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On the Kinetics of Apatite Growth on Substrates under Physiological Conditions K. H. Prakash,*,† R. Kumar,‡ S. C. Yu,† K. A. Khor,§ and P. Cheang† School of Chemical and Biomedical Engineering, Nanyang Technological UniVersity, 50 Nanyang AVenue, Singapore 639798, Department of Materials Science and Engineering, Rhines Hall, UniVersity of Florida, Florida 32611, and School of Mechanical and Aerospace Engineering, Nanyang Technological UniVersity, 50 Nanyang AVenue, Singapore 639798 ReceiVed August 17, 2005. In Final Form: October 14, 2005 Derived from reaction kinetics, a simple but useful method, based on “apatite forming capacity” or AFC of solutions mimicking blood plasma, is proposed to decipher the rate of calcium phosphate mineralization. Apatite growth rate constants were calculated using this method for a model composite surface varying the volume fraction of synthetic hydroxyapatite (HA) in a polymer matrix. Previously reported data for mineralized surfaces on Ta, Ti, and its alloys are also analyzed similarly and compared. Utilizing the growth rate constant, the bioactivity of the materials was indexed in vitro. Complementarily, semiempirical quantum mechanical calculation (ZINDO method) showed that the interaction of cations with TRIS-hydroxymethyl aminomethane molecules in the solution is stronger than that with the polymer substrate considered, but weaker than hydrated Ti and TiO2 surfaces. This analysis then quantifies for example the extent of polymer inertness and the “bioactivity” of alkali treated Ti. The growth rate constants for the model materials prepared in this work are explained on the basis of localized dissolution of HA, the amount of which simply increases with increasing volume fraction of HA in the composite.
Introduction It is commonplace now to ascertain the bioactivity of a surface from its ability to form an apatitic layer in vitro using simulated body fluid (SBF), as demonstrated by Kokubo et al.1 It has become a popular method owing to its relative ease in terms of experimentation and interpretation. SBF is easily synthesized by dissolving appropriate quantities of reagent grade NaCl, NaHCO3, KCl, K2HPO4‚3H2O, MgCl2‚6H2O, CaCl2, and Na2SO4 into distilled water and buffering the solution at pH 7.4 with TRIShydroxymethyl aminomethane-(CH2OH)3CNH2 and HCl at 37 °C to bring the ionic concentration close to physiological conditions (Table 1). Furthermore, the apatite induced in the presence of SBF on suitable substrates is thought to closely mimic the chemical composition of biological apatite; (Ca,Mg,Na)5-x (HPO4,CO3)x(PO4)3-x(OH,CO3)1-x‚yH2O, where 0 < x < 1.2,3 Testing the bioactivity of metals,4-12 ceramics,13-20 and * To whom correspondence should be addressed. † School of Chemical and Biomedical Engineering, Nanyang Technological University. ‡ University of Florida. § School of Mechanical and Aerospace Engineering, Nanyang Technological University. (1) Kokubo, T.; Kushitani, H.; Kitsugi, S.; Yammamuro, T. J. Biomed. Mater. Res. 1990, 24, 721-734. (2) Dorozhkin, S. V.; Dorozhkina, E. I.; Epple, M. Cryst. Growth Des. 2004, 4, 389-395. (3) Li, P.; Ohtsuki, C.; Kokubo, T. J. Biomed. Mater. Res. 1994, 28, 7-15. (4) Miyazaki, T.; Kim, H.-M.; Kokubo, T.; Ohtsuki, C.; Kato, H.; Nakamura, T. Biomaterials 2002, 23, 827-832. (5) Takadama, H.; Kim, H.-M.; Kokubo, T.; Nakamura, T. J. Biomed. Mater. Res. 2001, 55, 185-193. (6) Takadama, H.; Kim, H.-M.; Kokubo, T.; Nakamura, T. Sci. Tecnol. AdV. Mater. 2001, 2, 389-396. (7) Kim, H.-M.; Takadma, H.; Kokubo, T.; Nishiguchi, S.; Nakamura, T. Biomaterials 2000, 21, 353-358. (8) Kim, H.-M.; Miyaji, F.; Kokubo, T.; Nakamura, T. J. Mater. Sci.: Mater. Med. 1997, 8, 341-347. (9) Jona´sˇova´, L.; Mu¨ller, F. A.; Helebrant, A.; Strnad, J.; Greil, P. Biomaterials 2002, 23, 3095-3101. (10) Ha, S.-W.; Eckert, K.-L.; Wintermantel, E.; Gruner, H.; Guecheva, M.; Vonmont, H. J. Mater. Sci.: Mater. Med. 1997, 8, 881-886. (11) Uchida, M.; Kim, H.-M.; Miyaji, F.; Kokubo, T.; Nakamura, T. Biomaterials 2002, 23, 313-317.
