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Elastic Modulus Measurement of Hydrogels

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Book cover Cellulose-Based Superabsorbent Hydrogels

Abstract

Hydrogels have been employed for a wide variety of applications, and their mechanical properties need to be modulated based on the applications. In particular, the Young’s modulus, or elastic modulus, of hydrogels is a critical property for understanding their mechanical behaviors. In principle, the Young’s modulus of a hydrogel can be measured by finding a relationship between a force applied to the hydrogel and the resultant deformation of the hydrogel. On a macroscale, Young’s modulus is usually obtained by measuring the stress-strain curves of a hydrogel specimen through the compression method or the tensile method and then finding the slope of the curve. Also, the shear modulus of a hydrogel is measured using a rheometer with parallel plates and then converted into Young’s modulus considering Poisson’s ratio. On a mesoscale, the elastic modulus can be measured by the imaging-based indentation methods which measure the indentation depth of a hydrogel sample deformed by a static ball indenter on the gel. The measured indentation depth is converted to the Young’s modulus of the hydrogel via a contact mechanics model. The mesoscale indentation method and pipette aspiration method are also available. On a microscale, the elastic modulus is usually measured using the atomic force microscopy (AFM)-based indentation method. A hydrogel specimen is locally indented by a sharp or colloidal tip of an AFM probe, and the Young’s modulus of the hydrogel is obtained by fitting an appropriate indentation model against the recorded force-distance curves. An appropriate elastic modulus measurement method needs to be chosen depending on the application, length scale and expected elastic property of the hydrogels.

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References

  1. Anseth KS, Bowman CN, Brannon-Peppas L (1996) Mechanical properties of hydrogels and their experimental determination. Biomaterials 17:1647–1657

    Article  CAS  Google Scholar 

  2. Ahearne M, Yang Y, Liu K-K (2008) Mechanical characterization of hydrogels for tissue engineering application. Topics in tissue Engineering 4:1–16

    Google Scholar 

  3. Oyen ML (2014) Mechanical characterization of hydrogel materials. Int Mater Rev 59:44–59

    Article  CAS  Google Scholar 

  4. Vedadghavami A, Minooei F, Mohammadi MH, Khetani S, Rezaei A, Mashayekhan S, Sanati-Nezhad A (2017) Manufacturing of hydrogel biomaterials with controlled mechanical properties for tissue engineering applications. Acta Biomater 62:42–63

    Article  CAS  Google Scholar 

  5. Schramm-Baxter J, Katrencik J, Mitragotri S (2004) Jet injection into polyacrylamide gels: investigation of jet injection mechanics. J Biomech 37:1181–1188

    Article  Google Scholar 

  6. Buckley CT, Thorpe SD, O’Brien FJ, Robinson AJ, Kelly DJ (2009) The effect of concentration, thermal history and cell seeding density on the initial mechanical properties of agarose hydrogels. J Mech Behav Biomed Mater 2:512–521

    Article  Google Scholar 

  7. Delaine-Smitha RM, Burneya S, Balkwillb FR, Knight MM (2016) Experimental validation of a flat punch indentation methodology calibrated against unconfined compression tests for determination of soft tissue biomechanics. J Mech Behav Biomed Mater 60:401–415

    Article  Google Scholar 

  8. Lee KY, Mooney DJ (2012) Alginate: properties and biomedical applications. Prog Polym Sci 37:106–126

    Article  CAS  Google Scholar 

  9. Boontheekul T, Kong H-J, Mooney DJ (2005) Controlling alginate gel degradation utilizing partial oxidation and bimodal molecular weight distribution. Biomaterials 26:2455–2465

    Article  CAS  Google Scholar 

  10. Ouwerx C, Velings N, Mestdagh MM, Axelos MAV (1998) Physico-chemical properties and rheology of alginate gel beads formed with various divalent cations. Polym Gels Netw 6:393–408

