Temperature dependence of nickel ion release from nitinol medical devices

Abstract

Nitinol exhibits unique (thermo)mechanical properties that make it central to the design of many medical devices. However, nitinol nominally contains 50 atomic percent nickel, which if released in sufficient quantities, can lead to adverse health effects. While nickel release from nitinol devices is typically characterized using in vitro immersion tests, these evaluations require lengthy time periods. We have explored elevated temperature as a potential method to expedite this testing. Nickel release was characterized in nitinol materials with surface oxide thickness ranging from 12 to 1564 nm at four different temperatures from 310 to 360 K. We found that for three of the materials with relatively thin oxide layers, ≤ 87 nm nickel release exhibited Arrhenius behavior over the entire temperature range with activation energies of 80 to 85 kJ/mol. Conversely, the fourth “black-oxide” material, with a much thicker, complex oxide layer, was not well characterized by an Arrhenius relationship. Power law release profiles were observed in all four materials; however, the exponent from the thin oxide materials was approximately 1/4 compared with 3/4 for the black-oxide material. To illustrate the potential benefit of using elevated temperature to abbreviate nickel release testing, we demonstrated that a > 50 day 310 K release profile could be accurately recovered by testing for less than 1 week at 340 K. However, because the materials explored in this study were limited, additional testing and mechanistic insight are needed to establish a protective temperature scaling that can be applied to all nitinol medical device components.

1 |. INTRODUCTION

Nitinol is a commonly used medical device alloy comprised of nickel (Ni) and titanium (Ti). The pseudoelasticity and shape memory features of nitinol enables development of novel products for a wide-range of medical device applications.¹ However, the high Ni content of the alloy (≈ 54.5–57 wt %) gives rise to concerns regarding Ni ion release (i.e. leaching) contributing to clinical pathologies. For example, Ni may cause toxic effects following exposure to high levels² or provoke a systemic allergic response in as much as 16.2 % of the general population at relatively low concentrations.³ The amount of Ni that leaches from a nitinol device is largely dictated by manufacturing parameters (including alloy processing and surface finish) and a variety of environmental factors.^4,5

During processing and shaping at high temperatures (> 500 °C) nitinol develops a thick surface oxide layer.⁶ While the oxide layer is comprised primarily of titanium dioxide, subsurface Ni-rich phases are also present and are susceptible to releasing Ni both into the peri-implant environment and systemically following implantation.^7,8 Because the oxide layer of a treated surface is generally much thinner and more uniform than after thermal exposure, significantly decreased Ni release rates, as well as higher voltage breakdown potentials, have been observed following surface treatment.^4,9 For example, wires may be chemical etched by treatment with hydrofluoric acid and nitric acid followed by aging in boiling ultrapure de-ionized water to remove surface Ni. This process has been shown to improve electrochemical stability and corrosion resistance relative to native wires.¹⁰ Most nitinol-based medical implants are finished with an electropolish process that improves its corrosion resistance by removing the thick thermal oxide layer and imparting a relatively thin, uniform, and defect-free titanium dioxide surface.¹¹

To evaluate the susceptibility of a nitinol medical device component to Ni ion release, in vitro testing is often conducted. This testing typically involves static immersion in a physiologically-relevant electrolyte for an extensive time period (≥ 60 days) with frequent sampling.¹² While this testing provides a means to evaluate Ni leach from devices, it is unclear whether the results are indicative of in vivo release, which may be influenced by dynamic loads,^13,14 and/or the presence of inflammatory cells.¹⁵ Thus, current Ni ion release evaluations require relatively lengthy time periods, and it is unclear if the results of are representative of the release characteristics in the use environment. Recently, an in vitro test method has been developed for accelerating metal ion release from medical devices using elevated temperature and reactive oxygen species.¹⁶ Accelerated testing under aggressive conditions can potentially expedite device development and reduce the resources required to demonstrate the metal ion release will not pose an unacceptable risk to patients. However, there is a need to establish the extent to which the aggressive conditions accelerate ion release, such that the results of the testing can be interpreted in a clinically relevant context.

In this study, we evaluate the prospect of using temperature to increase the rate of Ni ion release from nitinol medical device components. To do so, we probe the impact of elevated temperature on Ni ion release from nitinol wires with a range of surface finishes. These data served as the basis to discern a time scaling factor for each distinct temperature and material (i.e. surface finish). The temperature dependence of the scaling factor was then probed in the context of two common empirical models for temperature dependent rates, the Arrhenius and $Q_{10}$ temperature coefficient equations. Next, we illustrated the application of these relations to reduce the time required to evaluate Ni ion release from nitinol devices. Finally, we discuss the need to obtain more data and elucidate the mechanisms governing Ni ion release from nitinol devices to establish statistically rigorous bounds on the scaling factor. Thus, the approach could be applied generally to nitinol devices in the future, which would allow for significant reduction in test duration, while ensuring the Ni release estimates remain conservative.

2 |. MATERIALS AND METHODS

2.1 |. Nitinol wires

Straight annealed nitinol wires (diameter = 0.5 mm) manufactured in conformance with ASTM F2063¹⁷ having three different finishes, chemically etched, amber oxide, and black oxide, were purchased from a commercial source (Memry Corporation). After acquiring the wires, a portion of the CE wire stock underwent an electropolishing treatment (Able Electropolishing). Thus, nitinol wires with four distinct surface oxides were evaluated in this study: electropolished (EP), chemically etched (CE), amber oxide (AO), and black oxide (BO). Because the details of wire processing and surface treatments are proprietary, we have conducted additional testing to characterize the final surface oxides of the wire samples.

