Abstract

In tissue engineering, porous biodegradable scaffolds are developed with morphological, chemical and mechanical properties to promote cell response. Therefore, the scaffold characterization at a (sub)micrometer and (bio)molecular level is paramount sincecells are sensitive to the chemical signals, the rigidity, and the spatial structuring of their microenvironment. In addition to the analysis at room temperature by conventional quasi-static (0.1–45 Hz) mechanical tests, the ultrasonic (10 MHz) and μ-Brillouin inelastic light scattering (13 GHz) were used in this study to assess the dynamical viscoelastic parameters at different frequencies of elastomeric scaffolds. Time-temperature superposition principle was used to increase the high frequency interval (100 MHz–100 THz) of Brillouin experiments providing a mean to analyse the viscoelastic behavior with the fractional derivative viscoelastic model. Moreover, the μ-Raman analysis carried out simultaneously during the μ-Brillouin experiment, gave the local chemical composition.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Corrections

7 March 2019: A typographical correction was made to the author affiliations.


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References

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2017 (1)

K.J.I. Ember, M.A. Hoeve, S.L. McAughtrie, M.S. Bergholt, B.J. Dwyer, M.M. Stevens, K. Faulds, S.J. Forbes, and C.J. Campbell, “Raman spectroscopy and regenerative medicine: a review,” npj Regen. Medicine 2, 12 (2017).
[Crossref]

2016 (1)

G. Antonacci and S. Braakman, “Biomechanics of subcellular structures by non-invasive Brillouin microscopy,” Sci. Reports 6, 37217 (2016).
[Crossref]

2015 (2)

S. Changotade, G. Radu-Bostan, A. Consalus, F. Poirier, J. Peltzer, J.-J. Lataillade, D. Lutomski, and G. Rohman, “Preliminary in vitro assessment of stem cell compatibility with cross-linked poly(ϵ -caprolactone urethane) scaffolds designed through high internal phase emulsions,” Stem Cells Int. 2015, 283796 (2015).
[Crossref]

L. Rouleau, R. Pirk, B. Pluymers, and W. Desmet, “Characterization and Modeling of the Viscoelastic Behavior of a Self-Adhesive Rubber Using Dynamic Mechanical Analysis Tests,” J. Aerosp. Technol. Manag., São José dos Campos 7(2), 200–208 (2015).
[Crossref]

2014 (1)

G. Pallares, M. El Mekki Azouzi, M.A. González, J.L. Aragones, J.L.F. Abascal, C. Valeriani, and F. Caupin, “Anomalies in bulk supercooled water at negative pressure,” Proc. Natl. Acad. Sci. USA 111, 7936 (2014).
[Crossref] [PubMed]

2013 (3)

L. Rouleau, J. -F. Deü, A. Legay, and F. Le Lay, “Application of Kramers-Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

Q. Chen, S. Liang, and G.A. Thouas, “Elastomeric biomaterials for tissue engineering,” Prog. Polym. Sci. 38, 584–671 (2013).
[Crossref]

I.K. Ko, S.J. Lee, A. Atala, and J.J. Yoo, “In situ tissue regeneration through host stem cell recruitment,” Exp. & Mol. Medicine 45, e57 (2013).
[Crossref]

2011 (5)

S.-Y. Tee, J. Fu, C.S. Chen, and P.A. Janmey, “Cell shape and substrate rigidity both regulate cell stiffness,” Biophys. J. 100, L25–L27 (2011).
[Crossref] [PubMed]

R. M. Guedes, “A viscoelastic model for a biomedical ultra-high molecular weight polyethylene using the time-temperature superposition principle,” Polym. testing 30, 294–302 (2011).
[Crossref]

M. Chollet and M. Horgnies, “Analyses of the surfaces of concrete by Raman and FT-IR spectroscopies: comparative study of hardened samples after demoulding and after organic post-treatment,” Surf. Interface Analysis 43, 714–725 (2011).
[Crossref]

G. Scarcelli, P. Kim, and S. H. Yun, “In vivo measurement of age-related stiffening in the crystalline lens by Brillouin optical microscopy,” Biophys. J. 101, 1539–1545 (2011).
[Crossref] [PubMed]

