The cellular response of osteocytes to commercially pure titanium (α) and its alloys (α + β and β) has been tested in a culture media, and the results have been supplemented by analyses from various techniques such as inductively coupled plasma atomic emission spectroscopic (ICP-AES) analysis, X-ray photoemission spectroscopy (XPS), scanning electron microscopy (SEM), metallography, and electrochemical measurements. These results have been correlated with respect to the presence of various alloying elements in these alloys to qualify them for human application. The newer β alloys have been examined for their potential use as implants. These results serve as a preliminary baseline to characterize the best alloy system for a comprehensive long-term investigation.

Corrosion resistant and biocompatible metallic biomaterials are composed of the metals titanium, niobium, tantalum and their alloys, followed by cobalt-based alloys and lastly the stainless steel grades.13 Commercially pure titanium and its alloys are known for their use in medical application owing to their good corrosion resistance, biocompatibility, and bioactivity in the human body.4 Titanium is readily oxidized during exposure to air and electrolytes to form oxides and suboxides (especially firmly adherent TiO2 covering of variable thickness), hydrated complexes, and aqueous cationic species. These oxides and hydrated complexes act as barriers between the titanium surface and the surrounding tissues. If the barrier layer gets disrupted, it can be reformed easily, leading to spontaneous repassivation. However, toxicity can still be manifested in the human body by the release of various alloying elements which can elicit a potential allergic reaction, localized systemic tissue toxicity, and a carcinogenic response. Following implantation, the prosthesis should thus have the ability to exhibit an appropriate host response in order to be biocompatible with the tissues.5,6 

Commercially pure titanium started gaining importance for use as implants in the 1970s due to its high corrosion resistance and tissue tolerance.7 However, its usage became limited, owing to its low strength and unfavorable wear properties. Later, commercially pure titanium was replaced by Ti-6Al-4V, which possesses higher strength and lower elastic modulus over the commercially pure titanium.79 Recently, studies have shown high levels of vanadium and aluminum in the tissues surrounding the Ti-6Al-4V alloy as an implant, under conditions of high wear such as knee and modular head components.7 There are also concerns regarding the toxicity of aluminum and vanadium released from the material.1013 β titanium alloys, composed of β stabilizers such as molybdenum, zirconium, niobium, tantalum, and iron, possess lower elastic modulus and better strength as compared to α + β alloys such as the Ti-6Al-4V alloy and are the newer materials of interest in contemporary implantology.7,1419 

The chemical composition of an implant determines the characteristics of its surface. These surface characteristics include surface charge,20 surface free energy,21 presence of grain boundaries,22 chemistry and stoichiometry of surface ions,23 and the crystallinity of surface salts24 and oxides.25 These surface features influence the interaction of an implant with its biological environment and affect cellular properties such as cell morphology, proliferation, differentiation, and adhesion.2631 It thus becomes extremely significant to correlate the presence of various alloying elements in an implant to cellular adhesion. In the present work, osteoblast cell response of various crystallographic forms of titanium alloys such as α, α + β, and β, varying in the compositions of alloying elements, has been investigated and correlated with the electrochemical results. Three newer β alloys, TiOs, Ti15Mo, and TMZF, which are considered to be superior in their material properties for implant applications, have been studied, and results obtained have been compared to those for α and α + β alloys.

Cell culture and expansion

Titanium alloys Ti1, Ti2, Ti64, TiOs, Ti15Mo, and TMZF (composition listed in the Table) were used for the present investigation. Available cuboidal and cylindrical rods were cut to expose cross section areas of 1.828 mm2 for Ti1, 1.19 mm2 for Ti2, 5.682 mm2 for Ti64, 12.7 mm2 for TiOs, 8.026 mm2 for Ti15Mo, and 20.052 mm2 for TMZF underwater jet to prevent work hardening and to retain the microstructure. The specimens were finished and polished with different grades of SiC grit papers and polished over the diamond abrasive wheel to a 0.25-micron finish. They were then washed with detergent, double distilled water, and acetone, and dried.

