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Measurement of Thermal Diffusivity of Bone, Hydroxyapatite and Metals for Biomedical Application Gabriel Peña Rodríguez*‡, Antonio Calderón Arenas*†, Rocío A. Muñoz Hernández*, Suren Stolik*, Alfredo Cruz Orea** and Feliciano Sánchez Sinencio** * Physics Laboratory, Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del IPN, Legaria 694, Colonia Irrigación, México D.F., C. P. 11500, México. ‡ Universidad Francisco de Paula Santander, A.A. 1055, Cúcuta, Colombia. ** Department of Physics, Centro de Investigación y Estudios Avanzados del IPN, A. P. 14740, México D.F., C. P. 07000, México. We present a microstructural study and thermal diffusivity measurements at room temperature in two different sections of bull dense bone, bull bone and commercial hydroxyapatite, the last two in powder form. A comparison was made between these measured values and those obtained from metallic samples frequently used in implants such as high purity titanium and 316L stainless steel. Our results show that the porosity and its orientation in the bone are two important factors for the heat flux through the bone. The hydroxyapatite, in compact powder form, presents a thermal diffusivity value very near to those obtained for the bone samples which give a good thermal agreement between these materials. Finally, one order of magnitude of difference among the thermal diffusivity values of metallic samples and those corresponding values to bone and hydroxyapatite was obtained, this difference being greater in titanium than in stainless steel. (Received June 29, 2000; Accepted October 31, 2000) Stainless steel and titanium are used in odontology and orthopaedia like screws, plates, prothesis, etc. These materials are also used as substrates that will be covered by bioceramics like hydroxyapatite,1 improving the interface biocompatibility of implant with bone tissue. The biomaterials derived from calcium phosphates, have proven to be biocompatible with human bone tissues, which present a composition structure that consists, among others, of bioceramic crystals like hydroxyapatite (HA), which is in the bone in an organic matrix medium. The HA is the most important mineral component of bone tissue, 60 to 70% (by volume) in bone and up to 98% (by volume) in dental enamel.2,3 The study and determination of physical, chemical and biological properties of biomaterials used in implants for medical or dental applications is fundamental from the point of view of the biocompatibility that these materials must present with the tissue which they will replace because of the prolonged contact which they must maintain with alive tissues of the body.2 The thermal diffusivity (α) measures how fast (m/s) heat propagates through each meter (m) of material. Its importance lies in it is a unique value for each material.4 It is know that, α is extremely sensitive to material † To whom correspondence should be addressed e-mail:
[email protected]
microstructure and composition.5,6 Thermal properties in porous materials, depend in addition, on the type of porous structure and its porosity degree.7 Nowadays, this kind of materials has not been studied enough, however, its scientific and technological research are becoming very important in many applications. In this work we report the thermal diffusivity measurements, by means of the photoacoustic (PA) technique in a heat transmission configuration,8,9 of two different sections of bull dense bone, bull bone and commercial HA, the last two in compact powder form. We performed a comparison among them and those values that we obtained from metallic samples frequently used in biomedical applications, like titanium and stainless steel 316L. The microstructure of the samples was studied by means of scanning electron microscopy. Experimental The samples have a disk shape of 1 cm of diameter and thickness between 200 and 239 µm. In table 1 we show the set of the studied samples with their corresponding thickness. The samples 1 and 2 are stainless steel 316L and high purity titanium, respectively. The bone used in making the samples 3-5 comes from the upper part of one of the back legs of a 18 to 20 month old mature male bull. The bone was cleaned of flesh with a scalpel and boiled in
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water for 2 hours in order to remove residual bone tissue and fat. The bone was dried in air for one week at room temperature. After this, it was baked in a microwave oven for 5 minutes in order to eliminate residual humidity. Using a low speed cutter several cuts were realized. Sample 3 was obtained from a longitudinal cut, in the same direction of the bone porosity and sample 4 was obtained from a transversal cut in relation of the porosity direction, Fig. 1. The samples were cleaned in alcohol and then in ultrasonic treatment to remove residual dust. Sample 5 consists of a pill of bull bone powder compressed at 10 tons. This bone powder was obtained from the dust when the dense bone was cut with a fine handsaw. Sample 6 is a pill obtained from commercial HA powder compressed at 10 tons. All the samples were humidity-free stored. Table 1 Type of samples and their thickness. Sample type 1. Stainless steel 316L 2. High purity titanium 3. Bull dense bone (longitudinal cutting) 4. Bull dense bone (transversal cutting) 5. Compressed bull bone powders 6. Compressed hydroxyapatite powders
Thickness µm 239 + 5 200 + 4 232 + 4 239 + 4 203 + 6 227 + 7
photoacoustic cell, Fig. 3. The photoacoustic chamber is connected to a sensitive detector (Bruel & Kjaer microphone). The PA voltage signal obtained is detected by a lock-in amplifier SR-850 (Stanford Research Systems) interfaced to a personal computer, which permits recording of the data (amplitude and phase of the signal) as a function of the modulation frequency.
