Theoretical modeling of tunable vibrations of three-dimensional serpentine structures for simultaneous measurement of adherent cell mass and modulus

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.