Table 1. Concentration of Different Ions in SBF and in Human Blood Plasma (mmol/L) ion species Ca2+ Na+ K+ Mg2+ Cl- HCO3- HPO42- SO42SBF 2.5 142.0 5.0 human blood 2.5 142.0 5.0 plasma
1.5 1.5
147.8 103.0
4.2 27.0
1.0 1.0
0.5 0.5
polymers21-26 in this way is very popular, but it remains rather qualitative. It is also known that the apatite, which forms via nucleation and growth, has a relatively low solubility product, and therefore, its solubility, specifically in TRIS-buffer and not in water, should be of paramount importance. Another simplification, through assumption, is that the solubility product and the ionic activity product calculated with respect to the formed apatite are generally the same as stiochiometric HA. The reasons for this are (1) lack of control over the composition of the apatite and (2) the crystal structure of biological apatite and stiochiometric HA are similar. (12) Ning, C. Q.; Zhou, Y. Biomaterials 2002, 23, 2909-2915. (13) Khor, K. A.; Li, H.; Cheang, P.; Boey, S. Y. Biomaterials 2003, 24, 723-735. (14) Gu, Y. W.; Khor, K. A.; Cheang, P. Biomaterials 2003, 24, 1603-1611. (15) Shi, D.; Jiang, G.; Wen, X. J. Biomed. Mater. Res. (Appl. Biomater.) 2000, 53, 457-466. (16) Shi, D.; Jiang, G.; Bauer, J. J. Biomed. Mater. Res. (Appl. Biomater.) 2002, 63, 71-78. (17) Ragel, C. V.; Vallet-Regi, M.; Rodriguez-Lorenzo, L. M. Biomaterials 2002, 23, 1865-1872. (18) Leonor, I. B.; Ito, A.; Onuma, K.; Kanzaki, N.; Zhong, Z. P.; Greenspan, D.; Reis, R. L. J. Biomed. Mater. Res. 2002, 62, 82-88. (19) Takadama, H.; Kim, H.-M.; Kokubo, T.; Nakamura, T. Chem. Mater. 2001, 13, 1108-1113. (20) Vallet-Regi, M.; Salinas, A. J.; Roma´n, J.; Gill, M. J. Mater. Chem. 1999, 9, 515-518. (21) Rhee, S.-H. Biomaterials 2004, 25, 1167-1175. (22) Li, S. H.; Liu, Q.; de Wijn, J. R.; Zhou, B. L.; de Groot, K. Biomaterials 1997, 18, 389-395. (23) Leonor, I. B.; Ito, A.; Onuma, K.; Kanzaki, N.; Reis, R. L. Biomaterials 2003, 24, 579-585. (24) Huang, Y.; DiSilvio, L.; Wang, M.; Rehman, I.; Ohthsuki, C.; Bonfield, W. J. Mater. Sci. Mater. Med. 1997, 8, 809-813. (25) Wang, M.; Wang, J.; Ni, J. Biomechanics 2000, 192-1, 741-744. (26) Wang, M.; Yue, C. Y.; Chua, B. J. Mater. Sci. Mater. Med. 2001, 12, 821-826.
10.1021/la0522348 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/08/2005
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In a slightly more rigorous treatment in vivo, the bioactivity index, Ib, of a material is related to the time taken for it to form more than 50% bond with bone upon implantation (100/t0.5bb, bb - bond to bone).27 From this it is rather obvious that the bioactivity index entails the kinetics of apatite formation. The higher the Ib, faster the growth of apatite and more bioactive the material. Although in vitro assessments, which just establish the presence, and if so how much, or absence of apatite, are economical and fast, attempts to study the kinetics of apatite growth is less satisfactory and not thorough enough to be quantitative. Therefore, presently, one has to depend on in vivo studies, which can be time-consuming and uneconomical to assess the bioactivity index of newly developed materials and correspondingly grade them as potentials for implantation. As the apatite layer grows, on most so-called bioactive materials upon immersion in SBF, the ions, predominantly Ca2+ and HPO42- ions, a source for PO43-, gradually decrease in concentration with immersion time till equilibrium is reached. Frequently, in most of the literature pertaining to in vitro bioactivity assessment, a plot of the concentrations measured against immersion time can be found. Such plots yield empirical information on the decrease in concentration, and the level of decrease varies from one material to another. Other than this, it is rather difficult to decipher any useful information on the growth rate from such plots. It is also difficult to compare the reported results because the level of decrease in concentration depends on the geometry of substrate and the ratio of surface contact area (S) to the volume of SBF (V) used. As the volume of SBF used, shape, size, and geometry of the immersed samples are not standardized thus far, it is, at first glance, inappropriate to quantitatively compare the various results. The present work describes a simple method, based on precipitation kinetics, to assess the bioactivity index in vitro and discusses apatite nucleation and apposition onto a substrate. In doing so, it postulates a way to quantitatively link bioactivity to the growth rate constant. It also emphasizes the importance of standardizing in vitro testing parameters, such as, volume of SBF, shape and size of the substrate, and duration of immersion.
Theory and Postulation Growth Rate ConstantsConcentration. The apatite layer, as mentioned in the previous section, grown from SBF is not stiochiometric HA but its structure is similar to HA. Structural and compositional analysis of the apatite layer formed from SBF has also been done extensively by Kim et al.28 It is reported that the Ca/P ratio for the apatite is 1.51 and the lattice constant c is 0.687 nm. The Ca/P ratio for the stoichiometric HA is 1.67 and the lattice constant c is 0.688 nm.29 This indicates that impurity ions are present as substitutions in Ca2+ and PO43- sites of the HA lattice. Moreover, if the deviation from stoichiometry has any effect on the growth of the layer, this effect would be the same in all apatite layers in SBF. Therefore, it is safe to assume that the apatite layer is synonymous to stiochiometric HA, for macroscopic calculation purposes. Also, a complete dissociation of HPO42- ions in SBF into PO43- ions is assumed. The formation of HA can then be expressed as
5Ca2+ + 3PO43- + OH- f Ca5(PO4)3(OH)
(1)
(27) Hench, L. L. Biomaterials 1998, 19, 1419-1423. (28) Kim, H.-M.; Kishimoto, K.; Miyaji, F.; Kokubo, T.; Yao, T.; Suetsugu, Y.; Tanaka, J.; Nakamura, T. J. Biomed. Mater. Res. 1999, 46, 228-235. (29) Narasaraju, T. S. B.; Phebe, D. E. J. Mater. Sci. 1996, 31, 1-21.
