骨構材料的黏彈塑性建模及其應用

Abstract

許多生物材料都具有很高的韌性以及抵抗外力的能力，特別是骨頭，在過往的研究中發現在微觀尺度下骨組織是由軟材（膠原纖維）以及硬材（礦物質）所組合而成的複合材料，而這兩種材料又以交錯的方式排列著，其外觀就跟水泥磚牆結構類似，故具有此微結構的材料，本研究稱為軟硬疊層材料。根據先前學者所提出的拉伸剪切鏈模式（tension-shear chain model, TSC model)，可知此種微結構由硬材乘載正向力，軟材傳遞剪力來增加韌性，硬軟材相輔相成形成一個力學性質良好的複合材料。然而在拉伸剪切鏈模式中，硬軟材都為線彈性，此行為並不符合膠原纖維的力學特性，因此在我們先前的研究，已經將軟材的模式推廣成黏彈性，發展出黏彈性拉伸剪切鏈模式（viscoelastic tension-shear chain model, VE TSC model)。本研究，首先深入談討材料微結構對於軟硬疊層材料的能量吸收與耗散能力的影響。接著，有鑒於傳統尤拉梁理論應用在骨頭的三點彎矩實驗會造成骨頭力學行為的低估，本研究將黏彈拉伸剪切鏈模式結合尤拉梁理論，考慮骨頭的真實斷面，發展出黏彈性微觀力學骨骼梁理論；同時進行大鼠腿骨的三點彎矩試驗，並透過電腦斷層掃描擷取鼠骨的真實斷面幾何，以驗證本研究提出之理論正確性。考量真實骨組織的力學行為，本研究再進一步將硬材推廣至彈塑性模式，發展黏彈塑性拉伸剪切鏈模式（viscoelastoplastic tension-shear chain model, VEP TSC model)。在此模式下，討論微結構幾何、軟硬材性質，對於軟硬疊層材料的能量吸收與耗散能力的影響。並且更進一步以此模式模擬骨組織在不同年齡或者不同健康情況下的力學行為。我們發現了模式中黏滯性和礦物體含量與人骨纖維中糖化終產物(advanced glycation end products, AGEs) 產物以及骨密度（bone mineral density, BMD）之間相對應的關係，透過這些關係我們的模式可以預測隨年齡或是疾病改變的骨頭力學性質以及骨折風險。本模式也結合破壞力學來探討礦物質的裂紋拓展以及裂紋尖端的應力場。最終我們發現相較於單調加載，循環加載下的骨組織力學特性更符合臨床上的趨勢。

Many biological materials exhibit high toughness and resistance to external forces, particularly bone. Previous research has revealed that at the microscopic scale, bone tissue is a composite material composed of soft material (collagen fibril) and hard material (minerals platlete) arranged in an interlocking pattern similar to the structure of a cement brick wall. Therefore, materials with this microstructure are referred to in this study as soft-hard layered materials. According to the previously proposed tension-shear chain (TSC) model, this type of microstructure features the hard material bearing normal forces and the soft material transmitting shear forces to enhance toughness. The synergy between the hard and soft materials forms a composite material with excellent mechanical properties. However, in the TSC model, both the hard and soft materials are linearly elastic, which does not align with the mechanical properties of collagen fibers. Consequently, our previous research has extended the model of soft material to viscoelasticity, developing the TSC model. This study first delves into the impact of the material microstructure on the energy absorption and dissipation capacity of soft-hard layered materials. Next, due to the traditional Euler-Bernoulli beam theory underestimates the mechanical behavior of bones in three-point bending tests, this study combines the viscoelastic TSC model with Euler-Bernoulli beam theory, taking into account the actual cross-section of the bone. This leads to the development of the Viscoelastic Micromechanical Bone Beam Theory. Concurrently, three-point bending tests were conducted on rat femurs, and computed tomography (CT) scans were used to capture the actual cross-sectional geometry of the bones to verify the accuracy of the proposed theory. Taking into account the real mechanical behavior of bone tissue, this study further extends the hard material to an elastoplastic model, developing the viscoelastoplastic TSC model. This model discusses the influence of microstructural geometry and the properties of soft and hard materials on the energy absorption and dissipation capacity of soft-hard laminated materials. Moreover, this model simulates the mechanical behavior of bone tissue under different ages or health conditions. We discovered correlations in the model between viscosity, mineral content, and advanced glycation end products (AGEs) in human bone fibers, as well as bone mineral density (BMD). Through these relationships, our model can predict changes in bone mechanical properties and fracture risk with age or disease. This model also incorporates fracture mechanics to explore the crack propagation of minerals and the stress field at crack tips. Ultimately, we found that the mechanical characteristics of bone tissue under cyclic loading are more consistent with clinical trends compared to monotonic loading.