Fig. 2 Experimental arrangement of the photoacoustic technique for thermal diffusivity measurement: a, laser; b, mechanical chopper; c, mirror; d, sample; e, photoacoustic cell; f, lock-in amplifier; g, computer. (d) (a)
(c)
(b)
Fig. 3 Scheme of the photoacoustic cell in a heat transmission configuration: a, sample; b, photoacoustic chamber; c, detector; d, modulated light beam. Fig. 1 Bull bone photography obtained from upper part of one of the back legs. It is shown in two cuts, sample 3 was obtained from a longitudinal cut and sample 4 was obtained from a transversal cut. The thermal diffusivity measurements were made by means of the PA technique in a heat transmission configuration.8,9 In our experimental setup, shown in Fig. 2, a 100 mW Ar+ ion laser (Omnichrome 543-200 MA) was used as a light source and its monochromatic light beam intensity was modulated at a frequency f by a variable speed mechanical chopper SR-540 (Stanford Research Systems) before it normally impinged on the surface of the sample. The sample was placed on the entrance orifice of the
According to the thermal diffusion model for the photoacoustic effect,10 the signal amplitude and phase as function of the modulation frequency f are given respectively by,9 A=C
1
(1)
f cosh(2 f / f c ) − cos(2 f / f c )
tan( f f c ) −π 2 ∆φ = − atan tanh( f f ) c
(2)
Where C is a constant related to thermal properties and pressure of air inside PA cell, light intensity, geometrical
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characteristics of the cell and thermal and optical properties of the sample. The parameter fc = α/πls2 is named critical frequency. fc represents the modulation frequency for which the thermal diffusion length µ=(α/πf)1/2 is equal to the sample thickness ls. The thermal diffusivity α of the studied sample is obtained by fitting Eq. (1) or (2) to the experimental data of the PA amplitude or phase versus modulation frequency.
In Fig. 4 and 5 we show the experimental amplitude and phase analysis of the photoacoustic signal obtained as a function of the modulation frequency for samples 3 to 6. The fitting curves shown in Fig. 4 represent the best fitting of the Eq. (1) to the experimental data. The fitting curves shown in Fig. 5 represent the best fitting of Eq. (2) to the phase of the experimental data. In Table 2 we show the measured values of the thermal diffusivity for the studied samples. The experimental data of samples 1 and 2 are not included in Fig. 4 and 5 because the frequency range for fitting occurs above 50 Hz. 2.2
Sample Sample Sample Sample
2.0
A m p l i t u d e (mV)
1.8
Sample 3 Sample 4 Sample 5 Sample 6
0.7
0.6
0.5
∆φ (Rad)
Results and discussion
0.8
0.4
0.3
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0.1
0.0 8
10
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16
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20
F r e q u e n c y (Hz)
Fig. 5. PA signal phase versus frequency. The curves indicate the best fitting to the experimental data.
3 4 5 6
Table 2 Critical frequency (fc) and measured values of the thermal diffusivity. Sample Amplitude analysis Phase analysis fc (Hz) α(10–7 m2/s) fc (Hz) α(10–7 m2/s) 21 38 + 2 1 20 36 + 2 2 73 92 + 4 74 93 + 3 2.6 4.4 + 0.1 3 2.6 4.4 + 0.1 3.1 5.6 + 0.1 4 3.0 5.4 + 0.1 2.4 3.1 + 0.1 5 2.4 3.1 + 0.1 2.5 4.0 + 0.2 6 2.5 4.0 + 0.2
1.6
1.4
1.2
1.0
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0.6 8
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F r e q u e n c y (Hz)
Fig. 4 Photoacoustic signal amplitude versus frequency. The curves indicate the best fitting to the experimental data. The microstructure of the samples was studied by means of scanning electron microscopy (SEM, Cambridge 360). In Fig. 6 a microphotography is shown corresponding to sample 3. The bone microstructure in the normal direction to the porosity structure can be observed. Fig. 7 correspond to a microphotograph of the sample 4, in which the bone microstructure in the same direction of the porosity structure can be observed.
