Gamma and X-ray radiation compatibility of Ti-Ta-Hf-Zr alloys used for coronary stent applications

LOW ENERGY ACCELERATOR, RAY AND APPLICATIONS

Gamma and X-ray radiation compatibility of Ti-Ta-Hf-Zr alloys used for coronary stent applications

L. Seenappa，

H.C. Manjunatha，

K.N. Sridhar，

Chikka Hanumantharayappa

Nuclear Science and Techniques

Vol.29, No.1

Article number 3

Published in print 01 Jan 2018

Available online 21 Dec 2017

DOI：10.1007/s41365-017-0339-z

45101

We have studied the gamma and X-ray radiation compatibility of Ti based alloys such as Ti-37Ta-26Hf-13Zr-24 (wt.%) [Alloy 1], Ti-40Ta-22Hf-11.7Zr-26.3 (wt.%) [ Alloy 2], Ti-45Ta-18.4Hf-10Zr-26.6 (wt.%) [ Alloy 3], Ti-50Ta-15Hf-8Zr-27 (wt.%) [Alloy 4], Ti-55Ta-12Hf-7Zr-26 (wt.%) [Alloy 5], and Ti-60Ta-10Hf-5Zr-25 (wt.%) [Alloy 6]. Gamma and X-ray radiation compatibility is studied by evaluating the mass attenuation coefficient, mean free path, HVL, TVL effective atomic number, effective electron density, exposure buildup factor, and relative dose. We have compared these parameters for studied alloys with that of arteries. The alloys Ti-55Ta-12Hf-7Zr-26 and Ti-60Ta-10Hf-5Zr-25 have added properties such as gamma/ X-ray radiation compatibility, high elastic admissible strain, high mechanical strength, and excellent biocompatibility. Hence we may suggest that, among Ti-Ta-Hf-Zr alloys, these alloys are best materials for coronary stent applications.

StentalloysX-rayGammaMass attenuation coefficient

I. Introduction

Ti based alloys are widely used in the bio medical application. Vasilescu et al.^[1] studied the microstructure, surface characterization, and long-term stability of the Ti-Zr-Ta-Ag alloy for implant use. Sreenivasa Reddy and Kanchana^[2] studied the dynamical properties such as pressure and temperature effects on ternary Ni-based Ti, V, Zr, Nb, Hf, and Ta alloys. Zheng et al.,^[3] investigated the effect of Zr content on the thermal stability of a Ti–Ta alloy. Patrik Stenlund et al.,^[4] developed a Ti–Ta–Nb–Zr alloy to use implant material for bone and teeth. Xu et al.,^[5] studied the corrosion behavior of the Ti–Nb–Ta–Zr–Fe alloy for biomedical applications. Ma and Sun^[6] studied the characterization of biomedical Ti-Nb–Ta–Zr alloy.Zhang et al.^[7] investigated the microstructures, phase transformations, mechanical properties, and shape memory effect of Ti-Zr-Nb-Al alloys. Kim et al.,^[8] investigated the hydroxyapatite formation on biomedical Ti–Ta–Zr alloys by magnetron sputtering and electrochemical deposition. Song et al.,^[9] studied the microstructure and fatigue behaviors of a biomedical Ti–Nb–Ta–Zr alloy containing trace amounts of CeO₂. Wei et al.,^[10] investigated the effects of oxygen concentration on the microstructure and thermal expansion properties of Ti–Nb–Zr–Ta–O alloys. Elias et al.,^[11] studied the microstructural and mechanical characterization of biomedical Ti–Nb–Ta–Zr and Ti–Nb–Zr alloys. Jeong et al.,^[12] studied the control of nanotube shape and morphology on Ti–Nb(Ta)–Zr alloys. Sakaguchi et al.,^[13] studied the relationships between tensile deformation behavior and microstructure in Ti–Nb–Ta–Zr system alloys. Málek et al.,^[14] studied the influence of chemical composition and thermo-mechanical treatment on Ti–Nb–Ta–Zr alloys. Xu et al.,^[15] investigated the effects of cold deformation on the microstructure, texture evolution, and mechanical properties of the Ti–Nb–Ta–Zr–Fe alloy. Wei et al.,^[16] studied the influence of oxygen content on microstructure and mechanical properties of a Ti–Nb–Ta–Zr alloy. Vasilescu et al.,^[17] proposed a new Ti-Zr-Ta-Ag alloy for bio medical applications.