    Article  CAS  Google Scholar 

  11. Chan E-S, Lim T-K, Voo W-P, Pogaku R, Tey BT, Zhang Z (2011) Effect of formulation of alginate beads on their mechanical behavior and stiffness. Particuology 9:228–234

    Article  CAS  Google Scholar 

  12. Normand V, Lootens DL, Amici E, Plucknett KP, Aymard P (2000) New insight into agarose gel mechanical properties. Biomacromolecules 1:730–738

    Article  CAS  Google Scholar 

  13. Brujan E-A, Nahen K, Schmidt P, Vogel A (2001) Dynamics of laser-induced cavitation bubbles near an elastic boundary. J Fluid Mech 433:251–281

    Article  CAS  Google Scholar 

  14. Roeder BA, Kokini K, Sturgis JE, Robinson JP, Voytik-Harbin SL (2002) Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure. J Biomech Eng 124:214–222

    Article  Google Scholar 

  15. Engler A, Bacakova L, Newman C, Hategan A, Griffin M, Discher D (2004) Substrate compliance versus ligand density in cell on gel responses. Biophys J 86:617–628

    Article  CAS  Google Scholar 

  16. Peyton SR, Putnam AJ (2005) Extracellular matrix rigidity governs smooth muscle cell motility in a biphasic fashion. J Cell Physiol 204:198–209

    Article  CAS  Google Scholar 

  17. Sun J-Y, Zhao X, Illeperuma WRK, Chaudhuri O, Oh KH, Mooney DJ, Vlassak JJ, Suo Z (2012) Highly stretchable and tough hydrogels. Nature 489:133–136

    Article  CAS  Google Scholar 

  18. Gross W, Kress H (2017) Simultaneous measurement of the Young’s modulus and the Poisson ratio of thin elastic layers. Soft Matter 13:1048–1055

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. Kong HJ, Wong E, Mooney DJ (2003) Independent control of rigidity and toughness of polymeric hydrogels. Macromolecules 36:4582–4588

    Article  CAS  Google Scholar 

  21. Janmey PA, Georges PC, Hvidt S (2007) Basic rheology for biologists. In: Wang Y-L, Discher DE (eds) Cell mechanics. Academic, San Diego, pp 3–27

    Google Scholar 

  22. Chippada U, Yurke B, Langrana NA (2010) Simultaneous determination of Young’s modulus, shear modulus, and Poisson’s ratio of soft hydrogels. J Mater Res 25:545–555

    Article  CAS  Google Scholar 

  23. Hammond NA, Kamm RD (2013) Mechanical characterization of self-assembling peptide hydrogels by microindentation. J Biomed Mater Res B 101:981–990

    Article  Google Scholar 

  24. Lee D, Rahman MM, Zhou Y, Ryu S (2015) Three-dimensional confocal microscopy indentation method for hydrogel elasticity measurement. Langmuir 31:9684–9693

    Article  CAS  Google Scholar 

  25. Lee D, Ryu S (2017) A validation study of the repeatability and accuracy of atomic force microscopy indentation using polyacrylamide gels and colloidal probes. J Biomech Eng 139:044502

    Article  Google Scholar 

  26. Kandow CE, Georges PC, Janmey PA, Beningo KA (2007) Polyacrylamide hydrogels for cell mechanics: steps toward optimization and alternative uses. In: Wang Y-L, Discher DE (eds) Cell mechanics. Academic, San Diego, pp 29–46

    Chapter  Google Scholar 

  27. Tse JR, Engler AJ (2010) Preparation of hydrogel substrates with tunable mechanical properties. Curr Protoc Cell Biol 16:10–16

    Google Scholar 

  28. Ross KA, Scanlon MG (1999) Analysis of the elastic modulus of agar gel by indentation. J Texture Stud 30:17–27

    Article  Google Scholar 

  29. Peng X, Huang J, Qin L, Xiong C, Fang J (2009) A method to determine Young’s modulus of soft gels for cell adhesion. Acta Mech Sin 25:565–570