F. Renaud, J. L. Dion, G. Chevallier, I. Tawfiq, and R. Lemaire, “A New Identification Method of Viscoelastic Behavior: Application to the Generalized Maxwell Model,” Mech. Syst. Signal Process.  25(3), 991–1010 (2011).
[Crossref]

2010 (1)

F.P.W. Melchels, A.M.C. Barradas, C.A. van Blitterswijk, J. de Boer, J. Feijen, and D.W. Grijpma, “Effects of the architecture of tissue engineering scaffolds on cell seeding and culturing,” Acta Biomater. 6, 4208–4217 (2010).
[Crossref] [PubMed]

2009 (2)

D. Fioretto and F. Scarponi, “Dynamics of a glassy polymer studied by Brillouin light scattering,” Mater. Sci. Eng., A 521-522, 243–246 (2009).
[Crossref]

J. Dealy and D. Plazek, “Time-Temperature Superposition- a User’s Guide,” Rheol. Bull. 78, 16–31 (2009).

2008 (2)

R.D. Widdle Jr, A.K. Bajaj, and P. Davies, “Measurement of the Poisson 's ratio of flexible polyurethane foam and its influence on a uniaxial compression model,” Int. J. Eng. Sci. 46, 31–49 (2008).
[Crossref]

R.G.M. Breuls, T.U. Jiya, and T.H. Smit, “Scaffold stiffness influences cell behavior: opportunities for skeletal tissue engineering,” The Open Orthop. J. 2, 103–109 (2008).
[Crossref] [PubMed]

2006 (3)

M. Mastrogiacomo, S. Scaglione, R. Martinetti, L. Dolcini, F. Beltrame, R. Cancedda, and R. Quarto, “Role of scaffold internal structure on in vivo bone formation in macroporous calcium phosphate bioceramics,” Biomaterials 27, 3230–3237 (2006).
[Crossref] [PubMed]

W. M. Madigosky, G. F. Lee, and J. M. Niemiec, “A method for modeling polymer viscoelastic data and the temperature shift function,” J. Acoust. Soc. Am. 119, 3760–3765 (2006).
[Crossref]

J. Yang, A.R. Webb, S.J. Pickerill, G. Hageman, and G.A. Ameer, “Synthesis and evaluation of poly(diol citrate) biodegradable elastomers,” Biomaterials 27, 1889–1898 (2006).
[Crossref]

2005 (2)

G. Rohman, D. Grande, F. Lauprêtre, S. Boileau, and P. Guérin, “Design of porous polymeric materials from interpenetrating polymer networks (IPNs): poly(DL-lactide)/poly(methyl methacrylate)-based semi-IPN systems,” Macromolecules 38, 7274–7285 (2005).
[Crossref]

W.C. Oliver and G.M. Pharr, “Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology,” J. Mater. Res. 19, 3–20 (2005).
[Crossref]

2003 (3)

Q. Hou, D. W. Grijpma, and J. Feijen, “Porous polymeric structures for tissue engineering prepared by a coagulation, compression moulding and salt leaching technique,” Biomaterials 24, 1937–1947 (2003).
[Crossref] [PubMed]

H. Janik, B. Pałys, and Z. S. Petrovic, “Multiphase-separated polyurethanes studied by micro-Raman spectroscopy,” Macromol. Rapid Commun.  24(3), 265–268 (2003).
[Crossref]

T. Pritz, “Five-Parameter Fractional Derivative Model for Polymeric Damping Materials,” J. Sound Vib. 265(5), 935–952 (2003).
[Crossref]

2001 (1)

B. Fabry, G.N. Maksym, J.P. Butler, M. Glogauer, D. Navajas, and J.J. Fredberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[Crossref] [PubMed]

1998 (1)

P. Sollich, “Rheological constitutive equation for a model of soft glassy materials,” Phys. Rev. E. 58, 738–759 (1998).
[Crossref]

1997 (2)

