基於諧振與同調觀點之血液壓力波分析

Abstract

在這篇論文中我們提出一個新的觀點來分析血液循環，也就是將血液循環系統視為一個電訊號激發的機械振動系統，並且用一個以橫向振動為主的血液壓力波方程式來描述血液循環時的諧振現象，接著我們把ECG與BPW(血液壓力波)視為此系統的輸入與輸出，並探討它的頻域特性，首先我們發現對於健康的受測者，其ECG與BPW的功率頻譜有相當大的重疊，頻譜耦合係數(Spectral coupling coefficient)趨近於1，而心血管相關疾病的患者則有較大的差異，頻譜耦合係數小於1，此乃因為健康者的動脈系統彈性極佳，能將心臟搏動的頻率變化完整地耦合至動脈系統，也就是心臟與動脈系統發生諧振; 而心血管相關疾病的患者，則因動脈系統彈性較差或其它阻力而無法完整地耦合心臟搏動的頻率到動脈系統，其諧振特性較差; 另一方面，其三階頻譜(Bicoherence) 趨近於1，顯示對於健康的受測者，其ECG與BPW有較強的相位耦合，而心血管相關疾病的患者其相位耦合則較弱; 此外健康的受測者其轉移函數(Transfer function)也較心血管相關疾病的患者有較平坦的曲線，這些結果都顯示健康者的動脈系統彈性較心血管相關疾病的患者好。我們也建立此系統的頻域電路模型，並計算其諧振品質因素，結果顯示健康的受測者有較高的諧振品質因素。 此外ECG的頻率調變及振幅調變效應、血管壁的欠阻尼與過阻尼效應也被探討，在輸入的電刺激信號與輸出的血管壁振動信號間，我們計算其同調函數(Coherence function) ，因此我們可以計算輸入(心臟) 與輸出(動脈系統) 間同調及干擾的程度，前五個諧波的平均同調值被用來衡量同調的程度，實驗結果顯示健康的受測者其平均同調值趨近於1，同調的程度較心血管相關疾病的患者高，也就是干擾的程度較小，根據上述這些觀念，我們得以建立一個血液循環的系統模型。 最後我們研究靜坐前後對心血管循環系統時域特性的影響，我們觀察BPW中P波的上升斜率、T波的高度、降中峽的高度、D波的高度等參數，實驗結果顯示實驗組(靜坐者)的P波的上升斜率、T波及D波的高度皆較控制組明顯地(P<0.05)增加而降中峽的高度明顯地減少，顯示經由靜坐的訓練能使心血管循環系統的特性有明顯地改善。

In this dissertation, we presented a novel idea for analyzing blood circulation that is viewed as an electrically-driven, mechanical-pumping mechanism. Besides, a blood pressure wave equation (BPW)with radial dilation is used to describe the resonance effect in blood circulation. Considering the ECG (electrocardiograph) and BPW as the input and output signals of the system, we aim to apply the spectral analysis approach for evaluating the property of blood circulation from the viewpoint of resonance and coherence. First, the power spectrum of the ECG coincides well with that of the BPW for healthy subjects, but deviates significantly from the BPW’s for vascular patients. According to the results, we may infer that the artery wall of healthy subjects exhibits better elasticity of artery wall for healthy subjects than that of cardiovascular-related patients. Thus, the spectrum of ECG can be completely coupled to BPW’s. In other words, heart resonates with the arterial system. Second, bispectral analysis demonstrates a strong phase coupling between ECG and BPW for the healthy subjects and a weaker coupling for subjects with vascular problems. Third, the transfer function for healthy subjects exhibits a flatter magnitude than that for patients. All the results demonstrate that healthy subjects possess better artery elasticity for healthy subjects than that for cardiovascular patients. In addition, we propose a resonance circuit model in frequency domain to characterize the behavior of blood circulation. The quality factor of a healthy model also reveals better resonance characteristic than the one of an abnormal model. In addition, this thesis presents the results of investigating the FM (frequency modulation) and AM (amplitude modulation) effects on ECG, as well as the under-damping and over-damping effects in the blood circulation system are studied. Coherence function is used to measure the degree of BPW in resonance with ECG, from which perturbations of the system can be determined. System model based on the above concepts is accordingly established. The average of the first five peaks (S) is used to quantify the power coherence effect. The evaluated p-value (< 0.01) reveals that the distinction of power coherence between the healthy subjects and cardiovascular patients is significant. Consequently, we conclude that if the S approaches a value close to one, the output is almost completely attributed to the input. In the case, the system’s operation involves fewer perturbation signals so that the cardiovascular system will remain in a better condition. Conversely, if S is much below one, the cardiovascular system operates under high perturbation and tends to decay or become diseased. Finally, we study the effect of Zen meditation on the characteristics of cardiovascular system, mainly based on the time-domain features of blood pressure waveform. Four parameters derived from the BPW include the rising slope ( ) of P wave, the normalized height of T wave ( ), the normalized height of valley ( ), and the normalized height of D wave ( ), where t1 and hi, i = 1, …, 5 are quantitative features of the BPW waveform pattern. A larger value of reflects better heart ejection ability and aorta compliance. A larger value of may infer an arterial system with good elasticity. The decrease (increase) of parameter indicates the decrease (increase) of peripheral resistance of vessels. A larger value of indicates the better artery elasticity and aortic valve function. In comparison with the control group, Zen-meditation practitioners have the post-meditation , , and increase more, while decrease more, with statistical significance (P<0.05). The observation allows us to infer that Zen meditation effectively improves some important characteristics relevant to the health condition of cardiovascular system.