To acquire depth profiles of elemental composition for the different nitinol finishes, wire samples were sent to Evans Analytical Group Laboratories (Sunnyvale, CA) for analysis using Auger electron spectroscopy (AES). A PHI 670 Auger Nanoprobe with an argon ion beam source was used to obtain Auger spectra. The sputter rate of 82 Å/min was used for depth profiling. To determine the sputter rate of the ion beam, an SiO₂ wafer was used. Therefore, all thickness measurements are with respect to SiO₂. The oxide thicknesses were determined by the distance between location of the maximum in the oxygen concentration and the location where the oxygen concentration decayed to one-half of the maximum value. Auger depth profiles were acquired from one location for each nitinol surface finish. Thus, while these data provide a detailed description of the chemical composition of the oxide layer, they are limited to a single location on the surface.

To provide a more general assessment of the overall quality and inter-sample variability of the final oxide layers, we have also conducted complementary potentiodynamic polarization testing in accordance with ASTM F2129¹⁸ on six samples for each of the four surface finishes. For this testing, Interface 1000 potentiostats (Gamry) with graphite carbon rod counter electrode and saturated calomel electrode (SCE) reference electrode were used. Samples were first mounted onto holders using fast drying silver paint (Ted Pella). The cut wire ends and portion of the wire having silver paint were further insulated with MICCROstop (Tolber Chemicals). Phosphate buffered saline (PBS) test solutions were de-aerated by nitrogen bubbled through at 150 cc/min for 30 min. The samples were then immersed in the PBS and the open circuit potential (OCP) was monitored for 1 hr. The OCP at the end of 1 hr was recorded as the rest potential, $E_r$. The samples were then subjected to potentiodynamic scans to a vertex potential of 1000 mV vs. SCE and back to the rest potential at a scan rate of 1 mV/sec. The scan was reversed when either the vertex potential was reached or the current density exceeded 25 mA/cm². The occurrence of pitting corrosion was inferred if the current density on the forward scan exhibited a two-decade increase at (near) constant potential, that is, breakdown potential, $E_b$. Pitting was confirmed in all samples that met this criterion through microscopic inspection.

2.2 |. Ni ion release

To characterize the time and temperature dependence of Ni ion release for each surface finish we employed the methods described in ASTM F3306.¹² First, the wires were cut into 1.6 cm lengths and the ends were capped with MICCROstop (Tolber Chemicals). The wires were subsequently submerged in 2 ml of PBS (FLB661, Fisher Scientific) and maintained at temperatures of 310, 325, 340, and 360 K. At prescribed time points of 1, 2, 4, 7, 14, 21, 28, 35, 42, 49, 54, and 63 days, the wires were transferred into a new container containing fresh PBS. After removal of the wires, the PBS media was diluted in a 1:5 ratio with 2 vol %/2 vol % hydrochloric acid/nitric acid (Optima grade, Fisher Scientific) prior to analysis with inductively coupled plasma mass spectrometry (ICP-MS). The concentration of Ni in each container was measured using an Xseries 2 ICP-MS (Thermo Scientific) in kinetic energy discrimination mode with 3.55% He, 30 ms dwell time, 0.02 AMU separation, and standard resolution. Sample injection was normalized using 10 ppb ¹¹⁵In as an internal standard.⁵⁸Ni and 60^Ni isotopes were quantified with respect to a Ni standard (ICP grade, Ricca) with a limit of quantification of 50 ppt (50 pg/ml). For each condition (temperature and surface finish), the immersion testing and chemical analysis were repeated in triplicate.

2.3 |. Data analysis

The Ni ion release procedure described above yielded the amount of Ni released as a function of time $\left(t\right)$, temperature $\left(T\right)$, and surface finish. To determine the extent that release rate is enhanced due to elevated $T$ we employed the following approach for each surface finish. First, we assume that the mechanisms governing Ni release result in self-similar release kinetics at all $T$. In other words, we assume that there is a time scaling with temperature, $\sigma \left(T\right)$, such that, at any $T$, the amount of Ni released over time, $M(T,t)$, is a function of only a scaled time, $\sigma \left(T\right)t$, that is, $M(T,t)=f\left(\sigma \right(T\left)t\right)$. Based on this assumption, $\sigma \left(T\right)$ values relative to the value at $T_0=310\mathrm{K}$, that is, ${\varphi }_i=\sigma \left(T_i\right)/\sigma \left(T_0\right)$, can be determined based on the Ni release profiles for each combination of elevated $\mathrm{T}$ and surface finish.

