Determination of cellular tractions on elastic substrate based on an integral Boussinesq solution

Journal of Biomechanical Engineering

Volumn 131, Issue 6, 2009, Pages

  Huang, Jianyong ^a   Peng, Xiaoling ^a   Qin, Lei ^a   Zhu, Tao ^a   Xiong, Chunyang ^a   Zhang, Youyi ^b   Fang, Jing ^a  

^a PEKING UNIVERSITY   (China)

^b PEKING UNIVERSITY THIRD HOSPITAL   (China)

Author keywords

Cardiac myocyte; Cell substrate interaction; Cellular traction recovery; Integral Boussinesq solution

Indexed keywords

ANALYTICAL SOLUTIONS; BOUSSINESQ SOLUTION; CARDIAC MYOCYTE CELLS; CARDIAC MYOCYTES; CELL FUNCTIONS; CELL-SUBSTRATE INTERACTION; CELL-SUBSTRATE INTERACTIONS; CELLULAR FORCE; CELLULAR TRACTION; COEFFICIENT MATRIX; CONDITION NUMBERS; CYTOMETRY; DATA SAMPLING; DEFORMATION IMAGES; DIGITAL IMAGE CORRELATION TECHNIQUE; DISCRETE GREEN'S FUNCTIONS; DISPLACEMENT NOISE; EFFICIENT METHOD; ELASTIC SUBSTRATE; FLEXIBLE SUBSTRATE; FORCE RECONSTRUCTION; HIGH EFFICIENCY; ILL POSED; ILL-POSED INVERSE PROBLEM; INVERSE SOLUTION; MATRIX; NOISE AMPLIFICATION; NUMERICAL SIMULATION; PHYSIOLOGICAL PROCESS; POTENTIAL APPLICATIONS; RECTANGULAR AREA; REGULAR MESHES; REGULARIZATION SCHEMES; SAMPLING DENSITIES; SUBSTRATE DEFORMATION; TANGENTIAL TRACTION; TRACTION FORCES;

AMPLIFICATION; COMPUTER SIMULATION; DEFORMATION; FOURIER TRANSFORMS; GREEN'S FUNCTION; HEART; INVERSE PROBLEMS; NUMBER THEORY; RECOVERY; REPAIR; SUBSTRATES; WAVELET TRANSFORMS;

TRACTION (FRICTION);

ANIMAL CELL; ARTICLE; BOUSSINESQ SOLUTION; CELL FUNCTION; FOURIER TRANSFORMATION; HEART MUSCLE CELL; MATHEMATICAL MODEL; NONHUMAN; RAT; SIMULATION; ANIMAL; CELL CULTURE; COMPUTER SIMULATION; ELASTICITY; FOURIER ANALYSIS; PHYSIOLOGY; ULTRASTRUCTURE;

ANIMALS; CELLS, CULTURED; COMPUTER SIMULATION; ELASTICITY; FOURIER ANALYSIS; MYOCYTES, CARDIAC; RATS;

EID: 67650779318     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.3118767     Document Type: Article

References (32)

