, where Compton scattering is dominant. It follows that XMuDat calculates (Z_{eff})_{XMuDat} by assuming photoelectric absorption is the main interaction process. In contrast, (N_{el})_{XMuDat} has been calculated assuming that Compton scattering is dominating. Thus, users of XMuDat should be aware that the calculations of the two single values, (Z_{eff})_{XMuDat} and (N_{el})_{XMuDat} are based on two different assumptions.
Kerma values relative to air and absorbed dose rate
The energy dependence of kerma relative to air is tabulated in [Table 7]. For Gallamine triethiodide kerma values relative to air increases up to 0.05 MeV; thereafter, it keeps on decreases and becomes minimum at 1.5 MeV. At higher energies, these values increase. For Mephenesin kerma values relative to air increases with increase in energy and becomes maximum at 0.3 MeV. It shows slight increasing trend at higher energies. For pancuronium bromide, kerma values decreases with energy from 0.1 MeV to 0.4 MeV. After this energy, kerma values remain almost constant. For Suxamethonium chloride and Tubocurarine chloride kerma values decreases with energy, thereafter it becomes constant.
The evaluated absorbed dose rate at a distance 1 m from a point gamma sources such as Na21, Cs137, Mn52, Co60, and Na22 in skeletal muscle relaxants are as shown in [Table 8]. Absorbed dose rate at of relaxants is maximum for Na21 and minimum for Mn52.
Conclusion   
We have measured the mass attenuation coefficients of some commonly used skeletal muscle relaxants such as tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide, and mephenesin for various gamma energies (84 keV to 1330 keV). The measured values agree with the theoretical values. The measured effective atomic numbers (Z_{eff}) and electron density (N_{e}) are compared with theoretical values. We have also calculated CT numbers, kerma values relative to air, and dose rate for relaxants. These parameters are useful in the radiation medicine.
Financial support and sponsorship
Nil.
Conflicts off interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8]
