The human meniscus behaves as a functionally graded fractional porous medium under confined compression conditions

Bulle, Raphaël, Alotta, Gioacchino, Marchiori, Gregorio, Berni, Matteo, Lopomo, Nicola F., Zaffagnini, Stefano, Bordas, Stéphane P. A. ORCID: https://orcid.org/0000-0001-8634-7002 and Barrera, Olga 2021. The human meniscus behaves as a functionally graded fractional porous medium under confined compression conditions. Applied Sciences 11 (20) , 9405. 10.3390/app11209405

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Abstract

In this study, we observe that the poromechanical parameters in human meniscus vary spatially throughout the tissue. The response is anisotropic and the porosity is functionally graded. To draw these conclusions, we measured the anisotropic permeability and the “aggregate modulus” of the tissue, i.e., the stiffness of the material at equilibrium, after the interstitial fluid has ceased flowing. We estimated those parameters within the central portion of the meniscus in three directions (i.e., vertical, radial and circumferential) by fitting an enhanced model on stress relation confined compression tests. We noticed that a classical biphasic model was not sufficient to reproduce the observed experimental behaviour. We propose a poroelastic model based on the assumption that the fluid flow inside the human meniscus is described by a fractional porous medium equation analogous to Darcy’s law, which involves fractional operators. The fluid flux is then time-dependent for a constant applied pressure gradient (in contrast with the classical Darcy’s law, which describes a time independent fluid flux relation). We show that a fractional poroelastic model is well-suited to describe the flow within the meniscus and to identify the associated parameters (i.e., the order of the time derivative and the permeability). The results indicate that mean values of λβ,β in the central body are λβ=5.5443×10−10m4Ns1−β, β=0.0434, while, in the posterior and anterior regions, are λβ=2.851×10−10m4Ns1−β, β=0.0326 and λβ=1.2636×10−10m4Ns1−β, β=0.0232, respectively. Furthermore, numerical simulations show that the fluid flux diffusion is facilitated in the central part of the meniscus and hindered in the posterior and anterior regions.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Additional Information:	This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/
Publisher:	MDPI
ISSN:	2076-3417
Date of First Compliant Deposit:	4 November 2021
Date of Acceptance:	13 September 2021
Last Modified:	12 May 2023 04:02
URI:	https://orca.cardiff.ac.uk/id/eprint/145234

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