最佳控制理論於力學生物學之應用：刺激細胞生長的最佳週期性施力之設計

Abstract

細胞對機械刺激的反應在組織工程、再生醫學和力學生物學中扮演關鍵角色，然而根據現有的施力策略多依賴經驗法則來去設計，缺乏系統性與可量化的依據。本研究提出一套以最佳控制理論為核心，結合細胞生物力學的建模與數值模擬的分析，嘗試設計出細胞於特定時間內所受到的最佳週期性弦波施力策略，以最大化細胞變形響應、兼顧能量消耗效率以及保護細胞內部結構。 本研究分別建立線性彈性模型與非線性彈性模型，以描述細胞在力學刺激下之動態行為，並應用前向-後向疊代法進行數值模擬。透過時間網格數與容許誤差值之收斂性分析，選定適合之模擬參數後，進一步探討不同的控制輸入條件下細胞變形響應與目標函數的變化。模擬結果顯示，細胞變形與控制輸入呈現正相關；此外，最佳控制策略相較於任意振幅輸入可顯著提升系統效益。進一步於頻率掃描中亦發現最佳頻率點可使目標函數達最大值，說明控制輸入之動態參數設計具關鍵影響。 綜合而言，本研究驗證了最佳控制理論於細胞機械刺激設計中之可行性，並提出具彈性與擴展潛力之施力優化架構。未來若能結合實驗驗證與更複雜之生物動態模型，將有望應用於智能化細胞刺激平台之開發，提升再生醫學與生物工程之應用效益。

The cellular response to mechanical stimulation plays a pivotal role in tissue engineering, regenerative medicine, and mechanobiology. However, existing force application strategies are often designed based on empirical rules, lacking systematic structure and quantitative justification. This study proposes a framework centered on optimal control theory, integrating cellular biomechanical modeling with numerical simulation analysis, to design an optimal sin wave stimulation strategy applied within a specific time window. The objective is to maximize cellular deformation responses while balancing energy efficiency and protecting internal cellular structures. Two mechanical models were constructed: a linear elastic model and a nonlinear elastic model, to describe the dynamic behavior of cells under mechanical loading. A forward–backward iterative method was employed for numerical simulation. Convergence analysis was performed with respect to time grid density and tolerance values to determine suitable simulation parameters. The effects of various control input conditions on cell deformation and the objective function were further examined. Simulation results indicated a positive correlation between cell deformation and control input amplitude. In addition, the optimized control strategy significantly outperformed fixed-amplitude inputs in terms of system performance. Frequency analysis also revealed an optimal frequency that maximized the objective function, highlighting the critical role of dynamic parameter design in stimulation effectiveness. In conclusion, this study demonstrates the feasibility of applying optimal control theory to the design of cell mechanical stimulation strategies, and proposes a flexible, extensible framework for stimulation optimization. Future work combining experimental validation with more complex biological dynamic models is expected to facilitate the development of intelligent cell stimulation platforms, contributing to advancements in regenerative medicine and biomedical engineering.