Influence of sperm impact angle on successful fertilization through mZP oscillatory spherical net model Andjelka Hedrih a,n , Mihailo Lazarevic b , Ana Mitrovic-Jovanovic c a Department for Bio-medical Science, State University of Novi Pazar, Novi Pazar, Vuka Karadzica bb, 36 300 Novi Pazar, Serbia b Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia c School of Medicine, University of Belgrade, Dr Subotica 8, 11 000 Belgrade, Serbia article info Article history: Received 5 September 2014 Accepted 12 January 2015 Keywords: Zona pellucid Discrete oscillatory spherical net model Oscillations Lissajous curves Sperm impact angle abstract According to the available literature, penetrating sperm creates an oblique path trough Zona pellucida (ZP) – the most outer surface of oocytes. Considering fertilization process as an oscillatory phenomenon, the influence of sperm impact angle relative to the oscillatory behavior of mouse ZP is described by using the discrete continuum mechanical model in the form of a spherical net model. A parametric frequency analysis of oscillatory behavior of knot material particles in the mouse ZP (mZP) spherical net model is conducted by using generalized Lussajous curves. The influence of impact angles of sperm cells on the corresponding knot mass particles’ resultant trajectory is discussed. Favorable sperm impact angles for successful fertilization are identified. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Studying the sperm–oocyte interaction is important for under- standing the process of fertilization. The precise molecular mechanism of mammalian fertilization is still not known, but from biochemical point of view it is considered that fertilization passes through several phases: recognition and specific receptor binding of sperm cell to ZP, acrozome reaction, penetration of sperm head trough zona pelucida, and cortical reaction [1]. In the process of fertilization both oocyte and spermatozoa pass through structural and biochemical changes [2]. “During the activation of the sperm cell (i.e. capacitation) in the female genital tract, dramatic reorganizations take place in the sperm plasma mem- brane in order to achieve the ability to fertilize the oocyte [3].” Certain amount of spermatozoa that undergo acrosome reaction at the time of insemination is required for fertilization to be successful. By using images of boar spermatozoa obtained with an optical phase-contrast microscope and learning vector quanti- zation, Alegre et al. [4] automatically classify individual sperm cells as acrosome-intact or acrosome-damaged with an overall test error of 6.8%. Clark [5] gave an alternative theory for successful sperm–ZP binding events and post-fertilization inhibition of sperm binding. According to this theory, content of the cortical granules causes modification of ZP2 that leads to modification of ZP3 that lacks sperm receptor and acrosome-inducing activity. Modified ZP2 and ZP3 are unsuitable for binding either acrosome reacted or acro- some intact sperm cells. The precise mechanism of how sperma- tozoa pass through ZP is still unclear. This process should have particular timing as ZP dynamically changes its mechanical prop- erties during the processes of oogenesis, fertilization, and pre- implantation development [6–12]. Ultrastructural analysis of mammal ZP by using transmission electronic microscopy (TEM) showed that the spermatozoid penetrated ZP by an oblique path [13,14], but the specific angle is still not known. “Binding of the sperm head by its flat surface could initiate the oblique angle of its subsequent penetration through the eutherian zona. The tangen- tial trajectory of that path ensures that it then closes as the zona stretches and thins during expansion of the blastocyst, so pre- venting the development of a hole(s)” [14]. Neither in vivo nor in vitro conditions of fertilization are always successful. Bayesian classifiers can be used to predict suitability of an embryo to succeed implantation [15]. Corani et al. [16] made a network model for predicting pregnancy after in vitro fertilization (IVF). The authors compare the proposed model with classification algorithms in the analysis of a data set containing IVF cycles performed at reproductive institute. There are several biomecha- nical models describing sperm–oocyte interaction from the bio- mechanical point of view [17–19]. Using contact mechanics based modeling Gefen [17] modeled relationship between sperm velocity and pressures applied to the ZP during early sperm–oocyte Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/cbm Computers in Biology and Medicine http://dx.doi.org/10.1016/j.compbiomed.2015.01.009 0010-4825/& 2015 Elsevier Ltd. All rights reserved. n Correspondence to: Trg Ucitelj Tase 3/9, 18 000 Nis, Serbia. Tel.: þ381 64 801 33 20; fax: þ381 18 42 41 663. E-mail addresses: handjelka@hm.co.rs, handjelka@gmail.com (A. Hedrih). Computers in Biology and Medicine 59 (2015) 19–29