Table

Compositions of the alloys studied*†

Compositions of the alloys studied*†
Compositions of the alloys studied*†

Roughness measurements were performed on the samples to determine the Ra, Rq, and Rt using a Veeco32 (Wyko Inc, Greenback, TN) roughness measurement equipment and an optical sensor with a ×2.0 objective. Finally, they were boiled in acetone separately for 10 minutes and individually wrapped in sterile sterilization foils for wet heat sterilization. All the wrapped samples were sterilized at 121°C at 15 pounds of pressure for 30 minutes. A color indicator was used to ascertain the sterilization effectively. The sterilized samples were subsequently inoculated into the 12-well culture plates, and cell culturing, expansion, and fixing protocol was followed as described below.

Cell culturing, expansion, and fixing protocol for bone cells

Cell Culturing

A human fetal osteoblast cell line (hFOB 1.19 ATCC CRL-11372) was used as a starting material in osteocyte culturing and expansion. Work was performed in a bio-safety cabinet disinfected with 90% ethanol 15 minutes prior to manipulations and was run under ultraviolet light for 15 minutes.

Cell-specific culture media (10% fetal bovine serum, 3 mg/mL G418 in 1∶1 DMEM/F-12) were kept in a 37°C water bath before beginning the thawing process for the cell lines.

Once the media was ready, the cells were removed from cryogenic storage and placed in a double boiler water bath to ensure getting them completely thawed in 5 minutes.

A 25 cm2 working area (T-25) cell culture flask was labeled in the hood with appropriate culture information (cell type, date, passage #). Once the cells were completely thawed, they were transferred to the hood. Contents of the cryotube were then pipetted down the culture surface side of the T-25 flask using a sterile, disposable 5-mL glass pipette. Following that, a 10-mL pipette was used to pour 10 mL of nutrient media along the side of the (T-25) flask. Culture flasks were lid tightened and were laid down by their flat surface and rocked gently to homogenize the cell mixture. Flasks were finally placed in an incubator at 34°C with a relative humidity of 5% CO2.

Media Change

Change of media was performed in accordance with the ATCC recommended media turnover time (2–3 days), keeping in mind the cell density within the flask. Culture media for media change was kept in a water bath at 37°C for 20 minutes to allow it to stabilize at that temperature. Subsequently, the culturing media and cell culture flasks were transferred to the bio-safety cabinet under complete disinfection.

Following strict asepsis and using a new pipette for each flask, all media was aspirated out of the culture flask(s). Newer culture media was finally compensated back to the culture flasks and kept for incubation.

Cell Expansion

Once the cell culture area appeared 80% confluent, it was expanded.

Culture media was kept in a water bath at 37°C for 20 minutes, along with 0.25% trypsin EDTA left out at room temperature (from frozen), to let them attain appropriate temperatures for use and finally transferred to the bio-safety cabinet for aseptic procedure.

Using a Pasteur pipette the culture flask contents were aspirated, and using another 10-mL pipette correct amounts of trypsin EDTA contents were poured down along the side of the culture flasks. Flasks were laid flat by their bottom and were rocked to allow complete and homogeneous detachment of cells. They were incubated for 10–15 minutes for complete detachment. Once the cells were detached completely, the trypsin/cell solution contents were added to new culture flasks, and additional cell culture media was added up to the working volume of the new flask.

Cell Seeding and Differentiation

Plate preparation

A 12-well sterile tissue culture polystyrene plate was prepared in a bio-safety cabinet using sterile techniques. Metal samples were then placed in the plate wells (as shown in Figure 1) using sterile forceps. Plates were prepared in triplicates.

Figure 1.

Twelve-well sterile tissue culture plate with samples in position.

Figure 1.

Twelve-well sterile tissue culture plate with samples in position.

Close modal
Cell seeding

A 1.5-mL solution of detached trypsin/cells having a cell density of approximately 500 cells/mm2 was added to each well over the metallic samples. Final volume of each well was made to 4 mL by adding 2.5 mL of culture media over the added solution. Plates were kept for incubation at a temperature of 37°C with 5% CO2 and 98% relative humidity. Following the seeding, plates were examined every 24 hours for any signs of contamination.

Cell sampling

On day 1, 14, and 21, 1.5 mL of media from the sterile plate well was transferred to the sterile Eppendorf tube and stored at 4°C for inductively coupled plasma atomic emission spectroscopic (ICP-AES) analysis.

