The Nonlinear Material Properties of Liver Tissue Determined From No-Slip Uniaxial Compression Experiments

[+] Author and Article Information
Esra Roan

CAE Research Laboratory, Department of Mechanical, Industrial, and Nuclear Engineering,  University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072roane@email.uc.edu

Kumar Vemaganti

CAE Research Laboratory, Department of Mechanical, Industrial, and Nuclear Engineering,  University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072Kumar.Vemaganti@uc.edu

J Biomech Eng 129(3), 450-456 (Nov 19, 2006) (7 pages) doi:10.1115/1.2720928 History: Received July 10, 2006; Revised November 19, 2006

The mechanical response of soft tissue is commonly characterized from unconfined uniaxial compression experiments on cylindrical samples. However, friction between the sample and the compression platens is inevitable and hard to quantify. One alternative is to adhere the sample to the platens, which leads to a known no-slip boundary condition, but the resulting nonuniform state of stress in the sample makes it difficult to determine its material parameters. This paper presents an approach to extract the nonlinear material properties of soft tissue (such as liver) directly from no-slip experiments using a set of computationally determined correction factors. We assume that liver tissue is an isotropic, incompressible hyperelastic material characterized by the exponential form of strain energy function. The proposed approach is applied to data from experiments on bovine liver tissue. Results show that the apparent material properties, i.e., those determined from no-slip experiments ignoring the no-slip conditions, can differ from the true material properties by as much as 50% for the exponential material model. The proposed correction approach allows one to determine the true material parameters directly from no-slip experiments and can be easily extended to other forms of hyperelastic material models.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of the uniaxial compression experiment

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Figure 2

Schematic of the model used in the finite element analysis of the no-slip compression experiment

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Figure 3

Bovine liver: (a) Samples are obtained from the portion to the right of the vertical line. (b) A cylindrical sample at the end of a typical no-slip unconfined compression experiment.

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Figure 4

Experimental stress-stretch results from the nearly frictionless unconfined compression experiments (n=13). The exponential strain energy function provides an excellent fit to the data.

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Figure 5

Contour plots of the correction factors f (top) and g (bottom) as functions of d∕h and B2

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Figure 6

Contour plot of the product of the correction factors f and g, which may be considered the correction factor for the elastic modulus of the material

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Figure 7

Experimental stress-stretch results from the no-slip unconfined compression experiments. The solid line shows the considerably softer response from the nearly frictionless experiments.

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Figure 8

Mean stress-stretch curve obtained using the correction factor approach. The spread in the corrected response is much smaller than that in the nearly frictionless response.

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Figure 9

Validation of the correction factor approach. Stress-stretch responses computed using the corrected material parameters and no-slip boundary conditions show good agreement with results from no-slip compression experiments on bovine liver tissue.

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Figure 10

Proposed correction approach applied to porcine liver data from Chui (16). The corrected response is significantly softer than the no-slip data.



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