我們透過理論計算和水管實驗模擬探討動脈系統。以徑向振動血液壓力波動方程式計算末端封閉的TY 型、TO 型和T 型主動脈系統的天然頻率和血液壓力波分佈，並探討血液壓力脈波響應各諧頻分佈和左心室輸血時間佔整個心跳週期的比例的關係。我們以不同材質的乳膠管模擬主動脈血管，並透過電腦設定控制訊號驅動步進馬達輸出脈衝水量或週期水量模擬心臟的血液輸出。我們發現兩種不同材質的水管相接成T 型或TY 型時，當兩種水管的長度比例和兩者的波速比例相同時，水管系統的各個天然震盪頻率會是整數倍(諧頻)。TO 型和TY 型主動脈系統的天然頻率和血液壓力波分佈是一致的。在主動脈系統中，血液壓力脈波響應各諧頻分佈會和左心室輸血時間佔整個心跳週期的比例有關，且當血液壓力波以不同頻率的供水輸入，發現在一些特定頻率時壓力脈波響應有峰值。

The blood pressure wave of different structures of ventricular-arterial system was studied theoretically and by tube simulations. The natural frequencies and the pressure distributions of the T、TY、TO arterial systems were predicted by solving the blood pressure wave equation. The effect of heart on the blood pressure response in the arterial system was analyzed. We used latex tubes to simulate the arterial system, and a pump driven by PC controlled stepping motor to simulate the heart. A T shape system (or a symmetric TY shape system) is constructed by connecting two different kind of elastic latex tubes. When the ratio of the length for the two latex tubes is proportional to the ratio of their pressure wave velocity, the natural frequencies of the system are in harmonics. The natural frequencies and the pressure distributions of the TY system and the TO system are similar. The harmonic components of the blood pressure response in the arterial system are correlated with the ejection time of the left ventricle. And the pressure response of the tube attains extreme values for some particular pumping frequencies.

(1). Taylor, M .G . (1957), A n A pproach to the A nalysis of the A rterial Pulse W ave. II Fluid O scillation in an Elastic Tube. Phys. M ed. B iol. 1:321-329
(2)M . F. O ’R ourke and A . A dji, “A n updated clinical prim er on large artery m echanics: im plications of pulse w aveform analysis and arterial tonom etry,” C urr. O pin. C ardiol., 20: 275-281, 2005.
(3)A . R . K hoshdel, “Tim e to end a doubt: Is pulse w ave analysis a valid m easure for central arterial blood pressure and arterial stiffness?” J. H ypertens., 25: 724-725, 2007.
(4)H arvey, W . (1628), M ovem ent of the H eart and B lood in A nim als, Frankurt : W illiam Fitzer
(5)W ang Lin, Y .Y . ,C hang , S.L. ,W u , Y .E. ,H su, T.L. ,W ang , W .K . (1911). “ R esonance ” The M issing Phenom enon in H em odyam ics. C ir. R ex. 69:246-248
(6)Y .Y . Lin W ang, W .C . Lia, S. H sin, M .Y . Jan, W .K . W ang, Effect of length on the Fundam ental R esonance Frequency of arterial m odels having radial dilatation. IEEE, Transactions on B iom edical Engineering, in press.
(7) Y uh-Y ing LinW ang,et al (2004) The N atural Frequencies of the A rterial System and Their R elation to the H eart R ate. IEEE TR A N SA C TIO N S O N B IO M ED IC A L EN G IN EER IN G , V O L. 51, N O . 1, JA N U Y (2004),pp193-195
(8)Y uh –Y ing W ang,et al (2007)A nalysis of transverse w ave as a propagation m ode for the pressure pulse in large arteries.J. A ppl. Phys.102, 064702 (2007)
(9) Y uh-Y ing LinW ang, et al (2008)The ventricular-arterial coupling system can be analyzed by the eigenw ave m odes of the w hole arterial system .A ppl. Phys. Lett.92, 153901 (2008)
(10)M ilnor W .R . : H em odynam ics(2nd ed). W ILLIA M S& W ILK IN S, 1989
(11).賴文哲: 主動脈振動天然頻率之探討. 國立台灣師範大學物理研究所, 碩士論文, 1996
(12) 陳忠誠: 壓力波在血管中行進的模擬與探討. 國立台灣師範大學物理研究所, 碩士論文, 1994
(13) 詹明宜: 共振對血壓波之模擬. 國立陽明醫學院醫學工程研究所, 碩士論文, 1992
(14) 徐清秀：彈性血管壓力波動方程式之初步應用. 國立台灣師範大學物理研究所, 碩士論文, 1996
(15)Y uh-Y ing Lin W ang1,2 Tse-Lin H su2 M ing-Y ie Jan2 W ei-K ung W ang2,* (2010)R eview :Theory and A pplications of the H arm onic A nalysis of A rterial Pressure Pulse W aves.Journal of Medical and Biological Engineering, 30(3): 125-131(2010)