From Table 1 and eq 1, 2.5 mmol/L of Ca2+ ions can yield 0.5 mmol/L of HA, whereas 1.0 mmol/L of PO43- ions can only yield 0.33 mmol/L of HA. The concentration of OH- ions, however, does not change much because the pH of the solution is constant throughout the experiment. Thus, the SBF contains an excess of Ca2+ ions compared to PO43- ions to form stiochiometric HA. Therefore, it can be approximated according to reaction kinetics that the rate of apatite growth depends on the rate of consumption of PO43- ions, which is related to its concentration in SBF at any given time by the following rate law:
-
dCp,t ∝ (Cp,t)3 dt
(2)
where, Cp,t is the concentration of PO43- ions in SBF at any given time. Solving eq 2 for Cp,t by integrating it with the initial condition, at t ) 0, Cp,t ) Cp,0 (1.0 mmol/L), yields
1 1 ) + 2Kt Cp,t2 Cp,02
(3)
where K is the rate constant, (mmol/L)-2 s-1. From eq 3, a plot of the inverse square of PO43- ion concentration in SBF after immersion against the immersion time can be fitted with a straight line. Then very simply, the slope of the line gives the growth rate of the apatite layer. Growth Rate ConstantsLayer Thickness. The concentration of PO43- ions in SBF after immersion can also be used to calculate the thickness of the apatite layer formed on the disks. It was observed that the concentration of Na+ ions in SBF continuously increased with time when glass substrates of composition 45SiO224.5CaO-24.5Na2O-6P2O5 (wt %)18 and 20Na2O-80SiO2 (mol %)19 are used. In the case of 26CaO-70SiO2-4P2O5 (mol %) glass, it was observed that the Ca2+ ion concentration decreased gradually after an initial steep increase, whereas the concentration of PO43- ions decreased steeply with immersion time.17 In all of the above three cases, the apatite layer grew in thickness. This suggests that the dissolution of substrate material and growth of apatite layer occurs simultaneously. If this is the case, there are two possibilities: (1) the substrate material dissolves through the pores present in the growing apatite layer and/or (2) the apatite layer does not grow on the periphery of the substrate disks to the extent it does on the top surface so that dissolution could occur from the periphery. In the former mechanism, the dissolution depends on the pore size in the apatite layer as well as the mobility of ions. Leonor et al.18 reported the Na+ ion concentration in SBF had increased by 9 mmol/L in 7 days, which is about 3.5% of Na2O present in the disk. It is not clear whether submicrometer pores in the growing apatite layer17,30 are sufficient to account for this much quantity of dissolution. Moreover, the surface treatments such as grinding and manual cleaning are generally done on the top surface of the disks. Therefore, it can be best approximated that the apatite layer grows only on the top surface of the substrates (A) and not on the whole of the surface area (S) in contact with SBF as a smooth continuous layer and that the density of the apatite layer formed is equal to that of stiochiometric HA. Thus, the thickness of apatite layer, xt, formed at time t on a given area of crosssection, A (in cm2), of the substrate immersed in a predetermined volume of SBF, V (in cm3), may be calculated from eq 4. (30) Yu, S.; Prakash, K. H.; Kumar, R.; Cheang, P.; Khor, K. A. Biomaterials 2005, 26, 2343-2352.
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Figure 1. Surface morphology of pure PEEK, PEEK-10 vol. %HA and PEEK-40 vol. % HA (a, c, and e) before and (b, d, and e) after 28 days of immersion in SBF, respectively.
