Dynamic Simulation of Red Blood Cell Rheology in a U-shaped Microtube

2012 年 4 月 兩岸力學科技論壇論文摘要集 臺北、臺南

Dynamic Simulation of Red Blood Cell Rheology in a

U-shaped Microtube

LIN San-Yih

1

, CHIN Ya-Hsien

2

, HU Jeu-Jiun

3

, CHUNG Ai-Jung

1

1 _{Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan} 2 _{Department of Marketing and Distribution Management, Overseas Chinese University, Taichung, Taiwan}

3_{Department of Information Management, Shu-Te University, Yan Chau, Kaohsiung County, Taiwan}

Abstract: A spring model is applied to simulate the skeleton of a red blood cell (RBC) membrane and to study the RBC rheology in a U-shaped micro-tube. An RBC membrane is modeled by an assembly of triangular elements in which stretch/compression and bending springs is placed to express planar shear and out-of-plane bending deformation, respectively. The areal incompressibility of the membrane and a volumetric constraint of the RBC are taken account. The total elastic energy of the RBC membrane is evaluated by the stretch/compression, bending, total areal, and local areal elastic energies. The biconcave RBC in static plasma has been captured in this spring model by adjusting the spring constants and its volumetric constraint. Then, an immersed-boundary (IB) pressure correction method is developed to simulate the flow-fields of the micro-tube flows. The history of the RBC shape changes and the flow structures of the RBC rheology in the U-shaped micro-tube are investigated.

Key words: red blood cell; rheology; immersed boundary method; pressure correction method.

紅血球之流變在

U 型微管中的動態模擬

林三益

1

, 秦雅嫻

2

, 胡舉軍

3

, 鍾艾蓉

1 1_{國立成功大學 航空太空工程學系 台灣台南} 2_{僑光科技大學 行銷與流通管理系 台灣台中} 3_{樹德科技大學 資訊管理系 台灣高雄} 摘要：由彈簧模型來模擬紅血球(RBC)膜的骨架和研究在U型微管中紅血球之流變 學。紅血球膜是模型藉由拉伸/壓縮和彎曲的彈簧被放置於三角形元素組合上，分 別表示剪切平面和外部平面彎曲變形。此需考慮紅血球膜的面不可壓縮性和紅血 球的體積約束。紅血球膜的彈性總能量是由拉伸/壓縮、彎曲、總面和局部面的彈 性能量所求得的數值。在靜態血漿中，雙凹型紅血球的彈簧模型已被獲得藉由調 整彈簧常數和體積約束。然後沉浸邊界(IB)壓力修正法來模擬微管流之流場。紅血 球形狀變化的經歷和紅血球流變學在U型微管流場結構進行了研究。 關鍵字：紅血球；流變；沉浸邊界法；壓力修正法 Project: NSC 99-2221-E-006-055

Corresponding author: LIN San-Yih, Professor. Research interest: Two Phase Flow. Email: sylin@mail.ncku.edu.tw