P. Sollich, F. Lequeux, P. Hébraud, and M.E. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78, 2020–2023 (1997).
[Crossref]

J. W. Rosthauser, K. W. Haider, C. Steinlein, and C.D. Eisenbach, “Mechanical and dynamic mechanical properties of polyurethane and polyurethane/polyurea elastomers based on 4,4 '-diisocyanatodicyclohexyl methane,” J. Appl. Polym. Sci. 64(5), 957–970 (1997).
[Crossref]

1996 (1)

G. Ben-Dor, G. Mazor, G. Cederbaum, and O. Igra, “Stress-strain relations for elastomeric foams in uni-, bi- and tri-axial compression modes,” Arch. Appl. Mech. 66, 409–418 (1996).
[Crossref]

1993 (1)

Y. Tamada and Y. Ykada, “Effect of preabsorbed proteins on cell adhesion to polymer surfaces,” J. Colloid Interface Sci. 155, 334–339 (1993).
[Crossref]

1992 (1)

M. Barikani and C. Hepburn, “Determination of crosslink density by swelling in the castable polyurethane elastomer based on 1/4-cyclohexane diisocyanate and para-phenylene diisocyanate,” Iran. J. Poly. Sci. & Technol. 1(1), 1–5 (1992).

1987 (1)

R. Lakes, “Foam structures with a negative Poisson 's ratio,” Sciences 235, 1038–1040 (1987).
[Crossref]

1951 (1)

D. W. Davidson and R. H. Cole, “Dielectric Relaxation in Glycerine,” J. Chem. Phys. 18, 1417 (1951).
[Crossref]

Abascal, J.L.F.

G. Pallares, M. El Mekki Azouzi, M.A. González, J.L. Aragones, J.L.F. Abascal, C. Valeriani, and F. Caupin, “Anomalies in bulk supercooled water at negative pressure,” Proc. Natl. Acad. Sci. USA 111, 7936 (2014).
[Crossref] [PubMed]

Ameer, G.A.

J. Yang, A.R. Webb, S.J. Pickerill, G. Hageman, and G.A. Ameer, “Synthesis and evaluation of poly(diol citrate) biodegradable elastomers,” Biomaterials 27, 1889–1898 (2006).
[Crossref]

Antonacci, G.

G. Antonacci and S. Braakman, “Biomechanics of subcellular structures by non-invasive Brillouin microscopy,” Sci. Reports 6, 37217 (2016).
[Crossref]

Aragones, J.L.

G. Pallares, M. El Mekki Azouzi, M.A. González, J.L. Aragones, J.L.F. Abascal, C. Valeriani, and F. Caupin, “Anomalies in bulk supercooled water at negative pressure,” Proc. Natl. Acad. Sci. USA 111, 7936 (2014).
[Crossref] [PubMed]

Atala, A.

I.K. Ko, S.J. Lee, A. Atala, and J.J. Yoo, “In situ tissue regeneration through host stem cell recruitment,” Exp. & Mol. Medicine 45, e57 (2013).
[Crossref]

Bajaj, A.K.

R.D. Widdle Jr, A.K. Bajaj, and P. Davies, “Measurement of the Poisson 's ratio of flexible polyurethane foam and its influence on a uniaxial compression model,” Int. J. Eng. Sci. 46, 31–49 (2008).
[Crossref]

Barikani, M.

M. Barikani and C. Hepburn, “Determination of crosslink density by swelling in the castable polyurethane elastomer based on 1/4-cyclohexane diisocyanate and para-phenylene diisocyanate,” Iran. J. Poly. Sci. & Technol. 1(1), 1–5 (1992).

Barradas, A.M.C.

F.P.W. Melchels, A.M.C. Barradas, C.A. van Blitterswijk, J. de Boer, J. Feijen, and D.W. Grijpma, “Effects of the architecture of tissue engineering scaffolds on cell seeding and culturing,” Acta Biomater. 6, 4208–4217 (2010).
[Crossref] [PubMed]

Beltrame, F.

