醫療植入材的臨床應用中，較常出現下列的問題：第一點、長期植入後，因為材料應力遮蔽，造成健康骨組織流失，甚至有再手術的風險；第二點、植入後，材料生物相容性不夠理想，與骨組織結合穩定度不足；第三點、復原期程長，對於病患生活造成不便。近年來，業界朝多孔性植體材料發展，致力於使力學性質能夠匹配人體骨質，以避免應力遮蔽效應，而多孔表面具備生物誘導與生成的特性，可以與病患的骨組織形成良好的骨質結合，使上述的臨床問題獲得初步的解決。而目前針對不同患部需求所進行特殊設計之仿生多孔材料，更是重要的發展趨勢之一。
本實驗以椎間盤的雙層結構為參考，設計出不同孔隙率雙層同心圓的結構，採用傳統粉末冶金製備多孔鈦，在造孔劑移除方面使用水熱法移除氯化鈉造孔劑，並且參考多孔材料孔隙率與細胞存活率文獻中較佳的孔隙率參數，在試片內圈區域使用高孔隙率的多孔鈦粉末；參考多孔材料孔隙率與機械強度文獻中較合適的孔隙率參數，在試片外圈區域使用低孔隙率的多孔鈦粉末，兩不同孔隙率區域間以可食用的糯米紙隔開，糯米紙將會在燒結以及水熱程序後被消去。於化性方面以XRD、EDS對試片做成份以及晶相分析，物性方面以SEM與AFM分析試片的表面形貌、並以阿基米德原理測量孔隙率、以壓縮試驗分析試片的抗壓強度，檢驗是否達到法規ISO 5833對人體植入材規範的最低強度70 MPa，以及使用奈米壓痕試驗儀的壓痕模式和刮痕模式分別測量試片微硬度及雙層結構的力學表現。在生物相容性測試方面，培養L929纖維母細胞進行細胞毒性(LDH)以及細胞活性(MTS)測試，確認試片對人體無害後，進一步在試片上培養人類成骨細胞hFOB 1.19，並且用螢光試驗觀察骨細胞的成長情況。
從EDS元素分析和XRD分析及晶格常數計算結果得知試片經過製程後，仍然是以純鈦為主體的tetragonal結構，並沒有產生相變，且由EDS元素分析和XRD峰值的結果看出C以及O的元素含量微少，並且XRD結果並未出現TiC以及TiO₂的訊號，可推測其含量在XRD偵測極限以下。阿基米德法孔隙率測定結果中，試片的整體孔隙率和由體積占比所計算出的整體試片孔隙率預期值趨勢一致，因此可以藉由事先計算內外圈孔隙率的分配，讓試片整體孔隙率落在控制範圍。再綜合化性分析的結果，確認了本實驗的製程以及設計為穩定且具有再現性。結構方面，從SEM結果可以看出內圈以及外圈不同孔隙率區域分別擁有疏鬆以及緻密的表面形貌，搭配刮痕試驗的結果，證實試片雙層結構確實存在。最後綜合壓縮試驗以及孔隙率分析的結果，和其他的單一孔隙率多孔結構研究做比較，顯示出在孔隙率相同的前提下，本實驗的結構設計能讓抗壓強度提升一倍以上。生物相容性測試的部分，MTS和LDH測試結果呈現出除了內圈-外圈孔隙率組合65 %-30 %的試片，因為孔隙率太高導致細胞不易在表面附著生長，造成細胞存活率下降以外，其餘多孔鈦試片隨著孔隙率提高，其細胞存活率對照純鈦試片皆有顯著性提升，而細胞死亡率對照純鈦試片皆顯示出下降的趨勢，證實本實驗的材料選用以及結構設計沒有生物毒性，並且孔洞結構有助於細胞存活率的提升。最後由人類成骨細胞的細胞活性實驗中，以螢光染色觀察存活細胞的結果顯示隨著試片孔隙率增加，存活的成骨細胞數目能夠有倍數的成長。
綜合以上討論，藉由本實驗的試片雙層同心圓結構設計，確實能讓結構外圈較低孔隙率區域提供整體試片所需的強度，配合孔隙率的調整，讓機械強度在預期範圍，同時結構中內圈較高孔隙率的區域可以提供良好生物相容性，有助於骨細胞的附著生長，其中內圈-外圈孔隙率組合55 %-20 %的試片因為抗壓強度符合ISO規範且擁有相對高的孔隙率與細胞存活率，適合做為未來臨床應用的參數。

關鍵字：多孔鈦、粉末冶金、結構設計、仿生

Porous materials have been widely used, there are many applications of porous materials, such as electrodes, catalysts, filters and intervertebral cage. Take intervertbral cage as example, recent researches and products still focus on solid or uniform porosity porous structure, but there is a need for porous material with more biomimetic structure.
