A hybrid characterization framework to determine the visco-hyperelastic properties of a porcine zona pellucida

The zona pellucida (ZP) is a specialized extracellular matrix surrounding the developing oocyte. This thick matrix consists of various types of glycoprotein that play different roles in the fertilization process. Nowadays, several techniques are available for assessing ZP's mechanical response. The basic assumption behind these methods is that the ZP behaves like an elastic body: hence, dissipative forces are neglected and Young's modulus remains unaffected by probe dynamics. However, dissipative forces are strongly regulated by the slippage of ZP chains past one another while reaction forces related to elastic deformations (driven by the ability of each chain to stretch) depend on the ZP structure (i.e. number of cross-links and distances between knots). Although viscous reaction forces generated by the ZP are one of the main factors regulating sperm transit, their peculiar behaviour along the ZP structure remains poorly understood and rarely investigated. In order to overcome this limitation, a novel visco-hyperelastic model describing the porcine ZP reaction forces generated by nanoindentations at different probe rates is developed and verified in this study. Visco-hyperelastic parameters of porcine ZP membranes are determined by means of a hybrid characterization framework combining atomic force microscopy nanoindentation measurements, nonlinear finite-element analysis and nonlinear optimization. Remarkably, it is possible to separate the contributions of hyperelastic and viscous terms to ZP mechanical response and evaluate the error made in the determination of ZP mechanical properties if viscous effects were not considered.