The molar density of HA, Ω, is 6280 mmol/L
xt )
V Cp,0 - Cp,t ΩA 3
(4)
At the limiting conditions, that is, at t ) 0, Cp,t ) Cp,0, and therefore, x0 ) 0; that is, the thickness of apatite layer before immersion is zero. After immersion, as the layer grows in thickness, Cp,t decreases with time, and at extremely long duration of immersion, Cp,t reaches 0.02064 mmol/L, the equilibrium concentration of PO43- ions in TRIS-buffer, calculated from the solubility product of stoichiometric HA in TRIS-buffer (2.92 × 10-42) at 37 °C and pH 7.3.31 Thus, as t f ∞, Cp,0 - Cp,t ≈ Cp,0 (1.0-0.02064 ≈ 0.9794 mmol/L) or x∞ ) 0.52(V/A) µm, the maximum thickness of the apatite layer that can form on a substrate. Therefore, after any given immersion time, the thickness of the apatite layer that can be formed from the SBF corresponds to the remaining concentration of PO43- ions after that time, Cp,t. We refer to this quantity hereafter as the apatite forming capacity (AFC), symbolized as X, of SBF and it can be expressed as
AFC ≡ X )
Cp,t V 3Ω A
(5)
The physical meaning of AFC is as follows: if the apatite layer thickness on a surface, for example, a disk of diameter 10 mm immersed in 30 cm3 of SBF, after 28 days is 12.500 µm, the layer thickness would have increased another 7.357 µm if the disk was removed after the completion of precipitation. That is, the AFC of SBF has decreased from the initial 19.857 µm (x∞) to 7.357 µm after 28 days of immersion and would eventually become zero after extremely long periods of time. Equation 4 calculates the thickness of apatite layer formed at a given immersion time, t, whereas eq 5 calculates the thickness that can still form after that time, t, up to infinite time. Therefore, it follows that
X ) x∞ - x t
(6)
over the substrate at a fixed rate.32 As such it is rather impossible for the analysis to be carried out using eq 3. However, the thickness of the layer can be measured at different immersion time and hence, the AFC of SBF can be calculated using eq 6. By substituting eq 5 in eq 3 for Cp,t, we get
1 1 ) + 2kt X2 X02
(7)
where k is the rate constant, µm-2 s-1 which is related to K as
k)
K (3ΩA V ) 2
(8)
Methodology The kinetic analysis proposed in this work is tested for validity using a model composite surface composed of polyetheretherketone (PEEK) and 10-40 volume % HA. The material preparation and characterization procedures are detailed elsewhere.30 Composite disks of diameter 10 mm and 3 mm height were immersed in 30 cm3 of SBF at 37 °C for up to 28 days. The immersed samples were carefully dried using a critical point drier (BAL-TEC CPD030, BAL-TEC, Germany) and sectioned delicately using a diamond cutoff wheel. One sample was used to measure the apatite layer thickness from digitized SEM images (cross-sectional view) using image analysis software. For each sample, measurements were made in 30 locations at regular intervals across the micrograph, and the average of the 30 measurements is used in the data analysis (eq 7). In the present work, the concentration of Ca2+ and PO43- ions in SBF after immersion was measured using inductively coupled plasma atomic emission spectrometry (ICP-AES, Thermo-Elemental, IRIS Intrepid, USA). After removing the disks, the solution was filtered using 0.45-µm cellulose acetate membrane and then a drop of concentrated HNO3 was added to stabilize it. The measurements were carried out after calibrating the equipment for Ca2+ and PO43- ions with the respective standard solutions provided by the manufacturer. An average of three measurements was taken in the analysis.
Results The x∞ corresponds to the initial AFC of SBF, X0. Equation 6 is useful when bioactivity assessment is performed under dynamic conditions, where the concentration of ions in SBF does not decrease much with immersion time as it continuously flows (31) Fulmer, M. T.; Ison, I. C.; Hankermayer, C. R.; Constantz, B. R.; Ross, J. Biomaterials 2002, 23, 751-755.
Concentration of Ions in SBF after Immersion. The surface of the pure PEEK and HA/PEEK materials immersed in SBF (Figure 1) shows the surface morphology at selected time frames. As it can be seen, the surface of 10 and 40 vol % HA/PEEK (32) Ra´mila, A.; Vallet-Regi, M. Biomaterials 2001, 22, 2301-2306.
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Figure 4. Representative micrograph used to measure the apatite layer thickness, 40 vol. % HA/PEEK composite after 14 days of immersion into SBF.
Figure 2. Thin-film XRD pattern of (a) 10 and (b) 40 vol. % HA/ PEEK composites immersed in SBF up to 28 days.
Figure 3. FTIR spectra of HA in the used to prepare the composite and apatite layer formed on the surface.
composites are completely covered by a layer after 28 days of immersion in SBF, whereas the pure PEEK surface is not. X-ray diffraction (XRD) and Fourier transformed infrared (FTIR) spectroscopy studies (Figures 2 and 3, respectively) of the layer confirmed that the layer is poorly crystalline carbonatedhydroxyapatite with crystal structure similar to stoichiometric HA. Detailed results of this work are found in our previous work.30 Figure 4 shows a representative cross-section of the apatite layer used to measure the thickness, and Figure 5 shows the variation of Ca2+ and PO43- ions concentration in SBF with immersion time. The Ca2+ ion concentration in SBF increased
Figure 5. Plot of Ca2+ and PO43- ions concentration in SBF against immersion time for different composites.
slightly at the start of immersion (within 1 day), whereas no increase in PO43- ion concentration is observed. Similar trends have been observed when HA is used as a substrate or as coatings on other materials.11,12,14 This could indicate that the HA in the composite may not have dissolved stoichiometrically, but stray CaO and/or calcium containing impurities present in HA did. The dissolution of substrates in SBF is also common for Na2O- CaO-P2O5-SiO2 glasses.17-20 In this study, the measured Ca2+ ions concentrations in SBF were 2.597 and 2.501 mmol/L after 1 day of immersion for 40 and 20 vol. % HA/PEEK composites, respectively. In general, Figure 3 only shows the level of decrease in concentration of ions and it is higher for composites with higher HA content. This qualitatively, if at all, only indicates the bioactivity of the composites increases with increasing HA content in the composite. It is shown, however, in the subsequent sections that more subtle information can be obtained from these experiments. Thickness of Apatite Layer. The apatite layer thickness calculated using eq 4 and measured using SEM (Figure 4) for various composites and duration of immersion is tabulated in Table 2. For samples with low HA content, particularly at shorter immersion time, the apatite layer is not uniform through out the surface or the thickness is not large enough to consistently measure from SEM and thus they are omitted. At short immersion time, the apatite crystals nucleated sparsely where HA is exposed, as evident from Figure 6. With prolonged immersion, they grow into a continuous layer. The layer thickness calculated from concentration measurements, using eq 4, at shorter immersion
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Table 2. Calculated (cal.) and Measured (mea.) Thickness of the Apatite Layer Formed on the Composite Disks thickness of the apatite layer (µm) pure PEEK
10 vol. % HA
time (days)
cal.
cal.