To account for the experimental variation at each time point, a standard bootstrap method was employed. This involved first generating synthetic data sets by randomly assigning Ni release values based on the observed mean and standard deviation at each experimental time point. Next, we define a new quantity ${\xi }_i$ as the scaling between an elevated $T_i$ and the next lowest temperature, $T_{i-1}$, that is, ${\xi }_i=\sigma \left(T_i\right)/\sigma \left(T_{i-1}\right)$. For each adjacent pair of $T$, the optimal value of $\xi$ was determined based on maximization of the overlap between the data sets. This procedure was repeated a large number $\left(n=1\times {10}^5\right)$ of times for each surface finish, which allowed the mean and standard deviation of ${\xi }_i$ to be specified. Finally, the ${\varphi }_i$ between adjacent $T$ were renormalized relative to the reference $T_0=310\mathrm{K}$, that is, ${\varphi }_i=\prod _{j=1}^i{\xi }_j$. We note that while ${\varphi }_i$ potentially could have been solved for directly based on the data, using the data from adjacent $T$ maximizes the time frames, and therefore the number of data points, that overlap for each best fit value of ${\xi }_i$, providing a more robust fit.

3 |. RESULTS

To establish the characteristics of the final surface oxide layer for the nitinol wires used in this study, we conducted both chemical depth profiling using AES and potentiodynamic polarization testing. While details of the results of this testing, including the composition profiles and polarization scans, are provided as supplemental information, a summary is provided in Table 1. We note that potentiodynamic polarization testing assesses pitting corrosion, and therefore, will not necessarily correlate to Ni ion release. Thus, the results of this testing are provided for reference only. As expected, materials with a final surface treatment following thermal exposure (i.e. EP and CE), displayed relatively thin oxide layers with no apparent enrichment of Ni at or near the surface. While the oxide thickness of the AO material was enhanced (87 nm), no enrichment of Ni at the surface was observed. However, the BO material not only exhibited an increase in Ni concentration in the primarily TiO₂ surface layer, but also the profiles suggest a subsurface mixed oxide layer with Ni, Ti, and O in approximately equimolar quantities.

TABLE 1.

Summary of oxide layer characterization for each of the four wire surface finishes. Both the oxide layer thickness from AES depth profiling and the range and median values of rest $E_{\mathrm{r}}$ and breakdown $E_{\mathrm{b}}$ potentials observed during potentiodynamic polarization testing are provided. Note that all voltages are vs. SCE

Surface finish	Thickness (nm)	Er (mV) [min, median, max]	Eb (mV) [min, median, max]	Eb-Er (mV) [min, median, max]
EP	12	[−161, −126, −90]	[489, ≥1000, ≥1000]	[616, ≥1111, ≥1161]
CE	12	[−89, −74, −53]	[440, 555, ≥1000]	[503,639, ≥1072]
AO	87	[−80, −62, −43]	[386, 534, 631]	[452,594, 680]
BO	1564	[−296, −261, −225]	[360, 468, 497]	[591,729, 766]

Based on the results of the oxide layer characterization, one would anticipate the amount of Ni release will tend to increase with oxide thickness.^4,19 Roughly consistent with this trend, the results of our Ni release testing for each of the four surface finishes and four temperatures (T) are shown in Figure 1 in terms of cumulative Ni release over time. Inspection of the figure reveals that while three of the surface finishes (EP, CE, and AO) exhibited fairly comparable release behavior at 310 K, the cumulative release over 63 days followed this trend with values of 0.068 ± 0.015, 0.108 ± 0.008, and 0.237 ± 0.168 μg/cm², for the EP, CE, and AO material, respectively. Conversely, BO material exhibited significantly enhanced Ni release compared to the other surface finishes with a 63-day cumulative Ni release of 21.124 ± 0.426 μg/cm².

FIGURE 1.

Results of Ni release testing of nitinol wires at four different temperatures (310, 325, 340, and 360 K) prepared using four different surface finishing methods: (a) EP = electropolish, (b) CE = chemical etch, (c) AO = amber oxide, and (d) BO = black oxide. The data points and error bars represent the mean and standard deviation of the measurements at each time point, respectively

While the Ni ion release measurements at 310 K could potentially be used to infer a maximum exposure dose of Ni deriving from these materials, extensive testing was required to assess the maximum Ni release rates. For example, the maximum weekly release in AO material was not observed until the fourth week of testing. Thus, we have also explored the potential of using temperature $\left(T\right)$ to accelerate these types of aging studies on nitinol. The results of testing of the same surface finishes at elevated $T$ are also shown in Figure 1. As expected, increasing $T$ resulted in an increase in the rate of Ni release for all surface finishes, with two exceptions. Single observations in the day 28 measurements in AO material at 310 K and day 1 measurements in CE material at 325 K that were uncharacteristically high and low, respectively, resulted in high variability and inverted the expected trend in mean cumulative release for time points at and beyond the anomalous observations at lower $T$.

Although increasing $T$ generally increased the rate of Ni release over the duration of testing, the extent of impact varied with both time $\left(t\right)$ and $T$. This is not surprising considering the release of Ni from nitinol is expected to be highly non-linear. Even in the simplest scenario of diffusion limited release from a homogeneous medium into an infinite sink, at early times one would likely expect the mass of Ni release $\left(M\right)$ to be proportional to $\sqrt{Dt}$, where $D$, the diffusion coefficient, increases with $T^{20}$ However, because the release of Ni from nitinol can be complex and does not necessarily follow a simple diffusion limited release model, we assumed a more general functional form, $M(t,T)=f\left(\sigma \right(T\left)t\right)$, in our (bootstrap) analysis of the data. Thus, the release profile $M\left(t\right)$ at an elevated $T$ can be transformed to the release profile at $T_0=310\mathrm{K}$ by simply multiplying $t$ by the ratio ${\varphi }_i=\sigma \left(T_i\right)/\sigma \left(T_0\right)$.