Fig. 6 Microphotography by SEM of longitudinal cutting of bull dense bone.
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CEGEPI-IPN through 200154 and 200173 projects. The authors want to thank to Eng. José Antonio García, Eng. Armando Gómez, Eng. Esther Ayala Maycotte and Eng. Marcela Guerrero for their technical assistance. References 1.
Fig. 7 Microphotography by SEM of transversal cutting of bull dense bone. The thermal diffusivity values obtained for dense bone, samples 3 and 4, are larger than that of compact form powder, sample 5 in 42 % and 74%, respectively. This difference in the thermal diffusivity corresponds mainly to the porous structure which is present in samples 3 and 4 and absent in sample 5. The α value of sample 4 is greater by 23% than the sample 3. These results show that the porosity and its orientation are important factors in the flow of heat through the bone. The heat diffusion is remarkably better in the direction of the porosity (transverse cutting) than heat flow corresponding to perpendicular direction (longitudinal cutting). We observe similar α values between the compressed hydroxyapatite powders, sample 6, and the bone samples, samples 3 to 5. These diffusivity values reveal a similar thermal behavior between these materials. Thermal diffusivity measurements of HA coatings in titanium substrates prepared by plasma-spraying report a value of 2.9 x 10-7 m2/s for this bioceramic,11 which is very near to the value that we obtained for the compressed HA powders, sample 6. Finally, we observed a difference of one order of magnitude among the thermal diffusivity of metals, samples 1 and 2, with the other samples. For the case of titanium we observe that the α value is around tree times larger than that of stainless steel 316L. We are shown that the porosity and its direction are important factors in the heat flow through the bone. The similar α values obtained between the commercial hydroxyapatite powders and the bone samples indicate an excellent thermal compatibility between these materials. On the other hand, the α values of titanium and stainless steel 316L show a big difference with those measured in bone which would be important to take into account in biomedical applications, mainly in the titanium case. Acknowledgment This work was partially supported by PIFI program of
P.A. Campbell, H.C. Gledhill, S.R. Brown and I.G. Turnes, J. Vac. Sci. Technol. B, 1996, 14, 1167. 2. D. F. Williams, J. Mat. Sci, 1987, 22, 3421. 3. M. Nagai, Y. Shibuy, T. Nishino, H. Owada, K. Yamashita and T. Umegaki, J. Mat.Sci., 1991, 26, 2949. 4. A. Rosencwaig, “Photoacoustics and Photoacoustic Spectroscopy”, 1980, John Wiley & Sons, New York. 5. C. Vázquez López, A. Calderón, M. E. Rodriguez, E. Velazco, S. Cano, R. Colas and S. Valtierra, Journal of Materials Research, 2000, 15, 85. 6. G. Ziegler and D. P. H. Hasselman, J. Mat. Sci., 1981, 16, 495. 7. A. Calderón, J. J. Alvarado Gil, Y. G. Gurevich, A. Cruz Orea, I. Delgadillo, H. Vargas and L. C. M. Miranda, Phys. Rev. Lett., 1997, 79, 5022. 8. M. V. Marquezini, N. Cella, A. M. Mansanares, H. Vargas and L. C. M. Miranda, Means Sci. Technol., 1991, 2, 396. 9. A. Calderón, R. A. Muñoz Hernández, S.A. Tomas, A. Cruz Orea and F. Sánchez Sinencio, J. Appl. Phys. 1998, 84, 6327. 10. A. Rosencwaig and A. Gersho, J. Appl. Phys., 1976, 47, 64. 11. A. C. Bento, D. P. Almond, S. R. Brown and I. G. Turner, J. Appl. Phys., 1996, 79, 6848.