The present study designs a porous titanium with double concentric structure by powder metallurgy. The inner concentric circle area of samples is loose structure with low porosity (10 %, 20 %, 30 %), which provide good cell viability, and the outer concentric circle area of samples is dense structure with high porosity (45 %, 55 %, 65 %), which provide the required mechanical properties. Mechanical and chemical tests were conducted on the bulk and powder of samples, and cell viability and morphology tests were conducted on the cross section of samples. The results show that the experimental design is reproducible, and the designed structure performed better mechanical properties than structure with uniform porosity.

Key words: porous titanium, powder metallurgy, structure design, biomimetic

[1] A. S. Kanter, A. R. Asthagiri, and C. I. Shaffrey, "Aging spine: challenges and emerging techniques," Clinical neurosurgery, vol. 54, p. 10, 2007.
[2] H. Kienapfel, C. Sprey, A. Wilke, and P. Griss, "Implant fixation by bone ingrowth," The Journal of arthroplasty, vol. 14, no. 3, pp. 355-368, 1999.
[3] H. U. Cameron, "Six-year results with a microporous-coated metal hip prosthesis," Clinical orthopaedics and related research, no. 208, pp. 81-83, 1986.
[4] S. H. Wu, Y. Li, Y. Q. Zhang, X. K. Li, C. F. Yuan, Y. L. Hao, Z. Y. Zhang, and Z. Guo, "Porous titanium‐6 aluminum‐4 vanadium cage has better osseointegration and less micromotion than a poly‐ether‐ether‐ketone cage in sheep vertebral fusion," Artificial organs, vol. 37, no. 12, pp. E191-E201, 2013.
[5] A. Nouri, P. D. Hodgson, and C. e. Wen, Biomimetic porous titanium scaffolds for orthopaedic and dental applications. InTech, 2010.
[6] J. Bobyn, G. Stackpool, S. Hacking, M. Tanzer, and J. Krygier, "Characteristics of bone ingrowth and interface mechanics of a new porous tantalum biomaterial," The Journal of bone and joint surgery. British volume, vol. 81, no. 5, pp. 907-914, 1999.
[7] L. D. Zardiackas, D. E. Parsell, L. D. Dillon, D. W. Mitchell, L. A. Nunnery, and R. Poggie, "Structure, metallurgy, and mechanical properties of a porous tantalum foam," Journal of Biomedical Materials Research: An Official Journal of The Society for Biomaterials, The Japanese Society for Biomaterials, and The Australian Society for Biomaterials and the Korean Society for Biomaterials, vol. 58, no. 2, pp. 180-187, 2001.
[8] M. Assad, P. Jarzem, M. A. Leroux, C. Coillard, A. V. Chernyshov, S. Charette, and C. H. Rivard, "Porous titanium‐nickel for intervertebral fusion in a sheep model: Part 1. Histomorphometric and radiological analysis1," Journal of Biomedical Materials Research Part B: Applied Biomaterials: An Official Journal of The Society for Biomaterials, The Japanese Society for Biomaterials, and The Australian Society for Biomaterials and the Korean Society for Biomaterials, vol. 64, no. 2, pp. 107-120, 2003.
[9] M. Assad, A. Chernyshov, P. Jarzem, M. Leroux, C. Coillard, S. Charette, and C. Rivard, "Porous titanium‐nickel for intervertebral fusion in a sheep model: Part 2. Surface analysis and nickel release assessment," Journal of Biomedical Materials Research Part B: Applied Biomaterials: An Official Journal of The Society for Biomaterials, The Japanese Society for Biomaterials, and The Australian Society for Biomaterials and the Korean Society for Biomaterials, vol. 64, no. 2, pp. 121-129, 2003.
