Visco-Hyperelastic Characterization of the Equine Immature Zona Pellucida

Abstract

This article presents a very detailed study on the mechanical characterization of a highly nonlinear material, the immature equine zona pellucida (ZP) membrane. The ZP is modeled as a visco-hyperelastic soft matter. The Arruda–Boyce constitutive equation and the two-term Prony series are identified as the most suitable models for describing the hyperelastic and viscous components, respectively, of the ZP’s mechanical response. Material properties are identified via inverse analysis based on nonlinear optimization which fits nanoindentation curves recorded at different rates. The suitability of the proposed approach is fully demonstrated by the very good agreement between AFM data and numerically reconstructed force–indentation curves. A critical comparison of mechanical behavior of two immature ZP membranes (i.e., equine and porcine ZPs) is also carried out considering the information on the structure of these materials available from electron microscopy investigations documented in the literature.

Mechanical Characterization of Soft Membranes with One-Shot Projection Moiré and Metaheuristic Optimization

“…The observed residual errors in the hybrid numerical-experimental identification process hence were fully consistent with the level of uncertainty normally entailed by FEMU-based characterization. Optically measured (d) Remarkably, HS-JAYA solved variants 1 and 2 of the identification problem including, respectively, 324 and 110 unknown material/structural parameters, a significantly larger number of unknowns than those usually reported in the literature for elastomers and rubberlike materials [66][67][68][69][70][71][72] (from two to six unknown material parameters or neural networks depending on three input characteristics), visco-hyperelastic materials [73][74][75] (from six to nine unknown material parameters including tangent modulus and softening index, Prony constants and relaxation times), biological tissues [76][77][78][79][80][81] (from five to sixteen unknowns accounting also for visco-elastic effects and stochastic variation of material properties), non-homogeneous hyperelastic structures [37,63,[82][83][84] (from four to sixteen unknown material parameters for the global model, or two unknown material parameters for each local inverse problem at the element level) or anisotropic hyperelastic materials modeled with much more complicated constitutive equations [27,34,[84][85][86] (from three to seventeen unknown material parameters). A very recent study by Borzeszkowski et al [38] considered identification problems of nonlinear shells subject to various loading conditions (i.e., uniaxial tension, pure bending, sheet inflation and abdominal wall pressurization).…”

Finite Element Modeling of Cells Adhering to a Substrate: An Overview

“…This review article presents an overview of useful guidelines for implementing accurate finite element simulation of cellular adhesion phenomena. By adopting ap-propriate modeling approaches, it is possible to reproduce findings obtained through experiments [61][62][63][64][65] and develop numerical frameworks capable of predicting cell behavior evolution, thus providing an in-depth insight into cell adhesion mechanisms.…”

In Situ TEM and AFM for Investigation of Materials

“…The last article of the Special Issue regarded the mechanical characterization of a complex biological structure, the immature equine zona pellucida (i.e., the extracellular membrane surrounding oocytes) [ 10 ]. For that purpose, Ficarella et al developed a hybrid framework combining AFM nanoindentation experiments, visco-hyperelastic models, nonlinear finite element analysis and nonlinear optimization.…”