To simulate a short segment of the aorta, we studied wave propagation in an elastic tube with a side branch balloon. The small balloon simulated the organ (group of arterioles). Ligation of this side branch would reduce the moduli of the higher harmonics when the length of the side branch was appropriate. Electrical analogy of vessels was used to analyze this phenomenon. This simulation can explain the ligation results we found in rats. It may also clarify the discrepancies between the prediction of the Womersley equation and the experimental results. We suggest that the aorta and the closely attached organ can produce coupled oscillation; theoretically, this structure is equivalent to a resonance circuit.
The pressure wave of the abdominal aorta and the flow wave of the renal artery were recorded simultaneously from a rat. The impedance of a kidney system that is derived by dividing the pressure of the corresponding frequency by that of the flow was studied in six rats. The data show that the system has two resonant frequencies, at the second and third harmonics. At the second harmonic, the pressure wave and fluid flow in a round trip through the branch of the kidney. Whereas it is difficult for the third harmonic flow to enter the kidney, it flows directly through the aorta. To obtain further proof, we compared the frequency components of the two flows measured simultaneously on the abdominal aorta and the renal artery and found the same result. The kidney, renal artery, and aorta combined show a coupled oscillation that is analogous to that of resonance circuits. The kidney vascular system exhibits a resonant frequency at the second harmonic of the heartbeat.
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