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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Eilaghi, A., Flanagan, J. G., Brodland, G. W., and Ethier, C. R., 2009, “Strain Uniformity in Biaxial Specimens is Highly Sensitive to Attachment Details,” ASME J. Biomech. Eng., 131(9), p. 091003. [CrossRef]
Sun, W., Sacks, M. S., and Scott., M. J., 2005, “Effects of Boundary Conditions on the Estimation of the Planar Biaxial Mechanical Properties of Soft Tissues,” ASME J. Biomech. Eng., 127(4), pp. 709–715. [CrossRef]
Fung, Y. C., 1973, “Biorheology of Soft Tissues,” Biorheology, 10(2), pp. 139–155. [PubMed]
Sacks, M. S., and Gloeckner, D. C., 1999, “Quantification of the Fiber Architecture and Biaxial Mechanical Behavior of Porcine Intestinal Submucosa,” J. Biomed. Mater. Res., 46(1), pp. 1–10. [CrossRef] [PubMed]
Waldman, S., and Lee, J., 2002, “Boundary Conditions During Biaxial Testing of Planar Connective Tissues Part II Fiber Orientation,” J. Mater. Sci. Lett., 21(15), pp. 1215–1221. [CrossRef]
Waldman, S., Sacks, M., and Lee, J., 2002, “Boundary Conditions During Biaxial Testing of Planar Connective Tissues. Part 1: Dynamic Behavior,” J. Mater. Sci.: Mater. Med., 13(10), pp. 933–938. [CrossRef] [PubMed]
Jacobs, N. T., Cortes, D. H., Vresilovic, E. J., and Elliott, D. M., 2013, “Biaxial Tension of Fibrous Tissue: Using Finite Element Methods to Address Experimental Challenges Arising From Boundary Conditions and Anisotropy,” ASME J. Biomech. Eng., 135(2), p. 021004. [CrossRef]
Miller, K. S., Connizzo, B. K., Feeney, E., Tucker, J. J., and Soslowsky, L. J., 2012, “Examining Differences in Local Collagen Fiber Crimp Frequency Throughout Mechanical Testing in a Developmental Mouse Supraspinatus Tendon Model,” ASME J. Biomech. Eng., 134(4), p. 041004. [CrossRef]
Miller, K. S., Edelstein, L., Connizzo, B. K., and Soslowsky, L. J., 2012, “Effect of Preconditioning and Stress Relaxation on Local Collagen Fiber Re-Alignment: Inhomogeneous Properties of Rat Supraspinatus Tendon,” ASME J. Biomech. Eng., 134(3), p. 031007. [CrossRef]
Sacks, M. S., 2000, “Biaxial Mechanical Evaluation of Planar Biological Materials,” J. Elast., 61(1–3), pp. 199–245. [CrossRef]
Skaggs, D. L., Weidenbaum, M., Latridis, J. C., Ratcliffe, A., and Mow, V. C., 1994, “Regional Variation in Tensile Properties and Biochemical Composition of the Human Lumbar Anulus Fibrosus,” Spine, 19(12), pp. 1307–1417. [CrossRef] [PubMed]
Holzapfel, G. A., Schulze-Bauer, C. A. J., Feigl, G., and Regitnig, P., 2005, “Single Lamellar Mechanics of the Human Lumbar Anulus Fibrosus,” Biomech. Model. Mechanobiol., 3(3), pp. 125–140. [CrossRef] [PubMed]
Pezowicz, C., 2010, “Analysis of Selected Mechanical Properties of Intervertebral Disc Annulus Fibrosus in Macro and Microscopic Scale,” J. Theor. Appl. Mech., 48, pp. 917–932.
Bass, E. C., Ashford, F. A., Segal, M. R., and Lotz, J. C., 2004, “Biaxial Testing of Human Annulus Fibrosus and Its Implications for a Constitutive Formulation,” Ann. Biomed. Eng., 32(9), pp. 1231–1242. [CrossRef] [PubMed]
O'Connell, G. D., Sen, S., and Elliott, D. M., 2012, “Human Annulus Fibrosus Material Properties From Biaxial Testing and Constitutive Modeling Are Altered With Degeneration,” Biomech. Model. Mechanobiol., 11(3–4), pp. 493–503. [CrossRef] [PubMed]
Malgorzata, Z., and Pezowicz, C., 2013, “Spinal Sections and Regional Variations in the Mechanical Properties of the Annulus Fibrosus Subjected to Tensile Loading,” Acta Bioeng. Biomech., 15(1), pp. 51–59.
