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Research Papers

Finite Element Analysis of Traction Force Microscopy: Influence of Cell Mechanics, Adhesion, and Morphology

[+] Author and Article Information
Rachel Zielinski

Biomedical Engineering Department,
The Ohio State University,
Columbus, OH 43210

Cosmin Mihai

Biomedical Engineering Department,
The Ohio State University,
Columbus, OH 43210;
Department of Internal Medicine,
Division of Pulmonary, Allergy,
Critical Care and Sleep Medicine,
Wexner Medical Center,
The Ohio State University,
Columbus, OH 43210

Douglas Kniss

Biomedical Engineering Department,
The Ohio State University,
Columbus, OH 43210;
Department of Obstetrics and Gynecology,
Wexner Medical Center,
The Ohio State University,
Columbus, OH 43210

Samir N. Ghadiali

Biomedical Engineering Department,
The Ohio State University,
Columbus, OH 43210;
Department of Internal Medicine,
Division of Pulmonary, Allergy,
Critical Care and Sleep Medicine,
Wexner Medical Center,
The Ohio State University,
Columbus, OH 43210;
Dorothy M. Davis Heart and Lung Research Institute,
Wexner Medical Center,
The Ohio State University,
Columbus, OH 43210
e-mail: ghadiali.1@osu.edu

1Corresponding author.

Present address: Department of Biomedical Engineering, The Ohio State University, 270 Bevis Hall, 1080 Carmack Road, Columbus, OH 43210.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received December 14, 2012; final manuscript received April 26, 2013; accepted manuscript posted May 8, 2013; published online June 11, 2013. Assoc. Editor: Edward Sander.

J Biomech Eng 135(7), 071009 (Jun 11, 2013) (9 pages) Paper No: BIO-12-1619; doi: 10.1115/1.4024467 History: Received December 14, 2012; Revised April 26, 2013; Accepted May 08, 2013

The interactions between adherent cells and their extracellular matrix (ECM) have been shown to play an important role in many biological processes, such as wound healing, morphogenesis, differentiation, and cell migration. Cells attach to the ECM at focal adhesion sites and transmit contractile forces to the substrate via cytoskeletal actin stress fibers. This contraction results in traction stresses within the substrate/ECM. Traction force microscopy (TFM) is an experimental technique used to quantify the contractile forces generated by adherent cells. In TFM, cells are seeded on a flexible substrate and displacements of the substrate caused by cell contraction are tracked and converted to a traction stress field. The magnitude of these traction stresses are normally used as a surrogate measure of internal cell contractile force or contractility. We hypothesize that in addition to contractile force, other biomechanical properties including cell stiffness, adhesion energy density, and cell morphology may affect the traction stresses measured by TFM. In this study, we developed finite element models of the 2D and 3D TFM techniques to investigate how changes in several biomechanical properties alter the traction stresses measured by TFM. We independently varied cell stiffness, cell-ECM adhesion energy density, cell aspect ratio, and contractility and performed a sensitivity analysis to determine which parameters significantly contribute to the measured maximum traction stress and net contractile moment. Results suggest that changes in cell stiffness and adhesion energy density can significantly alter measured tractions, independent of contractility. Based on a sensitivity analysis, we developed a correction factor to account for changes in cell stiffness and adhesion and successfully applied this correction factor algorithm to experimental TFM measurements in invasive and noninvasive cancer cells. Therefore, application of these types of corrections to TFM measurements can yield more accurate estimates of cell contractility.

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Figures

Grahic Jump Location
Fig. 1

Representative plots of Young's modulus versus absolute value of strain for the strain-stiffening material model parameters including (a) Young's modulus Eo, (b) slope of strain-stiffening curve m, and (c) strain at which material begins to stiffen εo. Eo was varied between 0.1 kPa and 10 kPa, m was varied between 0 kPa and 10 kPa, and εo was varied between 0 and 1.

Grahic Jump Location
Fig. 2

Representative 3D finite element mesh and loading vectors for (a) 2D TFM and (b) 3D TFM models. Representative plots of traction stress fields from (c) 2D TFM model gel surface and (d) 3D TFM model gel tractions projected onto cell surface.

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Fig. 3

Maximum resultant traction versus applied contractility at different cell stiffness values in the (a) 2D TFM model and (b) 3D TFM model. Net contractile moment versus applied contractility at different cell stiffness values in the (c) 2D TFM model and (d) 3D TFM model.

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Fig. 4

Maximum resultant traction versus applied contractility at different cell-gel adhesion energy density levels in the (a) 2D TFM model and (b) 3D TFM model. Net contractile moment versus applied contractility at different cell-gel adhesion energy density levels in the (c) 2D TFM model and (d) 3D TFM model.

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Fig. 5

Maximum resultant traction versus applied contractility at different cell aspect ratios in the (a) 2D TFM model and (b) 3D TFM model. Net contractile moment versus applied contractility at different cell aspect ratios in the (c) 2D TFM model and (d) 3D TFM model.

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Fig. 6

Sensitivity values for maximum resultant traction in the (a) 2D TFM model and (b) 3D TFM model. Sensitivity values for net contractile moment in the (c) 2D TFM model and (d) 3D TFM model. (e) Representative resultant variable versus parameter curve for sensitivity calculation.

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Fig. 7

Effect of (a) initial cell stiffness, (b) slope of strain stiffening curve, and (c) strain at which stiffening begins on maximum resultant traction in strain-stiffening models. Effect of (d) initial cell stiffness, (e) slope of strain stiffening curve, and (f) strain at which stiffening begins on net contractile moment in strain-stiffening models. (All data is from 2D TFM simulations).

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Fig. 8

(a) Maximum resultant traction versus applied contractility at different cell bulk modulus values. (b) Effect of bulk modulus on maximum resultant traction. Shaded area represents the range of Poisson's ratio for biological cells typically reported in the literature. (All data is from 3D TFM simulations).

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Fig. 9

(a) Measurement of maximum traction in wild-type MD-AMB-231 control cells (WT) and myoferlin-deficient MD-AMB-231 cells. (b) Application of correction factor to Tmax data results in an estimated contractile stress that is dramatically lower in the noninvasive MYOF-KD as compared to the invasive WT cells. * is with respect to WT conditions.

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