    Article  CAS  Google Scholar 

  30. Lo C-M, Wang H-B, Dembo M, Wang Y-L (2000) Cell movement is guided by the rigidity of the substrate. Biophys J 79:144–152

    Article  CAS  Google Scholar 

  31. Munevar S, Wang Y-L, Dembo M (2001) Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts. Biophys J 80:1744–1757

    Article  CAS  Google Scholar 

  32. Reinhart-King CA, Dembo M, Hammer DA (2003) Endothelial cell traction forces on RGD-derivatized polyacrylamide substrata. Langmuir 19:1573–1579

    Article  CAS  Google Scholar 

  33. Damljanovic V, Lagerholm BC, Jacobson K (2005) Bulk and micropatterned conjugation of extracellular matrix proteins to characterized polyacrylamide substrates for cell mechanotransduction assays. Biotechniques 39:847–851

    Article  CAS  Google Scholar 

  34. Frey MT, Engler A, Discher DE, Lee J, Wang YL (2007) Microscopic methods for measuring the elasticity of gel substrates for cell culture: microspheres, microindenters, and atomic force microscopy. In: Wang Y-L, Discher DE (eds) Cell mechanics. Academic, San Diego, pp 47–65

    Chapter  Google Scholar 

  35. Long R, Hall MS, Wu M, Hui C-Y (2011) Effects of gel thickness on microscopic indentation measurements of gel modulus. Biophys J 101:643–650

    Article  CAS  Google Scholar 

  36. D’Sa DJ, de Juan Pardo EM, de las Rivas Astiz R, Sen S, Kumar S (2009) High-throughput indentational elasticity measurements of hydrogel extracellular matrix substrates. Appl Phys Lett 95:063701

    Article  Google Scholar 

  37. Peng X, Huang J, Deng H, Xiong C, Fang J (2011) A multi-sphere indentation method to determine Young’s modulus of soft polymeric materials based on the Johnson–Kendall–Roberts contact model. Meas Sci Technol 22:027003

    Article  Google Scholar 

  38. Kuznetsova TG, Starodubtseva MN, Yegorenkov NI, Chizhik SA, Zhdanov RI (2007) Atomic force microscopy probing of cell elasticity. Micron 38:824–833

    Article  CAS  Google Scholar 

  39. Yoffe EH (1984) Modified Hertz theory for spherical indentation. Philos Mag A 50:813–828

    Article  Google Scholar 

  40. Mahaffy RE, Shih CK, MacKintosh FC, Käs J (2000) Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells. Phys Rev Lett 85:880–883

    Article  CAS  Google Scholar 

  41. Mahaffy RE, Park S, Gerde E, Käs J, Shih CK (2004) Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy. Biophys J 86:1777–1793

    Article  CAS  Google Scholar 

  42. Dimitriadis EK, Horkay F, Maresca J, Kachar B, Chadwick RS (2002) Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys J 82:2798–2810

    Article  CAS  Google Scholar 

  43. Yang Y, Bagnaninchi PO, Ahearne M, Wang RK, Liu K-K (2007) A novel optical coherence tomography-based micro-indentation technique for mechanical characterization of hydrogels. J R Soc Interface 4:1169–1173

    Article  Google Scholar 

  44. Lee SJ, Sun J, Flint JJ, Guo S, Xie HK, King MA, Sarntinoranont M (2011) Optically based-indentation technique for acute rat brain tissue slices and thin biomaterials. J Biomed Mater Res B 97:84–95

    Article  CAS  Google Scholar 

  45. Jacot JG, Dianis S, Schnall J, Wong JY (2006) A simple microindentation technique for mapping the microscale compliance of soft hydrated materials and tissues. J Biomed Mater Res A 79:485–494

    Article  Google Scholar 

  46. Frey MT, Wang Y-L (2009) A photo-modulatable material for probing cellular responses to substrate rigidity. Soft Matter 5:1918–1924

