Investigation of Cellular Contraction Forces in the Frequency Domain Using a PDMS Micropillar-Based Force Transducer

Polydimethylsiloxane (PDMS) micropillar-based biotransducers are extensively used in cellular force measurements. The accuracy of these devices relies on the appropriate material characterization of PDMS and modeling to convert the micropillar deformations into the corresponding forces. Cellular contraction is often accompanied by oscillatory motion, the frequency of which ranges in several hertz. In this paper, we developed a methodology to calculate the cellular contraction forces in the frequency domain with improved accuracy. The contraction data were first expressed as a Fourier series. Subsequently, we measured the complex modulus of PDMS using a dynamic nanoindentation technique. An improved method for the measurement of complex modulus was developed with the use of a flat punch indenter. The instrument dynamics was characterized, and the full contact region was identified. By incorporating both the Fourier series of contraction data and the complex modulus function, the cellular contraction force was calculated by finite-element analysis (FEA). The difference between the Euler beam formula and the viscoelastic FEA was discussed. The methodology presented in this work is anticipated to benefit the material characterization of other soft polymers and complex biological behavior in the frequency domain.