Elliott, D. M., and Setton, L. A., 2001, “Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions,” ASME J. Biomech. Eng., 123(3), pp. 256–263. [CrossRef]
Gaudette, G. R., Todaro, J., Krukenkamp, I. B., and Chiang, F.-P., 2001, “Computer Aided Speckle Interferometry: A Technique for Measuring Deformation of the Surface of the Heart,” Ann. Biomed. Eng., 29(9), pp. 775–780. [CrossRef] [PubMed]
Doehring, T. C., Kahelin, M., and Vesely, I., 2009, “Direct Measurement of Nonuniform Large Deformations in Soft Tissues During Uniaxial Extension,” ASME J. Biomech. Eng., 131(6), p. 061001. [CrossRef]
Quinn, K. P., and Winkelstein, B. A., 2010, “Full Field Strain Measurements of Collagenous Tissue by Tracking Fiber Alignment Through Vector Correlation,” J. Biomech., 43(13), pp. 2637–2640. [CrossRef] [PubMed]
Raghupathy, R., Witzenburg, C., Lake, S. P., Sander, E. A., and Barocas, V. H., 2011, “Identification of Regional Mechanical Anisotropy in Soft Tissue Analogs,” ASME J. Biomech. Eng., 133(9), p. 091011. [CrossRef]
Keyes, J. T., Haskett, D. G., Utzinger, Urs., Azhar, M., and Geest, J. P. V., 2011, “Adaptation of a Planar Microbiaxial Optomechanical Device for the Tubular Biaxial Microstructural and Macroscopic Characterization of Small Vascular Tissues,” ASME J. Biomech. Eng., 133(7), p. 075001. [CrossRef]
Witzenburg, C., Raghupathy, R., Kren, S. M., Taylor, D. A., and Barocas, V. H., 2012, “Mechanical Changes in the Rat Right Ventricle With Decellularization,” J. Biomech., 45(5), pp. 842–849. [CrossRef] [PubMed]
Li, W. G., Luo, X. Y., Hill, N. A., Ogden, R. W., Smythe, A., Majeed, A. W., and Bird, N., 2012, “A Quasi-Nonlinear Analysis of the Anisotropic Behaviour of Human Gallbladder Wall,” ASME J. Biomech. Eng., 134(10), p. 101009. [CrossRef]
Barbone, P. E., and Oberai, A. A., 2007, “Elastic Modulus Imaging: Some Exact Solutions of the Compressible Elastography Inverse Problem,” Phys. Med. Biol., 52(6), pp. 1577–1593. [CrossRef] [PubMed]
Pellot-Barakat, C., Frédérique, F., Insana, M. F., and Herment, A., 2004, “Ultrasound Elastography Based on Multiscale Estimations of Regularized Displacement Fields,” IEEE Trans. Med. Imaging, 23(2), pp. 153–163. [CrossRef] [PubMed]
Kim, J., and Srinivasan, M. A., 2005, “Characterization of Viscoelastic Soft Tissue Properties From in Vivo Animal Experiments and Inverse FE Parameter Estimation,” Medical Image Computing and Computer-Assisted Intervention – MICCAI (Lecture Notes in Computer Science), J. S.Duncan and G.Gerig, eds., Springer, Berlin, Heidelberg, Vol. 3750, pp. 595–606.
Raghupathy, R., and Barocas, V. H., 2009, “A Closed-Form Structural Model of Planar Fibrous Tissue Mechanics,” J. Biomech., 42(10), pp. 1424–1428. [CrossRef] [PubMed]
King, M. R., and Mody, N. A., 2010, Numerical and Statistical Methods for Bioengineering: Applications in MATLAB, Cambridge University, http://books.google.com/books?id = gEDRKeoIHmcC&pgis = 1.
Draper, N. R., and Smith, H., 1981, Applied Regression Analysis (Applied Regression Analysis), 2nd ed., Wiley, New York, Vol. 709.
See the “Supplemental Data” tab for this paper on the ASME Digital Collection. [CrossRef]
Knapp, D. M., Barocas, V. H., Moon, A. G., Yoo, K., Petzold, L. R., and Tranquillo, R. T., 1997, “Rheology of Reconstituted Type I Collagen Gel in Confined Compression,” J. Rheol., 41(5), pp. 971–993. [CrossRef]
Nagel, T. M., Raghupathy, R., Ellingson, A. M., Nuckley, D. J., and Barocas, V. H., 2011, “A Non-Linear Model to Describe the Material Properties of Single Lamellae in the Human Annulus Fibrosus,” ASME Paper No. SBC2011-53848. [CrossRef]
Raghupathy, R., Wiztenburg, C., Lake, S. P., Sander, E. A., and Barocas, V. H., 2011, “Identification of Regional Mechanical Anisotropy in Soft Tissue Analogs,” ASME J. Biomech. Eng., 133(9), p. 091011. [CrossRef]
Boriek, A. M., Rodarte, J. R., and Reid, M. B., 2001, “Shape and Tension Distribution of the Passive Rat Diaphragm,” Am. J. Physiol.: Regul., Integr. Comp. Physiol., 280(1), pp. R33–R41.
Flynn, C., and Rubin, M. B., 2014, “An Anisotropic Discrete Fiber Model With Dissipation for Soft Biological Tissues,” Mech. Mater., 68, pp. 217–227. [CrossRef]
Sun, W., and Sacks, M. S., 2005, “Finite Element Implementation of a Generalized Fung-Elastic Constitutive Model for Planar Soft Tissues,” Biomech. Model. Mechanobiol., 4(2–3), pp. 190–199. [CrossRef] [PubMed]
Wan, C., Hao, Z., and Wen, S., 2013, “The Effect of the Variation in ACL Constitutive Model on Joint Kinematics and Biomechanics Under Different Loads: A Finite Element Study,” ASME J. Biomech. Eng., 135(4), p. 041002. [CrossRef]
Martufi, G., and Christian, G. T., 2013, “Review: The Role of Biomechanical Modeling in the Rupture Risk Assessment for Abdominal Aortic Aneurysms,” ASME J. Biomech. Eng., 135(2), p. 021010. [CrossRef]
Avril, S., Badel, P., Gabr, M., Sutton, M. A., and Lessner, S. M., 2013, “Biomechanics of Porcine Renal Arteries and Role of Axial Stretch,” ASME J. Biomech. Eng., 135(8), p. 081007. [CrossRef]
Raghupathy, R., and Barocas, V. H., 2010, “Generalized Anisotropic Inverse Mechanics for Soft Tissues,” ASME J. Biomech. Eng., 132(8), p. 081006. [CrossRef]


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.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In