At present, the most commonly used stent materials include metal and polymer materials. Metallic stents exhibit a more stable performance than the polymer materials. The most commonly used metallic biomaterials for manufacturing stents are Nitinol (Ni-Ti), stainless steel (316L SS), cobalt-chromium (Co-Cr) alloy, tantalum (Ta), pure iron (Fe), platinum-iridium (Pt-Ir) alloy, and magnesium (Mg). Ni provides a local immune response and inflammatory reactions. Ta possesses excellent corrosion resistance, but has poor mechanical properties. The material which is used for a stent should not have high magnetic susceptibility because they are not appropriate for magnetic resonance imaging diagnostic in surgeries. There has been increasing research interest in the Titanium alloys for the development of metallic stent materials due to their biocompatibility, corrosion resistance, and non-magnetism. Ti-Ta-Hf-Zr (TTHZ) alloys are anticipated to be promising metallic stent materials by virtue of the unique combination of extraordinarily high elastic admissible strain, high mechanical strength, and excellent biocompatibility^[18]. X-ray and gamma radiation compatibility of stent alloys are important for radiation diognisis and therapy aspects. From the detailed literature survey, it is clear that there is no study on the gamma and X-ray radiation compatibility of stent alloys. In the present work, we have studied the gamma and X-ray radiation compatibility of Ti based alloys such as Ti-37Ta-26Hf-13Zr-24 (wt.%) [Alloy 1], Ti-40Ta-22Hf-11.7Zr-26.3 (wt.%) [ Alloy 2], Ti-45Ta-18.4Hf-10Zr-26.6 (wt.%) [ Alloy 3], Ti-50Ta-15Hf-8Zr-27 (wt.%) [Alloy 4], Ti-55Ta-12Hf-7Zr-26 (wt.%) [Alloy 5], and Ti-60Ta-10Hf-5Zr-25 (wt.%) [Alloy 6].

II.Theory

II.1. Gamma/X-ray interaction parameters

In the present work, the mass attenuation coefficients (MAC) and photon interaction cross sections in the energy range from 1 keV to 100 GeV are generated using WinXCom^[19]. The total linear attenuation coefficient (μ) can be evaluated by multiplying the density of compounds to mass attenuation coefficients.

μ = {(\frac{μ}{ρ})}_{c} \times ρ

(1)

The total linear attenuation coefficient (μ) is used in the calculation of Half Value Layer (HVL). HVL is the thickness of an interacting medium that reduces the radiation level by a factor of 2, so to half the initial level, and is calculated by the following equation

H V L = \frac{\ln 2}{μ} = \frac{0 .693}{μ} .

(2)

The total linear attenuation coefficient (μ) is also used in the calculation of Tenth Value Layer (TVL). TVL is the thickness of the interacting medium for attenuating a radiation beam to 10% of its radiation level and is computed by

T V L = \frac{\ln 10}{μ} = \frac{2.303}{μ} .

(3)

The average distance between two successive interactions is called the relaxation length (λ). It is also called the photon mean free path (MFP), which is determined by the equation:

λ = \frac{\int_{0}^{\infty} x \exp (- μ x) dx}{\int_{0}^{\infty} \exp (- μ x) d x} = \frac{1}{μ}

(4)

The gamma interaction parameters, such as linear attenuation coefficients (cm^-1), HVL (in cm), TVL (in cm), and mean free path (in cm) are calculated using the above Eqs. (1)-(4).

The total molecular cross section, σ_m [milli barn], is computed from the following equation using the values of mass attenuation coefficients [(µ/ρ)_c]

σ_{m} (E) = (\frac{1}{N}) {(\frac{μ (E)}{ρ})}_{c} \sum_{i} n_{i} A_{i},

(5)

where n_i is the number of atoms of i^th element in a given molecule, (µ/ρ)_c is the mass attenuation coefficient of compound, N is the Avogadro's number, and A_i is the atomic weight of element i. The effective (average) atomic cross section for a particular atom in the compound σ_a [milli barn] is estimated using the equation,

σ_{a} = \frac{σ_{m}}{\sum_{i} n_{i}} = \frac{(\frac{1}{N}) {(\frac{μ (E)}{ρ})}_{c} \sum_{i} n_{i} A_{i}}{\sum_{i} n_{i}} .

(6)

The effective electronic cross section, σ_e [milli barn], is computed from the mass attenuation coefficient (µ/ρ)_i of the i^th element in the given molecule using following equation:

σ_{e} = (\frac{1}{N}) \sum_{i} {(\frac{f_{i} A_{i}}{Z_{i}}) {(\frac{μ}{ρ})}_{i}},

(7)

where f_i is the fractional abundance (a mass fraction of the i^th element in the molecule) and Z_i is the atomic number of the i^th element in a molecule. Finally the Z_eff is estimated as

Z_{eff} = \frac{σ_{a}}{σ_{e}} .

