Technical Brief

Combining Displacement Field and Grip Force Information to Determine Mechanical Properties of Planar Tissue With Complicated Geometry

[+] Author and Article Information
Tina M. Nagel

Department of Mechanical Engineering,
University of Minnesota,
1100 Mechanical Engineering,
111 Church St. S.E.,
Minneapolis, MN 55455

Mohammad F. Hadi, Amy A. Claeson

Department of Biomedical Engineering,
University of Minnesota,
7-105 Nils Hasslemo Hall,
312 Church St. S.E.,
Minneapolis, MN 55455

David J. Nuckley

Department of Physical Medicine and Rehabilitation,
University of Minnesota,
420 Delaware St. S.E.,
MMC 297,
Minneapolis, MN 55455

Victor H. Barocas

Department of Biomedical Engineering,
University of Minnesota,
7-105 Nils Hasselmo Hall, 312 Church St. S.E.,
Minneapolis, MN 55455
e-mail: baroc001@umn.edu

For further information on strain uniformity and boundary conditions see Refs. [1] and [2].

This parameter set is from a previous test of a different annulus fibrosus lamella sample, fitted prior to improving the technique as shown in the current study.

This code is available for licensing at http://license.umn.edu/technologies/20130022_robust-image-correlation-based-strain-calculator-for-tissue-systems. There is no charge for an academic license.

Manuscript received April 4, 2014; final manuscript received July 7, 2014; accepted manuscript posted August 7, 2014; published online September 10, 2014. Assoc. Editor: Kristen Billiar.

J Biomech Eng 136(11), 114501 (Sep 10, 2014) (5 pages) Paper No: BIO-14-1149; doi: 10.1115/1.4028193 History: Received April 04, 2014; Revised July 07, 2014; Accepted August 07, 2014

Performing planar biaxial testing and using nominal stress–strain curves for soft-tissue characterization is most suitable when (1) the test produces homogeneous strain fields, (2) fibers are aligned with the coordinate axes, and (3) strains are measured far from boundaries. Some tissue types [such as lamellae of the annulus fibrosus (AF)] may not allow for these conditions to be met due to their natural geometry and constitution. The objective of this work was to develop and test a method utilizing a surface displacement field, grip force-stretch data, and finite-element (FE) modeling to facilitate analysis of such complex samples. We evaluated the method by regressing a simple structural model to simulated and experimental data. Three different tissues with different characteristics were used: Superficial pectoralis major (SPM) (anisotropic, aligned with axes), facet capsular ligament (FCL) (anisotropic, aligned with axes, bone attached), and a lamella from the AF (anisotropic, aligned off-axis, bone attached). We found that the surface displacement field or the grip force-stretch data information alone is insufficient to determine a unique parameter set. Utilizing both data types provided tight confidence regions (CRs) of the regressed parameters and low parameter sensitivity to initial guess. This combined fitting approach provided robust characterization of tissues with varying fiber orientations and boundaries and is applicable to tissues that are poorly suited to standard biaxial testing. The structural model, a set of C++ finite-element routines, and a Matlab routine to do the fitting based on a set of force/displacement data is provided in the on-line supplementary material.

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Grahic Jump Location
Fig. 1

Lamella of the AF. The sample is attached to bone, labeled, and is anisotropic with fibers aligned 30 deg from the horizontal testing axis, along the dotted line. The dissected tissue is too small to be removed from the bone and cut to align the fibers to the direction of pull for biaxial testing.

Grahic Jump Location
Fig. 2

Sensitivity of force (F) and displacement (U) error to model parameters. The parameter κ has been multiplied by 10 for visual clarity. Sensitivities of nodal measurements in the one and two directions are different due to the anisotropy of the model. A and B affect grip force but have less influence on the displacements, whereas displacements are more sensitive to μ and κ.

Grahic Jump Location
Fig. 3

Parameter error using simulated data perturbed with White Gaussian noise. Relative error for the fitted parameter is shown for each parameter: κ (•), μ (◻), A (▲), and B (▽). Parameters, κ, μ, and B are plotted on the left axis and parameter A is plotted on the right. Parameters κ, μ, and B are largely unchanged by the noise, and the relative error for A was less than 5% for signal to noise ratios greater than ten.

Grahic Jump Location
Fig. 4

Representative experiment grip force data fitted with the simple structural model based on grip force and nodal displacement data. A single arm along or near the fiber axis is shown for each tissue type: SPM (⋄), FCL (◻), and AF lamella (△). Data at low Green strains are inset to better visualize the FCL and AF lamella data. Each data set is fitted well considering all four grip forces as well as nodal displacements are fitted simultaneously.

Grahic Jump Location
Fig. 5

Representative experiment parameter estimates with each fitting approach based on the ratio of parameter value to the width of the CR. The fitting approaches shown refer to the data used to inform the model: grip forces and nodal displacements (BOTH), grip forces alone (FORCE), and nodal displacements alone (DISP). The tissue data fitted are (a) SPM, (b) FCL, and (c) AF lamella. The horizontal line represents the location where the fitted parameter value is equivalent to the width of the CR. Fitted parameters above the line are a more precise estimate than those below. The BOTH approach consistently fits three of the four parameters more precisely than the other approaches in the FCL and the AF lamella. The BOTH approach has a ratio larger than one for each parameter in each tissue type as opposed to the FORCE and DISP approaches.



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