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Compression testing of very soft biological tissues using semi-confined configuration—A word of caution

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Abstract

We analyse semi-confined (i.e. using no-slip boundary conditions) compression experiment of very soft tissue sample using finite element method. We show that the assumption that the planes perpendicular to the direction of the applied force remain plane during the experiments is not satisfied for compression levels lower than previously stated in Miller [2005. Method for testing very soft biological tissues in compression. Journal of Biomechanics 38, 153–158]. Therefore, we recommend that the parameters for constitutive models of very soft tissues be determined by fitting a solution of the finite element models of the experimental set-up to the measurements obtained using semi-confined compression experiments.

Introduction

The mechanical properties of very soft biological tissues—such as the brain, liver and kidney—are of interest to several fields, including computer-integrated surgery and biomechanical analysis of injury due to impacts. Determination of the mechanical properties of these soft tissues remains an experimental and analytical challenge.

In our previous publications, we suggested a way to reliably test very soft tissues in compression (Miller, 2005) and extension (Miller, 2001) using a semi-confined configuration. This method relies on attaching cylindrical samples of low aspect ratio to stress–strain machine platens using surgical glue, which allows using no-slip boundary conditions in the analysis of measurement results. The semi-confined test configuration has been used by a number of researchers, e.g. Cheng and Bilston (2007), Cheng and Chen (2003), Miller and Chinzei (2002), and Snedeker et al. (2005).

The applicability of the analytical relationships between stress and strain derived in our previous papers depends on the major assumption that the planes within the sample perpendicular to the direction of the applied force remain plane during the test is satisfied. In this paper, we analyse in detail the semi-confined compression experiment using the finite element method in an attempt to evaluate the validity of this assumption.

Section snippets

Finite element analysis of compression experiment

The semi-confined compression experiment set-up proposed by Miller (2005) is essentially the same as those used previously (Estes and McElhaney, 1970; Miller and Chinzei, 1997) but replaces a no-friction boundary condition at the tissue–platen interfaces, that is difficult to implement in practice, by a no-slip boundary condition (see Fig. 1).

We constructed a finite element model of the semi-confined compression experiment using the ANSYS software (ANSYS, Inc., Canonsburg, PA, USA). Cylindrical

Results

When simulating the compression experiment, we found that the cylindrical surface of the material sample came in contact with the platens at much lower compressions than initially thought. This material behaviour is best observed in Fig. 2.

Clearly, the increase of the contact surface demonstrates that the assumption stating that the planes perpendicular to the direction of the applied force remain plane is violated. Consequently, part of the measured reaction force is carried through the

Discussion and conclusions

Assumption 3 of Miller (2005) states: ‘the planes perpendicular to the direction of the applied force remain plane’. This assumption is invalid when the cylindrical surface of the material sample comes in contact with the compressing platen (formation of the expansion ring). Thus the model proposed by Miller (2005) for analysis of semi-confined compression experiments of very soft tissues is limited to analysis before formation of the expansion ring. We find that this occurs at a compression of

Conflict of interest

We have no conflicts of interest to report. All other than the employment sources of financial support (The Australian Research Council and The National Institute of Health) are disclosed in Acknowledgements.

Acknowledgements

The financial support of the Australian Research Council (Grants no. DP0770275 and DP0664534) and the National Institute of Health (Grant no. R03 CA126466-01A1) is gratefully acknowledged.

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