Numerical investigation of force and deflection of nanoneedle penetration into cell using finite element approach: Parameter study and experimental validation of results

This paper aims to develop a numerical methodology to investigate the penetration process of nanoneedles into cells and the corresponding force and indentation length. The finite element approach via the explicit dynamic method handles convergence difficulties in the nonlinear phenomenon. The cell is modeled as an isotropic elastic hemiellipsoidal shell with a thickness of 200 nm, which represents the lipid membrane and actin cortex, encapsulating cytoplasm that is regarded as an Eulerian body because of its fluid-type behavior. Nanoneedles with diameters 400, 200, and 50 nm are considered for model development based on available experimental data. The Von Mises strain failure criterion is used for rupture detection. A parameter study using 1, 2.5, 5, 7.5, and 10 kPa shows that Young's modulus of the HeLa cell membrane is about 5 kPa. Moreover, a failure strain of 1.2 chosen among 0.2, 0.4, 0.6, 0.8, 1, and 1.2 matches best the experimental data. In addition, a diameter study shows that the relations between force-diameter and indentation length-diameter are linear and polynomial, respectively. Furthermore, regarding the experimental data and by using contour of minimum principal stress around needle and an analytical equation for calculation of buckling force of a woven fabric, we proposed that for a given cell, membrane structural stability-a function of the coupled effect of Young's modulus and actin meshwork size-contributes directly to needle insertion success rate for that type of cell.

Profiling oocytes with neural networks from images and mechanical data

The success rate of assisted reproductive technologies could be greatly improved by selectively choosing egg cells (oocytes) with the greatest chance of fertilization. The goal of mechanical profiling is, thus, to improve predictive oocyte selection by isolating the mechanical properties of oocytes and correlating them to their reproductive potential. The restrictions on experimental platforms, however - including minimal invasiveness and practicality in laboratory implementation - greatly limits the data that can be acquired from a single oocyte. In this study, we perform indentation studies on human oocytes and characterize the mechanical properties of the zona pellucida, the outer layer of the oocyte. We obtain excellent fitting with our physical model when indenting with a flat surface and clearly illustrate localized shear-thinning behavior of the zona pellucida, which has not been previously reported. We conclude by outlining a promising methodology for isolating the mechanical properties of the cytoplasm using neural networks and optical images taken during indentation.

Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes

Probing mechanical properties of cells has been identified as a means to infer information on their current state, e.g. with respect to diseases or differentiation. Oocytes have gained particular interest, since mechanical parameters are considered potential indicators of the success of in vitro fertilisation procedures. Established tests provide the structural response of the oocyte resulting from the material properties of the cell's components and their disposition. Based on dedicated experiments and numerical simulations, we here provide novel insights on the origin of this response. In particular, polarised light microscopy is used to characterise the anisotropy of the zona pellucida, the outermost layer of the oocyte composed of glycoproteins. This information is combined with data on volumetric changes and the force measured in relaxation/cyclic, compression/indentation experiments to calibrate a multi-phasic hyper-viscoelastic model through inverse finite element analysis. These simulations capture the oocyte's overall force response, the distinct volume changes observed in the zona pellucida, and the structural alterations interpreted as a realignment of the glycoproteins with applied load. The analysis reveals the presence of two distinct timescales, roughly separated by three orders of magnitude, and associated with a rapid outflow of fluid across the external boundaries and a long-term, progressive relaxation of the glycoproteins, respectively. The new results allow breaking the overall response down into the contributions from fluid transport and the mechanical properties of the zona pellucida and ooplasm. In addition to the gain in fundamental knowledge, the outcome of this study may therefore serve an improved interpretation of the data obtained with current methods for mechanical oocyte characterisation.

Zona pellucida shear modulus, a possible novel non-invasive method to assist in embryo selection during in-vitro fertilization treatment

The present study investigated the association between oocyte zona pellucida shear modulus (ZPSM) and implantation rate (IR). Ninety-three oocytes collected from 38 in-vitro fertilization patients who underwent intracytoplasmic sperm injection were included in this case–control study. The ZP was modeled as an isotropic compressible hyperelastic material with parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{10}$$\end{document}C10, which represents the ZPSM. Computational methodology was used to calculate the mechanical parameters that govern ZP deformation. Fifty-one developed embryos were transferred and divided into two groups—implanted and not implanted. Multivariate logistic regression analysis was performed to identify the association between ZPSM and IR while controlling for confounders. Maternal age and number of embryos per transfer were significantly associated with implantation. The IR of embryos characterized by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{10}$$\end{document}C10 values in the range of 0.20–0.40 kPa was 66.75%, while outside this range it was 6.70%. This range was significantly associated with implantation (p < 0.001). Geometric properties were not associated with implantation. Multivariate logistic regression analysis that controlled for relevant confounders indicated that this range was independently associated with implantation (adjusted OR 38.03, 95% confidence interval 4.67–309.36, p = 0.001). The present study suggests that ZPSM may improve the classic embryo selection process with the aim of increasing IR.

