Free Access
Issue
ESAIM: M2AN
Volume 48, Number 1, January-February 2014
Page(s) 27 - 52
DOI https://doi.org/10.1051/m2an/2013093
Published online 15 November 2013
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [Google Scholar]
  2. L. Baffico, C. Grandmont, Y. Maday and A. Osses, Homogenization of elastic media with gaseous inclusions. Multiscale Model. Simul. 7 (2008) 432–465. [CrossRef] [Google Scholar]
  3. M. Baumgaertel and H.H. Winter, Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheologica Acta 28 (1989) 511–519. [CrossRef] [Google Scholar]
  4. A. Blasselle and G. Griso, Mechanical modeling of the skin. Asymptotic Analysis 74 (2011) 167–198. [MathSciNet] [Google Scholar]
  5. S. Boyaval, Reduced-basis approach for homogenization beyond the periodic setting. Multiscale Model. Simul. 7 (2008) 466–494. [CrossRef] [Google Scholar]
  6. R. Burridge and J. Keller, Biot’s poroelasticity equations by homogenization, in Macroscopic Properties of Disordered Media, vol. 154 of Lecture Notes in Physics. Springer (1982) 51–57. [Google Scholar]
  7. J.P. Butler, J.L. Lehr and J.M. Drazen, Longitudinal elastic wave propagation in pulmonary parenchyma. J. Appl. Phys. 62 (1987) 1349–1355. [CrossRef] [Google Scholar]
  8. J. Clegg and M.P. Robinson, A genetic algorithm used to fit Debye functions to the dielectric properties of tissues. 2010 IEEE Congress on Evolutionary Computation (CEC) (2010) 1–8. [Google Scholar]
  9. F. Dunn, Attenuation and speed of ultrasound in lung: Dependence upon frequency and inflation. J. Acoust. Soc. Am. 80 (1986) 1248–1250. [CrossRef] [PubMed] [Google Scholar]
  10. M. Fabrizio and A. Morro, Mathematical problems in linear viscoelasticity, vol. 12 of SIAM Studies in Applied Mathematics. SIAM, Philadelphia, PA (1992). [Google Scholar]
  11. M. Fang, R.P. Gilbert and X. Xie, Deriving the effective ultrasound equations for soft tissue interrogation. Comput. Math. Appl. 49 (2005) 1069–1080. [CrossRef] [Google Scholar]
  12. R.P. Gilbert and A. Mikelić, Homogenizing the acoustic properties of the seabed. I. Nonlinear Anal. 40 (2000) 185–212. [Google Scholar]
  13. Q. Grimal, A. Watzky and S. Naili, A one-dimensional model for the propagation of transient pressure waves through the lung. J. Biomech. 35 (2002) 1081–1089. [CrossRef] [PubMed] [Google Scholar]
  14. A. Hanygan, Viscous dissipation and completely monotonic relaxation moduli. Rheologica Acta 44 (2005) 614–621. [CrossRef] [Google Scholar]
  15. F. Hecht, FreeFem++ manual (2012). [Google Scholar]
  16. J.S. Hesthaven and T. Warburton, Nodal discontinuous Galerkin methods, vol. 54 of Texts in Applied Mathematics. Springer, New York (2008). [Google Scholar]
  17. A. Kanevsky, M.H. Carpenter, D. Gottlieb and J.S. Hesthaven, Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. J. Comput. Phys. 225 (2007) 1753–1781. [CrossRef] [Google Scholar]
  18. D.F. Kelley, T.J. Destan and R.J. Luebbers, Debye function expansions of complex permittivity using a hybrid particle swarm-least squares optimization approach. Antennas Propagation IEEE Trans. 55 (2007) 1999–2005. [CrossRef] [Google Scholar]
  19. C.A. Kennedy and M.H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44 (2003) 139–181. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Kloeckner, Hedge: Hybrid and Easy Discontinuous Galerkin Environment. http://www.cims.]nyu.edu/˜kloeckner/ (2010). [Google Scholar]
  21. S.S. Kraman, Speed of low-frequency sound through lungs of normal men. J. Appl. Phys. (1983) 1862–1867. [Google Scholar]
