本文發展了光滑粒子流體動力學法(SPH)應用在二維紅血球於微流道中的變形，紅血球的細胞膜以一群粒子離散並與相鄰的細胞膜粒子以線性彈簧連接，而血漿及細胞質由一群不可壓縮牛頓流體粒子所表示。為驗證SPH算法，模擬紅血球於壓力驅動流中的變形，紅血球往下游移動並由原先的雙凹透鏡形變成特徵形狀降落傘形(parachute shape)，與文獻結果一致，為模擬紅血球變形提供了另一種可行的途徑。較早的研究，大多假設紅血球的細胞內液和血漿的性質是相同的，因此本文模擬不同密度比、黏滯係數比對紅血球在微流道中的變形的影響，結果顯示改變彈簧常數、密度比、黏滯係數比皆影響其變形和速度，其中以改變細胞膜的彈簧常數影響最大。最後模擬了紅血球進入微流道的變形過程，兩翼向中心線靠攏並向後延伸，中間增厚。通過流道的時間隨彈簧常數的增大而增加，但此表現在常數變小較不明顯。

This thesis presents a smooth particle hydrodynamics (SPH) model for simulation of two dimensional deformation of a red blood cell (RBC) in micro-channel. In the model, the RBC membrane is discretized by membrane particles that are connected to neighboring membrane particles by linear spring. The plasma and cytoplasm are modeled as incompressible homogeneous Newtonian fluids, discretized by SPH particles. In order to verify the model, the deformation of a RBC in capillary, with the RBC moving downstream and processing a characteristic parachute shape in the steady state, results is well-agreement of previously reported. Then the effects of parameter were also investigated, which include the spring modulus, density and viscosity ratios of the fluid to RBC. The simulation results reveals that all of the parameters have effects on the dynamic behavior of the RBC. Finally, the dynamic behavior of an RBC entering a contraction micro-channel was presented. As the RBC moves, two wings fold toward each other, and bending of the membrane is increased. The result agrees well with the experiment results of reported previously in the literature, and the traveling time increases as the spring modulus is increased.

[1] Constantine Pozrikidis. (2010). Computational hydrodynamics of capsules and biological cells.
[2] Fischer, T. M. and Sch¨onbein, H. S. (1977)., Tank tread motion of red cell membranes in viscometric flow: Behavior of intracellular and extracellular markers. Blood Cells, 3 : 351–365.
[3] Fisher, T. M. (1980)., On the energy dissipation in a tank-tread human red blood cell. Biophysical J., 32 : 863–868.
[4] Fung, Y. C. (1984) Biodynamics: Circulation. Springer–Verlag, New York.
[5] Goldsmith, H. L. (1971). Red cell motions and wall interactions in tube flow. Fed. Proc.,30 : 1578–1588.
[6] Hosseini, S.M., Amanifard, N. (2007). Presenting a modified SPH algorithm for numerical studies of fluid-structure interaction problems. Int. J. Eng. Trans. B 20, 167–178.
[7] Hosseini, S.M., Manzari, M.T., Hannani, S.K. (2007). A fully explicit three-step SPH algorithm for simulation of non-Newtonian fluid flow. Int. J. Num. Methods Heat Fluid Flow 7, 715–735.
[8] Hashemi, M. R., Fatehi, R., Manzari, M.T., (2011) SPH simulation of interacting solid bodies suspended in a shear flow of an Oldroy-B fluid. J. Non-Newtonian Fluid Mechanics, 166, 1239-1252.
[9] Hashemi, M.R., Fatehi, R., Manzari, M.T. (2012) A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows. J. Non-Linear Mechanics, 47, 626–638.
[10] Karnis, A., Goldsmith, H. L. and Mason, S. G. (1966). The flow of suspensions through tubes. Canadian J. Chem. Eng., 44 : 181–193.
[11] Liu, G.R., Liu, M.B., (2005).Smoothed Particle Hydrodynamics: A Meshfree Particle Method.
[12] Lee, G.Y.H., Lim, C.T., (2007). Biomechanics approaches to studying human diseases. Trends Biotech. 25, 111-118.
[13] Liu, MouBin., Shao, JiaRu., Chang, JianZong., (2012). On the treatment of solid boundary in particle hydrodynamics. J. Science China Technological Sciences, 55, 244-254.
[14] Monaghan, J.J., (1992). Smoothed particle hydrodynamics. Annual Review of Astronomical and Astrophysics, 30, 543-574.
[15] Monaghan, J. J. (1994). Simulating free surface flows with SPH. J. Comput. Phys., 110 :399–406.
[16] Morris, J.P. (1996). Analysis of Smoothed Particle Hydrodynamics with Applications, Department of Mathematics, Monash University.
[17] Morris, J.P., Fox, P.J., Zhu, Y.J., (1997). Modelling low Reynolds number incompressible flows using SPH. J. Computational Physics, 136, 214–226.
[18] Monaghan, J.J., Kajtar, J. (2008). SPH simulations of swimming linked bodies. J. Comput. Phys.,, 227, 8568–8587.
[19] Monaghan, J.J., Kajtar, J.B., (2009). SPH particle boundary forces for arbitrary boundaries. Computer Physics Communications 180 (2009) 1811–1820.
[20] Pozrikidis, C. (2003). Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. 31, 1194–1205.
[21] Pivkin, I.V., Karniadakis, G.E., (2008). Accurate coarse-grained modeling of red blood cells. J. Phys. Rev. Lett. 101, 118-105.
[22] Skalak, R., Branemark, P.-I. (1969)., Deformation of red blood cells in capillaries.Science 164, 717–719.
[23] Skalak, R., ¨Ozkaya, N., Skalak, T.C. (1989). Biofluid mechanics. Ann. Rev. Fluid Mech. 21, 167–204.
[24] Suresh, S., (2006). Mechanical response of human red blood cells in health and disease: some structure–property–function relationships. J. Mater. Res. 21, 1871-1877.
[25] Tsubota, K. et al , (2001), Direct measurement of erythrocyte deformability in diabetesmellitus with a transparent microchannel capillary model and high-speed video camera system. J. Microvasc. Res. 61, 231–239.
[26] Tsubota, K. et al , (2005), A particle method for blood flow simulation application to flowing red blood cell and platelets. J. Earth Sim. 5, 2-7.
[27] Tanaka, N., Takano, T. (2005).Microscopic-scale simulation of blood flow using SPH method. International Journal of Computational Methods, 2(04), 555-568.
[28] Tsubota, K., Wada, S., Yamaguchi, T., (2006), Particle method for computer simulation of red blood cell motion in blood flow, Computer Methods and Programs in Biomedicine, 83, 139-146.
[29] Tsubota, K., Wada, S., Yamaguchi, T., (2006), Simulation study on effects of hematocrit on blood flow properties using particle method, J. Biomechanical Science and Engineering, 6, 159-170.
[30] Ye T., Li H., Lam K.Y.,(2010), Modeling and simulation of microfluid effects on deformation behavior of a red blood cell in a capillary. Microvasc Res. 80(3):453-63.
[31] Yap, B., Kamm, R.D., (2005b) Mechanical deformation of neutrophils into narrow channels induces pseudopod projection and changes in biomechanical properties. J. Appl. Physiol. 98, 1930–1939.
[32] Zhang, C., Zhang, Y. X., Wan, D. C., (2011). Comparative study of SPH and MPS methods for numerical simulations of dam breaking problems. J. Hydrodynamics Ser. 26, 736-746.
[33] 韓旭、楊綱、強洪夫.(2005).光滑粒子流體動力學-一種無網格粒子法.