Vibration-based methods can be used effectively to characterize the physical properties of biological materials, with an increasing interest focused on the mechanics of individual, living cells. Real-time measurements of cell properties, such as mass and Young's modulus, can yield important insights into many aspects of cell growth and metabolism as well as the interaction of cells with external stimuli (e.g., drugs). Vibrational test structures designed for the study of such cell properties often use fixed configurations and operational modes, with associated limitations in determining multiple characteristics of the cell, simultaneously. Recent development of mechanics-guided techniques for deterministic assembly of three-dimensional (3D) microstructures provides a route to vibrational frameworks that offer tunable configurations, vibration modes, and resonant frequencies. Here we propose a method that exploits such tunable vibrational structures to simultaneously determine the mass and modulus of a single adherent cell, or of other biological materials or small-scale living systems (e.g., organoids), through theoretical modeling and finite element analysis. The idea involves a 3D architecture that supports two different vibrational structures and can be converted from one to the other through application of strain to an elastomeric substrate. Specifically, tailored designs for serpentine ribbons in these systems enable a decoupling of the dependence of the resonant frequencies of the two structures to the cell mass and modulus, with an associated ability to measure these two properties accurately and independently. These same concepts can be scaled to apply to various types of cells, as well as to organoids (3D clusters of cells) and other biological materials with small geometries, across a range of values of mass and modulus. This method could serve as the foundation for microelectromechanical systems capable of monitoring mass and modulus in real time for use in research in biomechanics and dynamic biological processes.

基于振动的方法可以有效地用于表征生物材料的物理特性，并且越来越多地关注单个活细胞的力学。诸如质量和杨氏模量之类的细胞特性的实时测量可以对细胞生长和代谢的许多方面以及细胞与外部刺激（例如药物）的相互作用产生重要的见解。为研究这种电池特性而设计的振动测试结构通常使用固定的配置和操作模式，同时在确定电池的多个特性方面受到相关限制。用于确定性组装三维（3D）微结构的力学指导技术的最新发展提供了通往振动框架的途径，该振动框架可提供可调整的配置，振动模式和共振频率。在这里，我们提出一种方法，通过理论建模和有限元分析，利用这种可调谐的振动结构来同时确定单个贴壁细胞或其他生物材料或小规模生物系统（例如类器官）的质量和模量。这个想法涉及一种3D架构，该架构支持两种不同的振动结构，并且可以通过向弹性体基底施加应变来将其从一种转换为另一种。具体而言，在这些系统中为蛇形带设计的定制设计可以使两个结构的共振频率与细胞质量和模量之间的依赖性脱钩，并具有准确，独立地测量这两个性质的相关能力。这些相同的概念可以缩放以适用于各种质量和模量值范围内的各种类型的细胞，以及类器官（细胞的3D簇）和其他具有小几何形状的生物材料。该方法可作为能够实时监测质量和模量的微机电系统的基础，以用于生物力学和动态生物过程的研究。