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 Title: 血壓與交感神經活性訊號數學關係之探討;A discussion of mathematical relations of blood pressure and sympathetic nerve signals Authors: 張雅筑;Yea-jwu Chang Contributors: 數學研究所 Keywords: 交感神經;阻尼函數;方盒函數;血壓;damping function;blood pressure;sympathetic nurve;box function Date: 2007-06-18 Issue Date: 2009-09-22 11:09:18 (UTC+8) Publisher: 國立中央大學圖書館 Abstract: 觀察受刺激狀態下血壓與交感神經兩生物訊號，採用阻尼函數與方盒函數分別來模擬此兩生物訊號，並利用數學模型找出其對應的參數，根據這些參數去討論在不同刺激頻率下，頻域為0至1Hz兩數學模型比值之對數關係，使用最小平方法求得直線關係。且利用此直線去分析在不同的刺激強度或不同的刺激時間下，對此直線關係的影響為何。並定義方盒函數的振幅倍率α與阻尼函數的振幅倍率f(α)為非線性關係，方盒函數與阻尼函數的持續時間關係為線性。本研究針對相同的刺激強度、不同刺激強度、相同刺激時間，以及不同刺激時間等各種情況下分析直線關係的改變，並得知在改變刺激強度時，則直線關係的y截距亦隨之改變，且α在0.8至1.4之間，當α值愈大，y截距愈大；改變阻尼函數的持續時間時，則改變了直線關係的斜率變化，當阻尼函數持續時間β愈大，斜率也愈大。且發現不同的方盒函數持續時間，所對應的交會點，隨著持續時間愈大而愈接近頻率小的地方。 The blood pressure and sympathetic nerve in the stimulated state were observed. We used the damping function and box function to simulate those two signals respectively, and experimented data were used to find the parameters of two mathematical models. Using the resulted parameters, we discussed the relationship between two mathematical models at the frequencies between 0 and 1 Hz with different stimulated frequencies. The least square method was used to determine the linear relation. We defined that the relation of amplitude of the box function and damping function to be nonlinear, and the relation of duration of the box function and damping function to be linear. Finally, we found that the y-intercept of the line obtained by the least square method changes when the stimulation intensity changes, while the slope changes when the duration of damping function changes. Appears in Collections: [數學研究所] 博碩士論文

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