水晶體在眼球中之動態力學特徵分析

Abstract

水晶體作為眼球中關鍵的光學與調焦結構，其力學穩定性與動態響應能力對維持清晰視覺扮演重要角色。然而，目前對於水晶體在視線轉動、眼壓變化或外力激發下之力學行為仍缺乏量化理解。因此，本研究旨在建立簡化振動理論於豬眼水晶體，在外力激發產生之動態行為，可推算水晶體彈性係數與阻尼特性。理論部分以單自由度與雙自由度的響應分析方法，並輔以協方差分析其特徵值，探討模態間的耦合關係。實驗部分，採用敲擊、噴氣與聲波驅動等外力輸入方式，並以紅外線測距儀記錄水晶體位移響應。另設計質量變動實驗以驗證模型適用性，並將振動參數代入根據理論自行撰寫的求解程式模擬其動態行為。分析結果顯示，水晶體振動頻率主要分布於10至20 Hz，阻尼比約為0.1至0.2，整體行為符合彈性體理論的趨勢；且於不同激發與邊界條件下均以單向振動模態為主。進一步配合有限元素分析，建立具懸韌帶與液體邊界條件之水晶體動態模型，要模態解析水晶體於外力激發下之位移響應與應力分佈，結果與對應之第一模態特徵值與實驗觀測結果一致。本研究透過單自由度與多自由度模型的第一模態響應確認水晶體在單顆與置於眼球中的頻率在10到20Hz之間。提出之實驗與數據，為未來眼球動態力學建模提供基礎依據。

The crystalline lens is a key optical and focusing structure in the eye, and its mechanical stability and dynamic response play an essential role in maintaining clear vision. However, the dynamic behavior of the lens under eye rotation, intraocular pressure changes, or external forces has not yet been fully characterized. This study aims to apply simplified vibration theory to describe the dynamic response of porcine lenses under external excitation, and to estimate their elastic modulus and damping ratio. Both single-degree-of-freedom (SDOF) and two-degree-of-freedom (2DOF) models were analyzed, with covariance analysis used to explore the coupling between vibration modes. Experimentally, lenses were stimulated by tapping, air puff, and acoustic input, and their displacement responses were measured using infrared sensors. A mass variation test was also designed to verify model applicability, and lens dynamics were simulated using custom MATLAB solvers. Results showed that lens vibration frequencies were mostly between 10–20 Hz, with damping ratios around 0.1–0.2, consistent with elastic system theory. Finite element modeling including zonular fibers and fluid boundaries further validated the lens’s primary mode behavior under force. The proposed experimental and modeling framework provides a biomechanical basis for future studies on ocular dynamics and intraocular lens design.