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.

Effect of acupuncture at Tsu San Li (St-36) was examined by investigating the pulse variation of the radial artery. Our results indicated that acupuncture at Tsu San Li has a specific effect on the Fourier components of the pulse. The harmonic proportions were redistributed (C2, C4 decreased, C5, C6, C8 and C9 increased), and the phase angle of the 5th and 8th harmonic waves were decreased (propagating faster). This specific frequency effect was not found when acupuncture needle was applied on a non-acupuncture point. These results can be explained by the resonance theory, which provides a scientific explanation of the acupuncture effect from the hemodynamic view point.

We investigated the pulse spectrum variation of the human radial artery when Hsien- Ku (St 43), an acupoint on the stomach meridian, was needled and compared the results with the acupuncture effects of two other acupoints, Tsu-San-Li (St-36) and Tai-Shih (K-3), reported previously. For Hsien-Ku, the harmonic proportions were redistributed: the second harmonic (C2) decreased, C3, C5, C6, C7, C8 and C9 increased, C3, C6 and C9 became the relative peaks to their neighboring harmonics and C2, C4 became the relative minimums. The phase angles of the 2nd harmonic (P2) and 5th harmonic (P5) decreased, propagating faster. These effects were similar to that of Tsu-San-Li which is also on the stomach meridian. A totally different pattern was found for Tai-Shih on the kidney meridian. These results strengthen the theory that a meridian can be classified according to its effects on the pulse spectrum, and that all the meridian related effects such as those caused by acupuncture or meridian specific herbs are frequency specific.

Laser Doppler flowmetry (LDF) is a popular method for monitoring the microcirculation, but it does not provide absolute measurements. Instead, the mean flux response or energy distribution in the frequency domain is generally compared before and after stimulus. Using the heartbeat as a trigger, we investigated whether the relation between pressure and flux can be used to discriminate different microcirculatory conditions. We propose the following three pulsatile indices for evaluating the microcirculation condition from the normalized pressure and flux segment with a synchronized-averaging method: peak delay time (PDT), pressure rise time and flux rise time (FRT). The abdominal aortic blood pressure and renal cortex flux (RCF) signals were measured in spontaneously hypertensive rats (SHR) and Wistar Kyoto rats (WKY). The mean value of the RCF did not differ between SHR and WKY. However, the PDT was longer in SHR (87.14 +/- 5.54 ms, mean +/- SD) than in WKY (76.92 +/- 2.62 ms; p < 0.001). The FRT was also longer in SHR (66.56 +/- 1.98 ms) than in WKY (58.02 +/- 1.77 ms; p < 0.001). We propose that a new dimension for comparing the LDF signals, which the results from the present study show, can be used to discriminate RCF signals that cannot be discriminated using traditional methods.

The frequency specific acupuncture effect on Tai-Tsih (K-3) was examined by investigating pulse variations at the radial artery. The harmonic proportions of the 2nd, 3rd, and the 4th harmonics were increased but the 5th, 6th and 9th harmonics were decreased significantly. The phase angles of all except the 2nd harmonic were increased (wave propagated slower). These results are compared with the frequency specific acupuncture effect on Tsu-San-Li (St-36) which we reported previously (Wang et al., 1995a). This study solidified the weak coupling resonance theory, which successfully explains these frequency specific effects as well as the acupuncture mechanism.