Dynamic Simulation of Red Blood Cell Rheology in a U-shaped Microtube S.Y. Lin, Y.H. Chin, J.J. Hu, and A.J. Chung Department of Aeronautics and Astronautics National Cheng Kung University 2012 兩岸力學科技論壇 2012 年 4 月 日

Introduction 以彈性之彈簧模型模擬紅血球結構變化， 紅血球將由球體變形成雙凹圓盤型形狀。 並研究在不同形狀微血管之管流中紅血球 變化的動態情形。

紅血球 Red Blood Cell 形狀 Shape  呈中央雙凹圓盤狀  直徑 ( Diameter ) ： 6.0~9.5μm  厚度 ( Thickness ) ： 中心 1.0μm ；周圍 2.0μm  平均表面積 (Average area) ： 120  平均體積 (Volume area) ： 87 圖解生理學 中野 昭一著 趙德彰 譯

Spring Network Model of Elastic RBC Membrane K.I. Tsubota, and S. Wada ”, International Journal of Mechanical Sciences, 2010.

Level 0 Level 1 Level 3 Level 4 W.X. Huang, C.B. Chang, and H.J. Sung, Journal of Computational Physics, Unstructured Triangular Mesh 3D level 0~3 sphere of the nodal positions in the Cartesian coordinates.

Spring Network Model of Elastic RBC Membrane Level =21 Nodes =2402 Edges =7200 Areas =4800

Spring Network Model of Elastic RBC Membrane

Level =21; Nodes =2402; Edges =7200; Areas =4800 Various Shape Changes of Red Blood Cells

Various Shape Changes of a Swollen Red Blood t=0.1 t=0.3 t=0.5 t=0.7 t=1.0 t=0

PISO Scheme Step 1: Predictor Step 2: a) First corrector b) Second corrector

Staggered Grids W P E SW S SE NW N NE U i,j,k u i-1,j,k v i,j,k v i,j-1,k AB CD p j,k p i-1,j,k p i+1,j,k

The Flow Induced Deformation of Red Blood Cells in the U Tube U Tube: PISO Scheme, Stagger Grid MI=80, MJ=80, MK=120 Radius = 5μm Initial data: U=0, V=0, W=0, P=1, ρ=1 Red Blood Cell: Level=9, Nodes=386, Edges=1152, Areas=768

The Flow Induced Deformation of Red Blood Cells in the U Tube U Tube: PISO Scheme, Stagger Grid MI=80, MJ=80, MK=120 Radius = 5μm Initial data: U=0, V=0, W=0, P=1, ρ=1 Red Blood Cell: Level=9, Nodes=386, Edges=1152, Areas=768

The Flow Induced Deformation of Red Blood Cells in the Y Tube Y Tube: PISO Scheme, Stagger Grid MI=160, MJ=80, MK=120 Initial data: U=0, V=0, W=0, P=1, ρ=1 Red Blood Cell: Level=9, Nodes=386, Edges=1152, Areas=768

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