[10] C. Gaillard, J. Despois, and A. Mortensen, "Processing of NaCl powders of controlled size and shape for the microstructural tailoring of aluminium foams," Materials Science and Engineering: A, vol. 374, no. 1-2, pp. 250-262, 2004.
[11] B. Li, C. Wang, and X. Lu, "Effect of pore structure on the compressive property of porous Ti produced by powder metallurgy technique," Materials & Design, vol. 50, pp. 613-619, 2013.
[12] G. E. Ryan, A. S. Pandit, and D. P. Apatsidis, "Porous titanium scaffolds fabricated using a rapid prototyping and powder metallurgy technique," Biomaterials, vol. 29, no. 27, pp. 3625-3635, 2008.
[13] N. Gui, W. Xu, A. N. Abraham, D. E. Myers, E. L. Mayes, K. Xia, R. Shukla, and M. Qian, "A comparative study of the effect of submicron porous and smooth ultrafine‐grained Ti‐20Mo surfaces on osteoblast responses," Journal of Biomedical Materials Research Part A, 2018.
[14] A. B. Khoda and B. J. C.-A. D. Koc, "Functionally heterogeneous porous scaffold design for tissue engineering," vol. 45, no. 11, pp. 1276-1293, 2013.
[15] D. Yoo, "Heterogeneous minimal surface porous scaffold design using the distance field and radial basis functions," Medical engineering & physics, vol. 34, no. 5, pp. 625-639, 2012.
[16] L. Zhang, Z. He, J. Tan, M. Calin, K. Prashanth, B. Sarac, B. Völker, Y. Jiang, R. Zhou, and J. Eckert, "Designing a multifunctional Ti-2Cu-4Ca porous biomaterial with favorable mechanical properties and high bioactivity," Journal of alloys and compounds, vol. 727, pp. 338-345, 2017.
[17] G. Kotan and A. Ş. Bor, "Production and characterization of high porosity Ti-6Al-4V foam by space holder technique in powder metallurgy," Turkish Journal of Engineering and Environmental Sciences, vol. 31, no. 3, pp. 149-156, 2007.
[18] Z. Esen and Ş. Bor, "Processing of titanium foams using magnesium spacer particles," Scripta Materialia, vol. 56, no. 5, pp. 341-344, 2007.
[19] N. Jha, D. Mondal, J. D. Majumdar, A. Badkul, A. Jha, and A. Khare, "Highly porous open cell Ti-foam using NaCl as temporary space holder through powder metallurgy route," Materials & Design, vol. 47, pp. 810-819, 2013.
[20] S. W. Kim, H.-D. Jung, M.-H. Kang, H.-E. Kim, Y.-H. Koh, and Y. Estrin, "Fabrication of porous titanium scaffold with controlled porous structure and net-shape using magnesium as spacer," Materials Science and Engineering: C, vol. 33, no. 5, pp. 2808-2815, 2013.
[21] Z. Wang, X. Jiao, P. Feng, X. Wang, Z. Liu, and F. Akhtar, "Highly porous open cellular TiAl-based intermetallics fabricated by thermal explosion with space holder process," Intermetallics, vol. 68, pp. 95-100, 2016.
[22] C. Wen, M. Mabuchi, Y. Yamada, K. Shimojima, Y. Chino, and T. Asahina, "Processing of biocompatible porous Ti and Mg," Scripta Materialia, vol. 45, no. 10, pp. 1147-1153, 2001.
[23] O. Smorygo, A. Marukovich, V. Mikutski, A. Gokhale, G. J. Reddy, and J. V. Kumar, "High-porosity titanium foams by powder coated space holder compaction method," Materials Letters, vol. 83, pp. 17-19, 2012.
[24] A. Bansiddhi and D. C. Dunand, "Shape-memory NiTi foams produced by solid-state replication with NaF," Intermetallics, vol. 15, no. 12, pp. 1612-1622, 2007.
[25] Y. Torres, J. Pavón, and J. Rodríguez, "Processing and characterization of porous titanium for implants by using NaCl as space holder," Journal of Materials Processing Technology, vol. 212, no. 5, pp. 1061-1069, 2012.
[26] T. Aydoğmuş and Ş. Bor, "Processing of porous TiNi alloys using magnesium as space holder," Journal of alloys and compounds, vol. 478, no. 1-2, pp. 705-710, 2009.