1 3 7 14 28
0.128 0.182 0.304 0.264 0.446
0.138 0.547 2.595 6.131 7.931
20 vol. % HA
mea.
cal.
5.434 ( 0.63 7.158 ( 0.43
0.223 0.851 4.359 6.865 9.545
time represents the thickness of the apatite layer if it were formed uniformly through out the surface at that immersion time. It is also worth mentioning that the sample preparation to measure the apatite layer thickness is demanding and extra care has to be taken as the layer may sometimes delaminate on sectioning. As evident from Table 2, the measured thickness of the apatite layer does not differ much from the calculated thickness. The maximum variation in thickness between the calculated and measured is close to 1 µm, whereas the error in thickness measurement is about 0.65 µm. In addition, assumptions, such as, (1) the layer forms only on the top surface of the substrate and (2) a fully compacted, smooth, and continuous layer is formed, made in deriving eq 4, might be some reasons for the variation. In reality, the layer is not fully compacted and the bulk density of the layer is, therefore, slightly lower than the theoretical density. The microstructural features such as grain boundaries and pores which are in submicrometer size17,30 would also lead to the deviation from theoretically calculated thickness. Growth Rate Constants. The concentration data plotted in Figure 5 are re-plotted as the inverse square of concentration
30 vol. % HA
40 vol. % HA
mea.
cal.
mea.
cal.
mea.
7.821 ( 0.57 9.264 ( 0.48
0.730 2.696 5.876 8.448 11.106
4.905 ( 0.47 7.353 ( 0.43 9.383 ( 0.52 11.592 ( 0.45
1.622 5.156 8.203 9.884 12.550
5.127 ( 0.34 8.060 ( 0.52 10.383 ( 0.51 12.500 ( 0.48
against time in Figure 7. Now the data points for all samples fit well linearly and the slope is proportional to the growth rate constant (K). Similarly, the thickness data is converted into AFC using eq 6 which is then plotted as the inverse square of AFC of SBF against immersion time in Figure 8. The initial AFC of SBF (X0 or x∞) is 19.857 µm for the samples used in this study (A ) 0.7854 cm2 and VSBF ) 30 cm3). Again the data points fit well linearly with a slope proportional to the growth rate constant (k). The growth rate constants obtained from both concentration and thickness measurements are tabulated in Table 3 for comparison. As mentioned earlier, the K values can be converted to k values using eq 8. The conversion factor in this study is 2.433 × 10-3 µm-2 (mmol/L)2. As evident from Table 3, the growth rate constants obtained from both concentration measurements and thickness measurements are comparable to each
Figure 7. Plot of the inverse square of the concentration of PO43ions in SBF against immersion time for different composites. The slope of straight line is proportional to the growth rate constant (K).
Figure 6. Surface morphology of (a) PEEK-10 vol. %HA and (b) PEEK-40 vol. % HA after 1 day of immersion in SBF.
Figure 8. Plot of inverse square of AFC of SBF against immersion time for different composites. The slope of straight line is proportional to the growth rate constant (k).
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Table 3. Growth Constants Obtained from Thickness and ICP Measurements growth rate constants vol. % of HA
K× , (mmol/L)-2 s-1
0 10 20 30 40
0.0077 ( 0.0054 3.75 ( 0.85 5.48 ( 0.50 8.14 ( 0.55 12.02 ( 0.79
10-7
k × 10-9, µm-2 s-1 converted thickness 0.91 ( 0.24 1.33 ( 0.12 1.98 ( 0.13 2.93 ( 0.20
0.76 ( 0.20 1.32 ( 0.28 2.44 ( 0.34 3.26 ( 0.30
other for the given composite, within the error limits. Now, from the K values, it can be quantitatively said that pure PEEK is bio-inert as the absolute growth rate constant is very low. However, the bioactivity, or more aptly, the “mineralizing ability”, based on the growth constant of apatite layer, increased about 3.2 times when the HA content is increased from 10 to 40 vol. % in the HA/PEEK composite. This increase in bioactivity, then, is likely the result of the increase in surface reactivity, modulated by the increase in initial dissolution, with increasing HA content. The differences between the K values obtained from ICP and thickness measurements may be due to (1) the usage of theoretical density of HA, (2) nonstiochiometry and flaky structure of apatite layer,17,30 (3) artifacts induced errors in sample preparation leading to variation in thickness measurement, (4) exclusion of layer formation on the curved surfaces of the samples, and (5) inaccuracy in calculating the initial AFC of SBF (x∞) because the apatite is nonstiochiometric, not exactly HA and its solubility in SBF is different. It is worth