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Three-dimensional Full-field Measurements of Large Deformations in Soft Materials Using Confocal Microscopy and Digital Volume Correlation

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Abstract

A three-dimensional (3-D) full-field measurement technique was developed for measuring large deformations in optically transparent soft materials. The technique utilizes a digital volume correlation (DVC) algorithm to track motions of subvolumes within 3-D images obtained using fluorescence confocal microscopy. In order to extend the strain measurement capability to the large deformation regime (>5%), a stretch-correlation algorithm was developed and implemented into the Fast Fourier Transform (FFT)-based DVC algorithm. The stretch-correlation algorithm uses a logarithmic coordinate transformation to convert the stretch-correlation problem into a translational correlation problem under the assumption of small rotation and shear. Estimates of the measurement precision are provided by stationary and translation tests. The proposed measurement technique was used to measure large deformations in a transparent agarose gel sample embedded with fluorescent particles under uniaxial compression. The technique was also employed to measure non-uniform deformation fields near a hard spherical inclusion under far-field uniaxial compression. Introduction of the stretch-correlation algorithm greatly improved the strain measurement accuracy by providing better precision especially under large deformation. Also, the deconvolution of confocal images improved the accuracy of the measurement in the direction of the optical axis. These results shows that the proposed technique is well-suited for investigating cell-matrix mechanical interactions as well as for obtaining local constitutive properties of soft biological materials including tissues in 3-D.

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References

  1. Ingber DE, Dike L, Hansen L, Karp S, Liley H, Maniotis A, McNamee H, Mooney D, Plopper G, Sims J, Wang N (1994) Cellular tensegrity—exploring how mechanical changes in the cytoskeleton regulate cell-growth, migration, and tissue pattern during morphogenesis. Int Rev Cytol-A Survey of Cell Biology 150:173–224.

    Google Scholar 

  2. Lo CM, Wang HB, Dembo M, Wang YL (2000) Cell movement is guided by the rigidity of the substrate. Biophys J 79(1):144–152.

    Google Scholar 

  3. Petronis S, Gold J, Kasemo B (2003) Microfabricated force-sensitive elastic substrates for investigation of mechanical cell-substrate interactions. J Micromechanics Microengineering 13(6):900–913.

    Article  Google Scholar 

  4. Wong JY, Velasco A, Rajagopalan P, Pham Q (2003) Directed movement of vascular smooth muscle cells on gradient-compliant hydrogels. Langmuir 19(5):1908–1913.

    Article  Google Scholar 

  5. Tan JL, Tien J, Pirone DM, Gray DS, Bhadriraju K, Chen CS (2003) Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc Natl Acad Sci USA 100(4):1484–1489.

    Article  Google Scholar 

  6. Gray DS, Tien J, Chen CS (2003) Repositioning of cells by mechanotaxis on surfaces with micropatterned Young’s modulus. J Biomed Materi Res Part A 66A(3):605–614.

    Article  Google Scholar 

  7. Zaari N, Rajagopalan P, Kim SK, Engler AJ, Wong JY (2004) Photopolymerization in microfluidic gradient generators: microscale control of substrate compliance to manipulate cell response. Adv Mater 16(23–24):2133–2137.

    Article  Google Scholar 

  8. Cukierman E, Pankov R, Stevens DR, Yamada KM (2001) Taking cell-matrix adhesions to the third dimension. Science 294(5547):1708–1712.

    Article  Google Scholar 

  9. Even-Ram S, Yamada KM (2005) Cell migration in 3D matrix. Curr Opin Cell Biol 17(5):524–532.

    Article  Google Scholar 

  10. Zaman MH, Kamm RD, Matsudaira P, Lauffenburger DA (2005) Computational model for cell migration in three-dimensional matrices. Biophys J 89(2):1389–1397.

    Article  Google Scholar 

  11. Berfield TA, Patel HK, Shimmin RG, Braun PV, Lambros J, Sottos NR (2006) Fluorescent image correlation for nanoscale deformation measurements. Small 2(5):631–635.

    Article  Google Scholar 

  12. Luo PF, Chao YJ, Sutton MA, Peters WH (1993) Accurate measurement of 3-dimensional deformations in deformable and rigid bodies using computer vision. Exp Mech 33(2):123–132.

    Article  Google Scholar 

  13. Vendroux G, Knauss WG (1998) Submicron deformation field measurements: part 2. Improved digital image correlation. Exp Mech 38(2):86–92.

    Article  Google Scholar 

  14. Sutton MA, Cheng MQ, Peters WH, Chao YJ, McNeill SR (1986) Application of an optimized digital correlation method to planar deformation analysis. Image Vis Comput 4(3):143–150.

