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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Multi-parametric Dependence of DeformationWork of Zona Pelucida in Fertilization Process Trough Quasi-static Continual Shell-like ZP Model

Discontinuity, Nonlinearity, and Complexity 6(4) (2017) 465--476 | DOI:10.5890/DNC.2017.12.005

Andjelka Hedrih$^{1}$, Katica (Stevanovic) Hedrih$^{1}$,$^{2}$

$^{1}$ Department of Mechanics, Mathematical Institute of Serbian Academy of Sciences and Arts, (MI SANU), 11000 Belgrade Serbia, Mathematical institute SANU, 11000 Belgrade, Serbia

$^{2}$ Faculty of Mechanical engineering, University of Nis, 18 000 Nis, Serbia

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Zona Pelucida (ZP) is highly specialized glycosylated and sulfated polymer gel that surrounds mammalian oocyte, exhibits elastic or viscoelastic properties and change of diameter in different maturation stages. In process of in vitro fertilization, sperm cells affect the external ZP surface and transfer certain amount of energy to the ZP structure that goes through the deformation work. ZP thickness and number of motile sperm cells are important factors that may influence the fertility. Using the quasi-static approximate ZP model in the form of hollow sphere the numerical analysis of how specific deformation work depends of different variables like: ZP thickness, specific point in ZP, external pressure that comes from sperm cells were done. According to the model, sperm that make pressure upon ZP surface are in the form of homogeny discrete continuum distribution in radial directions. For specific ZP point in the model, analytical expressions of component stresses and strains were obtained as well as deformations and volume dilatation in ZP. The results are discussed from biomechanical aspect of fertilization. Limitations of the model are also discussed.


This work was supported by the Ministry of Education, Sciences and Technology of the Republic of Serbia through Mathematical Institute SANU, Belgrade and Faculty of Mechanical Engineering, University of Niš, Grant ON174001. Authors would like to thank reviewers for critical review of the manuscript and for useful suggestions.


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