mentioning that the solubility of stiochiometric HA in pure TRIS-buffer would be different from that in SBF because of the differences in ionic strength between these two solutions. Therefore, growth rate constants obtained from concentration measurements are more reliable than those obtained from thickness measurements because the inherent errors are comparably lower in the former measurements. However, utilizing the thickness data to perform kinetic analysis is invaluable in cases where the apatite growth takes place under dynamic conditions and the only way to carry out the kinetic analysis is from thickness measurements. The errors listed earlier can, however, be minimized by using appropriate density values of the apatite, solubility of apatite in SBF (for accurate initial AFC) and careful thickness measurements. Indexing in Vitro Bioactivity. According to eqs 4 and 5, the thickness of the apatite layer, and hence the AFC of SBF, depends on the ratio of the volume of SBF to the area of cross-section of substrate. Clearly, for the given volume of SBF, the thickness would be higher for smaller area of cross section and vice versa. However, a literature survey on the in vitro bioactivity test reveals that this ratio varies considerably among different authors. Still, the concentration of PO43- ions in SBF at various immersion times, reported by the same research group, were collected from the literature for Ta,4 Ti,5 Ti6Al4V,6 and Ti15Mo5Zr3Al.7 These results are plotted in Figure 9 after normalizing the concentration values to per unit VSBF/A ratio. The growth rate constants both normalized and absolute are given in Table 4 along with those for HA/PEEK composites. Based on the normalized growth rate constant, K′ the bioactivity of the materials can be arranged in increasing order as follows: Ti6Al4V < 10 vol. % HA/PEEK < Ti < 20 vol. % HA/PEEK < Ti15Mo5Zr3Al < Ta < 30 vol. % HA/PEEK < 40 vol. % HA/PEEK. When the absolute growth rate constant is used, this order completely changes as evident from Table 4. This could not be done here due to the differences in the ratio VSBF/A, and hence the initial AFC of SBF (X0) used in different studies. Until this ratio is universally standardized, the absolute growth rate
Figure 9. Plot of inverse square of normalized AFC of SBF against immersion time. The slope of the straight line is proportional to growth rate constant (K′). Table 4. Growth Constants Obtained from Thickness and ICP Measurements growth rate constants materials
normalized, K′, s-1
ICP-converted k × 10-9, µm-2 s-1
Ib, day-1
10 vol. % HA 20 vol. % HA 30 vol. % HA 40 vol. % HA Ta4 Ti5 Ti6Al4V6 Ti15Mo5Zr3Al7
133.0790 194.5915 288.8040 427.4595 269.1410 184.4715 79.1870 220.7940
0.91 1.33 1.98 2.93 2.99 4.61 1.98 3.83
1.215 1.776 2.636 3.902 2.457 1.684 0.723 2.015
constants cannot be used for bioactivity comparison. Therefore, for the time being, the normalized growth rate constants are used to assess the bioactivity index of the considered materials. Following the arbitrary definition of in vivo bioactivity index, Ib, i.e., 100/t0.5bb, the time taken for 50% of bone bonding, a similar definition is assumed for the time taken to reduce the AFC of SBF by 50%. That is, the time taken for Cp,t to become equal to 0.5 Cp,0 is
t0.5 )
( )
1.5 3Ω 2 100 and Ib ) K′ Cp,0 t0.5
(9)
Thus, the in vitro bioactivity indexes, from the definition, are calculated and given in Table 4. Shi et al.33 immersed NaOH treated Ti coated Ti6Al4V substrates (12 mm diameter and 1.5 mm thickness) into 40 mL of SBF while refreshing the solution every 2 days and reported the changes in Ca2+ and PO43- ions concentration in SBF with time. After the first 2 days (0-2 days), the concentrations of Ca2+ and PO43- ions decreased by 10.7 and 8.11 µg/L, respectively. After the second 2 days (2-4 days), the level of decrease was 16.2 µg/L for Ca2+ and 14.3 µg/L for PO43- ions and after the fourth 2 days (6-8 days), it was 27.1 µg/L for Ca2+ and 27.7 µg/L for PO43- ions. It is easy to note how the level of decrease in concentration of Ca2+ and PO43- ions increased with successive refreshment of SBF and can be explained as follows. At the beginning, the surface is NaOH treated Ti; however, it becomes apatite coated after 2 days. When the SBF was refreshed, the apatite coating becomes the substrate surface and hence more bioactive than the original surface. This fact is evident in Table 4 where the bioactivity of 40 vol. % HA/PEEK composite is more than that of NaOH treated Ti. (33) Shi, J.; Ding, C.; Wu, Y. Surf. Coat. Technol. 2001, 137, 97-103.