    Article  Google Scholar 

  15. Bay BK, Smith TS, Fyhrie DP, Saad M (1999) Digital volume correlation: Three-dimensional strain mapping using X-ray tomography. Exp Mech 39(3):217–226.

    Article  Google Scholar 

  16. Roeder BA, Kokini K, Robinson JP, Voytik-Harbin SL (2004) Local, three-dimensional strain measurements within largely deformed extracellular matrix constructs. J Biomech Eng-Transactions of the Asme 126(6):699–708.

    Article  Google Scholar 

  17. Smith TS, Bay BK, Rashid MM (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42(3):272–278.

    Article  Google Scholar 

  18. Corle TR, Kino GS (1996) Confocal scanning optical microscopy and related imaging systems. Academic, San Diego: xv, p 335.

    Google Scholar 

  19. Sheppard C, Shotton D (1997) Confocal laser scanning microscopy. BIOS Scientific; Springer, in association with the Royal Microscopical Society. Oxford; New York: xii, p 106.

  20. Chen DJ, Chiang FP, Tan YS, Don HS (1993) Digital speckle-displacement measurement using a complex spectrum method. Appl Opt 32(11):1839–1849.

    Google Scholar 

  21. Takita K, Aoki T, Sasaki Y, Higuchi T, Kobayashi K (2003) High-accuracy subpixel image registration based on phase-only correlation. IEICE Trans Fundam Electron Commun Comput Sci E86A(8):1925–1934.

    Google Scholar 

  22. Hong S, Ravichandran G (2007) FFT-based digital image correlation algorithm for large deformation measurements. Galcit SM Technical Report, California Institute of Technology, Pasadena, CA.

  23. Born M, Wolf E (1970) Principles of optics; electromagnetic theory of propagation, interference and diffraction of light, 4th edn. Pergamon, Oxford, New York,: xxviii, p 808.

  24. Gu M (1996) Principles of three dimensional imaging in confocal microscopes. World Scientific. Singapore, River Edge, NJ: xii, p 337.

  25. Lucy LB (1974) Iterative technique for rectification of observed distributions. Astron J 79(6):745–754.

    Article  Google Scholar 

  26. Torok P, Varga P, Booker GR (1995) Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes — structure of the electromagnetic-field .1. J Opt Soc Am A, Opt Image Sci Vis 12(10):2136–2144.

    Article  MathSciNet  Google Scholar 

  27. Sheppard CJR, Torok P (1997) Effects of specimen refractive index on confocal imaging. J Microsc-Oxford 185:366–374.

    Article  Google Scholar 

  28. Visser TD, Oud JL, Brakenhoff GJ (1992) Refractive-index and axial distance measurements in 3-D microscopy. Optik 90(1):17–19.

    Google Scholar 

  29. Diaspro A, Federici F, Robello M (2002) Influence of refractive-index mismatch in high-resolution three-dimensional confocal microscopy. Appl Opt 41(4):685–690.

    Google Scholar 

  30. Ghahremani F (1980) Effect of grain-boundary sliding on anelasticity of polycrystals. Int J Solids Struct 16(9):825–845.

    Article  MATH  Google Scholar 

  31. Welsh ER, Tirrell DA (2000) Engineering the extracellular matrix: a novel approach to polymeric biomaterials. I. Control of the physical properties of artificial protein matrices designed to support adhesion of vascular endothelial cells. Biomacromolecules 1(1):23–30.

    Article  Google Scholar 

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Acknowledgements

We gratefully acknowledge the support provided by the National Science Foundation (DMR # 0520565) through the Center for Science and Engineering of Materials (CSEM) at the California Institute of Technology. GR acknowledges the support of the Army Research Office for providing the DURIP funds for the acquisition of the confocal microscope used in this study. GR also gratefully acknowledges the Ronald and Maxine Linde Venture Fund for enabling the acquisition of imaging instrumentation used in this investigation. We would like to thank Mr. Petros Arakelian for his valuable help with the experimental setup.

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Authors and Affiliations

  1. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, 91125, USA

    C. Franck, S. Hong & G. Ravichandran (SEM member)

  2. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA

    S. A. Maskarinec & D. A. Tirrell

Authors
  1. C. Franck
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  2. S. Hong
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  3. S. A. Maskarinec
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  4. D. A. Tirrell
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  5. G. Ravichandran
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Correspondence to G. Ravichandran.

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Franck, C., Hong, S., Maskarinec, S.A. et al. Three-dimensional Full-field Measurements of Large Deformations in Soft Materials Using Confocal Microscopy and Digital Volume Correlation. Exp Mech 47, 427–438 (2007). https://doi.org/10.1007/s11340-007-9037-9

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  • DOI: https://doi.org/10.1007/s11340-007-9037-9

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