Double-peak resonant mapping of cellular viscoelasticity in force-clamp detection of atomic force microscope

Abstract

The mechanical properties of cells are very important to their physiological functions and pathological states, and their variations are also potential indications for early identification of the relevant diseases such as various cancers. With the development of microcantilever sensor, the atomic force microscope (AFM) has become one of the most commonly used tools to detect nanoscale biomolecular mechanical properties. In this contribution, an integral type inhomogeneous viscoelastic moving boundary effect in AFM system is accurately delineated, and a potential conceptual proposal of using the double-peak resonance for microcantilever dynamic system is suggested to detect viscoelasticity of fixed cells. Mathematical models for the quasi-static and dynamic responses of microcantilever system with a viscoelastic moving boundary effect are presented. Laplace transform and its inverse transform, and differential method in the temporal domain and extended differential quadrature method (DQM) in the spatial domain are combined to obtain the relevant analytical solutions for quasi-static response and numerical solutions for dynamical response. Analytical results for quasi-static response agree well with the previous experiments and our simulations by the extended DQM. The results not only reveal that moving boundary conditions and cellular viscoelasticity cannot be ignored for signal extractions in the processes of cellular detection due to their significant influence on interaction force, bending deflection, natural frequency, and mode shape of microcantilever system, but also indicate a double-peak resonance-based method that could be potentially used to identify the transient-, steady-state modulus, and relaxation time of fixed cells.