The scaled Ni release data at $T=310\mathrm{K}$ for each surface finish based on the best-fit ${\varphi }_i$ values determined by the bootstrap method are shown in Figure 2. In all cases, the scaled data readily collapse onto a single well-defined curve, which supports the underlying assumption of $M(t,T)=f\left(\sigma \right(T\left)t\right)$. In the BO material, the analysis suggests that Ni release would exhibit a power-law dependence with an exponent of approximately 3/4 over the first year, after which the release levels out as the rate decays rapidly toward zero. This is in contrast to the other three surface finishes, which are all fairly comparable to one another. The scaled release data for the EP, CE, and AO data are characterized not only by significantly reduced Ni release compared to the BO material, but also a significantly different power law dependence with an exponent of approximately 1/4 over the first one to 2 years. In all three cases, this exponent increases at later times, albeit to different values. This suggests a similar release rate limiting mechanism among these three surface finishes, which is fundamentally different from the BO material, at least over the first year following exposure to the media. At longer times, which correspond to the highest T = 360 K, the exponents increase to approximately 1/2 for the CE and AO materials, which suggests a transition to Fickian type release kinetics. However, the EP material exhibits a more substantial increase in the exponent, which exceeds one at the longest T=310 K equivalent timeframes. Based on the data available it is unclear if these transitions are due to either or both the longer (equivalent) timeframes or the elevated T of the testing. We note that while the two anomalous observations in the CE and AO material do not substantively impact the mean values shown in the figure, they have a significant impact on the uncertainty. For reference, we have included the equivalent plots shown in Figure 2 that arise if these two observations are omitted from the analysis as part of the supplemental information.

FIGURE 2.

Results of the time scaling analysis. Best-fit scalings $\left({\varphi }_i\right)$ were used to transform Ni release observations at 325, 340, and 360 K to 310 K for each surface finish (EP = electropolish, CE = chemical etch, AO = amber oxide, and BO = black oxide). The data points and error bars represent the mean and standard deviation of the measurements at each time point, respectively, for both Ni release (y-axis) and time at 310 K (x-axis). Note that the time scaling varies with material and temperature; therefore, even though the test conditions were identical, the range of scaled time will not be consistent between different nitinol materials

Once the discrete time scalings ${\varphi }_i$ have been established for each $T$, it is instructive to probe the impact of $T$ quantitatively for each surface finish. Specifically, we explore the extent to which $\varphi \left(T\right)$ follows Arrhenius behavior by plotting $\varphi$ as a function of inverse $T$ in Figure 3. Visually, three of the surface finishes characterized by relatively low levels of Ni release (EP, CE, and AO) appear to exhibit Arrhenius-type behavior, where the logarithm of the scaling factor decays linearly with inverse $T$. While our analysis suggests the BO material is consistent with these observations at low $T$, the Arrhenius-type behavior associated with the other surface finishes increasingly overpredicts the scaling factors determined for the BO material as $T$ increases (inverse $T$ decreases). To quantify the extent to which our observations are consistent with Arrhenius-type behavior, we enforce $\varphi =1$ at $T_0=310\mathrm{K}$, which yields the following relationship:

$$ln\varphi =\frac{E}{R}\left[\frac{1}{T_0}-\frac{1}{T}\right],$$ (1)

where $E$ and $R$ are the activation energy and gas constant, respectively. We then fit the observations to determine an optimal $E$ value for each surface finish. The results of this fitting are summarized in Table 2. Note that the EP, CE, and AO materials are all comparable with $E\approx 80-85\mathrm{k}\mathrm{J}/\text{mol}$ and are well fit by the model in Equation 1 with $R^2\approx 1$. However, the BO material exhibits a much lower $E$ value with a reduced quality of fit.

FIGURE 3.

Arrhenius plots of the scaling ratio $\varphi$. Three of the surface finishes (i.e., EP = electropolish, CE = chemical etch, and AO = amber oxide) exhibit a linear relationship between ln $\varphi$ and 1/T. The fourth surface finish, BO = black oxide, deviates from linearity, suggesting the activation energy, E, in Equation 1, is not constant over the T range shown. The data points and error bars represent the mean and standard deviation of the best fit $\varphi$ values determined by the bootstrap method. For reference, the temperature coefficient model in Equation 2 is shown with $Q_{10}=2$

TABLE 2.

Results of fitting Equations 1 and 2 to the mean $\varphi$ values determined using the bootstrap method as a function of T

Surface finish	E (kJ/Mol)	R2 (Equation 1)	Q10	R2 (Equation 2)
EP	84.1	0.995	2.69	0.986
CE	79.8	0.997	2.41	0.996
AO	85.0	1.000	2.55	0.997
BO	57.3	0.945	1.87	0.918

An alternative model that is often used to describe the temperature dependence of the rate of change in a biological or chemical system is a $Q_{10}$ temperature coefficient,^21,22 This empirical approach assumes the increase in rate of change is a constant factor, $Q_{10}$, for every 10° increase in $T$. If we again enforce $\varphi =1$ at $T_0=310\mathrm{K}$, this implies:

$$ln\varphi =\frac{T-T_0}{10}ln{Q}_{10}.$$ (2)