M. Mastrogiacomo, S. Scaglione, R. Martinetti, L. Dolcini, F. Beltrame, R. Cancedda, and R. Quarto, “Role of scaffold internal structure on in vivo bone formation in macroporous calcium phosphate bioceramics,” Biomaterials 27, 3230–3237 (2006).
[Crossref] [PubMed]

Ben-Dor, G.

G. Ben-Dor, G. Mazor, G. Cederbaum, and O. Igra, “Stress-strain relations for elastomeric foams in uni-, bi- and tri-axial compression modes,” Arch. Appl. Mech. 66, 409–418 (1996).
[Crossref]

Bergholt, M.S.

K.J.I. Ember, M.A. Hoeve, S.L. McAughtrie, M.S. Bergholt, B.J. Dwyer, M.M. Stevens, K. Faulds, S.J. Forbes, and C.J. Campbell, “Raman spectroscopy and regenerative medicine: a review,” npj Regen. Medicine 2, 12 (2017).
[Crossref]

Boileau, S.

G. Rohman, D. Grande, F. Lauprêtre, S. Boileau, and P. Guérin, “Design of porous polymeric materials from interpenetrating polymer networks (IPNs): poly(DL-lactide)/poly(methyl methacrylate)-based semi-IPN systems,” Macromolecules 38, 7274–7285 (2005).
[Crossref]

Braakman, S.

G. Antonacci and S. Braakman, “Biomechanics of subcellular structures by non-invasive Brillouin microscopy,” Sci. Reports 6, 37217 (2016).
[Crossref]

Brannon-Peppas, L.

L. Brannon-Peppas and N.A. Peppas, “The equilibirum swelling behavior of porous and non-porous hydrogels,” in “Absorbent polymer technology,” L. Brannon-Peppas and R.S. Harland, eds. (Elsevier Science Publishers, 1990).
[Crossref]

Breuls, R.G.M.

R.G.M. Breuls, T.U. Jiya, and T.H. Smit, “Scaffold stiffness influences cell behavior: opportunities for skeletal tissue engineering,” The Open Orthop. J. 2, 103–109 (2008).
[Crossref] [PubMed]

Burdick, J. A.

J. A. Burdick and R. L. Mauck, “ Biomaterials for tissue engineering applications,” (Springer-Verlag, 2011).
[Crossref]

Butler, J.P.

B. Fabry, G.N. Maksym, J.P. Butler, M. Glogauer, D. Navajas, and J.J. Fredberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[Crossref] [PubMed]

Campbell, C.J.

K.J.I. Ember, M.A. Hoeve, S.L. McAughtrie, M.S. Bergholt, B.J. Dwyer, M.M. Stevens, K. Faulds, S.J. Forbes, and C.J. Campbell, “Raman spectroscopy and regenerative medicine: a review,” npj Regen. Medicine 2, 12 (2017).
[Crossref]

Cancedda, R.

M. Mastrogiacomo, S. Scaglione, R. Martinetti, L. Dolcini, F. Beltrame, R. Cancedda, and R. Quarto, “Role of scaffold internal structure on in vivo bone formation in macroporous calcium phosphate bioceramics,” Biomaterials 27, 3230–3237 (2006).
[Crossref] [PubMed]

Cates, M.E.

P. Sollich, F. Lequeux, P. Hébraud, and M.E. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78, 2020–2023 (1997).
[Crossref]

Caupin, F.

G. Pallares, M. El Mekki Azouzi, M.A. González, J.L. Aragones, J.L.F. Abascal, C. Valeriani, and F. Caupin, “Anomalies in bulk supercooled water at negative pressure,” Proc. Natl. Acad. Sci. USA 111, 7936 (2014).
[Crossref] [PubMed]

Cederbaum, G.

G. Ben-Dor, G. Mazor, G. Cederbaum, and O. Igra, “Stress-strain relations for elastomeric foams in uni-, bi- and tri-axial compression modes,” Arch. Appl. Mech. 66, 409–418 (1996).
[Crossref]

Chang, H.-I.