Planar AFM macro-probes to study the biomechanical properties of large cells and 3D cell spheroids

The ability to measure mechanical response of cells under applied load is essential for developing more accurate models of cell mechanics and mechanotransduction. Living cells have been mechanically investigated by several approaches. Among them, atomic force microscopy (AFM) is widely used thanks to its high versatility and sensitivity. In the case of large cells or 3D multicellular aggregates, standard AFM probes may not be appropriate to investigate the mechanical properties of the whole biological system. Owing to their size, standard AFM probes can compress only a single somatic cell or part of it. To fill this gap, we have designed and fabricated planar AFM macro-probes compatible with commercial AFM instruments. The probes are constituted of a large flat compression plate, connected to the chip by two flexible arms, whose mechanical characteristics are tuned for specific biological applications. As proof of concept, we have used the macro-probes to measure the viscoelasticity of large spherical biological systems, which have a diameter above 100 μm: human oocytes and 3D cell spheroids. Compression experiments are combined with visual inspection, using a side-view configuration imaging, which allows us to monitor the sample morphology during the compression and to correlate it with the viscoelastic parameters. Our measurements provide a quantitative estimate of the relaxation times of such biological systems, which are discussed in relation to data present in literature. The broad applicability of the AFM macro-probes can be relevant to study the biomechanical features in any biological process involving large soft materials. STATEMENT OF SIGNIFICANCE: The understanding of the role of physical factors in defining cell and tissue functions requires to develop new methods or improve the existing ones to accurately measure the biomechanical properties. AFM is a sensitive and versatile tool to measure the mechanical features from single proteins to single cells. When cells or cell aggregates exceed few tens of microns, AFM suffers from limitations. On these biological systems the control of the contact area and the application of a precise uniform compression becomes crucial. A modification of the standard cantilevers fabrication allowed us obtaining AFM macro-probes, having large planar contact area and spring constant suitable for biological investigations. They were demonstrated valuable to characterize the mechanical properties of large hierarchical biological systems.

Separating the contributions of zona pellucida and cytoplasm in the viscoelastic response of human oocytes

The successful characterization of the mechanical properties of human oocytes and young embryos is of crucial relevance to reduce the risk of pregnancy arrest in in-vitro fertilization processes. Unfortunately, current study has been hindered by the lack of accuracy in describing the mechanical contributions of each structure (zona pellucida, cytoplasm) due to its high heterogeneity. In this work, we present a novel approach to model the oocyte response taking into account the effect of both zona and cytoplasm, as well as different loading conditions. The model is then applied to develop an experimental protocol capable of accurately separating the viscoelastic contribution of zona and cytoplasm by simply varying the loading condition. This new protocol has the potential to open the door to improving our understanding the mechanical properties of oocytes at different stages, and provide a quantitative predictive ability to the evaluation of oocyte quality. STATEMENT OF SIGNIFICANCE: Assisted reproductive technologies, such as in vitro fertilization, often rely on identifying high quality oocytes or female egg cells. The viscoelastic properties of these cells, such as stiffness and stress relaxation time, have been identified as potential objective indicators of cell quality. However, their characterization has proven difficult due to the structural heterogeneity of the cell and inconsistent loading conditions. This paper presents a new model that, although simple, addresses the above difficulties to provide accurate estimations of the cell's mechanical properties. Learning from this model, we then propose a novel non-invasive testing protocol to allow oocyte characterization with increased accuracy. We believe this effort would improve consistency in measurements and enhance our knowledge on the mechanics of oocytes.

A Flexure-Guided Piezo Drill for Penetrating the Zona Pellucida of Mammalian Oocytes

Mammalian oocytes such as mouse oocytes have a highly elastic outer membrane, zona pellucida (ZP) that cannot be penetrated without significantly deforming the oocyte, even with a sharp micropipette. Piezo drill devices leverage lateral and axial vibration of the micropipette to accomplish ZP penetration with greatly reduced oocyte deformation. However, existing piezo drills all rely on a large lateral micropipette vibration amplitude ( 20 ) and a small axial vibration amplitude (0.1 ). The very large lateral vibration amplitude has been deemed to be necessary for ZP penetration although it also induces larger oocyte deformation and more oocyte damage. This paper reports on a new piezo drill device that uses a flexure guidance mechanism and a systematically designed pulse train with an appropriate base frequency. Both simulation and experimental results demonstrate that a small lateral vibration amplitude (e.g., 2 ) and an axial vibration amplitude as large as 1.2 were achieved. Besides achieving 100% effectiveness in the penetration of mouse oocytes (n = 45), the new piezo device during ZP penetration induced a small oocyte deformation of 3.4 versus larger than 10 using existing piezo drill devices.

Investigating the mechanical properties of zona pellucida of whole human oocytes by atomic force spectroscopy

The role of mechanics in numerous biological processes is nowadays recognized, while in others, such as the fertilization process, it is still neglected. In the case of oocytes the description of their mechanical properties could improve the comprehension of the oocyte-spermatozoon interaction and be helpful for application in in vitro fertilization (IVF) clinics. Herein the mechanical properties of whole human oocytes (HOs) immediately after retrieval are investigated by indentation measurements with atomic force spectroscopy under physiological conditions. Measurements are performed on immature (metaphase I - MI) and mature (metaphase II - MII) HOs. According to their morphological characteristics MII-HOs are classified as "suitable" and "rejected"; these latter would be usually rejected for intracytoplasmic sperm injection (ICSI). For all maturation stages we observe that the elastic response of the zona pellucida (ZP) outer layer was different and distinguishable from the rest of the ZP-HO. The elasticity of this ZP outer layer varies with maturation and quality: stiffness decreases from immature MI to good quality MII, up to poor-quality rejected MII. An indirect analysis with IVF outcome indicates that the ZP outer layer of analysed HOs donated by women who achieved pregnancy is stiffer than that of HOs from women with negative outcome. Our findings suggest that mechanical properties can represent important oocyte quality indicators that may be exploited for the design of innovative ICSI dedicated cell sorters.