Cell Fixing

Fixation was done to stabilize the cell membrane and to prevent cell degradation. Media from each well was aspirated using a sterile glass pipette. A 1.5% solution of freshly prepared glutaraldehyde was buffered with 0.01 M sodium cacodylate to obtain the working solution ratio of 1∶0.25. The buffered solution mixture was poured into each well, covering the metallic samples, and allowed to set for 2 minutes. The excess solution was aspirated off and the samples were allowed to harden for 4 hours. The samples were air dried for later viewing and microscopy. Cell count analysis was performed on day 1, 14, and 21 using a 100 and 400 micron mesh under a scanning electron microscope, and an average value was reported.

Electrochemical measurements

Nondestructive electrochemical impedance spectroscopic (EIS) measurements and cyclic potentiodynamic polarization measurements were performed for titanium alloys at 37°C. Titanium alloy grades Ti1, Ti2, Ti64, TiOs, Ti15Mo, and TMZF of compositions mentioned in the Table were used for the electrochemical measurements. Available cuboidal and cylindrical rods were cut to expose cross section areas of 0.855 cm2 for Ti1, 1.0 cm2 for Ti2, 1.5525 cm2 for Ti64, 1.3270 cm2 for TiOs, 0.4869 cm2 for Ti15Mo, and 2.7606 cm2 for TMZF for use as working electrodes.

A 3-electrode cell assembly consisting of titanium alloy as the working electrode, platinum wire as the counter electrode, and a saturated calomel electrode as the reference electrode were used. A 450-mL solution of PBS (0.137 M sodium chloride, 0.0027 M potassium chloride, and 0.01 M phosphate buffer) of pH 7.4 was taken for the electrochemical testing of the alloys. PAR Potentiostat 273A and 1255 FRA were employed to perform the potentiodynamic polarization and EIS tests.

X-ray photoelectron spectroscopic measurements

Surrogate samples prepared for all the titanium alloys (as mentioned in the Table), specifically for X-ray photoelectron spectroscopy (XPS) were initially treated in an identical fashion to the electrochemical testing and then removed from the PBS solution and dried.

The titanium alloys were allowed to passivate up to a potential of 1V, which was chosen as a common potential for all alloys from the polarization curve for the passive film formation. The alloys were then analyzed by XPS for the detection of the oxides formed on their surfaces. XPS measurements were performed on a Kratos HSi system with an Al Kα monochromatic source. Wide scans were acquired with 160 eV pass energy, and individual lines were measured with 40 eV pass energy. Depth profiling was performed with a MiniBeam I ion gun with 4 keV argon ions and an emission current of 10 mA.

Scanning electron microscopic and metallographic measurements

Scanning electron microscopic (SEM) measurements for various titanium alloys were performed using a FEI Quanta 600 microscope with a tungsten filament cathode of spot size 4 and voltage ranging from 10 to 40 kV. The measurements were performed in the environmental mode under low vacuum.

Metallographic analyses were performed using an Olympus PMG-3 optical microscope and PAX-it (MIS, Villa Park, Ill) software.

The roughness parameters, Ra (average arithmetic), Rq (average root mean square), and Rt (maximum peak to valley height) of α, α + β, and β titanium alloys such as Ti1, Ti2, Ti64, TiOs, TMZF, and Ti15Mo were measured and have been plotted in Figure 2 (a and b). The average values of Ra, Rq, and Rt for all the alloys were found to be 0.09, 0.125, and 2.5 µm, respectively. These values are within the range of the roughness parameters reported in the literature for a maximal cell attachment.3235 

Figure 2.

Roughness measurements (a and b) and total cell count analysis (c) for the titanium alloys.

Figure 2.

Roughness measurements (a and b) and total cell count analysis (c) for the titanium alloys.

Close modal

The average total cell count values for the alloys (shown in Figure 2c) follow the order TiOs>Ti15Mo>TMZF>Ti1 = Ti2>Ti64. On the basis of these results, it can be said that β alloys show a higher tendency towards cell adherence, followed by α and α + β alloys. This observation, however, does not indicate the vital cell count of the cells on the alloys. More experiments need to be performed to study the effect of leaching of alloying elements which could affect the cellular vitality and osteointegration.

ICP-AES analyses

ICP-AES analyses for all the alloys were performed in triplicate (plates 1, 2, and 3) after 1, 14, and 21 days of cell culturing to know the amounts of alloying elements leached from each alloy.

