這個研究是使用數值化運算模擬缺氧血流經過一個矩陣排列纖維的區域，而氧氣從纖維傳輸到缺氧血中。在這個分析中由於心臟並不是一個穩態的輸出來源，因此波動流的影響是非常重要的。在這研究之中，我使用一些無因次參數，例如，Reynolds numbers (Re), Womersley parameters (α), pulsation amplitudes (A) 來固定我的流場，並用 power-law model 模擬血液這個非牛頓流體以及 Hill equation 來描述氧氣融在血液中的數值，最後從這個研究可以觀察出，波動流對於氧氣分壓 (PO2) 和 氧氣融在血液中的濃度 (SO2) 以及 Sherwood numbers 的影響非常大。 然而，當血液流入矩陣排列纖維的區域後，氧氣分壓 (PO2) 的相位差延遲現象逐漸出現，而單獨一個纖維周邊的氧氣分壓 (PO2) 和 氧氣融在血液中的濃度 (SO2) 邊界層也完整的顯示於結果的部份，可以透過這部份的成果更加了解氧氣的擴散情形，最後探討了當PO2 設定最少需高於 100 mmHg 時，所需的矩陣排列纖維的區域長度與雷諾數的關係，雷諾數越大所需的矩陣排列纖維的區域長度越長，也造成壓差上升。

The target of this research is to computationally analyze deoxygenated blood flows passing through a multi-fiber bundle that releases oxygen to blood. The effect of pulsatile flow on the oxygen transport in blood is investigated. Dimensionless parameters for the physical model include Reynolds numbers (Re), Womersley parameters (α), pulsation amplitudes (A). The power law model is used to describe the non-Newtonian flow and the Hill equation is employed to simulate the oxygen saturation of hemoglobin. It is observed that flow pulsation significantly influences the velocity profile, partial pressure of oxygen (PO2), saturation of oxygen (SO2) and Sherwood numbers, in blood flows along a fiber bundle region. As blood flows into fiber bundle region, the downstream sinusoidal profiles of O2 partial show the phase lag with respect to that at the entrance. The variations of SO2 and PO2 boundary layers are documented. Finally, the mixing length where PO2 achieves 100 mmHg is determined against different Reynolds numbers.

論文審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
Table of Contents v
List of Figures vii
List of Tables ix
1 Introduction 1
2 Computational details 8
2.1 Governing equation 13
2.2 Analysis parameter 17
3. Numerical method 18
4. Numerical validation 19
5. Results and Discussion 21
5.1 The phase lag analysis 21
5.2 The SO2 contours analysi 24
5.3 Sherwood number 26
5.4 Boundary layers of partial pressure of O2 (PO2) and O2 saturation (SO2) 34
5.5 The mixing length of fiber bundle region and pressure drop 37
6 Conclusions 40
7. References 41
8. Appendix 45

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