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Porosity and Diffusion in Biological Tissues. Recent Advances and Further Perspectives

  • Raimondo PentaEmail author
  • Laura Miller
  • Alfio Grillo
  • Ariel Ramírez-Torres
  • Pietro Mascheroni
  • Reinaldo Rodríguez-Ramos
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 262)

Abstract

We present a review of porosity and diffusion in biological tissues from different perspectives. We first introduce the topic by illustrating experimental evidence related to diffusion in porous media and review a number of state of the art experimental techniques. We then proceed by providing a revisited derivation of the equations of poroelasticity from the microstructure (via asymptotic homogenization), which is especially aimed at giving a first insight on the topic to both students and scientists who are not familiar with the subject. Results based on this kind of models have only recently been presented in the literature and could possibly complement the experiments by getting a more thorough understanding on the complex interplay between porosity and diffusion. We investigate further the matter by exploring the role of diffusion in driving growth and stresses in the context of linear elastic modeling for tumors and cellular automata. We finally conclude the chapter by (a) discussing diffusion in nonlinear, “active” materials, i.e., those which are possibly characterized by growth and remodeling, and (b) offering an overview on cutting edge research problems on diffusion for this class of complex materials.

Notes

Acknowledgements

LM is funded by EPSRC with project number EP/N509668/1. ART and AG acknowledge the Dipartimento di Scienze Matematiche (DISMA) “G.L. Lagrange” of the Politecnico di Torino, Dipartimento di Eccellenza 2018–2022 (Department of Excellence 2018–2022, Project code: E11G18000350001). PM is supported by MicMode-I2T (01ZX1710B) from the German Federal Ministry of Education and Research (BMBF).

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Authors and Affiliations

  • Raimondo Penta
    • 1
    Email author
  • Laura Miller
    • 1
  • Alfio Grillo
    • 2
  • Ariel Ramírez-Torres
    • 2
  • Pietro Mascheroni
    • 3
  • Reinaldo Rodríguez-Ramos
    • 4
  1. 1.School of Mathematics and Statistics, Mathematics and Statistics BuildingUniversity of Glasgow, University PlaceGlasgowUK
  2. 2.Dipartimento di Scienze Matematiche “G. L. Lagrange”Politecnico di TorinoTurinItaly
  3. 3.Braunschweig Integrated Centre of Systems Biology (BRICS)Helmholtz Centre for Infection Research (HZI)BraunschweigGermany
  4. 4.Departamento de Matemáticas, Facultad de Matemática y ComputaciónUniversidad de La HabanaHavanaCuba

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