[27] K. Nishiyabu, S. Matsuzaki, K. Okubo, M. Ishida, and S. Tanaka, "Porous graded materials by stacked metal powder hot-press moulding," in Materials Science Forum, 2005, vol. 492, pp. 765-770: Trans Tech Publ.
[28] K. Nishiyabu, S. Matsuzaki, and S. Tanaka, "Net-shape manufacturing of micro porous metal components by powder injection molding," in Materials science forum, 2007, vol. 534, pp. 981-984: Trans Tech Publ.
[29] A. K. Gain, H.-Y. Song, and B.-T. Lee, "Microstructure and mechanical properties of porous yttria stabilized zirconia ceramic using poly methyl methacrylate powder," Scripta Materialia, vol. 54, no. 12, pp. 2081-2085, 2006.
[30] M. Köhl, T. Habijan, M. Bram, H. P. Buchkremer, D. Stöver, and M. Köller, "Powder metallurgical near‐net‐shape fabrication of porous NiTi shape memory alloys for use as long‐term implants by the combination of the metal injection molding process with the space‐Holder technique," Advanced Engineering Materials, vol. 11, no. 12, pp. 959-968, 2009.
[31] Y. Quan, F. Zhang, H. Rebl, B. Nebe, O. Keẞler, and E. Burkel, "Ti6Al4V foams fabricated by spark plasma sintering with post-heat treatment," Materials Science and Engineering: A, vol. 565, pp. 118-125, 2013.
[32] Y. Torres, S. Lascano, J. Bris, J. Pavón, and J. A. Rodriguez, "Development of porous titanium for biomedical applications: A comparison between loose sintering and space-holder techniques," Materials Science and Engineering: C, vol. 37, pp. 148-155, 2014.
[33] I.-H. Oh, N. Nomura, and S. Hanada, "Microstructures and mechanical properties of porous titanium compacts prepared by powder sintering," Materials Transactions, vol. 43, no. 3, pp. 443-446, 2002.
[34] M. Gahlert, T. Gudehus, S. Eichhorn, E. Steinhauser, H. Kniha, and W. Erhardt, "Biomechanical and histomorphometric comparison between zirconia implants with varying surface textures and a titanium implant in the maxilla of miniature pigs," Clinical oral implants research, vol. 18, no. 5, pp. 662-668, 2007.
[35] S. Muñoz, J. Pavón, J. Rodríguez-Ortiz, A. Civantos, J. Allain, and Y. Torres, "On the influence of space holder in the development of porous titanium implants: Mechanical, computational and biological evaluation," Materials Characterization, vol. 108, pp. 68-78, 2015.
[36] C. Pan, C. Lin, Y. Huang, T. Yang, S. Chen, C. Ou, L. Chen, J. Huang, J. Jang, and H. Lin, "Design of Interbody Fusion Cages of Ti6Al4V with Gradient Porosity Using a Selective Laser Melting Process for Spinal Fusion Arthroplasty," Journal of Laser Micro/Nanoengineering, vol. 12, no. 1, 2017.
[37] N. Yang, Y. Tian, and D. Zhang, "Novel real function based method to construct heterogeneous porous scaffolds and additive manufacturing for use in medical engineering," Medical engineering & physics, vol. 37, no. 11, pp. 1037-1046, 2015.
[38] A. Khoda, I. T. Ozbolat, and B. Koc, "Designing heterogeneous porous tissue scaffolds for additive manufacturing processes," Computer-Aided Design, vol. 45, no. 12, pp. 1507-1523, 2013.
[39] D. Yamashita, M. Machigashira, M. Miyamoto, H. Takeuchi, K. Noguchi, Y. Izumi, and S. Ban, "Effect of surface roughness on initial responses of osteoblast-like cells on two types of zirconia," Dental materials journal, vol. 28, no. 4, pp. 461-470, 2009.
[40] R. K. Alla, K. Ginjupalli, N. Upadhya, M. Shammas, R. K. Ravi, and R. Sekhar, "Surface roughness of implants: a review," Trends in Biomaterials and Artificial Organs, vol. 25, no. 3, pp. 112-118, 2011.
[41] H.-H. Huang, C.-T. Ho, T.-H. Lee, T.-L. Lee, K.-K. Liao, and F.-L. Chen, "Effect of surface roughness of ground titanium on initial cell adhesion," Biomolecular engineering, vol. 21, no. 3-5, pp. 93-97, 2004.