We note that Equation 2 is simply a rough approximation of the Arrhenius relationship given in Equation 1, which is only valid provided the range of T considered is relatively small. However, often Equation 2 is applied under the assumption of $Q_{10}=2$, which implies a specific E value in the corresponding Arrhenius relationship, at times in the absence of data to support this value. Thus, we feel it is instructive to compare our results to this model. For reference, we have included the $\varphi \left(T\right)$ relationship implied by the model with $Q_{10}=2$ in Figure 3. This comparison illustrates that, on average, the rate of Ni release scales more rapidly with increasing $T$ than this model predicts, with the exception of the BO material. The results of fitting the data in Figure 3 to Equation 2 are given in Table 2 for comparison to the Arrhenius model results. As expected, the best-fit $Q_{10}$ values for the EP, CE, and AO materials are comparable in the range of 2.41 to 2.69 and the data are reasonably well fit by the model $\left(R^2\ge 0.986\right)$. However, for BO material, the quality of fit is significantly reduced with a best-fit $Q_{10}=1.87$.

4 |. DISCUSSION

While often the risk associated with Ni ion release from nitinol medical devices is minimized by implementing surface finishing processes, such as electropolishing, to remove the thermal oxide that develops during tempering, this is not always possible or necessary. Thus, it is critical to demonstrate that Ni ion release will not pose unacceptable risk to patients. As part of this risk evaluation, patient exposure to Ni ions is routinely estimated based on extended immersion testing (≥ 60 days) under physiologically relevant conditions (310 K).¹² For example, in this study, the maximum average daily release observed at 310 K was 0.047 ± 0.004, 0.052 ± 0.006, and 0.021 ± 0.005 μg/cm² for the AO, CE, and EP material, respectively, over the duration of the testing. These levels would compare quite favorably to proposed toxicological limits for systemic exposure to Ni (≈ 0.5 μg/kg bw/day) for typical patient body weights (bw) and medical device surface areas,^7,8,23 Similarly, maxima in weekly release rates of 0.11 ± 0.15, 0.068 ± 0.007, and 0.037 ± 0.008 μg/cm²/week are, on average, below the migration limits of 0.2 μg/cm²/week for skin penetrating jewelry recommended by the European Union Ni directive for allergy.²⁴ Conversely, the BO material nitinol exhibited significantly enhanced Ni release compared to the other surface finishes with a maximum daily and weekly release rates of 0.88 ± 0.03μg/kg bw / day and 2.96 ± 0.05 μg/cm²/week, respectively. Therefore, BO nitinol specimens would well exceed local per surface area limits prescribed by the European Union Ni directive and likely the systemic exposure limit for devices with surface areas that exceed patient body weight by a ratio of more than about 0.55 cm²/kg, which is quite feasible for many nitinol devices.

While the results of the testing at 310 K imply potential toxicological concerns with BO nitinol in contrast to the other surface finishes, extensive testing was required to estimate a maximum exposure dose for Ni leaching from these materials. Therefore, we explored the potential to use elevated $T$ testing to reduce the time needed to assess Ni release from these materials. Our analysis of Ni release profiles at different $T$ suggest that common surface finishes used in medical devices, that is, EP, CE, and AO, exhibit Arrhenius behavior over the $T$ range of 310 K to 360 K, with activation energies, $E,\approx 80-85\mathrm{k}\mathrm{J}/\text{mol}$. While our analysis suggests the less commonly used BO material is consistent with these observations at low $T$, it is not well characterized by Arrhenius-type behavior over the entire $T$ range explored. Specifically, when $E$ are determined based on linear interpolation between adjacent (inverse) $T$ for the BO material, we find $E$ decays from a value of 81.1 to 36.0 kJ/mol over the $T$ range evaluated. Thus, it appears to be consistent with the other materials only up to around 325 K. Nevertheless, these data suggest that it should be possible to significantly reduce the time needed to establish Ni release rates at 310 K by testing at elevated $T$.

To illustrate the potential benefit of this approach, we conducted a secondary Ni leach study of the BO material at 340 K. However, the sampling frequencies were scaled down relative to those shown in Figure 1 by considering the mean value of $\varphi =8.4$ for this condition. In other words, the sample times covered only about a week instead of 63 days. The results of this testing are shown in Figure 4 as the light blue points. Based on the $\varphi$ value, the observations where then scaled to 310 K and compared the actual measurements made at 310 K. This comparison is also shown in the figure and illustrates that the scaled elevated T observations predict the behavior at 310 K with reasonable quantitative accuracy. We note that the scaled results based on the mean value of $\varphi$ do under-predict the 310 K measurements slightly at intermediate times; however, considering the uncertainty in the scaling factor, they are within the 95% confidence limit on $\varphi$. Thus, the results suggest that abbreviated testing at elevated $T$ can provide reasonable estimates of the response at 310 K, provided the relevant scaling factor $\varphi$ is known a priori.

FIGURE 4.