(8)

The effective electron density (N_e), the expressed interms of number of electrons per unit mass is closely related to the effective atomic number. For an element, the electron density is given by N_e = NZ/A[electrons/g]. This expression can be generalized for a compound using

N_{e} (g^{- 1}) = \frac{N}{\sum_{i} n_{i} A_{i}} Z_{eff} \sum_{i} n_{i} .

(9)

II.2. Secondary radiation during the interaction of gamma/X-ray

During the interaction of gamma/X-rays with the medium, it degrades their energy and produces secondary radiations through the different interaction process. The quantity of secondary radiations produced in the medium and energy deposited/absorbed in the medium is studied by calculating buildup factors. In the present work, we have estimated energy exposure build up factors (B_en) using GP fitting method^[20-22]. We have evaluated the G-P fitting parameters (b, c, a, X_k, and d) for different stent alloys using the following expression, which is based on Lagrange’s interpolation technique

P_{Z_{_{eff}}} = \sum (\frac{\prod_{Z' \neq Z} (Z_{eff} - Z)}{\prod_{z \neq Z} (z - Z)}) P_{z},

(10)

where lower case z is the atomic number of the element of known G-P fitting parameter, P_z is adjacent to the effective atomic number (Z_eff) of the given material of known whose G-P fitting parameter, $P_{Z_{eff}}$ is desired, and upper case Z are atomic numbers of other elements of known G-P fitting parameter adjacent to Z_eff. GP fitting parameters (b, c, a, X_k, and d) for elements adjacent to Z_eff are provided by the standard data available in literature^[23]. The computed G-P fitting parameters (b, c,a, X_k, and d) were then used to compute the EABF in the energy range 0.015MeV-15MeV up to a penetration depth of 40 mean free path with the help of G-P fitting formula, as given by the equations

B (E, X) = 1 + \frac{b - 1}{K - 1} (K^{X} - 1) for K \neq 1,

(11)

B (E, X) = 1 + (b - 1) X for K = 1,

(12)

K (E, X) = C X^{a} + d \frac{\tanh (\frac{X}{X_{K}} - 2) - \tanh (- 2)}{1 - \tanh (- 2)} For p e n e t r a t i o n depth (X) \leq 40 mfp,

(13)

where X is the source-detector distance for the medium in mean free paths (mfp), b is the value of build-up factor at 1mfp. K(E,X) is the dose multiplication factor, and b, c,a, X_k, and d are computed G-P fitting parameters that depend on attenuating medium and source energy.

II.3. Relative dose

The radial dependence of dose is e^-μrB/r², where μ denotes the linear attenuation coefficient for the appropriate photon energy, and B is the exposure build-up factor. Dose distribution at a distance r is given by [21]

D_{r} = D_{0} e^{- μ \times r} B / r .

(14)

Here D₀ is the initial dose delivered by the point gamma ray emitter. The relative dose distribution at a distance r is

\frac{D_{r}}{D_{0}} = e^{- μ \times r} B / r .

(15)

Hence the relative dose distribution can be evaluated using estimated exposure build-up for different penetration depths.

III. Results and discussions:

The calculated mass attenuation coefficient for Stent alloys is graphically represented in Fig.1. Mass attenuation coefficient values for Stent alloys are large in the low energy region and decrease progressively. Variation of the mass attenuation coefficient with incident photon energy can be explained on the basis of different photon interaction processes such as the photoelectric process, Compton scattering, and pair production. In the low energy region, the mass attenuation coefficient is observed to be high due to the dominant photoelectric interaction. In the high energy region, Compton scattering becomes dominent and depends linearly with atomic number. Hence, mass attenuation coefficient value becomes the minimum value.

Figure 1

Variation of total mass attenuation coefficient with photon energy for Stent alloys

The calculated HVL, TVL, and MFP for different incident energies of Stent alloys are graphically represented in Fig. 2. All these parameters increase progressively with an increase in photon energy up to few keV (250 keV) due to dominant photo electric absorption, beyond this energy these parameters increase slowly (up to 6 MeV) with energy due to Compton scattering. After 6 MeV, these parameters remain almost constant with energy due to pair production. The variation of effective atomic number with energy for stent alloys are as shown in Fig.3. The effective atomic number values for Stent alloys are large in the low energy region (due to photo electric effect) and decrease progressively, thereafter increases and becomes constant for high energy (due to pair production). Similar variations are observed in the case of effective electron density and is shown in Fig. 4.