  22. R.J. LeVeque, Numerical methods for conservation laws. Lectures in Mathematics ETH Zürich. Birkhäuser, Basel (1990). [Google Scholar]
  23. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, vol. 1 of Travaux et Recherches Mathématiques. Dunod, Paris (1968). [Google Scholar]
  24. M. Lourakis, levmar: Levenberg-Marquardt nonlinear least squares algorithms in C/C++. http://www.ics.forth.gr/˜lourakis/levmar/ (2004). [Google Scholar]
  25. Y. Maday, N. Morcos and T. Sayah, Reduced basis numerical homogenization for scalar elliptic equations with random coefficients: application to blood micro-circulation. Submitted to SIAM J. Appl Math. (2012). [Google Scholar]
  26. N. Morcos, Modélisation mathématique et simulation de systèmes microvasculaires. Ph.D. thesis, Université Pierre et Marie Curie (2011). [Google Scholar]
  27. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [CrossRef] [MathSciNet] [Google Scholar]
  28. M.R. Owen and M.A. Lewis, The mechanics of lung tissue under high-frequency ventilation. SIAM J. Appl. Math. 61 (2001) 1731–1761. [CrossRef] [Google Scholar]
  29. H. Pasterkamp, S.S. Kraman and G.R. Wodicka, Respiratory sounds. advances beyond the stethoscope. Am. J. Respir. Crit. Care Med. 156 (1997) 974. [CrossRef] [PubMed] [Google Scholar]
  30. D.A. Rice, Sound speed in pulmonary parenchyma. J. Appl. Physiol. 54 (1983) 304–308. [PubMed] [Google Scholar]
  31. E. Roan and M.W. Waters, What do we know about mechanical strain in lung alveoli? Am. J. Physiol. Lung Cell Mol. Physiol. 301 (2011) 625–635. [CrossRef] [Google Scholar]
  32. D. Rueter, H.P. Hauber, D. Droeman, P. Zabel and S. Uhlig, Low-frequency ultrasound permeates the human thorax and lung: a novel approach to non-invasive monitoring. Ultraschall Med. 31 (2010) 53–62. [CrossRef] [PubMed] [Google Scholar]
  33. E. Sanchez–Palencia, Vibration of mixtures of solids and fluids, in Non-Homogeneous Media and Vibration Theory, vol. 127 of Lecture Notes in Physics. Springer (1980) 158–190. [Google Scholar]
  34. R.A. Schapery, A simple collocation method for fitting viscoelastic models to experimental data. GALCIT SM 63 (1961) 23. [Google Scholar]
  35. M. Siklosi, O.E. Jensen, R.H. Tew and A. Logg. Multiscale modeling of the acoustic properties of lung parenchyma. ESAIM: Proc. 23 (2008) 78–97. [CrossRef] [EDP Sciences] [Google Scholar]
  36. J. Sorvari and J. Hämäläinen, Time integration in linear viscoelasticity – a comparative study. Mech. Time-Dependent Mater. 14 (2010) 307–328 [CrossRef] [Google Scholar]
  37. B. Suki, S. Ito, D. Stamenović, K.R. Lutchen and E.P. Ingenito, Biomechanics of the lung parenchyma: critical roles of collagen and mechanical forces. J. Appl. Physiol. 98 (2005) 1892–1899. [CrossRef] [PubMed] [Google Scholar]
  38. P. Suquet, Linear problems. In Homogenization Techniques for Composite Media, vol. 272 of Lecture Notes in Physics. Edited by Enrique Sanchez–Palencia and André Zaoui. Springer (1987) 209–230. [Google Scholar]
  39. L. Tartar, The general theory of homogenization. A personalized introduction, vol. 7 of Lecture Notes of the Unione Matematica Italiana. Springer (2009). [Google Scholar]
  40. Y.-M. Yi, S.-H. Park and S.-K. Youn, Asymptotic homogenization of viscoelastic composites with periodic microstructures. Int. J. Solids Struct. 35 (1998) 2039–2055. [CrossRef] [Google Scholar]

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