本論文旨在發展一套適合反脈動循環輔助的動力模式，結合一維流場與區塊參數法(Lumped Parameter Method)，提出全新的混合循環模式(Hybrid Circulation Model)。利用一維流場模型來模擬動脈的波傳現象，而區塊參數法則負責模擬其餘的血管系統。並針對此一維血液循環方程式發展出上風Roe近似里曼算子(Roe Approximate Riemann Solver)，且用朗吉-庫塔(Runge-Kutta)時間步進法來積分此耦合的混合循環模式。隨時間變化的左右心室功能以壓力–體積關係(Pressure-Volume Relationship)來描述，藉由調整心肌收縮彈性係數來模擬健康及心衰竭狀態下之血動力特性，並於心衰竭狀態下使用主動脈氣球泵浦 (Intra-Aortic Balloon Pump，簡稱IABP)及側主動脈氣球泵浦(PABP)輔助，分析以不同相位、驅動強度、心跳頻率及氣球體積對反脈動循環輔助效果的影響。模擬結果顯示增加氣球體積可以降低左心後負載(After Load)及增加心博量(Cardiac Output)的輸出。在氣球體積為40 ml的狀態下，使用IABP及PABP可以增加心博量分別為4% 和11%。此外，相較於IABP，PABP的效能並不隨著心跳頻率的改變而有太大的影響。反脈動循環輔助綜合性指標endocardical viability ratio (EVR) 顯示兩者的趨勢相同，表示輔助的效能並沒有很明顯的差異。使用波強度分析法可以發現，PABP舒張灌流時可以產生比IABP更強烈的壓縮波，而收縮卸載輔助可以使左心收縮時產生較大的順向壓縮波峰值。本研究使用波動強度分析法探討反脈動循環輔助，顯示出PABP產生反脈動波動能量優於IABP。

The present research aims at developing a system dynamic model that can simulate various hemodynamic and wave characteristics associated with the counter-pulsation circulation support. A novel hybrid circulation model consisting of a one-dimensional flow model and a lumped parameter circulation model was constructed. Wave propagation phenomenon in the arteries is simulated using the one-dimensional flow model with other parts of the vasculature represented by the lumped parameter circulation model. Roe-splitting upwind scheme was developed for this one-dimensional vascular equations and Runge-Kutta marching was used for time-stepping this coupled hybrid circulation system. Suga-Sagawa pressure-volume relationship was adopted to describe the time-varying left and right ventricular function. By adjusting the time-varying elastance of the ventricles, the healthy and failed heart conditions can be simulated. Failing heart supported either by intra-aortic balloon pump (IABP) or by para-aortic balloon pump (PABP) was simulated. These simulation results indicate that increasing pumping volume may result in left ventricular afterload reduction and cardiac output enhancement. For 40 ml pumping support, cardiac output was elevated to 4% and 11% for IABP and PABP, respectively. Moreover, contrary to the IABP support characteristics, heart rate does not show strong influence on PABP perfusion augmentation. Endocardical viability ratio (EVR), however, shows similar trend for both counter-pulsation devices. Using the wave intensity analysis, it was observed that, first, for diastolic augmentation, PABP produces stronger compression wave than does IABP; and second, left ventricle may generate steeper forward-going compression pressure waveform when assisted by PABP systolic unloading. The present wave intensity analysis (WIA) approach shows that counter-pulsation supported by PABP is more effective than that of the IABP.

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