Example of using Ni ion release measurements at elevated T to predict the release behavior over longer times at 310 K. 12 measurements were made over the course of ≈ 7 days at 340 K on the BO material (light blue). Based on the mean value of $\varphi$ determined for this condition, the results were scaled to the predicted value at 310 K (dark blue). For comparison, the actual Ni release measurements made at 310 K are also shown on the plot (black). The x-axis error bars represent standard deviation in $\varphi$ determined using the bootstrap method (dark blue only). The error bars along the y-axis for Ni release are all within the size of the symbols

The example above demonstrates that it should be possible to significantly reduce the time needed to evaluate Ni ion release from nitinol device components by testing at elevated $T$. However, it is first necessary to determine a time scaling for the specific material and test conditions. While several nitinol materials were probed in this study, it is unclear if these are representative of the breadth of materials resulting from the wide range of manufacturing conditions used in medical device applications. Establishing system-specific parameters for materials derived from all potential nitinol manufacturing routes would be prohibitive. Despite this, it may be possible to define suitable conservative bounds on the $T$ dependence of Ni release. For example, the results shown in Figure 3 suggest that $Q_{10}=2$ may be an appropriately conservative scaling for most nitinol devices when $T$$\le 340\mathrm{K}$. However, because only a limited number of different materials were probed and large uncertainties resulted in the final time scalings due to apparent outliers, a conservative (lower) bound cannot be established with any statistical reliability based on the current data. Nevertheless, with additional data, it should be possible to develop a generally applicable protective time scaling as a function of $T$ by applying the approaches used in this study.

The data requirements to develop a protective lower bound could potentially be reduced, if the mechanism(s) governing Ni ion release and its variation with $T$ and different nitinol materials were better elucidated. For example, the empirical power law release behavior implied in Figure 2 suggests the mass of Ni ion release over time is $\mathrm{M}\left(t\right)\propto t^{\alpha }$, where $\alpha$ is either approximately 1/4 (EP, CE, and AO) or 3/4 (BO) over relevant timeframes. When compared to the expected value of $\alpha =1/2$ for a normal Fickian diffusion process,²⁰ our observed values are consistent with sub-diffusive $(\alpha =1/4)$ and super-diffusive $(\alpha =3/4)$ transport. We note that these observations are potentially underpinned by an array of complex phenomena, including spatial and time dependent chemical and electrical potential gradients from multiple species that derive from the complex microstructure within and beneath the oxide layer. Capturing all of these potential contributions, would be extremely challenging, if not prohibitive. However, these observations can potentially be described phenomenologically using fractional diffusion processes.²⁵ In the Appendix, we provide a demonstration of applying this approach to describe Ni release from nitinol. In the example, we show that $\alpha =1/4$ release behavior can be described by a fractional diffusion equation of the form:

$$\frac{\partial C}{\partial t}=D\frac{{\partial }^{\beta }C}{\partial x^{\beta }},$$ (3)

with $\beta$ equal to 4/3. The resulting analytical solution is not only consistent with $M\propto t^{1/4}$, but also suggests $M\propto c_0\Delta x^{2/3}{D}_0^{1/4}$, where $c_0$ and $D_0$ are the Ni concentration and oxide layer diffusivity, respectively, and $\Delta x$ is the length scale of the microstructure features within the oxide layer that dictate Ni ion transport. If we assume that the $c_0$ and $D_0$ are comparable between the EP, CE, and AO materials, power law fits to the data shown in Figure 2 suggest ratios of $\Delta x$ between CE:EP and AO:EP of 1.7 and 2.9, respectively. This may imply, for example, corresponding differences in the length scale of defects that facilitate Ni ion transport within the oxide layers. Thus, fractional transport processes may represent a promising framework to provide insight into the factors that dictate the release of Ni from the physico-chemically complex oxide layers of nitinol device components.

In addition to discerning the appropriate governing equation(s) to describe Ni release, establishing the $T$ dependence of the coefficients (i.e. transport properties) is also paramount to gaining insight into the rate limiting mechanism and establishing rigorously protective scaling factors and their potential variation. For nitinol materials explored herein, our observations suggest the mass release per unit area $M/A=(\sigma t{)}^{\alpha }$. Further, over the $T$ range of interest, $\sigma$ exhibits mean activation energies, $E$, of ≤ 85 kJ/mol based on an Arrhenius description. In contrast, for diffusion of Ni through ${\text{Ti}\mathrm{O}}_2$, previous observations imply an activation energy of approximately 130 kJ/mol, albeit at much higher $T$²⁶ Thus, one might expect a significant enhancement of Ni release with increasing $T$ relative to our observations if it were rate-limited by Ni ion diffusion through a solid TiO₂ oxide layer. If the corrosion of Ni-rich phases within the oxide layer were the rate limiting factor, one would likely expect a much lower apparent activation energy. For example, although measured at low pH, activation energies for the corrosion of pure Ni have been reported in the range of 35–63 kJ/mol,^27,28 which would imply a smaller impact of $T$ relative to our observations, with the exception of the black-oxide material at high $T$.

Because the complexities of the physico-chemical composition of nitinol oxide layers and the associated phenomena that can impact ion release (e.g. chemical reactions, ion transport, the semiconducting nature of the oxide layer, and structural changes such as oxide hydration and growth), explicitly modeling the salient physics and capturing the $T$ dependence of the relevant material properties would be extremely difficult, if not prohibitive. However, it should be possible to develop protective (i.e. worst-case) models for Ni release as a function of $T$. These models could help to facilitate specification of appropriate scaling factors for Ni release at elevated $T$. These scaling factors would then, in turn, enable a more rapid assessment of in vitro Ni ion release, thereby reducing the resources needed to evaluate the toxicological risk associated with nitinol medical device components.