Kinetics of Apatite Growth
Langmuir, Vol. 22, No. 1, 2006 275
Discussion Apatite Growth MechanismsBioceramics. Figure 9 indicates that the apatite growth kinetics differs with respect to the surface activity of the substrates. Though it is reported that the SBF is supersaturated with respect to apatite and precipitation occurs through nucleation and growth,28,34 the precipitation is not spontaneous and an active surface is required to induce this process. As such, apatite does not precipitate on materials such as PEEK. Therefore, before analyzing the apatite formation mechanism, it is necessary to calculate the super saturation level (SSL) of SBF with respect to HA. In the absence of active surfaces, that is, for homogeneous nucleation, the driving force for precipitation, ∆GHA, depends on the super saturation level (SSL), which is given by
∆GHA ) -
RT IP IP ln and SSL ) -1 υ ksp ksp
(10)
where IP is the ionic activity product, ksp is the solubility product, υ is the number of ions (3 + 5 + 1 ) 9), R is the universal gas constant, and T is the absolute temperature. The IP is given by
IP ) γCa2+5[Ca2+]5γPO43-3[PO43-]3γOH- [OH-]
(11)
where γ’s are the activity coefficients and [ions] is the concentration of each ion. The activity coefficients are calculated using Debye-Huckel equation and the calculation is detailed as below
log γi ) -
A)
1
Azi2xµ 1 + BRixµ
( )( ) e2
4π ln 10 kT
3/2
FNA 2
1/2
; B)2
+ Cµ
(12)
( )( ) e2
1/2
FNA 2
kT
µ)
1
1/2
;
∑i cizi2
2
(13)
where A and B are temperature-dependent constants, R is the ionic radius (these data are taken from literature for Ca2+, OHand HPO42- 35), C is ionic system specific constant (0.055 in this case), µ is the ionic strength, and the i refers to a particular ionic species. The terms in eq 13 are defined as follows: e is the electronic charge, k is the Boltzman constant, T is the absolute temperature, F is the density (the density of TRIS-buffer is taken same as that of water because of low concentration of TRIS), NA is the Avogadro number, () or) is the dielectric constant (r for TRIS-buffer is about 35 at 37 °C36), c is the ionic concentration, and z is the ionic charge. The ionic strength, µ of SBF is calculated using HPO42- instead of PO43- ions because SBF contains HPO42- ions which dissociate into PO43- ions as the latter are consumed to form the apatite layer. The dissociation constant for the equilibrium HPO42- T H+ + PO43- in water is 6.61 × 10-13,28 high enough not to be an apatite formation rate controlling step; however, it is not known in TRIS-buffer. We have now calculated the ionic activity product with respect to apatite in SBF. Thus, the calculated activity coefficients of Ca2+, HPO42-, and OH- ions using eq 12 are (34) Tsuru, K.; Ohtsuki, C.; Osaka, A.; Iwamoto, T.; Mackenzie, J. D. J. Mater. Sci. Mater. Med. 1997, 8, 157-161. (35) Montastruc, L.; Azzaro-Pantel, C.; Biscans, B.; Cabassud, M.; Domenech, S. Chem. Eng. J. 2003, 194, 41-50. (36) Tamarit, J. L.; Perez-Jubindo, M. A.; de la Fuentez, M. R. J. Phys. Condens. Mater. 1997, 9, 5469-5478.
Figure 10. Schematic representation of the HOMO and LUMO of the Lewis acid, Lewis base, and adduct showing the criteria for the formation of adduct.
0.063, 0.035, and 0.410, respectively, and the IP with respect to apatite in SBF (not in water), calculated using eq 11 and pH of the SBF, is 4.187 × 10-40. From the reported ksp (2.92 × 10-42) of stoichiometric HA in 0.03 M TRIS-buffer at 37 °C and pH of 7.4,31 the SSL is calculated to be 1.434 × 102 (eq 10). Kim et al28 reported the IP with respect to apatite is 5.012 × 10-49 by considering various dissociation constants of H3PO4 into ions in aqueous medium and association constants of Ca2+ ions with phosphates and hydrogen phosphates ions. The ksp of stoichiometric HA in water at 37 °C is reported as 2.34 × 10-59,37 giving a SSL of 2.142 × 1010 in water. Since the ions in SBF are in TRIS-buffer and not in aqueous medium, one should use the data reported for TRIS-buffer and not for water. It seems that the incubation time for homogeneous nucleation, that is, the time taken to form the first stable nuclei of HA, would be very short for a solution with SSL of the order of 1010, according to Posner et al.38 They had reported an incubation time of about 24 h at a SSL of the order of 105 for HA in water. Our calculation shows a SSL of the order of 102 and this could explain the longer incubation time (and stability) of SBF (more than 30 days), as this increases exponentially with decreasing SSL. Also, the apatite growth on substrates such as bioglasses is then due to the initial dissolution of CaO, P2O5, etc., in the glass. This dissolution increases the IP of SBF hence causing continuous apatite precipitation. It then follows that the growth rate constant depends on the extent of dissolution of the substrate. The greater the dissolution, the higher the IP resulting in a higher growth rate constant, as evident from Table 3. The increasing growth rate constant with increasing HA content is then expected from the same reasoning. Apatite Growth MechanismsMetals and Polymers. The growth mechanism of apatite on metals and polymers cannot be considered the same as that on ceramics because the dissolution of substrate, if any, will not increase the IP of SBF with respect to apatite. This warrants a separate treatment and we propose one based on the Lewis acid-base interactions. Since the TRIS molecule is a Lewis base (unshared electron pairs on N and O), it forms adducts with Lewis acids such as Ca2+, Mg2+, etc. Also the most common polymer substrates such as polyetheretherketone (PEEK), polysulfone (PS), and polyamide (PA) and metallic substrates such as Ti and its alloys (which only forms a layer of TiO2 on the surface after NaOH treatment5) contain functional groups that are Lewis bases. Therefore, for the substrate materials to have the ability to form apatite, it should be able to break the cation-TRIS adduct and form adduct of its own with the cation. These interactions can be studied by calculating the energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) (37) McDowell, H.; Gregory, T. M.; Brown, W. E. J. Res. Natl. Bur. Stand. (U.S.) 1977, 81A, 273-281. (38) Boskey, A. L.; Posner, A. S. J. Phys. Chem. 1976, 80, 40-45.