Figure 3 shows the change in the amounts of alloying elements leached in addition to the change in amounts of calcium and phosphorus (from the nutrient media) with time for the 3 plates studied for all the alloys. The amounts of these elements as plotted in these curves reveal the results obtained under the detectable limit of the instrumentation. The amounts of the elements plotted in Figure 3 have been normalized to the areas of the samples, volumes of the solutions within the well, and the controls used.

Figure 3.

Inductively coupled plasma atomic emission spectroscopic (ICP-AES) analyses showing the amounts of alloying elements leached from the alloys, in addition to calcium and phosphorus from the nutrient media, as a function of time.

Figure 3.

Inductively coupled plasma atomic emission spectroscopic (ICP-AES) analyses showing the amounts of alloying elements leached from the alloys, in addition to calcium and phosphorus from the nutrient media, as a function of time.

Close modal

Figure 4 shows the average profiles for various common elements in these alloys such as molybdenum and iron (calculated from the results obtained in triplicate) which as a function of time, in addition to calcium and phosphorus coming from the nutrient media. On comparing the overall calcium profile for all alloys over 3 weeks in Figure 4, it is found that the amount of calcium has decreased, suggesting its uptake either for bone mineralization or the formation of calcium phosphates (apatites) on the alloy surface owing to an adsorption process. The amount of phosphorus, on the other hand, has decreased on the whole, thereby indicating an increase in the calcium to phosphorus ratio available for bone mineralization. This result might suggest that calcium and phosphorus may be actively participating in bone metabolism. The molybdenum and iron profiles reveal an increase in their amounts with time, suggesting an active leaching of iron and molybdenum from TMZF, Ti15Mo, and TiOs β alloys, which might be detrimental to the cellular health as discussed in the later section on SEM.

Figure 4 and 5.

Figure 4. Inductively coupled plasma atomic emission spectroscopic (ICP-AES) analyses showing average profiles for various common elements in the alloys as a function of time, in addition to calcium and phosphorus coming from the nutrient media. Figure 5. Impedance plots (Nyquist and Bode) for TMZF alloy in PBS solution at 37°C.

Figure 4 and 5.

Figure 4. Inductively coupled plasma atomic emission spectroscopic (ICP-AES) analyses showing average profiles for various common elements in the alloys as a function of time, in addition to calcium and phosphorus coming from the nutrient media. Figure 5. Impedance plots (Nyquist and Bode) for TMZF alloy in PBS solution at 37°C.

Close modal

Electrochemical analyses

Figure 5 (a and b) shows the impedance plots obtained at different immersion times for a TMZF β alloy. After performing circuit modeling on the data obtained, the curves were found to follow a 2-time constant circuit model shown in Figure 6. All other titanium alloys followed the same circuit model. The circuit model shown is based on the duplex structure of an oxide film formed on titanium alloys, composed of an inner barrier layer and an outer porous layer. The barrier layer is compact, having a high resistance, whereas the porous layer contains microscopic pores. Rs, Rp and Rb represent the solution, porous layer, and barrier layer resistance, respectively. Cb is the capacitance of the barrier layer, and CPEp is the capacitance of the porous layer which is prepresented by a constant phase element to account for the porous nature of the porous outer layer. It has been suggested36,37 that the hydrated phosphate ions are adsorbed on hydrated titanium oxide with the release of water as:

Figure 6.

Equivalent electric circuit used to simulate titanium alloy-PBS interface.

Figure 6.

Equivalent electric circuit used to simulate titanium alloy-PBS interface.

Close modal

The porous outer oxide layer can accommodate the adsorbed ions in the oxide film matrix, and in the presence of calcium ions, stable bone-like structures (apatite) are formed, which can increase the biocompatibility of the implant.38 The ICP-AES calcium and phosphorus profiles also suggest a similar result by their active uptake from the solution for apatite formation. The culturing/ICP-AES and electrochemical measurements were performed independent of each other for generating these preliminary data, and it is intended as a next step to perform in situ cell culturing with the electrochemical measurements.

Figure 7 (a through f) shows the cyclic potentiodynamic polarization curves obtained for titanium alloys in PBS solution at 37°C. The corrosion current densities for these alloys follow the order Ti15Mo>TiOs>TMZF>Ti64>Ti2>Ti1, and the passivation current densities are in the order Ti15Mo>TiOs>Ti64>Ti2>TMZF>Ti1. Ti15Mo shows the highest and Ti1 the lowest values of both the corrosion and passivation current densities.

