2017
DOI: 10.1007/s11012-017-0625-1
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Homogenized modeling for vascularized poroelastic materials

Abstract: A new mathematical model for the macroscopic behavior of a material composed of a poroelastic solid embedding a Newtonian fluid network phase (also referred to as vascularized poroelastic material ), with fluid transport between them, is derived via asymptotic homogenization. The typical distance between the vessels/channels (microscale) is much smaller than the average size of a whole domain (macroscale). The homogeneous and isotropic Biot's equation (in the quasistatic case and in absence of volume forces) f… Show more

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Cited by 43 publications
(47 citation statements)
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“…Morover, in [23] and [19], the authors solve the homogenized fluid and drug transport models developed in [34] and [24] for vascularized tumors, respectively. Their analysis, which was extended to mechanic deformations in [26], supports the argument that geometric regularization of the microvasculature improves transport of blood and advected drugs transported into the tumor mass. Cancer evolution is extremely complex and cannot be reduced only to its mechanical stress response; however some features in the tumor progression can be associated with the generation and accumulation of mechanical stresses.…”
Section: Introductionmentioning
confidence: 56%
“…Morover, in [23] and [19], the authors solve the homogenized fluid and drug transport models developed in [34] and [24] for vascularized tumors, respectively. Their analysis, which was extended to mechanic deformations in [26], supports the argument that geometric regularization of the microvasculature improves transport of blood and advected drugs transported into the tumor mass. Cancer evolution is extremely complex and cannot be reduced only to its mechanical stress response; however some features in the tumor progression can be associated with the generation and accumulation of mechanical stresses.…”
Section: Introductionmentioning
confidence: 56%
“…Enforcing the multiplicative decompositions (100) and (101) in the cell problem for the first order displacements (42)(43)(44)(45), the local force f y that appears on the righ hand sides rewrites as…”
Section: Multiplicative Decomposition Of the Potentialsmentioning
confidence: 99%
“…We then apply the asymptotic homogenization technique via formal expansions and by adopting a strong form formulation approach (see [43,44]), which has been recently enforced also to investigate various problems of practical interest such as bone modeling [46], filter efficiency [14], cardiac electrical activity [48], transport, growth, and heat exchange in tumors ( [27,40,41,42,45,47,54]). We admit both macroscale and microscale variations of the elastic coefficients of the individual phases of the composite, as well as possible discontinuities of the elastic moduli across the interface between two different phases.…”
Section: Introductionmentioning
confidence: 99%
“…Multiscale composites organized across two or more length scales are often encountered in nature, as well as in artificial materials designed to optimize specific properties (see, e.g., [10]). Relevant applications involving hierarchical systems include, but are not limited to, rocks and fracture [11], biomechanics and nanomedicine [28], poroelasticity [21], and the bone tissue [26].…”
Section: Introductionmentioning
confidence: 99%