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

Penta, Raimondo; Miller, Laura; Grillo, Alfio; Ramírez-Torres, Ariel; Mascheroni, Pietro; Rodrı́guez-Ramos, Reinaldo

doi:10.1007/978-3-030-31547-4_11

Cited by 18 publications

(23 citation statements)

References 116 publications

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“…where representation ( 32) is implied in relationships (34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45) and indicated by the superscript . We also have periodic conditions on the cell boundary ∂Ω \Υ .…”

Section: The Global Double Poroelastic Resultsmentioning

confidence: 99%

“…When zooming in on each of these subdomains separately, Fig. 1c), we find that Ω M and Ω η have a standard poroelastic structure (see [10,38]).…”

Section: Formulation Of the Problemmentioning

confidence: 96%

“…The C M and C η are the effective elasticity tensors which would be obtained from the homogenization at the finer hierarchical level. C M and C η are the effective elasticity tensors obtained in [10,38] for a standard poroelastic material. These effective elasticity tensors also possess major and minor symmetries as proved in [28].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…[41] for an example related to elastic composites. We refer to the underlying porescale microstructure as the equations used here are those that would arise from upscaling of the porescale fluid-structure interaction between the fluid and solid phases, see [10,38]. These equations are Biot's anisotropic, heterogeneous, compressible equations for poroelasticity.…”

Section: Introductionmentioning

confidence: 99%

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Double poroelasticity derived from the microstructure

Miller

Penta

2021

Acta Mech

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We derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. We assume that the distance between the subphases (the local scale) is much smaller than the size of the domain (the global scale). We assume that at the local scale both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity (i.e. the porescale is already smoothed out). We then decompose the spatial variations by means of the two-scale homogenization method to upscale the interaction between the poroelastic phases at the local scale. This way, we derive the novel global scale model which is formally of poroelastic-type. The global scale coefficients account for the complexity of the given microstructure and heterogeneities. These effective poroelastic moduli are to be computed by solving appropriate differential periodic cell problems. The model coefficients possess properties that, once proved, allow us to determine that the model is both formally and substantially of poroelastic-type. The properties we prove are a) the existence of a tensor which plays the role of the classical Biot’s tensor of coefficients via a suitable analytical identity and b) the global scale scalar coefficient $$\bar{\mathcal {M}}$$ M ¯ is positive which then qualifies as the global Biot’s modulus for the double poroelastic material.

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Section: The Global Double Poroelastic Resultsmentioning

confidence: 99%

“…When zooming in on each of these subdomains separately, Fig. 1c), we find that Ω M and Ω η have a standard poroelastic structure (see [10,38]).…”

Section: Formulation Of the Problemmentioning

confidence: 96%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Double poroelasticity derived from the microstructure

Miller

Penta

2021

Acta Mech

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“…Based on the latter, we assume that PR ranges from 0.45 at the tumour core to 0.3 at the adjacent peripheral region and, for the sake of simplicity, solid matrix YM of 50 kPa is constant in the whole space and time domain. The reported values of the porosities of cancerous tissues are higher compared with the healthy tissues (see, for example, [58,59] and the references therein). The porosity of the highly cancerous tumour core is assumed 50%, which decreases to 20% at the peripheral region.…”

Section: Example: 2d Model Of a Tumour Tissuementioning

confidence: 99%

Poroelastic model parameter identification using artificial neural networks: on the effects of heterogeneous porosity and solid matrix Poisson ratio

Dehghani

Zilian

2020

Comput Mech

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Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests for model parameter identification.This problem motivates us to develop a more efficient approach to address complex problems with an acceptable computational cost. In particular, we employ artificial neural network (ANN) for reliable and fast computation of poroelastic model parameters. Based on the strong-form governing equations for the poroelastic problem derived from asymptotic homogenisation, the weighted residuals formulation of the cell problem is obtained. Approximate solution of the resulting linear variational boundary value problem is achieved by means of the finite element method. The advantages and downsides of macroscale properties identification via asymptotic homogenisation and the application of ANN to overcome parameter characterisation challenges caused by the costly solution of cell problems are presented. Numerical examples, in this study, include spatially dependent porosity and solid matrix Poisson ratio for a generic model problem, application in tumour modelling, and utilisation in soil mechanics context which demonstrate the feasibility of the presented framework. Keywords Artificial neural network • Multiscale and multiphysics problems • Poroelastic media • Material characterisation • Data-driven computational mechanics B Hamidreza Dehghani

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Porous Crystalline Organic Cages Made by Design

Ivanova,

Beuerle

2024

Israel Journal of Chemistry

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Shape‐persistent organic cages are an intriguing class of molecular porous materials. Through hierarchical molecular design, size and shape of the intrinsic molecular voids are controlled by dynamic covalent chemistry, while pore structure and topology are governed by noncovalent alignment in the solid state. However, the predictable and reliable crystallization of organic cages is still challenging since long‐range superstructures are solely based on weak and rather unidirectional supramolecular interactions. In this tutorial review, we provide a general classification of porous solid‐state materials and discuss specific design principles regarding the dynamic covalent reactions, the small‐molecule building blocks and solid‐state engineering. Furthermore, we introduce the most important analytical techniques for porous materials with a special focus on organic cages.

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

Cited by 18 publications

References 116 publications

Double poroelasticity derived from the microstructure

Double poroelasticity derived from the microstructure

Poroelastic model parameter identification using artificial neural networks: on the effects of heterogeneous porosity and solid matrix Poisson ratio

Porous Crystalline Organic Cages Made by Design

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