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Research Papers

Identification of Regional Mechanical Anisotropy in Soft Tissue Analogs

[+] Author and Article Information
Ramesh Raghupathy1

Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455Department of Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455

Colleen Witzenburg, Spencer P. Lake, Edward A. Sander

Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455Department of Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455

Victor H. Barocas

Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455baroc001@umn.eduDepartment of Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455baroc001@umn.edu

1

Corresponding author. Present address: Department of Biomedical Engineering 7-105 Nils Hasselmo Hall, 312 Church St. SE, Minneapolis, MN 55455

J Biomech Eng 133(9), 091011 (Oct 14, 2011) (7 pages) doi:10.1115/1.4005170 History: Received January 11, 2011; Revised September 09, 2011; Published October 14, 2011

In a previous work (Raghupathy and Barocas, 2010, “Generalized Anisotropic Inverse Mechanics for Soft Tissues,”J. Biomech. Eng., 132 (8), pp. 081006), a generalized anisotropic inverse mechanics method applicable to soft tissues was presented and tested against simulated data. Here we demonstrate the ability of the method to identify regional differences in anisotropy from full-field displacements and boundary forces obtained from biaxial extension tests on soft tissue analogs. Tissue heterogeneity was evaluated by partitioning the domain into homogeneous subdomains. Tests on elastomer samples demonstrated the performance of the method on isotropic materials with uniform and nonuniform properties. Tests on fibroblast-remodeled collagen cruciforms indicated a strong correlation between local structural anisotropy (measured by polarized light microscopy) and the evaluated local mechanical anisotropy. The results demonstrate the potential to quantify regional anisotropic material behavior on an intact tissue sample.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Samples with visual texture added for strain tracking: (a) PDMS cruciform (isotropic, homogeneous) textured with graphite powder. (b) PDMS cruciform (isotropic, heterogeneous) textured with spray paint. The central square region is of one-tenth the surrounding thickness. (c) Collagen TE (anisotropic, heterogeneous) with arm-width ratio of 1:0.5 textured by Verhoeff stain and incubated for seven days. (d) Collagen TE sample similar to (c) but incubated for 11 days.

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Figure 2

Each of the four arms of the cruciform sample are either extended or held fixed. A total of fifteen biaxial tests are performed by these five basic protocols: equibiaxial (1), two-adjacent arms (4), single arm (4), strip biaxial (2), and three arms (4), where the number in parenthesis represents the number of cyclic permutations of each test.

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Figure 3

GAIM alignment maps (a,b) and Kelvin moduli plots (c,d) for isotropic PDMS samples. The length of vectors in (a,b) is the relative anisotropy in each partition. (a) Homogeneous sample shows low anisotropy values at the belly, indicating a largely isotropic sample. (b) Heterogeneous sample also shows low anisotropy, indicating an isotropic sample. (c) Homogeneous sample has uniform values in Kelvin modulus at the belly. (d) Heterogeneous sample shows a relatively compliant region at the center which corresponds to the location of the thin section (shown in dashed lines).

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Figure 4

Polarized light alignment maps for 1:0.5 collagen TE incubated for 7 and 11 days shows variation in sample anisotropy from isotropic to completely aligned. Retardation from PLM is a measure of the strength of fiber alignment (high retardation values indicate high alignment). The contour shows the normalized retardation from polarimetry and the vectors indicate the direction of alignment with vector lengths corresponding to the normalized retardation value. (a) 7-day sample shows high alignment at arms and curved ends while most of the belly is less aligned. (b) 11-day shows moderate alignment in center along the wide axis, two isotropic regions offset from the center, and strong alignment at arms and curved ends.

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Figure 5

GAIM alignment maps and Kelvin modulus plots for 7-day and 11-day TE samples. The alignment maps from GAIM are indicative of the mechanical anisotropy of all elements in each partition. Alignment map for 7-day (a) and 11-day (b) samples show similar patterns to polarized light data, namely a large isotropic region for the 7-day, and increased alignment at 11-days. (c) Kelvin modulus (surface tension) plot for 7-day sample shows a range of values from 50-160 N/m at the belly. (d) Kelvin modului (surface tension) for 11-day sample are evaluated to be within 30-85 N/m at the belly.

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Figure 6

Comparison of alignment maps generated by the model (GAIM) and the experiment (polarized light microscopy) for 7-day and 11-day TE samples. The retardation and fiber alignment data from PLM were vector-averaged over each partition. The contour in the figures show the magnitude of difference in alignment angles between GAIM and PLM. The vectors indicate the relative anisotropy with the length given by the value of rGAIM (for model) and averaged retardation (for experiment) in each partition. The length of the vectors in the legend indicate the maximum anisotropy of 1. There is excellent match between the alignments from model and experiments. The regions with large differences in angles correspond to largely-isotropic partitions where any angle is acceptable since there is no preferred direction.

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