5 |. SUMMARY

We have probed the impact of $T$ on Ni ion release from nitinol wire manufactured using four different methods, resulting in distinct surface finishes. The resulting wires exhibited surface oxides that ranged from relatively thin (≈12 nm) primarily TiO₂ layers to thick (≈1500 nm), complex mixed oxide surface structures. By optimizing coincidence between profiles from adjacent $T$, we determined best-fit values of a scaling factor, $\varphi \left(T\right)$, for each nitinol material. We find that $\varphi \left(T\right)$ is well characterized by an Arrhenius relationship with comparable activation energies, $E$, in the range of 80 to 85 kJ/mol, for three of the four surface finishes, specifically those that were relatively thin (≤87 nm) and primarily ${\text{Ti}\mathrm{O}}_2$. The thick, black oxide material exhibited a temperature dependent $E$ that decreased from around 80 kJ/mol to 36 kJ/mol over the range of $T$. We also explored the adequacy of the $Q_{10}$ temperature coefficient model to describe our observations. Again, the three thinner oxide materials were comparable and were fit reasonably well by this model with $Q_{10}$ values of around 2.5. As with the Arrhenius relation, $\varphi \left(T\right)$ for the black oxide material was also not well fit by the $Q_{10}$ model. Despite some inconsistencies with these $T$ dependent models, the data and subsequent analysis can be used as a benchmark to establish accelerated aging test conditions, provided the scaling factor, $\varphi$, is established a priori. To demonstrate this potential, we showed that a >50 day 310 K release profile could be accurately recovered by testing for less than a week at 340 K. While it is likely prohibitive to evaluate $\varphi \left(T\right)$ for the range of possible nitinol chemistry and processing, it may be possible to specify a protective lower bound. This will require not only additional testing, but also insight into the transport processes that govern Ni ion release and the $T$ dependence of the transport parameters for these materials.

APPENDIX A: NICKEL LEACHING AND ANOMALOUS DIFFUSION

A simple, one-spatial-dimension mathematical model for nickel leaching consists of an oxide medium which begins at the origin with the spatial coordinate $x$ representing depth into the oxide layer. Since the concentration in the leaching medium is negligibly low (due to its large volume), a zero-concentration boundary condition at the origin is specified. At small timescales the oxide layer thickness is immaterial and a fixed concentration boundary condition at infinity is appropriate. The oxide layer is initially in equilibrium (constant concentration). The flux across the interface at $x=0$ and cumulative nickel leaching are obtained by first calculating the diffusion within the oxide layer. The natural domain of the problem is the half-line $x\in (0,\infty )$. However, extending the domain to the entire real line permits more convenient analysis by way of the Fourier transform. On this domain the initial condition is $c(x,0)=c_0\text{sgn}\left(x\right)$, where $c_0$ is the initial concentration of nickel in the oxide layer, and the boundary conditions $c(\pm \infty , t)=\pm c_0$ are implicit. On this domain the odd parity of the concentration $c(x,t)=-c(-x,t)$ is required to enforce the original boundary condition $c(0,t)=0$. Here, we first review the case of Fickian diffusion using this approach.

A.1 |. Fickian diffusion

In the case of Fickian diffusion the problem is written as a conservation law

$$\frac{\partial c}{\partial t}+\frac{\partial \varphi }{\partial x}=0$$

for concentration $c$ and flux $\varphi$ along with Fick’s law

$$\varphi =-D\frac{\partial c}{\partial x}$$

with diffusion constant $D$. The domain is the quadrant $x\in [0,\infty ),t\in [0,\infty )$ and the boundary conditions are

$$\begin{array}{rr}\hfill c\left(0,t\right)=0,c\left(\infty ,t\right)& \hfill =c_0,\\ \hfill c\left(x,0\right)& \hfill =c_0.\end{array}$$

Extending to the half plane $x\in (\infty ,\infty ),t\in [0,\infty )$ the boundary conditions become

$$\begin{array}{r}\hfill c\left(-\infty ,t\right)=-c_0,c\left(\infty ,t\right)=c_0,\\ \hfill c\left(x,0\right)=c_0\text{sgn}\left(x\right).\end{array}$$

Applying the Fourier transform obtains.

$$\frac{\partial \widehat{c}}{\partial t}=D{k}^2\widehat{c}$$ (A1)

$$\widehat{c}\left(k,0\right)=\frac{2i{c}_0}{k},$$ (A2)

where the hats indicate transformed variables, which are a function of the spatial frequency $k$. This ordinary differential equation yields the solution

$$\widehat{c}\left(k,t\right)=\frac{2i{c}_0}{k}\text{exp}\left(-Dt{k}^2\right).$$

In $k$-space, Fick’s law becomes

$$\widehat{\varphi }=ikD\widehat{c}=-2c_{0}D\text{exp}\left(-Dt{k}^2\right).$$

Applying the inverse Fourier transform obtains

$$\begin{array}{rr}\hfill \varphi \left(x,t\right)=& \hfill -\frac{c_{0}D}{\pi }\int e^{-Dt{k}^2-ikx}dk\\ \hfill =& \hfill -c_0\sqrt{\frac{D}{\pi t}}\text{exp}\left(-\frac{x^2}{4Dt}\right).\end{array}$$

The mass transfer per unit area across the interface is given by

$$\begin{array}{rr}\hfill \frac{m}{A}\left(0,t\right)=& \hfill {\int }_0^t\left|\varphi \left(0,t^{\prime }\right)\right|d{t}^{\prime }\\ \hfill =& \hfill 2c_0\sqrt{\frac{Dt}{\pi }}.\end{array}$$

Here we have the familiar result for Fickian diffusion; mass transfer is proportional to the square root of time.

