生理活動如心跳起伏等被認定為複雜行為並為非線性過程且非?定性質。 因此非線性數學方法被發展以應用在這些混沌系統。 多尺度熵(Multiscale entropy-MSE) 和去趨勢波動分析(Detrended fluctuation analysis-DFA)是最常用的方法去量化在不同的時間尺度上的複雜性，而且被認為對分辨健康和病人特別是患有心臟衰竭的病人上較傳統的以熵為基礎的運算法則更為優異。 無論如何，此兩種方法在生理上的意義仍未清楚瞭解。 乙型交感神經阻斷劑在過去數十年一直被用作治療心衰竭的有效治療藥物，雖然陸續有很多不同的理論和證明，但呼吸竇性心律不整(Respiratory Sinus Arrhythmia-RSA)在其作用機轉之角色很少被提及甚至證明。 因此我們假設呼吸竇性心律不整是乙型交感神經阻斷劑在治療心衰竭病人時的其中一個重要的關連，甚至呼吸竇性心律不整的比例和強度大小會影響治療效果。 因此我們首先收集心衰竭病人在使用乙型交感神經阻斷劑治療後的MSE和DFA分析結果；然後利用創新的數學方法模擬不同RSA的分數（fraction）和振幅(amplitude)計算出MSE和DFA的結果跟之前實際臨床病人的數據作比較。 在10位以乙型交感神經阻斷劑(atenolol)治療進階心衰竭病人獲得包括基準、治療一個月和三個月後連續24小時心電圖記錄(24-hour Holter)。 短段去趨勢波動分析在以乙型交感神經阻斷劑治療1至3個月後增加但中段去趨勢波動分析並沒有增加。 在多尺度熵分析中，斜度1-5在治療1個月後上升並在治療3個月後由負值轉為正值。在面積5 在治療1個月後亦明顯由4.03±2.11 增加至 4.69±1.28。 在多尺度熵的大尺度參數在治療後沒有明顯增加。 研究中創新以模擬不同比例的分數和振幅的呼吸竇性心律不整在多尺度模型于以計算。 在模擬的多尺度熵的短時間尺度參數相較於長時間尺度具有相對的結果和變化。 總而言之，在我們的研究中多尺度熵和去趨勢波動分析是一種有效的方法可用於監測心衰竭病人的治療效果，而且更重要的是本論文中我們證明了透過首創的數學模型指出呼吸竇性心律不整很可能是導致乙型交感神經阻斷劑治療心衰竭病人的MSE和DFA改變的重要機轉。 ;Physiological behaviors such as heart rate fluctuations have been recognized as complex behaviors originated from nonlinear processes and often with nonstationary property. So non-linear mathematic methods was developed to apply on these chaos system. Multiscale entropy (MSE) and detrended fluctuation analysis (DFA) are the most common methods to quantify complexity in multiple time scales and has been demonstrated to be superior to traditional entropy-based algorithms in discriminating healthy and disease conditions, especially in investigation of congestive heart failure. However, their physical interpretation remains unclear. ?-blocker was used for patients with congestive heart failure for decades. Although studies were approved many different mechanisms of it’s treatment, RSA was seldom be showed as a important role. So we assumed RSA is a major role of mechanism in the treatment o f patients with congestsive heart failure, even it’s fraction and amplitude will contribute to different effects and results . So we collected the MSE and DFA results of the patients treated by ?-blokcer in our clinical practice. After that we utilized the novel model of simulated different fraction and amplitude of RSA to calculate the results of MSE and DFAto compare with the clinical results. Sequential 24-hour Holter ECG recordings were obtained at baseline, and 1 and 3 months after addition of atenolol therapy for advanced congestive heart failure in 10 patients. Short-term DFA increased after 1 to 3 months of atenolol treatment (0.79±0.16 vs. 0.95±0.22 and1.11±0.19 , all P < 0.05 compared with baseline ) while the intermediate-term DFA did not change. The slope 1-5 increased after 1 month of atenolol treatment (-0.08±0.10 vs. -0.03±0.10, P < 0.05) and changed from negative to positive value after 3 months of treatment (-0.03±0.10 vs. 0.02±0.06, P < 0.05). The mean area5 also significantly increased from 4.03±2.11 to 4.69±1.28 after 1 month of atenolol treatment. The large time-scale parameter of MSE (area6-20) did not significantly change after atenolol treatment (14.80±5.85 vs. 19.26±3.49, P = 0.06). The novel model of MSE with simulated different fractioin and amplitude of RSA components was calculated. The simulated short time-scale of parameter MSE was compatible with the actual results rather than the large time-scale parameter of MSE. In summary, MSE and DFA were a useful nonlinear methods to monitor the treatment of CHF and more importantly we proved that the change of RSA is possibly a major mechanism of MSE and DFA change in the treatment of CHF by ?-blocker.