    Article  CAS  Google Scholar 

  47. Beekmans SV, Iannuzzi D (2016) Characterizing tissue stiffness at the tip of a rigid needle using an opto-mechanical force sensor. Biomed Microdevices 18:15

    Article  CAS  Google Scholar 

  48. Saxena T, Gilbert JL, Hasenwinkel JM (2009) A versatile mesoindentation system to evaluate the micromechanical properties of soft, hydrated substrates on a cellular scale. J Biomed Mater Res A 90:1206–1217

    Article  Google Scholar 

  49. Levental I, Levental KR, Klein EA, Assoian R, Miller RT, Wells RG, Janmey PA (2010) A simple indentation device for measuring micrometer-scale tissue stiffness. J Phys Condens Matter 22:194120

    Article  CAS  Google Scholar 

  50. Chevalier NR, Dantan P, Gazquez E, Cornelissen AJM, Fleury V (2016) Water jet indentation for local elasticity measurements of soft materials. Eur Phys J E 39:10

    Article  CAS  Google Scholar 

  51. Lin DC, Yurke B, Langrana NA (2004) Mechanical properties of a reversible, DNA-crosslinked polyacrylamide hydrogel. J Biomech Eng 126:104–110

    Article  Google Scholar 

  52. Lin DC, Yurke B, Langrana NA (2005) Inducing reversible stiffness changes in DNA-crosslinked gels. J Mater Res 20:1456–1464

    Article  CAS  Google Scholar 

  53. Boudou T, Ohayon J, Picart C, Tracqui P (2006) An extended relationship for the characterization of Young’s modulus and Poisson’s ratio of tunable polyacrylamide gels. Biorheology 43:721–728

    CAS  PubMed  Google Scholar 

  54. Buffinton CM, Tong KJ, Blaho RA, Buffinton EM, Ebenstein DM (2015) Comparison of mechanical testing methods for biomaterials: pipette aspiration, nanoindentation, and macroscale testing. J Mech Behav Biomed Mater 51:367–379

    Article  CAS  Google Scholar 

  55. Kleinberger RM, Burke NAA, Dalnoki-Veress K, Stöver HDH (2013) Systematic study of alginate-based microcapsules by micropipette aspiration and confocal fluorescence microscopy. Mater Sci Eng C 33:4295–4304

    Article  CAS  Google Scholar 

  56. Wyss HM, Franke T, Mele E, Weitz DA (2010) Capillary micromechanics: measuring the elasticity of microscopic soft objects. Soft Matter 6:4550–4555

    Article  CAS  Google Scholar 

  57. Engler AJ, Richert L, Wong JY, Picart C, Discher DE (2004) Surface probe measurements of the elasticity of sectioned tissue, thin gels and polyelectrolyte multilayer films: correlations between surface substrate stiffness and cell adhesion. Surf Sci 570:142–154

    Article  CAS  Google Scholar 

  58. Radmacher M (2007) Studying the mechanics of cellular processes by atomic force microscopy. In: Wang Y-L, Discher DE (eds) Cell mechanics. Academic, San Diego, pp 347–372

    Chapter  Google Scholar 

  59. Engler AJ, Rehfeldt F, Sen S, Discher DE (2007) Microtissue elasticity: measurements by atomic force microscopy and its influence on cell differentiation. In: Wang Y-L, Discher DE (eds) Cell mechanics. Academic, San Diego, pp 521–545

    Chapter  Google Scholar 

  60. Markert CD, Guo X, Skardal A, Wang Z, Bharadwaj S, Zhang Y, Bonin K, Guthold M (2013) Characterizing the micro-scale elastic modulus of hydrogels for use in regenerative medicine. J Mech Behav Biomed Mater 27:115–127

    Article  CAS  Google Scholar 

  61. Li C, Allen J, Alliston T, Pruitt LA (2011) The use of polyacrylamide gels for mechanical calibration of cartilage – a combined nanoindentation and unconfined compression study. J Mech Behav Biomed Mater 4:1540–1547