A.2 |. Anomalous diffusion

The experiments reported here show the concentration in the leaching medium deviates from the expected square-root of time dependence consistent with Fickian diffusion processes. Instead, it exhibits $t^{1/4}$ or $t^{3/4}$ behavior depending on the method of surface treatment. Thus, we seek to develop a simple mathematical model that simulates the anomalous diffusion observed in experiment.

To obtain an anomalous diffusion model, begin in analogy with Equations A-1 and A-2 with the Fourier-domain equation and initial data.

$$\begin{array}{c}\frac{\partial \widehat{c}}{\partial t}=-D_0|k{|}^{\beta }\widehat{c}\\ \widehat{c}\left(k,0\right)=\frac{2i{c}_0}{k},\end{array}$$

where the diffusion constant $D_0$ and fractional diffusion exponent $\beta$ are real and positive. Without the absolute value of $k$, spurious dispersive effects occur in the solution and the implicit boundary condition $c(0,t)=0$ is not satisfied. Solving this system and applying the inverse Fourier transform gives.

$$c\left(x,t;\alpha \right)=-\frac{c_0}{\pi }\int k^{-1}exp\left(-D_{0}t|k{|}^{\alpha }\right)\mathit{\text{sin}}\left(kx\right)dk$$ (A3)

however no closed-form solution exists.

For the subdiffusive case, where $1<\beta <2$, the fractional conservation law²⁹

$$\frac{\partial c}{\partial t}+\frac{\Delta x^{\beta -2}}{\Gamma \left(\beta \right)}\frac{{\partial }^{\beta -1}\varphi }{\partial x^{\beta -1}}=0,$$

is employed. While the traditional conservation law relies on the assumption that the control volume is infinitesimal, the fractional conservation law does not require a limiting process and thus accounts for fine structure within the control volume. Here $\Delta x$ is the characteristic scale of the structure of the oxide layer. In Fourier space the fractional conservation law is

$$\frac{\partial \widehat{c}}{\partial t}+\frac{\Delta x^{\beta -2}}{\Gamma \left(\beta \right)}{(-ik)}^{\beta -1}\widehat{\varphi }=0,$$

which, when combined with Equation A-3 gives

$$\begin{array}{rr}\hfill \widehat{\varphi }=& \hfill \frac{D_0\Gamma \left(\beta \right)}{\Delta x^{\beta -2}}\frac{|k{|}^{\beta }}{{(-ik)}^{\beta -1}}\widehat{c}\\ \hfill =& \hfill \frac{D_0\Gamma \left(\beta \right)}{\Delta x^{\beta -2}}\text{exp}\left[i\frac{\pi \beta }{2}\text{sgn}\left(k\right)\right]\left(-ik\right)\widehat{c}.\end{array}$$

Noting that $-ik$ is the Fourier-domain analog of first-order differentiation allows a return to the spatial domain using the convolution

$$\varphi =\frac{D_0\Gamma \left(\beta \right)}{\Delta x^{\beta -2}}{ℱ}^{-1}\left\{\text{exp}\left[i\frac{\pi \beta }{2}\text{sgn}\left(k\right)\right]\right\}\text{*}\frac{\partial c}{\partial x}.$$

Note that $\beta =2$ recovers Fick’s law, which suggests that this expression is its generalization to the subdiffusive case. Using Equation A-3, this convolution is soluble, yielding the flux expression:

$$\varphi \left(x,t;\beta \right)=\frac{2D_0{c}_0\Gamma \left(\beta \right)}{\pi \Delta x^{\beta -2}}{\int }_0^{\infty }\text{exp}\left(-D_{0}t{k}^{\beta }\right)\text{cos}\left(kx+\frac{\pi \beta }{2}\right)dk.$$

The mass transfer per unit area is given by

$$\begin{array}{rr}\hfill \frac{M}{A}\left(x,t;\beta \right)=& \hfill \left|{\int }_0^t\varphi \left(t^{\prime }\right)d{t}^{\prime }\right|\\ \hfill =& \hfill \frac{2c_0\Gamma \left(\beta \right)}{\pi \Delta x^{\beta -2}}{\int }_0^{\infty }\frac{1-\text{exp}\left(-D_{0}t{k}^{\beta }\right)}{k^{\beta }}\text{cos}\left(kx+\frac{\pi \beta }{2}\right)dk.\end{array}$$

Finally, choosing $\beta =4/3$ and evaluating this expression at the oxide layer interface $x=0$ yields

$$\frac{M}{A}\left(0,t;\frac{4}{3}\right)=\frac{3\Gamma \left(\frac{4}{3}\right)\Gamma \left(\frac{3}{4}\right)}{\pi }{c}_0\Delta x^{2/3}{\left(D_{0}t\right)}^{1/4}.$$

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.