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研究生： 廖于凱
Liao, Yu-Kai
論文名稱： 心臟腱索的超黏彈性分析
Visco-hyperelastic Analysis on Chordae Tendineae
指導教授： 劉立偉
Liu, Li-Wei
學位類別： 碩士
Master
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 76
中文關鍵詞： 心臟腱索 、超黏彈性模式 、廣義非線性Kelvin模式 、階梯潛變實驗 、階梯鬆弛實驗
外文關鍵詞： chordae tendineae, visco-hyperelastic model, generalized nonlinear Kelvin model, step-wise creep test, step-wise relaxation test
相關次數： 點閱：61  下載：0 
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    • 心臟腱索連接心臟房室瓣膜和乳突肌，它的功能是確保心臟瓣膜能夠正常的運作，防止血液逆流回心房。先前的研究多將心臟腱索以線性彈性或非線性彈性模式描述其力學行為。然而，心臟腱索的實驗證據卻呈現不同的力學現象。本研究以廣義黏彈性Kelvin模式結合超彈性Ogden模式，提出廣義非線性Kelvin模式來描述心臟腱索的力學行為，其中以較佳的超彈性部份來獲得更貼近軟組織的非線性力學行為，另一方面則以黏彈性部份達到材料的時間相依特性，企圖提出一個能很好描述心臟腱索黏彈性行為的模式。為了更了解此模式的內涵，在理論上，我們求出模式的切線模數，藉此研究位移、速度、力量與加力速度對切線斜率的影響。於位移與力量控制下，以四階Runge-Kutta數值方法來獲得模式反應，並分別求得鬆弛試驗與潛變試驗下的結果。在模擬實驗上，選用標準非線性固體模式(一階廣義非線性Kelvin模式與Ogden彈簧串聯)，並且根據心臟腱索的潛變實驗，決定模式參數。進一步，藉由階梯潛變實驗、階梯鬆弛實驗、單邊循環載重實驗與多階段複合路徑實驗來探索並了解廣義非線性Kelvin-Ogden模式的能力與心臟腱索的力學行為。在未來，模擬實驗將與真實的心臟腱索實驗進行比對，以便獲得更匹配的參數或者更好的廣義非線性Kelvin模式選擇。這項研究將加深對心臟腱索力學行為的理解，並希望在未來能進一步幫助我們改善腱索失效的治療方法。

    The chordae tendineae connects the atrioventricular heart valves and the papillary muscle. Its function is to ensure that the heart valve can function normally and prevent blood from flowing back to the atrium. Previous studies had mostly described the mechanical behavior of the chordae tendineae by linear elastic or nonlinear elastic models. However, the experimental evidence of chordae showed different mechanical phenomena. In this study, combining the generalized viscoelastic Kelvin model with the hyperelastic Ogden model, we formulated the generalized nonlinear Kelvin-Ogden model, which is capable of describing the mechanical behavior of the chordae tendineae. In this model, the hyperelastic part is used to obtain the nonlinear behavior of the chordae and the viscoelastic part is used to describe its time-dependent properties. In order to better understand the model, from a theoretical perspective, we focused on the tangent modulus of the model and studied the effects of displacement, velocity, force and loading rate on it. Under the displacement control and the force control, the model formulation was rearranged and the fourth-order Runge-Kutta was used to solve the model and obtained the response under the relaxation test as well as the response of the creep test. In the simulation, the standard nonlinear solid model (the first-order generalized nonlinear Kelvin mode and Ogden spring in series) was selected, and the model parameters were determined according to a creep test of the chordae tendineae. Furthermore, we explored the capacity of the generalized nonlinear Kelvin-Ogden model and the mechanical behavior of the chordae tendineae via the step-wise creep testing, the step-wise relaxation testing, the cyclic loading experiment and the multi-stage compound path experiment. In the future, simulations will be compared with experimental results of the chordae in order to obtain more proper parameters or better selection of generalized nonlinear Kelvin models. This study would underpin the understanding of the behavior of chordae tendineae and further enable us to improve the therapies for chordae failure.

    摘要 I Abstract II 致謝 IV List of figures VIII List of tables XI Nomemclature XII 1 Introduction 1 1.1 Background 1 1.1.1 Chordae tendineae 1 1.1.2 Hyperelastic model for biological soft tissues 2 1.1.3 Nonlinear viscoelastic model for biological soft tissues 4 1.2 Objective 5 1.3 Outline 7 2 Material model and response under arbitrary inputs 8 2.1 Experimental evidence 8 2.1.1 Tissue preparation 8 2.1.2 Mechanical testing 9 2.2 Hyperelastic models and finite deformation 10 2.2.1 Strain energy density function 10 2.2.2 Ogden model in uniaxial tests 12 2.3 Generalized Kelvin models and its nonlinear extensions 13 2.3.1 Standard linear solid models and generalized Kelvin model 13 2.3.2 Nonlinear Kelvin model 14 2.3.3 Standard nonlinear solid model 16 2.4 Generalized nonlinear Kelvin-Ogden models and its tangent modulus 17 3 Model formulations and responses under specific inputs 23 3.1 Mathematical formulations of generalized nonlinear Kelvin-Ogden models under force-controlled input 23 3.1.1 Arbitrary force-controlled input 23 3.1.2 Step-wise force-controlled input 25 3.2 Mathematical formulations of generalized nonlinear Kelvin-Ogden models under displacement-controlled input 26 3.2.1 Arbitrary displacement-controlled input 26 3.2.2 Step-wise displacement-controlled input 28 4 Numerical simulations and discussions 29 4.1 Parameter estimation for standard nonlinear solid model 29 4.2 Numerical approaches by solving SNS models 30 4.2.1 Approaches for cases under force-controlled history 30 4.2.2 Approaches for cases under displacement-controlled history 32 4.3 Numerical simulation of the first-order GNK-Ogden model 33 4.3.1 Limitation of the NK model 33 4.3.2 Monotonic stretch 34 4.3.3 Creep testing 35 4.3.4 Step-wise force-controlled input 35 4.3.5 Step-wise displacement-controlled input 36 4.3.6 Force-controlled testing with incrementally-increased amplitude of the SNS model 37 4.3.7 Displacement-controlled testing with incrementally-increased amplitude of the SNS model 38 4.3.8 Multi-stage experiment under load/displacement-controlled history 39 4.4 Discussion 42 5 Conclusions 65 Reference 67 Appendix 72 A1. Theory of large deformation 72 A2. Numerical method 74

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