Figure 2

(Color online) Variation of penetration thickness (mean free path, HVL and TVL) with energy of photon for Stent alloys

Figure 3

Variation of effective atomic number with energy of photon for Stent alloys

Figure 4

Variation of effective electron density with energy of photon for Stent alloys

The variation of energy exposure build up factor (EBF) for stent alloys are as shown in Fig. 5. It is observed that EBF increases up to the E_pe and then decreases. Here, E_pe is the energy value at which the photo electric interaction coefficients matches with Compton interaction coefficients for a given value of effective atomic number (Z_eff). The variation of EBF with energy is due to the dominance of photoelectric absorption in the lower end and dominance of pair production in the higher photon energy region. Similar variations are observed in cases of variation of relative dose with energy and are shown in Fig. 6. The variation of relative dose with mean free path for stent alloys at 0.5 MeV for different thickness of the medium (1, 2, 5, 10 mm) are as shown in Fig. 7. Relative dose values increase with an increase in mean free path. As mean free path increases, thickness of the interacting material increases, which results in an increase of scattering events. Hence, it results in large relative dose values.

Figure 5

(Color online) Variation of exposure build up factors with energy of photon for Stent alloys

Figure 6

Variation of Relative dose with energy of photon for Stent Alloys

Figure 7

Variation of Relative dose with penetration depth for Stent Alloys

The variation of relative dose with thickness of the medium for stent alloys at 0.5MeV for different mean free paths (1, 5, 10, 20, and 40) are as shown in Fig. 8. The computed relative dose decreases with an increase in the thickness of the medium. As the thickness of the medium increases, energy of incident gamma/x-ray decreases due to scattering or absorption. Hence, it results in a decreasing trend of relative dose with an increase in thickness of the medium.

Figure 8

Variation of Relative dose with thickness of the medium for Stent Alloys

Coronary stents are small, expandable tubes made up of alloys that are implanted in the arteries. To test the gamma and X-ray radiation compatibility of Ti-Ta-Hf-Zr alloys for coronary stent applications, we have compared gamma/ X-ray radiation interaction parameters such as mass attenuation coefficient, mean free path, HVL, TVL, and effective electron density of Ti-Ta-Hf-Zr alloys with that of Arteries. This comparison is as shown in Table 1. Among the studied alloys, gamma, and X-ray interaction parameters for alloy 5 [Ti-55Ta-12Hf-7Zr-26 (wt.%)] and alloy 6 [Ti-60Ta-10Hf-5Zr-25 (wt.%)] are nearly close to that of arteries. Thus, among the studied Ti-Ta-Hf-Zr alloys, Ti-55Ta-12Hf-7Zr-26 and Ti-60Ta-10Hf-5Zr-25 are gamma and x-ray radiation compatible than the other studied alloys. The alloys Ti-55Ta-12Hf-7Zr-26 and Ti-60Ta-10Hf-5Zr-25 have added properties such as radiation compatibility including high elastic admissible strain, high mechanical strength, and excellent biocompatibility [18]. Hence we may suggest that, among Ti-Ta-Hf-Zr alloys, these alloys are the best materials for coronary stent applications.

Comparison of total mass attenuation coefficient, mean free path, HVL, TVL and effective electron density of stent alloys with that of Arteries and veins.

