Elsevier

Journal of Biomechanics

Volume 37, Issue 12, December 2004, Pages 1923-1928
Journal of Biomechanics

An analysis of the complete strain field within FlexercellTM membranes

https://doi.org/10.1016/j.jbiomech.2004.02.022Get rights and content

Abstract

The purpose of the current investigation was to use finite element analysis to quantify the complete strain field for the membranes of the FlexercellTM apparatus, a device extensively used to study the effects of mechanical loading on cultured cells. Four vacuum pressure simulations were run for the membrane for both the uniaxial and biaxial loading post, yielding the distribution of longitudinal (Exx) and transverse (Eyy) strain for the uniaxial post, and the radial (Err) and the circumferential (Eθθ) strain for the biaxial post. The discrete values of each strain were evaluated at the center of the loading post as well as the region off of the post. Experimental measurements were made for both types of loading posts in order to validate our simulations. The biaxial post simulation was found to provide a central circular region of equal and constant Err and Eθθ in the membrane on the post. Likewise, the uniaxial post simulation provided a definitive region of constant Exx for a central rectangular region on the post. For the uniaxial simulation, the region on the post resulted in small compressive Eyy, while the region off the post resulted in tensile Eyy. The biaxial simulation resulted in large tensile Err and Eθθ on the post, while the region off the post resulted in large Err and smaller Eθθ. Our simulations were reasonably consistent with the experimental measurements made for both types of loading posts. We believe that the results of this study will allow scientists to more accurately describe the response of cells to known strains on all portions of the membrane, thus increasing the range of known strain regions for investigation in the FlexercellTM apparatus.

Introduction

The biomechanical environment to which cells are exposed is important to their normal growth, development and function, and in some cases in the development of disease (Burger and Klein-Nulen, 1999; Raghavan et al., 1996; Li and Xu, 2000). Accordingly, there has been much interest in studying the role of biomechanical forces in cell biology and pathophysiology. It is important in such studies to provide well-controlled, physiologically consistent biomechanical forces to the cell being studied. This need has led to the introduction and even commercialization of many experimental devices.

One such device is the FlexercellTM system (Flexcell Corp, McKeesport, PA). In this device, a flexible silicone membrane is stretched across a loading post by the application of a vacuum pressure. The user may apply either biaxial strain with the use of a circular shaped loading post, or uniaxial strain with the use of an oblong-shaped loading post. For both cases, a sizable portion of the silicone membrane is not contained in the region on the loading post, where the strain field is known based on calibrations performed by the manufacturer. As a result, any cells that are grown on the off-post region of the membranes are exposed to an unknown strain field.

To our knowledge, there has been no quantification of the strain fields within the membrane of the FlexercellTM device, either with the uniaxial or the biaxial loading posts, reported in the literature. Gilbert et al. (1994) used the finite element method to determine the strain field for a circular cell culture plate containing a flexible surface, but this was without a loading post. Later, Brown (2000) summarized the stresses and strains for a variety of mechano-stimulus instruments with the use of a fluid–structure analysis. However, this analysis did not include the FlexercellTM device with loading posts.

The purpose of the current investigation was to use finite element analysis to quantify the complete strain field—i.e. within both the on-post and off-post regions—for the FlexercellTM membranes using both the uniaxial and biaxial loading posts. We believe that characterization of the complete strain field on these deformable membranes will allow investigators who use the device to analyze and interpret their experiments more accurately.

Section snippets

Methods

The membrane and post-geometries of single uniaxial and biaxial FlexercellTM wells can be seen in Fig. 1. The uniaxial post is designed to provide uniaxial strain in the X-direction. Dimensions for the membrane and posts were obtained from the manufacturer and confirmed via direct measurement in our laboratory

Results

The preliminary stress relaxation tests of the silicone material showed minimal (<5%) relaxation at 10 min. Because the Flexcell device operates at ∼1 Hz, this result suggests viscoelastic effects of the silicone material could be neglected given the duration of the loading phase of a single cycle of the Flexcell device (0.5 s). An r2 value of 0.99 was reported for the regression fit of the uniaxial tensile testing data to Eq. (3). The value for C1 determined from the nonlinear regression was 0.282

Discussion

The present study utilized the finite element method to quantify the strain distributions in a single well of a FlexercellTM plate manufactured by Flexcell Corp (McKeesport, PA). Specifically, two loading posts were investigated, one designed for creating a biaxial strain field and the other for creating a constant uniaxial strain field. The strain for the biaxial simulation was indeed found to be approximately equal in the radial and tangential directions for a circular region on the post,

Acknowledgements

We would like to acknowledge FlexcellTM for their correspondence throughout this study as well as Ajay Bohra, Timothy Maul, and Mohammed El Kurdi for technical assistance. Dr. Douglas Hamilton provided insights on cellular response differences on and off the post, which helped serve to motivate this study. Funding for this work was provided in part by grants from the NIH (R01 HL069368-01A1 and R01-HL-60670) to DAV.

References (8)

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