Poroelastic and viscoelastic properties of soft materials determined from AFM force relaxation and force-distance curves

In the field of tissue engineering, determining the mechanical properties of hydrogels is a key prerequisite to develop biomaterials mimicking the properties of the extracellular matrix. In mechanobiology, understanding the relationships between the mechanical properties and physiological state of cells is also essential. Time-dependent mechanical characterization of these soft materials is commonly achieved by atomic force microscopy (AFM) experiments in liquid environment. However, the determination of an appropriate model to correctly interpret the experimental data is often missing, making it difficult to extract quantitative mechanical properties. Here, force relaxation and force-distance curves were combined to elucidate the origin of dissipative processes involved in hydrogels and cells, before applying the relevant poroelastic or viscoelastic theory to model the curves. By using spherical AFM tips, analytical equations were developed to transform these curves into mechanical parameters by describing the relationships between the exerted force and the elastic, poroelastic or viscoelastic responses of semi-infinite and finite-thickness materials. Poroelastic behavior was evidenced for a thermoresponsive hydrogel and a set of poroelastic parameters was extracted from the force relaxation curves. In contrast, cells exhibited viscoelastic properties characterized by a single power-law relaxation over three-decade time scales. In addition, compressive modulus and fluidity exponent of cells were obtained by fitting force relaxation curves and approach-retraction force-distance curves. This combined theoretical and experimental framework opens a rigorous way toward quantitative mechanical properties of soft materials by (1) systematically determining the origin of their relaxation mechanisms, (2) defining the theoretical models to correctly interpret the experimental data, (3) using analytically solved equations to extract the mechanical parameters.