[42] D. D. Deligianni, N. Katsala, S. Ladas, D. Sotiropoulou, J. Amedee, and Y. Missirlis, "Effect of surface roughness of the titanium alloy Ti–6Al–4V on human bone marrow cell response and on protein adsorption," Biomaterials, vol. 22, no. 11, pp. 1241-1251, 2001.
[43] H. Begam, B. Kundu, A. Chanda, and S. K. Nandi, "MG63 osteoblast cell response on Zn doped hydroxyapatite (HAp) with various surface features," Ceramics International, vol. 43, no. 4, pp. 3752-3760, 2017.
[44] T. S. N. Silva, D. C. Machado, C. Viezzer, S. Júnior, A. Novaes, and M. G. d. Oliveira, "Effect of titanium surface roughness on human bone marrow cell proliferation and differentiation: an experimental study," Acta cirurgica brasileira, vol. 24, no. 3, pp. 200-205, 2009.
[45] R. A. Gittens, T. McLachlan, R. Olivares-Navarrete, Y. Cai, S. Berner, R. Tannenbaum, Z. Schwartz, K. H. Sandhage, and B. D. Boyan, "The effects of combined micron-/submicron-scale surface roughness and nanoscale features on cell proliferation and differentiation," Biomaterials, vol. 32, no. 13, pp. 3395-3403, 2011.
[46] D. Buser, R. Schenk, S. Steinemann, J. Fiorellini, C. Fox, and H. Stich, "Influence of surface characteristics on bone integration of titanium implants. A histomorphometric study in miniature pigs," Journal of biomedical materials research, vol. 25, no. 7, pp. 889-902, 1991.
[47] P. Ducheyne and Q. Qiu, "Bioactive ceramics: the effect of surface reactivity on bone formation and bone cell function," Biomaterials, vol. 20, no. 23-24, pp. 2287-2303, 1999.
[48] D. W. Hutmacher, "Scaffolds in tissue engineering bone and cartilage," in The Biomaterials: Silver Jubilee Compendium: Elsevier, 2000, pp. 175-189.
[49] S. Bose, M. Roy, and A. Bandyopadhyay, "Recent advances in bone tissue engineering scaffolds," Trends in biotechnology, vol. 30, no. 10, pp. 546-554, 2012.
[50] L. Ponsonnet, K. Reybier, N. Jaffrezic, V. Comte, C. Lagneau, M. Lissac, and C. Martelet, "Relationship between surface properties (roughness, wettability) of titanium and titanium alloys and cell behaviour," Materials Science and Engineering: C, vol. 23, no. 4, pp. 551-560, 2003.
[51] 黃坤祥, 粉末冶金學. 中華民國粉末冶金協會, 2003.
[52] P. W. Voorhees, "Ostwald ripening of two-phase mixtures," Annual Review of Materials Science, vol. 22, no. 1, pp. 197-215, 1992.
[53] K. Byrappa and T. Adschiri, "Hydrothermal technology for nanotechnology," Progress in crystal growth and characterization of materials, vol. 53, no. 2, pp. 117-166, 2007.
[54] M. T. Reagan, J. G. Harris, and J. W. Tester, "Molecular Simulations of Dense Hydrothermal NaCl− H2O Solutions from Subcritical to Supercritical Conditions," The Journal of Physical Chemistry B, vol. 103, no. 37, pp. 7935-7941, 1999.
[55] T. Onoki, "Porous Apatite Coating on Various Titanium Metallic Materials via Low Temperature Processing," in Biomaterials Science and Engineering: InTech, 2011.
[56] M. C. de Andrade, M. R. T. Filgueiras, and T. Ogasawara, "Hydrothermal nucleation of hydroxyapatite on titanium surface," Journal of the European Ceramic Society, vol. 22, no. 4, pp. 505-510, 2002.
[57] S. Danwittayakul and J. Dutta, "Controlled growth of zinc oxide microrods by hydrothermal process on porous ceramic supports for catalytic application," Journal of alloys and compounds, vol. 586, pp. 169-175, 2014.
[58] A. Moradi, S. Pramanik, F. Ataollahi, T. Kamarul, and B. Pingguan-Murphy, "Archimedes revisited: computer assisted micro-volumetric modification of the liquid displacement method for porosity measurement of highly porous light materials," Analytical Methods, vol. 6, no. 12, pp. 4396-4401, 2014.
