在本研究中，我們對三尖瓣腱索的力學行為進行了理論方面的研究，在經過一系列的三尖瓣腱索單調拉伸實驗後，實驗結果顯示腱索呈現典型的J 型力-位移曲線，因此我們使用非線性彈簧替換掉Generalized Kelvin 模型的線性彈簧，建立一個新的非線性黏彈性模型。此外，我們考慮模型的參數以及模型的初始條件，推導出模型在受到逐步的力/位移、固定變化率的力/位移以及循環加載的力/位移下的解析解，將所得到的模型與腱索組織的實驗結果進行比對後，發現此模型能很好的描述腱索在受到潛變試驗以及單調拉伸試驗時的結果，接著我們也對模型的初始條件以及其他內部參數的變量進行了研究，以檢驗各個參數對模型在受到逐步以及固定變量的力時位移響應的影響。除此之外，我們透過模型的解析解以及Prony's method 設計出了一種參數識別的方法，並且成功的識別出模型的參數值。另外，我們也考慮了腱索在真實生理上的行為，透過動態力學分析以及體外試驗的結果，對模型實施長時間的模擬，在研究過程中，我們察覺到了模型在長時間模擬下的限制，並提出了解決辦法，包含（1）增加的參數與（2）使用帶有分數微分的黏彈性模型以進行長時間的模擬。

In the present study, the mechanical behavior of tricuspid valve (TV) chordae tendineae tissue is theoretically investigated. A series of uniaxial mechanical testing experiments of the TV chordae tendineae was conducted in Biomechanics and Biomaterials Design Laboratory hosted by Prof. Chung-Hao Lee and a viscoelastic model of chordae tendineae is developed by taking into account the initial condition of displacement of the tissue. This experimental result shows the typical J-shaped force-displacement curve of the TV chordae tendineae and the corresponding viscoelastic model is established via a nonlinear spring installed to replace the linear spring of the generalized Kelvin model. In addition, specified arrangements of the model parameters and the initial condition of the individual Kelvin element are proposed. The exact solutions of the model under step-wise, constant-rate, and cyclic loading forces/displacements are analytically derived. The resulted simulation is compared with the uniaxial mechanical testing of the TV chordae tendineae tissue and shows superior performance of the proposed model under creep and monotonic loading experiments. Furthermore, the parametric study of the model parameters are performed to examine the influence of initial conditions of displacement, as well as other internal variables, on the model response under step-wise and constant-rate forces. Also, we design a parameter identification method with the exact solution by Prony's method and successfully identify the parameters. Finally, we considered the operation in physiological heartbeat and conduct a long-term simulation by dynamic mechanical analysis (DMA) and in vitro experiment. In this research, we also realize the limitation of our model about yearlong simulation and come up with two solutions including (1) increasing the number of the Kelvin element or (2) establishing a new fractional viscoelastic model to tackle the long-term simulation.

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