本研究使用裝載球型探針之原子力顯微鏡對擬球藻細胞進行壓縮測試，並建立模型來分析壓縮測試得到的力曲線，而模型為一內含不可壓縮液體之薄膜球體被另一球體與一無限大平板做壓縮。

實驗部分將擬球藻細胞滴在載玻片上，載玻片經過Poly-L-Lysine處理增加細胞黏附性，原子力顯微鏡掃描表面與壓縮測試的過程均在液相中進行，壓縮測試至破壞擬球藻細胞。模型部份假設細胞壁為薄膜，為均質、等向與彈性的材料，並且壁厚不會變化；球體內含不可壓縮液體以替代細胞質。模型推導套用薄膜理論以得到不同接觸區與非接觸區的統御方程式組，搭配對應之邊界條件。數值解法部分將邊界條件問題換成初始條件問題，接著引用四階Runge-Kutta法求解。最後將模型計算值對實驗力曲線擬合，以最佳擬合結果做分析。相對於現有其他文獻針對尺寸介於數十微米至厘米等級細胞的壓縮試驗模型而言，本研究所提出的模型可運用在微米等級的擬球藻壓縮試驗，並且成功地描述相對變形量0.25前力曲線的反應。

[1] 林哲毅, “以微藻生產生質柴油之未來發展,” 能源報導, July, 11~13, 2008
[2] J. L. Ye, “Studies on lipid production from microalgae using two-step cultivation strategy in a photobioreactor,” Master Thesis, National Cheng Kung University, 2006
[3] S. Y. Chiu, C. Y. Kao, M. T. Tsai, S. C. Ong, C. H. Chen and C. S. Lin,“ Biosource Technology,” 100, 833~838, 2009
[4] C.T. Lim, E.H. Zhou and S.T. Quek, “Mechanical models for living cells—a review,” Journal of Biomechanics, 39, 195~216, 2006
[5] A. Yeung and E. Evans, “Cortical shell–liquid core model for passive flow of liquid-like spherical cells into micropipets,” Biophysical Journal, 56, 1, 139~149, 1989
[6] D. E. Ingber, “Cellular tensegrity：defining new roles of biological design that govern the cytoskeleton,” Journal of Cell Science, 104, 613~627, 1993
[7] 高永毅,焦群英與王荣, “植物细胞对外加压缩载荷的响应分析,” Chinese Journal of Applied mechanics, 22, 1, 79~82, 2005
[8] www.lab8.cn/biol/ 2006/20060822085140.html
[9] E. Reissner, “Stresses and Small Displacements of Shallow Spherical Shells,” Journal of Mathematics and Physics, 25, 80~85, 1946
[10] G. V. Ranjan and C. R. Steele, “Large Deflection of Deep Spherical Shells Under Concentrated Load,” Proceedings, AIAA/ASME 18th Structures, Structural Dynamics, and Materials Conference, San Diego, Mar. 21~23, 269~278, 1977
[11] A. E. H. Love, The Mathematical Theory of Elasticity, Cambridge University Press, 4th Ed., 553, 1927
[12] L. A. Taber, “Large Deflection of a Fluid-Filled Spherical Shell Under a Point Load,” Journal of Applied Mechanics, 49, 121~128, 1982
[13] L. A. Taber, “Compression of Fluid-Filled Spherical Shells by Rigid Indenters,” Journal of Applied Mechanics, 50, 717~722, 1983
[14] W. W. Feng and W. H. Yang, “On the Contact Problem of an Inflated Spherical Nonlinear Membrane,” ASME Journal of Applied Mechanics, 40, 209~214, 1973
[15] T. J. Lardner and P. Pujara, Mechanics Today, New York, 5, 1980
[16] K. K. Liu, D. R. Williams and B. J. Briscoe, “Compressive deformation of a single microcapsule,” Physical Review E, 54, 6, 6673~6680, 1996
[17] C. X. Wang, L. Wang and C. R. Thomas, “Modelling the Mechanical Properties of Single Suspension-Cultured Tomato Cells,” Annals of Botany, 93, 443~453, 2004
[18] B. P. Jena and H. J. K. Horber, “Methods in Cell Biology,” Elsevier Science, 68, 71~74, 2002
[19] G. Moeller and V. Domnich, “AFM Nanoindentation of Polymers,” Microsc Microanal, 13, 2007
[20] M. Ryohei and H. Haruki, “Unusual Nuclear Divisionin Nannochloropsis oculata (Eustigmatophyceae,Heterokonta) which May Ensure Faithful Transmission of Secondary Plastids,” Protist, 160, 41~49, 2009
[21] L. Y. Cheng, “Deformation analyses in cell and development biology Part I. Formal methodology,” Transactions of the American Society of Mechanical Engineers: Journal of Biomedical Engineering 109, 10~17, 1987
[22] R. Skalak, A. Tozeren, R. P. Zarda and S. Chien, “Strain energy function of red blood cell membranes,” Biophysical Journal, 13, 245~263, 1973
[23] A. E. Smith, K. E. Moxham and A. P. J. Middelberg, “Wall material properties of yeast cells. Part II. Analysis,” Chemical Engineering, 55, 2043~2053, 2000
[24] W. Gindl and H. S. Gupta, “Cell-wall hardness and Young's modulus of melamine-modified spruce wood by nano-indentation,” Composites Part A: Applied Science and Manufacturing, 33, 8, 1141~1145, 2002
[25] K. J. Niklas, “Mechanical Behavior of Plant Tissues as Inferred from the Theory of Pressurized Cellular Solids,” American Journal of Botany, 76, 6, 929~937, 1989
[26] B. Nadler, “On the contact of a spherical membrane enclosing a fluid with rigid parallel planes,” International Journal of Non-Linear Mechanics, 45, 294~300, 2010
[27] L. Zhao, D. Schaefer, H. Xu, S. J. Modi, W. R. LaCourse and M. R. Marten, “Elastic Properties of the Cell Wall of Aspergillus nidulans Studied with Atomic Force Microscopy,” Biotechnology Progress, 21, 292~299, 2005
[28] G. C. Davies, S. Hiller and D. M. Bruce, “A membrane model for elastic deflection of individual plant cell walls,” Journal of Texture Studies, 29, 645~667, 1998
[29] A. E. Smith, Z. Zhang, C. R. Thomas, K. E. Moxham and A. P. J. Middelberg, “The mechanical properties of
Saccharomyces cerevisiae,” Proceedings of the National Academy of Sciences of the United States of America, 97, 18, 9871~9874, 2000
[30] J. J. Thwaites and U. C. Suranat, “Mechanical Properties of Bacillus subtilis Cell Walls: Effects of Removing Residual Culture Medium,” Journal of Bacteriology, 173, 1, 197~203, 1991
[31] G. A. Toole, P. A. Gunning, M. L. Parker, A. C. Smith and K. W. Waldron, “Fracture mechanics of the cell wall of Chara coralline,” Planta, 212, 606~611, 2001
[32] M. Johnson, S. Shivkumar and L. Berlowitz-Tarrant, “Structure and properties of filamentous green algae,” Material Science and Engineering, B38, 103~108, 1996