Energy (MeV)		0.01	0.02	0.05	0.1	0.2	0.5	1	2	5	10
μ/ρ (cm ² /g)
	Arteries	16.492	2.365	0.328	0.182	0.138	0.096	0.070	0.049	0.031	0.023
	Alloy 1	180.262	56.974	5.033	2.953	0.546	0.116	0.063	0.043	0.038	0.042
	Alloy 2	169.852	56.175	4.944	2.757	0.515	0.114	0.063	0.043	0.037	0.041
	Alloy 3	167.193	54.601	4.787	2.543	0.481	0.111	0.062	0.043	0.037	0.040
	Alloy 4	158.086	52.841	4.611	2.296	0.442	0.107	0.062	0.043	0.036	0.039
	Alloy 5	137.080	50.683	4.404	2.082	0.409	0.105	0.061	0.043	0.035	0.038
	Alloy 6	142.943	48.311	4.175	1.842	0.371	0.101	0.061	0.042	0.035	0.036
λ cm
	Arteries	1.19E-1	7.80E-1	2.87E+0	3.86E+0	4.81E+0	6.81E+0	9.32E+0	1.33E+1	2.18E+1	2.98E+1
	Alloy 1	4.69E-4	1.48E-3	1.68E-2	2.86E-2	1.55E-1	7.26E-1	1.34E+0	1.96E+0	2.25E+0	2.03E+0
	Alloy 2	5.22E-4	1.58E-3	1.79E-2	3.22E-2	1.72E-1	7.80E-1	1.42E+0	2.06E+0	2.39E+0	2.18E+0
	Alloy 3	5.60E-4	1.72E-3	1.96E-2	3.68E-2	1.95E-1	8.45E-1	1.51E+0	2.18E+0	2.56E+0	2.36E+0
	Alloy 4	6.31E-4	1.89E-3	2.16E-2	4.35E-2	2.26E-1	9.29E-1	1.62E+0	2.33E+0	2.78E+0	2.58E+0
	Alloy 5	7.77E-4	2.10E-3	2.42E-2	5.12E-2	2.60E-1	1.02E+0	1.74E+0	2.50E+0	3.01E+0	2.83E+0
	Alloy 6	7.94E-4	2.35E-3	2.72E-2	6.16E-2	3.06E-1	1.12E+0	1.86E+0	2.67E+0	3.27E+0	3.11E+0
HVLcm
	Arteries	1.72E-1	1.13E+0	4.14E+0	5.56E+0	6.94E+0	9.82E00	1.35E+1	1.93E+1	3.14E+1	4.30E+1
	Alloy 1	3.25E-4	1.03E-3	1.16E-2	1.98E-2	1.07E-1	5.03E-1	9.31E-1	1.36E+0	1.56E+0	1.41E+0
	Alloy 2	3.62E-4	1.09E-3	1.24E-2	2.23E-2	1.19E-1	5.41E-1	9.83E-1	1.43E+0	1.66E+0	1.51E+0
	Alloy 3	3.88E-4	1.19E-3	1.36E-2	2.55E-2	1.35E-1	5.86E-1	1.04E+0	1.51E+0	1.77E+0	1.63E+0
	Alloy 4	4.37E-4	1.31E-3	1.50E-2	3.01E-2	1.56E-1	6.44E-1	1.12E+0	1.62E+0	1.92E+0	1.79E+0
	Alloy 5	5.38E-4	1.46E-3	1.68E-2	3.55E-2	1.81E-1	7.06E-1	1.20E+0	1.73E+0	2.09E+0	1.96E+0
	Alloy 6	5.50E-4	1.63E-3	1.88E-2	4.27E-2	2.12E-1	7.76E-1	1.29E+0	1.85E+0	2.26E+0	2.16E+0
TVLcm
	Arteries	3.97E-1	2.59E+0	9.55E+0	1.28E+1	1.60E+1	2.26E+1	3.10E+1	4.43E+1	7.23E+1	9.89E+1
	Alloy 1	1.08E-3	3.42E03	3.87E-2	6.59E-2	3.57E-1	1.67E+0	3.09E+0	4.51E+0	5.18E+0	4.69E+0
	Alloy 2	1.20E-3	3.64E-3	4.13E-2	7.41E-2	3.97E-1	1.80E+0	3.27E+0	4.75E+0	5.50E+0	5.02E+0
	Alloy 3	1.29E-3	3.95E-3	4.50E-2	8.48E-2	4.48E-1	1.95E+0	3.47E+0	5.03E+0	5.90E+0	5.42E+0
	Alloy 4	1.56E-3	4.35E-3	4.98E-2	1.00E-1	5.19E-1	2.14E+0	3.72E+0	5.38E+0	6.39E+0	5.94E+0
	Alloy 5	1.79E-3	4.84E-3	5.57E-2	1.18E-1	6.00E-1	2.35E+0	4.00E+0	5.75E+0	6.93E+0	6.52E+0
	Alloy 6	1.83E-3	5.41E-3	6.26E-2	1.42E-1	7.04E-1	2.58E+0	4.29E+0	6.15E+0	7.52E+0	7.17E+0
Nel g^-1×10²⁵
	Arteries	0.600	0.580	0.390	0.340	0.330	0.330	0.330	0.330	0.340	0.360
	Alloy 1	1.366	1.622	1.032	1.482	1.487	1.404	1.301	1.265	1.279	1.286
	Alloy 2	1.342	1.606	1.020	1.444	1.447	1.353	1.246	1.212	1.228	1.237
	Alloy 3	1.322	1.591	1.008	1.406	1.408	1.298	1.187	1.158	1.174	1.184
	Alloy 4	1.295	1.568	0.991	1.357	1.356	1.232	1.121	1.092	1.113	1.124
	Alloy 5	1.258	1.114	0.961	1.297	1.292	1.162	1.050	1.025	1.047	1.059
	Alloy 6	1.227	1.124	0.936	1.239	1.230	1.084	0.986	0.964	0.987	0.999

References

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Microstructure, surface characterization and long-term stability of new quaternary Ti-Zr-Ta-Ag alloy for implant use

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