Hyperelastic models for the human zona pellucida and their implications on shear modulus estimation in the clinical practice

It has long been speculated that the mechanical properties of the human oocyte can be an indicator for oocyte viability. Recent studies have demonstrated that embryo implantation rates, following Intra-Cytoplasmic Sperm Injection (ICSI) procedures, may be increased if the shear modulus value of the oocyte Zona Pellucida (ZP) is taken into consideration during embryo transfer. The shear modulus was determined by an iterative oocyte specific finite element (FE) analysis based on the clinical ICSI data. Nevertheless, the results obtained from the computational analysis may depend on the choice of the constitutive model used for the ZP. In the current study, three different hyper-elastic strain energy density functions (SEDF's) are considered. The Neo-Hookean (NH), Mooney-Rivlin (MR) and Ogden models (OG) were used to determine the ZP shear modulus from ICSI clinical data. The sensitivity of each SEDF in extracting the oocyte specific shear modulus is examined, for the first time. It is demonstrated that the NH and MR models are more sensitive than the OG model for determining the ZP shear modulus from clinical ICSI data. It is also demonstrated that the accuracy of ZP shear modulus identification process greatly depends on the value of suction pressure applied during the ICSI procedure.