Elsevier

Journal of Biomechanics

Volume 43, Issue 9, 18 June 2010, Pages 1806-1816
Journal of Biomechanics

Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

https://doi.org/10.1016/j.jbiomech.2010.02.011Get rights and content

Abstract

This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than ∼15% of global cell deformation in cell compression tests, or more than ∼3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.

Introduction

At the organ scale, image-based finite element (FE) modeling is currently considered a state-of-the-art biomechanical research methodology, where typically, computed tomography or magnetic resonance imaging are employed to obtain a set of planar images used to reconstruct a three-dimensional (3D) organ (Pistoia et al., 2004; Linder-Ganz et al., 2007; Portnoy et al., 2008; Lenaerts and van Lenthe, 2009). The equivalent of this at a cellular scale could be confocal microscopy imaging, which allows obtaining a set of planar images for individual cells; however, image-based modeling has not yet been employed at a cell-scale for large deformation analyses. The only attempt to develop a full-3D confocal-based cell model was made recently by Dailey et al. (2009) who reconstructed alveolar epithelial cells for FE modeling of shear flow effects, but employed the small strain theory to predict cell deformations. Another limitation of the Dailey study was the absence of cellular organelles, e.g. nucleus and cytoskeletal fibers. There was another recent publication by Gladilin et al. (2008) who studied topologies of nuclei reconstructed from fibroblasts using the FE modeling, but they also used small strain elasticity.

Utilization of confocal microscopy-based FE cell models with details of intracellular structures in large deformation analyses is likely to support experimental work in cellular mechanics. Specifically, it will allow realistic modeling of strains at a scale of individual cells in classic cell loading designs ,which typically involve large cell deformations, e.g. static and cyclic stretching, cell compression, micropipette aspiration, shear flow, and hydrostatic pressure. Nevertheless, 3D computational modeling of cell-specific strains in cellular structures subjected to large deformations presents a challenging task, particularly in numerically representing mechanical interactions at the cell-scale (μm-scale), coupled with interactions at scales that are orders-of-magnitude smaller, e.g. involving the plasma membrane or cytoskeletal fibers (for which characteristic dimensions are at a nm-scale).

In this study, confocal microscopy-based FE cell-specific models, consisting of nucleus, cytosol, plasma membrane and cytoskeletal fibers are analyzed under large deformations. Cellular strains occurring due to cell compression and stretching are investigated in the context of pressure ulcer research, selected here as an example of application. Specifically, large deformation analyses of skeletal muscle cells are important in studying the aetiology of deep tissue injury (DTI), a serious pressure ulcer that develops in muscle tissue overlying weight-bearing bony prominences, and may cause life-threatening complications (Agam and Gefen, 2007; Black, 2009). In a previous paper (Slomka et al., 2009), it was postulated that sustained compressive tissue deformations near bony prominences could cause muscle cell death by a mechanism of locally stretching plasma membranes of cells. This could increase membrane permeability, and perhaps also the permeability of the nucleus envelope, and eventually disrupt cellular homeostasis. The present models were therefore utilized for studying tensile strains in membranes and nuclei of myoblasts compressed and stretched in large deformations.

Section snippets

Cells

Skeletal muscle cells were used in their undifferentiated, myoblast form. Undifferentiated cells have not yet retained the morphological and functional characteristics they will acquire in their mature form. In the case of myoblasts, this refers to immature muscle cells that did not yet fuse together to form myotubes (Yun and Wold, 1996). Murine C2C12 myoblasts (cell line #CRL1722, ATCC, VA, USA) were maintained undifferentiated in a growth medium (GM) consisting of the Dulbecco's Modified

Compression simulations

Compressing the cells induced localized tensile strains in their membrane and NSA (see Fig. 5 for cell A) with peak and average tensile strains that increased in a power–law relationship with the GCD (Table 4; Fig. 6). Average tensile strains in the NSA were higher than in the membrane for both cells (Fig. 6). Peak and average membrane and NSA strains for the maximally reached GCD of 65% and 45% for cells A and B, respectively are detailed in Table 5. Plots of percentage membrane area and

Discussion

This study introduced a new confocal microscopy-based 3D cell-specific modeling methodology for simulating cellular mechanics experiments involving large cell deformations. This methodology was tested by simulating two specific setups, cell compression and cell stretching, which are physiological loading regimes, and are particularly used in pressure ulcer and DTI researches (Peeters et al., 2005a; Gawlitta et al., 2007; Gefen et al., 2008). Localized tensile strains in plasma membrane and NSA

Conflict of interest

The authors of the above paper state that they have no conflict of interest.

Acknowledgements

The authors appreciate the help of Dr. Eran Linder-Ganz and Ms. Sigal Portnoy from the Musculoskeletal Biomechanics Laboratory at the Department of Biomedical Engineering of the Faculty of Engineering at Tel Aviv University, for their technical assistance in using SolidWorks and ABAQUS. We are also thankful to Ms. Shira Or-Tzadikario from the same lab, for helping with the cell culturing. We appreciate the help of Mr. Shmulik Keidar (ADCOM Ltd., Givatayim, Israel) with technical issues related

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