A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding

Computational analyses have been used to study the biomechanical microenvironment of the chondrocyte that cannot be assessed by in vitro experimental studies; yet all computational studies thus far have focused on the effect of zonal location (superficial, middle, and deep) on the mechanical microenvironment of chondrocytes. The aim of this paper was to study the effect of both zonal and radial locations on the biomechanical microenvironment of chondrocytes in inhomogeneous cartilage under unconfined stress relaxation. A biphasic multiscale approach was employed and nine chondrocytes in different locations were studied. Hyperelastic biphasic theory and depth-dependent aggregate modulus and permeability of articular cartilage were included in the models. It was found that both zonal and radial locations affected the biomechanical stresses and strains of the chondrocytes. Chondrocytes in the mid-radial location had increased volume during the early stage of the loading process. Maximum principal shear stress at the interface between the chondrocyte and the extracellular matrix (ECM) increased with depth, yet that at the ECM-pericellular matrix (PCM) interface had an inverse trend. Fluid pressure decreased with depth, while the fluid pressure difference between the top and bottom boundaries of the microscale model increased with depth. Regardless of location, fluid was exchanged between the chondrocyte, PCM, and ECM. These findings suggested that even under simple compressive loading conditions, the biomechanical microenvironment of the chondrocytes, PCM and ECM were spatially dependent. The current study provides new insight on chondrocyte biomechanics.

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“…User defined strain energy density function in COMSOL was used to input the strain energy density function (Eq. 4) (Guo et al, 2014). …”

Section: Methodsmentioning

confidence: 99%

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

Guo

Maher

Torzilli

2014

Journal of Biomechanics

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“…The user defined strain energy density function in COMSOL was used to input the strain energy density function (Eqn. 4) (Guo et al, 2014b). …”

Section: Methodsmentioning

confidence: 99%

A biphasic finite element study on the role of the articular cartilage superficial zone in confined compression

Guo

Maher

Torzilli

2015

Journal of Biomechanics

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The aim of this study was to investigate the role of the superficial zone on the mechanical behavior of articular cartilage. Confined compression of articular cartilage was modeled using a biphasic finite element analysis to calculate the one-dimensional deformation of the extracellular matrix (ECM) and movement of the interstitial fluid through the ECM and articular surface. The articular cartilage was modeled as an inhomogeneous, nonlinear hyperelastic biphasic material with depth and strain-dependent material properties. Two loading conditions were simulated, one where the superficial zone was loaded with a porous platen (normal test) and the other where the deep zone was loaded with the porous platen (upside down test). Compressing the intact articular cartilage with 0.2 MPa stress reduced the surface permeability by 88%. Removing the superficial zone increased the rate of change for all mechanical parameters and decreased the fluid support ratio of the tissue, resulting in increased tissue deformation. Apparent permeability linearly increased after superficial removal in the normal test, yet it did not change in the upside down test. Orientation of the specimen affected the time-dependent biomechanical behavior of the articular cartilage, but not equilibrium behavior. The two tests with different specimen orientations resulted in very different apparent permeabilities, suggesting that in an experimental study which quantifies material properties of an inhomogeneous material, the specimen orientation should be stated along with the permeability result. The current study provides new insights into the role of the superficial zone on mechanical behavior of the articular cartilage.

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“… 1980 ), as it is often done for soft tissues (Guo et al. 2014 ; Di Stefano et al. 2019 ) where and m are model parameters, is a reference value for k taken in the natural state, and is the volume fraction of the solid phase in the natural state.…”

Section: Theory and Calculationsmentioning

confidence: 99%

Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model

Lucci

Agosti

Ciarletta

et al. 2022

Biomech Model Mechanobiol

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Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.

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A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding

Cited by 11 publications

References 37 publications

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

A biphasic finite element study on the role of the articular cartilage superficial zone in confined compression

Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model

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