The Human Meniscus Behaves as a Functionally Graded Fractional Porous Medium under Confined Compression Conditions

被引:13
作者
Bulle, Raphael [1 ]
Alotta, Gioacchino [2 ]
Marchiori, Gregorio [3 ]
Berni, Matteo [4 ]
Lopomo, Nicola F. [5 ]
Zaffagnini, Stefano [6 ]
Bordas, Stephane P. A. [1 ,7 ]
Barrera, Olga [8 ,9 ,10 ]
机构
[1] Univ Luxembourg, Inst Computat Engn Sci, L-4365 Luxembourg, Luxembourg
[2] Univ Mediterranea Reggio Calabria, Dept Civil Environm Energy & Mat Engn DICEAM, I-89124 Reggio Di Calabria, Italy
[3] IRCCS Ist Ortoped Rizzoli, Complex Struct Surg Sci & Technol, I-40136 Bologna, Italy
[4] IRCCS Ist Ortoped Rizzoli, Med Technol Lab, I-40136 Bologna, Italy
[5] Univ Brescia, Ipartimento Ingn Informaz, I-25121 Brescia, Italy
[6] IRCCS Ist Ortoped Rizzoli, Orthopaed & Traumatol Clin 2, I-40136 Bologna, Italy
[7] Cardiff Univ, Sch Engn, Cardiff CF10 3AT, Wales
[8] Oxford Brookes Univ, Sch Engn Comp & Math, Oxford OX3 0BP, England
[9] Univ Oxford, Dept Engn Sci, Oxford OX3 0BP, England
[10] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
来源
APPLIED SCIENCES-BASEL | 2021年 / 11卷 / 20期
基金
欧洲研究理事会;
关键词
poromechanics experiments; confined compression test; human meniscus; fractional darcy; constitutive model; ANOMALOUS DIFFUSION; BUILDING-MATERIALS; STRESS-RELAXATION; WATER-ABSORPTION; KNEE-JOINT; DERIVATION; CARTILAGE; FLOW;
D O I
10.3390/app11209405
中图分类号
O6 [化学];
学科分类号
0703 ;
摘要
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 ?beta,beta in the central body are ?beta=5.5443x10(-10)m(4)/Ns(1-beta), b=0.0434, while, in the posterior and anterior regions, are ?beta=2.851x10(-10)m(4)/Ns(1-beta), b=0.0326 and ?beta=1.2636x10(-10)m(4)/Ns(1-beta), b=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.
引用
收藏
页数:20
相关论文
共 31 条
[1]   High Resolution Micro-Computed Tomography Reveals a Network of Collagen Channels in the Body Region of the Knee Meniscus [J].
Agustoni, Greta ;
Maritz, Jared ;
Kennedy, James ;
Bonomo, Francesco P. ;
Bordas, Stephane P. A. ;
Barrera, Olga .
ANNALS OF BIOMEDICAL ENGINEERING, 2021, 49 (09) :2273-2281
[2]   A unified modelling and simulation for coupled anomalous transport in porous media and its finite element implementation [J].
Barrera, O. .
COMPUTATIONAL MECHANICS, 2021, 68 (06) :1267-1282
[3]   A procedure for slicing and characterizing soft heterogeneous and irregular-shaped tissue [J].
Bonomo, Francesco P. ;
Gregory, Jonathan J. S. ;
Barrera, Olga .
MATERIALS TODAY-PROCEEDINGS, 2020, 33 :2020-2026
[5]   Diffusion in porous layers with memory [J].
Caputo, M ;
Plastino, W .
GEOPHYSICAL JOURNAL INTERNATIONAL, 2004, 158 (01) :385-396
[6]   Compressive moduli of the human medial meniscus in the axial and radial directions at equilibrium and at a physiological strain rate [J].
Chia, Helena N. ;
Hull, M. L. .
JOURNAL OF ORTHOPAEDIC RESEARCH, 2008, 26 (07) :951-956
[7]   Water ingress in Y-type zeolite: Anomalous moisture-dependent transport diffusivity [J].
de Azevedo, Eduardo N. ;
da Silva, D. Vitoreti ;
de Souza, R. E. ;
Engelsberg, M. .
PHYSICAL REVIEW E, 2006, 74 (04)
[8]  
Detournay E., 1993, Comprehensive Rock Engineering: Principles, Practice & Projects, VII, P113, DOI 10.1016/b978-0-08-040615-2.50011-3
[9]   Neutron radiography study of water absorption in porous building materials: anomalous diffusion analysis [J].
El Abd, AEG ;
Milczarek, JJ .
JOURNAL OF PHYSICS D-APPLIED PHYSICS, 2004, 37 (16) :2305-2313
[10]   KNEE JOINT CHANGES AFTER MENISCECTOMY [J].
FAIRBANK, TJ .
JOURNAL OF BONE AND JOINT SURGERY-BRITISH VOLUME, 1948, 30 (04) :664-670