Figure 7 and 8.

Figure 7. Cyclic potentiodynamic polarization curves for titanium alloys in PBS solution at 37°C. Figure 8. X-ray photoemission spectrometer (XPS) standard angle scan of titanium alloys.

Figure 7 and 8.

Figure 7. Cyclic potentiodynamic polarization curves for titanium alloys in PBS solution at 37°C. Figure 8. X-ray photoemission spectrometer (XPS) standard angle scan of titanium alloys.

Close modal

XPS analyses

Figure 8 shows the XPS standard angle curves for the presence of various elements, their oxides, and suboxides on the surface of the alloys in the passive region.

The exposed surface of Ti1 showed primarily TiO2, with the 2p3/2 primary peak at 459 eV. Sputtering resulted in spectra that showed larger amounts of lower oxidation states, until only the metallic titanium remains after removal of about 16 nm of material, as shown by the asymmetric lineshape with 2p1/2 centered at 454.1 eV. Oxides of intermediate oxidation states are represented by a single broad doublet with binding energy between the metal and +4 oxidation state since there are several bonding contributions playing a role. The exposed surface was 64% TiO2, 18% lower oxidation states, and 17% metallic titanium. The presence of the metallic titanium indicates that the passivating TiO2 layer is sufficiently thin that photoelectrons from the underlying substrate penetrate. The presence of the suboxides indicated that a graded composition exists. The thinnest is shown by the removal of all oxides after 330 s sputtering.

Figure 8 also shows the evolution of the Ti 2p core level during depth profiling of the Ti64 alloy. As with the Ti1 alloy, the spectrum is predominately TiO2, with smaller contributions from the suboxides and metal. Other components of the alloy also show evolving oxidation states during depth profiling. Vanadium and iron are not detectable on the exposed surface, and the aluminum was in an oxidation state similar to the Al2O3, with a binding energy for the Al 2p of 75.7 eV. After removal of 10 nm of material, both vanadium and aluminum in metallic states are visible, although the aluminum remains primarily in the +3 oxidation state (90%). Titanium is approximately 50% metallic and the remainder is TiO2 and suboxides. The passivating layer for the Ti64 alloy is thicker than the Ti1 alloy. After removal of about 30 nm of the material, XPS showed only metallic titanium and vanadium, with the aluminum still partially oxidized. At this depth the composition was similar to the bulk.

The TMZF alloy showed the thickest passivating layer, as determined by the attenuation of the metallic component of the Ti 2p core level. Figure 8 also demonstrates the reduction of the surface from a passivating oxide layer to the metallic substrate after removal of about 30 nm of material during the depth profile. The Ti 2p was 88% TiO2, the Zr 3d was 91% ZrO2 (binding energy 182.8 eV), and the Mo 3d was a mixture of +6 (binding energy 232.2 eV, 34%), +4 (binding energy 229.6 eV, 40%), and metallic (binding energy 227.4 eV, 26%) oxidation states.

Ti2 showed a similar profile and oxidation states compared to the Ti1 except for a thicker oxide film compared to Ti1.

Ti15Mo shows the Ti 2p core level during depth profiling. As with the titanium and molybdenum elements, the spectra is predominately TiO2, with smaller contributions from the suboxides and oxides of Mo. Various oxides and suboxides of Mo are present on the surface but only +2 and +6 oxidation states are detectable.

TiOs alloy shows the presence of various oxides and suboxides, primarily TiO2, ZrO2, and suboxides of tantalum. Fe is present in elemental form and no oxide of iron is seen on the surface of the alloy.

Ti1 and Ti2 alloys show the presence of oxides, only of titanium but the β alloys show oxides of various β stabilizing elements as well in addition to those of titanium. The β alloys have also shown a higher total cell count in comparison to other alloys, hence implying that these oxides are playing a crucial role in the cellular processes.

SEM/metallographic analyses

Figure 9a and b shows the scanning electron micrographs and the optical microscopic images of the bone cells on various titanium alloys. The β alloys show a relatively higher cell count, as already shown in Figure 2c, as compared to the α and the Ti64 mixed alloy. The cells on the β alloys appear to be healthy, globular in shape with dark cytoplasmic inclusions (protoplasmic segregation), and the cytoplasm appears dark and swollen. The cells are connected through lamellar projections and are indistinct. The cells on α alloys, on the other hand, appear relatively healthier with long, projected spindle-shaped cell bodies, central protoplasm, and distinct and flattened cytoplasm. These cells are connected to one another through the dendritic lamellar-like projections. The cells over the Ti64 mixed alloy appear long and flat with distinct cellular inclusions.