276 Langmuir, Vol. 22, No. 1, 2006
Prakash et al.
Table 5. HUMO and LUMO Energy Levels of Different Molecules Considered and Its Adduct with Mg2+ Ion material
Mg2+
TRIS and adduct
PEEK and adduct
PA and adduct
PS and adduct
HOMO (eV) LUMO (eV)
-12.9
-10.8 +2.6
-8.1 -0.7
-9.3 -1.7
-8.1 -0.5
-16.3 -12.1
-13.3 -10.7
of the different molecules and adducts involved. The formation of adduct between two molecules is favored when the difference between HOMO of the Lewis base and LUMO of the Lewis acid is minimal as well as the HOMO of the adduct is lower than HOMO of the Lewis base and LUMO of the Lewis acid. This is schematically shown in Figure 10. As a start in this direction, we have used the semiempirical quantum mechanical method to calculate the HOMO and LUMO of the molecules and adducts. The Hamiltonians used are ZINDO (Zerner intermediate neglect of diatomic differential overlap) type.39,40 The molecule geometry is optimized using universal force field molecular mechanical method and that geometry of the molecule with nonbonded molecular interactions (e.g., Mg2+) is optimized with a cutoff radius range 0.8-1.0 nm. All of the calculations are carried out using Arguslab.41 Table 5 list the HOMO and LUMO of the molecules considered. The interaction of TRIS molecule with Mg2+ ion is considered instead with Ca2+, because ZINDO method does not include parameters required for Ca element while it includes first row transition elements (Sc, Ti, V, etc.). Since the purpose here is to compare the interaction of TRIS and/or the substrate molecule with cations, we used Mg2+ ion as a cation, which is closest to Ca2+ ions in terms of valence and the chemical properties as both elements are in group II of the periodic table. Still, it would be better, if we have parameters for Ca, as the Mg2+ ions (0.7 nm) are smaller in size compared to Ca2+ ion (0.99 nm).42 Also, the monomer or the repeat unit is considered for the polymer and metal (hydro) oxide layer. The monomer units in PEEK, PA, and PS are given in Figure 11. From Table 5, the HOMO of the adduct TRIS-Mg2+ is lower than that of the PEEK-Mg2+, hence explaining why apatite does not form on PEEK. Similarly, the HOMO for PS-Mg2+
-13.8 -11.5
-12.9 -10.5
Ti(OH)4 (or TiO2) and adduct -11.9 (-10.2) -2.8 (-2.4)
-17.6 (-17.3) -11.4 (-10.7)
and PA-Mg2+ adducts is higher than the TRIS-Mg2+ adduct. Hence, the apatite layer should not form on these polymer substrates. Accordingly, experimental results have shown that both PS43 and PA44 are bio-inert. However, the HOMO of the adduct Ti(OH)4-Mg2+ is lower than TRIS-Mg2+ adduct, and hence, an apatite layer forms. The alkali treated Ti and its alloys form a layer of TiO2,5 which hydrates to form Ti(OH)4 species when in contact with moisture or water.45 The extent of forming TiO2, and hence Ti(OH)4, depends on the alloy composition and this is reflected in the growth rate constant (Table 4). It is worth mentioning that the surface roughness and surface treatment methodology are also found to affect the growth of the apatite layer.8 With this treatment, one can then explain, more specifically, why certain polymers do not induce apatite formation and why certain metals with surface modification do.
Conclusions A method to kinetically analyze apatite formation from physiological media, using both the concentration of PO43- ions in SBF and the thickness of apatite layer on the substrate, after immersion, is proposed. This method utilizes a concept called apatite forming capacity (AFC) of SBF. The validity of method is tested on PEEK/HA composite substrates by measuring the PO43- ion concentration and thickness of apatite layer. The calculated and measured thickness agreed well giving impetus to the validity of this method. Based on the growth rate constant reported for various substrates, it is shown that bioactivity of different materials could be quantitatively indexed in vitro. The growth rate constants calculated for different materials are explained taking into consideration the apatite induction mechanism based on Lewis acid-base reactions for polymers and metals, whereas for ceramic substrates, it is based on the increase in ionic product of SBF due to localized initial dissolution. LA0522348
Figure 11. Monomer units of the polymers.
(39) Zerner, M. C.; Loew, G. H.; Kirchner, R. F.; Mueller-Westerhoff, U. T. J. Am. Chem. Soc. 1980, 102, 589-599. (40) Zerner, M. C. Semiempirical Molecular Orbital Methods, In ReViews in Computational Chemistry II; Libkowitz, K. B., Boyd, D. B., Ed.; VCS Publishers Inc.: New York, 1991; Chapter 8, pp 313-366. (41) Thompson, M. A. ArgusLab 4.0; Planaria Software LLC: Seattle, WA; http://www.arguslab.com. (42) Shannon, R. D. Acta Cryst. 1976, A32, 751-767. (43) Zhang, K.; Ma, Y.; Francis, L. F. J. Biomed. Mater. Res. 2002, 61, 551563. (44) Kawai, T.; Ohtsuki, C.; Kamitakahara, M.; Miyazaki, T.; Tanihara, M.; Sakaguchi, Y.; Konagaya, S. Biomaterials 2004, 25, 4529-4534. (45) Henderson, M. A. Langmuir 1996, 12, 5093-5098.
