Advancement of hemodynamics enables researchers to verify the resonance phenomenon in blood circulation The model of BPW can elaborate the following physiological phenomena, which are hard to be explained by the traditional theory of blood flow,
(1) With a small power (1.7W), the heart can push the blood to circulate all over the body day and night.
(2) The arch of aorta have a turn of 180 degrees.
(3) The blood can enter the organ which couple to the aorta with 90 degrees.
From the evolutionary viewpoint, resonance, corresponds to the most efficient energy transfer state of a system. It also enables the living beings to compete in the nature.
On the other hand, if a system deviates from its resonance state, diseases or death often arise.
From the macroscopic aspect, blood circulation is viewed as a forced oscillation which is electrically driven by the heart. In spite of the quite distinct wave patterns in the time domain, the power spectra of the ECG and BPW overlap well for the normal, healthy subjects, yet deviate significantly for the patients with vascular-related diseases. The results conform to the concept of frequency matching and imply that there are close spectral relationships and information shared between the ECG and the BPW, which can be used to measure the condition of blood circulation. The correlation coefficient estimated for the frequency band 0-20Hz further reflects much weaker coupling efficiency in the ECG-to-BPW system for the abnormal subjects (mean = 0.542) in comparison with the normal subjects (mean = 0.821). In the bicoherence analysis, a diseased circulation system exhibits poor cross
quadratic-phase coupling between ECG and BPW (healthy subjects: 0.828 > vascular patients: 0.619). Furthermore, the result of transfer function analysis for the patients indicates a low energy transmission efficiency from input to output (S.D. of healthy subjects: 0.206 < vascular patients: 0.301). In addition, we propose a frequency-domain equivalent circuit to model the blood circulation, and develop the quality factor (Q) to assess the resonance characteristic of each harmonic-related resonator. The results reveal that the patients who have poor coupling efficiency from the heart also tend to have poor resonance in their circulatory system (healthy subjects vs. vascular patients, f: 5.68 > 5.38, 2f: 10.59 > 9.77, 3f: 15.45 > 13.99, 4f: 20.65 >
18.19, 5f: 27.35 >24.19).
Why does a mechanical vibration signal (BPW) have almost the same spectral components as an electrophysiological signal (ECG) in a healthy cardiovascular system? We hypothesize that the BPW, transduced from the ECG of the heart, is optimally coupled from the heart to the arterial system due to the superior elasticity of the vessels. The spectral contents are thus preserved in the circulation under the well-elastic arterial system since the pressure wave encounters little perturbation, less reflection, and smaller peripheral resistance. Considering the circulatory system modeled as an electrically-driven, mechanical-pumping system, we developed several methods to quantitatively evaluate the effects of spectral coupling and resonance between ECG and BPW, in which the ECG and BPW represent, respectively, the electrically driving source and the mechanically responding output.
Next, Using coherence function analysis, we found that for healthy subjects, most spectral components of the input (ECG) are coherently coupled to those of the response (BPW) (S=0.97), so that less perturbation is found. On the other hand, for cardiovascular patients, the influence of perturbation signals on the output is relatively
important (S=0.92). In other words, the perturbation signals seriously interfere with the coherence power transfer. If S approaches one, the perturbation effect becomes smaller. The cardiovascular system can thus be maintained in a better condition. On the contrary, if S deviates from one, severe perturbation occurs in the cardiovascular system that will decay fast.
Although we cannot identify the perturbation source using the model, this method provides an approach for quantifying such macroscopic phenomenon as the coherence power transfer and perturbation in the system. Moreover, we have demonstrated that cardiovascular system exhibits some phenomena similar to the technologies and mechanisms employed in communication systems, for example, the FM and AM schemes. These analogies give us more insight into the cardiovascular system. In summary, the results provide us with a new scope to study blood circulation using power coherence. Due to the close relationship between spectral harmonics and various organs, this approach might be extended to the study of organ disease [11].
Cardiovascular-related diseases have been one of the major causes of death.
Furthermore, they often cause sudden death without warning. To identify the early sign of disease in advance, cardiovascular system characterization by spectral analysis may offer a non-invasive and affirmative approach for medical prognosis.
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