Figure 9.

(a) Scanning electron micrographs of the bone cells on various titanium alloys. (b) Optical microscopic images of the bone cells on various titanium alloys.

Figure 9.

(a) Scanning electron micrographs of the bone cells on various titanium alloys. (b) Optical microscopic images of the bone cells on various titanium alloys.

Close modal

Ti64 shows the least cell count value with an intermediate corrosion rate among all the alloys and shows an average mass release of 0.0103 mg/mm2 aluminum from ICP analysis after 21 days of testing. XPS analysis shows the presence of titania and alumina on the surface of the alloy. Vanadium, on the other hand, is not detectable on the alloy surface in its oxidized state. The relationship between the oxides present on the surface of the alloy, amount of aluminum ion released, and cell count value needs to be explored further.

For the α Ti1 and Ti2 alloys, the cell count values are higher as compared to the α + β Ti64 alloy. The corrosion rates for these alloys are lower than that of the Ti64 alloy and, in fact, are lowest out of the group, which also includes the β alloys. The XPS analyses of these 2 α alloys show the presence of titania, and nothing was observed from the results of the ICP analyses.

The β alloys TiOs, TMZF, and Ti15Mo show the highest cell count values, as compared to the α and α + β alloys. Of the 3 β alloys studied, TMZF shows the lowest corrosion rate and the lowest cell count value. ICP analysis shows an average mass release of 0.0039 mg/mm2 zirconium. XPS analysis reveals the presence of titania, zirconia, and several oxides and suboxides of molybdenum.

TiOs alloy, however, shows a higher corrosion rate and cell count, as compared to TMZF alloy. ICP analysis indicates an average mass release of 0.0013 mg/mm2 iron. XPS results show the presence of titania and various oxides and suboxides of molybdenum.

Ti15Mo alloy shows the highest corrosion rate and an intermediate average cell count among the 3 β alloys investigated. ICP results suggest an average release of 0.002 mg/mm2 molybdenum. Results from XPS reveal the presence of titania and various oxides and suboxides of molybdenum.

Molybdenum profile for Ti15Mo and TMZF conforms to the higher corrosion rate and an average release of 0.002 mg/mm2 molybdenum for Ti15Mo among the two.

Iron profile for TiOs and TMZF is in line with the higher corrosion rate and an average release of 0.0007 mg/mm2 iron for TiOs, compared to 0.0002 mg/mm2 iron for TMZF.

The average calcium and phosphorus profile for all the alloys reveals a decrease in the amounts of these elements, per unit area of the metal surface, compared with the profile of the control. This suggests a consumption of calcium and phosphorus in the biochemical calcium phosphate apatite metabolism or an active uptake of Ca and P by the bone matrix. The metabolism involving calcium and phosphorus may not be only a part of the surface phenomena occurring on the surface of the alloys, and this observation requires further investigation to affirm if the calcium and phosphorus are being utilized as an apatite to seal the outer porous layer of the duplex oxide film formed over the surface of the alloys, as already suggested by impedance measurements, or used by the osteoblasts for their mineralization and matrix formation.

The β alloys demonstrate the highest cell count value and the highest corrosion rate. Various oxides and suboxides of the substitutional elements are formed on the surface of these alloys and these elements are also found to leach out into the test solution.

The α alloys demonstrate an intermediate cell count value. These alloys are found to reveal the least corrosion rate from electrochemical measurements with the presence of titanium oxide as TiO2 on their surface. The mixed α + β alloy Ti64 demonstrates the least cell count value and an intermediate corrosion rate. The oxides formed on the surface of Ti64 are TiO2 and Al2O3. ICP analyses reveal a leaching of aluminum from this alloy.

ICP-AES

inductively coupled plasma atomic emission spectroscopy

SEM

scanning electron microscopy

XPS

X-ray photoelectron spectroscopy

The authors express their sincere thanks to Dr John R. Spear for his valuable guidance in this work. The authors also appreciate the help from Nina Vollmer and Amitabh Tewari towards the completion of this work.

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