H.-I. Chang and Y. Wang, “Cell responses to surface and architecture of tissue engineering scaffolds,” in “Regenerative medicine and tissue engineering - cells and biomaterials,” D. Eberli, ed. (InTech, 2011).
[Crossref]

Changotade, S.

S. Changotade, G. Radu-Bostan, A. Consalus, F. Poirier, J. Peltzer, J.-J. Lataillade, D. Lutomski, and G. Rohman, “Preliminary in vitro assessment of stem cell compatibility with cross-linked poly(ϵ -caprolactone urethane) scaffolds designed through high internal phase emulsions,” Stem Cells Int. 2015, 283796 (2015).
[Crossref]

Chen, C.S.

S.-Y. Tee, J. Fu, C.S. Chen, and P.A. Janmey, “Cell shape and substrate rigidity both regulate cell stiffness,” Biophys. J. 100, L25–L27 (2011).
[Crossref] [PubMed]

Chen, Q.

Q. Chen, S. Liang, and G.A. Thouas, “Elastomeric biomaterials for tissue engineering,” Prog. Polym. Sci. 38, 584–671 (2013).
[Crossref]

Chevallier, G.

F. Renaud, J. L. Dion, G. Chevallier, I. Tawfiq, and R. Lemaire, “A New Identification Method of Viscoelastic Behavior: Application to the Generalized Maxwell Model,” Mech. Syst. Signal Process.  25(3), 991–1010 (2011).
[Crossref]

Chollet, M.

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Figures (5)

Fig. 1
Fig. 1 (a) Photography of the porous PCLU scaffold (left) and non-porous material (right); (b) ESEM image of the porous PCLU scaffold; (c) FTIR-ATR analysis of the non-porous material and the porous PCLU scaffold; (d) μ-Raman analysis of the non-porous material and the porous PCLU scaffold. (dotted lines indicate urea functions).
Fig. 2
Fig. 2 Mechanical behavior of the PCLU scaffold under uni-axial (solid line) and tri-axial (dotted line) stress modes of compression: (a) all strain range; (b) low strain range.
Fig. 3
Fig. 3 Load-displacement curves of the dense PCLU from nanoindentation tests for three different frequency (1 Hz, 10 Hz and 45 Hz) and a fixed strain rate of 0.05 s−1.
Fig. 4
Fig. 4 (a) μ-Brillouin light scattering spectra of the non-porous material (dotted line) and the porous PCLU scaffold (solid line) at room temperature (20 °C). The peak is the inelastic scattering of the incident light by the longitudinal bulk acoustic wave with a Brillouin frequency shift fB ~ 13 GHz. (b) μ-Brillouin light scattering spectra of the non-porous material as a function of the temperature (−40 °C, + 60 °C).
Fig. 5
Fig. 5 Longitudinal storage modulus M′ as a function of the frequency f (log-log scale) of the PCLU dense polymer. The line (red-color on-line) is a fit using the fractional derivative model described in the text.

Equations (14)

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υ 2 a p p = m d r y × ρ s m d r y × ρ n o n p o r o u s × ( ρ s ρ p o r o u s 1 ) + m w e t × ρ n o n p o r o u s
1 υ 2 s = 1 υ 2 a p p P 1 P
M c ¯ = V s × ( υ 2 s 1 / 3 υ 2 s 2 ) υ ¯ × [ l n ( 1 υ 2 s ) + υ 2 s + χ × υ 2 s 2 ]
χ = 0.34 + V s R T × ( δ s δ p ) 2
k = 4 π n / λ L
V L = f B λ L / 2 n
η = ρ Γ B / k 2
M = ρ V L 2 + i η 2 π f B
l n ( a T ( T , T r ) ) = C 1 ( T T r ) C 2 + ( T T r )
  E 1 t h e o * = E n o n p o r o u s × ( 1 P ) N
M c ¯ = 3 ρ R T E 1 *
  E 3 t h e o * = E n o n p o r o u s × ( 1 P ) N ( 2 P ) × ( 1 2 υ * 2 1 υ * )
M = M 0 ( f f 0 ) α
M * = M 0 + M 1 ( i ω τ ) α 1 + ( i ω τ ) α

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