    Article  CAS  Google Scholar 

  62. Ondeck MG, Engler AJ (2016) Mechanical characterization of a dynamic and tunable methacrylated hyaluronic acid hydrogel. J Biomech Eng 138:021003

    Article  Google Scholar 

  63. Sneddon IN (1965) The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int J Eng Sci 3:47–57

    Article  Google Scholar 

  64. Heuberger M, Dietler G, Schlapbach L (1995) Mapping the local Young’s modulus by analysis of the elastic deformations occurring in atomic force microscopy. Nanotechnology 6:12–23

    Article  CAS  Google Scholar 

  65. Puricelli L, Galluzzi M, Schulte C, Podestà A, Milani P (2015) Nanomechanical and topographical imaging of living cells by atomic force microscopy with colloidal probes. Rev Sci Instrum 86:033705

    Article  Google Scholar 

  66. Hermanowicz P, Sarna M, Burda K, Gabryś H (2014) AtomicJ: an open source software for analysis of force curves. Rev Sci Instrum 85:063703

    Article  Google Scholar 

  67. Carl P, Schillers H (2008) Elasticity measurement of living cells with an atomic force microscope: data acquisition and processing. Pflugers Arch 457:551–559

    Article  CAS  Google Scholar 

  68. Harris AR, Charras GT (2011) Experimental validation of atomic force microscopy-based cell elasticity measurements. Nanotechnology 22:345102

    Article  Google Scholar 

  69. Lin DC, Horkay F (2008) Nanomechanics of polymer gels and biological tissues: a critical review of analytical approaches in the Hertzian regime and beyond. Soft Matter 4:669–682

    Article  CAS  Google Scholar 

  70. McKee CT, Last JA, Russell P, Murphy CJ (2011) Indentation versus tensile measurements of Young’s modulus of soft biological tissues. Tissue Eng B 17:155–164

    Article  Google Scholar 

  71. Lin DC, Dimitriadis EK, Horkay F (2007) Robust strategies for automated AFM force curve analysis-I. Non-adhesive indentation of soft, inhomogeneous materials. J Biomech Eng 129:430–440

    Article  Google Scholar 

  72. Chippada U, Yurke B, Georges PC, Langrana NA (2008) A nonintrusive method of measuring the local mechanical properties of soft hydrogels using magnetic microneedles. J Biomech Eng 31:021014

    Google Scholar 

  73. Kim K, Liu X, Zhang Y, Cheng J, Wu XY, Sun Y (2009) Elastic and viscoelastic characterization of microcapsules for drug delivery using a force-feedback MEMS microgripper. Biomed Microdevices 11:421–427

    Article  CAS  Google Scholar 

  74. Corbin EA, Millet LJ, Pikul JH, Johnson CL, Georgiadis JG, King WP, Bashir R (2013) Micromechanical properties of hydrogels measured with MEMS resonant sensors. Biomed Microdevices 15:311–319

    Article  CAS  Google Scholar 

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Acknowledgments

We acknowledge supports from the Nebraska Tobacco Settlement Biomedical Research Development Fund through (1) Bioengineering for Human Health Grant of the University of Nebraska-Lincoln (UNL) and the University of Nebraska Medical Center (UNMC) and (2) Biomedical Research Seed Grant of UNL. AFM measurements were performed at the NanoEngineering Research Core Facility of UNL, which is partially funded from Nebraska Research Initiative Funds.

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Correspondence to Sangjin Ryu .

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Lee, D., Zhang, H., Ryu, S. (2019). Elastic Modulus Measurement of Hydrogels. In: Mondal, M. (eds) Cellulose-Based Superabsorbent Hydrogels. Polymers and Polymeric Composites: A Reference Series. Springer, Cham. https://doi.org/10.1007/978-3-319-77830-3_60

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