1. Bershadsky, A. D., Balaban, N. Q., and Geiger, B., 2003, "Adhesion-Dependent Cell Mechanosensitivity," Annu. Rev. Cell Dev. Biol., 19, pp. 677-695.
2. Galbraith, C. G., and Sheetz, M. P., 1998, "Forces on Adhesive Contacts Affect Cell Function," Curr. Opin. Cell Biol., 10(5), pp. 566-571.
3. Vogel, V., and Sheetz, M., 2006, "Local Force and Geometry Sensing Regulate Cell Functions," Nat. Rev. Mol. Cell Biol., 7(4), pp. 265-275.
4. Chicurel, M. E., Chen, C. S., and Ingber, D. E., 1998, "Cellular Control Lies in the Balance of Forces," Curr. Opin. Cell Biol., 10(2), pp. 232-239.
5. Geiger, B., Bershadsky, A., Pankov, R., and Yamada, K. M., 2001, "Transmembrane Extracellular Matrix-Cytoskeleton Crosstalk," Nat. Rev. Mol. Cell Biol., 2(11), pp. 793-805.
6. Geiger, B., and Bershadsky, A., 2001, "Assembly and Mechanosensory Function of Focal Contacts," Curr. Opin. Cell Biol., 13(5), pp. 584-592. (Pubitemid 32817017)
7. Galbraith, C. G., and Sheetz, M. P., 1997, "A Micromachined Device Provides a New Bend on Fibroblast Traction Forces," Proc. Natl. Acad. Sci. U.S.A., 94(17), pp. 9114-9118.
8. Balaban, N. Q., Schwarz, U. S., Riveline, D., Goichberg, P., Tzur, G., Sabanay, I., Mahalu, D., Safran, S., Bershadsky, A., Addadi, L., and Geiger, B., 2001, "Force and Focal Adhesion Assembly: A Close Relationship Studied Using Elastic Micropatterned Substrates," Nat. Cell Biol., 3(5), pp. 466-472.
9. Tan, J. L., Tien, J., Pirone, D. M., Gray, D. S., Bhadriraju, K., and Chen, C. S., 2003, "Cells Lying on a Bed of Microneedles: An Approach to Isolate Mechanical Force," Proc. Natl. Acad. Sci. U.S.A., 100(4), pp. 1484-1489.
10. Dembo, M., and Wang, Y. L., 1999, "Stresses at the Cell-to-Substrate Interface During Locomotion of Fibroblasts," Biophys. J., 76(4), pp. 2307-2316. (Pubitemid 29266384)
11. Butler, J. P., Tolic-Norrelykke, I. M., Fabry, B., and Fredberg, J. J., 2002, "Traction Fields, Moments, and Strain Energy That Cells Exert on Their Surroundings," Am. J. Physiol. Cell Physiol., 282(3), pp. C595-C605. (Pubitemid 34663176)
12. Schwarz, U. S., Balaban, N. Q., Riveline, D., Bershadsky, A., Geiger, B., and Safran, S. A., 2002, "Calculation of Forces at Focal Adhesions From Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization," Biophys. J., 83(3), pp. 1380-1394.
13. Yang, Z. C., Lin, J. S., Chen, J. X., and Wang, J., 2006, "Determining Substrate Displacement and Cell Traction Fields - A New Approach," J. Theor. Biol., 242(3), pp. 607-616.
14. Ambrosi, D., 2006, "Cellular Traction as an Inverse Problem," SIAM J. Appl. Math., 66(6), pp. 2049-2060.
15. Harris, A., and Wild, P., 1980, "Silicone Rubber Substrata: A New Wrinkle in the Study of Cell Locomotion," Science, 208(4440), pp. 177-179. (Pubitemid 10072133)
16. Harris, A., Stopak, D., and Wild, P., 1981, "Fibroblast Traction as a Mechanism for Collagen Morphogenesis," Nature (London), 290(5803), pp. 249-251. (Pubitemid 11149655)
17. Sabass, B., Gardel, M. L., Waterman, C. M., and Schwarz, U. S., 2008, "High Resolution Traction Force Microscopy Based on Experimental and Computational Advances," Biophys. J., 94(1), pp. 207-220.
18. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 2007, Numerical Recipes: The Arts of Scientific Computing, Cambridge University Press, Cambridge, Chap. 19.
19. Merkel, R., Kirchgebner, N., Cesa, C. M., and Hoffmann, B., 2007, "Cell Force Microscopy on Elastic Layers of Finite Thickness," Biophys. J., 93(9), pp. 3314-3323.
20. Qin, L., Huang, J. Y., Xiong, C. Y., Zhang, Y. Y., and Fang, J., 2007, "Dynamical Stress Characterization and Energy Evaluation of Single Cardiac Myocyte Actuating on Flexible Substrate," Biochem. Biophys. Res. Commun., 360(2), pp. 352-356.
21. Sen, A., 1988, "Terminally Differentiated Neonatal Rat Myocardial-Cells Proliferate and Maintain Specific Differentiated Functions Following Expression of SV40 Large T Antigen," J. Biol. Chem., 263, pp. 19132-19136.
22. Sutton, M. A., Wolters, W. J., Peters, W. H., Ranson, W. F., and McNeill, S. R., 1983, "Determination of Displacements Using an Improved Digital Correlation Method," Image Vis. Comput., 1(3), pp. 133-139.
23. Peters, W. H., and Ranson, W. F., 1982, "Digital Imaging Techniques in Experimental Stress-Analysis," Opt. Eng. (Bellingham), 21(3), pp. 427-431.
24. Pan, B., Xie, H. M., Xu, B. Q., and Dai, F. L., 2006, "Performance of Sub-Pixel Registration Algorithms in Digital Image Correlation," Meas. Sci. Technol., 17(6), pp. 1615-1621. (Pubitemid 43787587)
25. Chang, S., Wang, C. S., Xiong, C. Y., and Fang, J., 2005, "Nanoscale In-Plane Displacement Evaluation by AFM Scanning and Digital Image Correlation Processing," Nanotechnology, 16(4), pp. 344-349.
26. Berfield, T. A., Patel, H. K., Shimmin, R. G., Braun, P. V., Lambros, J., and Sottos, N. R., 2006, "Fluorescent Image Correlation for Nanoscale Deformation Measurements," Small, 2(5), pp. 631-635.
27. Li, M., Zhang, J., Xiong, C. Y., Fang, J., Li, J. M., and Hao, Y., 2005, "Damage and Fracture Prediction of Plastic-Bonded Explosive by Digital Image Correlation Processing," Opt. Lasers Eng., 43(8), pp. 856-868.
28. Marganski, W. A., Dembo, M., and Wang, Y. L., 2003, "Measurements of Cell-Generated Deformations on Flexible Substrata Using Correlation-Based Optical Flow," Methods Enzymol., 361, pp. 197-211.
29. Tolic-Norrelykke, I. M., Butler, J. P., Chen, J. X., and Wang, N., 2002, "Spatial and Temporal Traction Response in Human Airway Smooth Muscle Cells," Am. J. Physiol.: Cell Physiol., 283(4), pp. C1254-C1266.
30. Landau, L. D., and Lifshitz, E. M., 1970, Theory of Elasticity, 2nd ed., Pergamon, Oxford, Chap. 1.
31. Hansen, P. C., 1992, "Analysis of Discrete Ill-Posed Problems by Means of the L-Curve," SIAM Rev., 34(4), pp. 561-580.
32. Hansen, P. C., and Oleary, D. P., 1993, "The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems," SIAM J. Sci. Comput., 14(6), pp. 1487-1503.