[59] S. J. Kim and T. Chung, "Cold atmospheric plasma jet-generated RONS and their selective effects on normal and carcinoma cells," Scientific reports, vol. 6, p. 20332, 2016.
[60] M. V. Berridge and A. S. Tan, "Characterization of the cellular reduction of 3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyltetrazolium bromide (MTT): subcellular localization, substrate dependence, and involvement of mitochondrial electron transport in MTT reduction," Archives of biochemistry and biophysics, vol. 303, no. 2, pp. 474-482, 1993.
[61] J. A. Barltrop, T. C. Owen, A. H. Cory, and J. G. Cory, "5-(3-carboxymethoxyphenyl)-2-(4, 5-dimethylthiazolyl)-3-(4-sulfophenyl) tetrazolium, inner salt (MTS) and related analogs of 3-(4, 5-dimethylthiazolyl)-2, 5-diphenyltetrazolium bromide (MTT) reducing to purple water-soluble formazans as cell-viability indicators," Bioorganic & Medicinal Chemistry Letters, vol. 1, no. 11, pp. 611-614, 1991.
[62] Y. Oshida, Bioscience and bioengineering of titanium materials. Elsevier, 2010.
[63] W. M. Haynes, CRC handbook of chemistry and physics. CRC press, 2014.
[64] S. Ponader, E. Vairaktaris, P. Heinl, C. v. Wilmowsky, A. Rottmair, C. Körner, R. F. Singer, S. Holst, K. A. Schlegel, and F. W. Neukam, "Effects of topographical surface modifications of electron beam melted Ti‐6Al‐4V titanium on human fetal osteoblasts," Journal of Biomedical Materials Research Part A: An Official Journal of The Society for Biomaterials, The Japanese Society for Biomaterials, and The Australian Society for Biomaterials and the Korean Society for Biomaterials, vol. 84, no. 4, pp. 1111-1119, 2008.
[65] J. Jia, K. Zhang, and S. Jiang, "Microstructure and mechanical properties of Ti–22Al–25Nb alloy fabricated by vacuum hot pressing sintering," Materials Science and Engineering: A, vol. 616, pp. 93-98, 2014.
[66] M. F. C. Ladd, R. A. Palmer, and R. A. Palmer, Structure determination by X-ray crystallography. Springer, 1985.
[67] S. Hengsberger, A. Kulik, and P. Zysset, "Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions," Bone, vol. 30, no. 1, pp. 178-184, 2002.
[68] 張瑞慶, "奈米壓痕技術與應用," 聖約翰科技大學, 2006.
[69] W. D. Callister and D. G. Rethwisch, Materials science and engineering: an introduction. John Wiley & Sons New York, 2007.
[70] P. Szymczyk, G. Ziółkowski, A. Junka, and E. Chlebus, "Application of Ti6Al7Nb alloy for the manufacture of Biomechanical Functional Structures (BFS) for custom-made bone implants," Materials, vol. 11, no. 6, p. 971, 2018.
[71] J. Li, X. Wang, R. Hu, and H. Kou, "Structure, composition and morphology of bioactive titanate layer on porous titanium surfaces," Applied Surface Science, vol. 308, pp. 1-9, 2014.
[72] L.-j. Chen, L. Ting, Y.-m. Li, H. Hao, and Y.-h. Hu, "Porous titanium implants fabricated by metal injection molding," Transactions of Nonferrous Metals Society of China, vol. 19, no. 5, pp. 1174-1179, 2009.
[73] 蘇宇涵, "以改良式水熱法製備仿生多孔鈦支架之研究," 成功大學材料科學及工程學系學位論文, pp. 1-75, 2015.
[74] L. Feng, M. Chittenden, J. Schirer, M. Dickinson, and I. Jasiuk, "Mechanical properties of porcine femoral cortical bone measured by nanoindentation," Journal of biomechanics, vol. 45, no. 10, pp. 1775-1782, 2012.
[75] H. Giambini, H.-J. Wang, C. Zhao, Q. Chen, A. Nassr, and K.-N. An, "Anterior and posterior variations in mechanical properties of human vertebrae measured by nanoindentation," Journal of biomechanics, vol. 46, no. 3, pp. 456-461, 2013.