Modeling sample/patient‐specific structural and diffusional responses of cartilage using DT‐MRI

Pierce, David M.; Ricken, Tim; Holzapfel, Gerhard

doi:10.1002/cnm.2524

Cited by 35 publications

(19 citation statements)

References 56 publications

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“…Indeed, both the strain energy density,Ŵ sκ , and the hydraulic conductivity, k, are isotropic [see (10a) and (29a)], and all the parameters appearing in their constitutive expressions, including the referential volumetric fraction of the solid phase, φ sR , are set equal to constants. If, on the one hand, the model could be acceptable for studying the structural evolution of tumour tissues, which are often assumed to be elastically and hydraulically isotropic [1,42,84], it fails to be accurate for tissues, such as articular cartilage, in which the presence of reinforcing collagen fibres induces anisotropy [35,78,79,94], and the constitutive laws are strongly dependent on material points. In these cases, whereas the balance laws (44a) and (44b) only need to account for the contribution of the fibres to the strain energy density and hydraulic conductivity, the plastic flow rule (44c) should be reformulated.…”

Section: Discussionmentioning

confidence: 99%

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Grillo

Prohl

Wittum

2015

Continuum Mech. Thermodyn.

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We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of "plastic" distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.

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Section: Discussionmentioning

confidence: 99%

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Grillo

Prohl

Wittum

2015

Continuum Mech. Thermodyn.

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“…Earlier studies have shown that fluid pressurization is enhanced by anisotropy of the elastic properties of the tissue (Huang et al, 2001;Huang and Gu, 2007). Furthermore, the anisotropy of cartilage permeability due to the glycosaminoglycan network deformation (Ateshian and Weiss, 2010;Quinn et al, 2001b;Reynaud and Quinn, 2006) and the collagen fiber orientation (Federico and Grillo, 2012;Federico andHerzog, 2008a, 2008b;Pierce et al, 2013aPierce et al, , 2013bTomic et al, 2014) affects the fluid pressurization at both small and large strains. Additionally, as mentioned earlier, there is evidence that flow-independent viscoelasticity of the cartilage matrix affects the strain-rate-dependent behavior of the tissue at small and large strain-rates (DiSilvestro et al, 2001;Edelsten et al, 2010;Huang et al, 2001).…”

Section: 7mentioning

confidence: 98%

Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability

Thibbotuwawa

Oloyede

Senadeera

et al. 2015

Journal of the Mechanical Behavior of Biomedical Materials

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Solid-interstitial fluid interaction, which depends on tissue permeability, is significant to the strain-rate-dependent mechanical behavior of humeral head (shoulder) cartilage. Due to anatomical and biomechanical similarities to that of the human shoulder, kangaroos present a suitable animal model. Therefore, indentation experiments were conducted on kangaroo shoulder cartilage tissues from low (10(-4)/s) to moderately high (10(-2)/s) strain-rates. A porohyperelastic model was developed based on the experimental characterization; and a permeability function that takes into account the effect of strain-rate on permeability (strain-rate-dependent permeability) was introduced into the model to investigate the effect of rate-dependent fluid flow on tissue response. The prediction of the model with the strain-rate-dependent permeability was compared with those of the models using constant permeability and strain-dependent permeability. Compared to the model with constant permeability, the models with strain-dependent and strain-rate-dependent permeability were able to better capture the experimental variation at all strain-rates (p < 0.05). Significant differences were not identified between models with strain-dependent and strain-rate-dependent permeability at strain-rate of 5 × 10(-3)/s (p = 0.179). However, at strain-rate of 10(-2)/s, the model with strain-rate-dependent permeability was significantly better at capturing the experimental results (p < 0.005). The findings thus revealed the significance of rate-dependent fluid flow on tissue behavior at large strain-rates, which provides insights into the mechanical deformation mechanisms of cartilage tissues.

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“…With this equation for the filtration velocity, the fact that the motions of both solid and liquid are connected by the interaction forcesp L = −p S , and considering thermodynamic restrictions (see, e.g., Ricken andBluhm (2009, 2010)), we propose the anisotropic intrinsic permeability of the liver tissue K F as (cf. Pierce et al 2013b)…”

Section: Transversely Isotropic Permeability and Remodelingmentioning

confidence: 99%

Modeling function–perfusion behavior in liver lobules including tissue, blood, glucose, lactate and glycogen by use of a coupled two-scale PDE–ODE approach

Ricken

Werner

Holzhütter

et al. 2014

Biomech Model Mechanobiol

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This study focuses on a two-scale, continuum multicomponent model for the description of blood perfusion and cell metabolism in the liver. The model accounts for a spatial and time depending hydro-diffusion-advection-reaction description. We consider a solid-phase (tissue) containing glycogen and a fluid-phase (blood) containing glucose as well as lactate. The five-component model is enhanced by a two-scale approach including a macroscale (sinusoidal level) and a microscale (cell level). The perfusion on the macroscale within the lobules is described by a homogenized multiphasic approach based on the theory of porous media (mixture theory combined with the concept of volume fraction). On macro level, we recall the basic mixture model, the governing equations as well as the constitutive framework including the solid (tissue) stress, blood pressure and solutes chemical potential. In view of the transport phenomena, we discuss the blood flow including transverse isotropic permeability, as well as the transport of solute concentrations including diffusion and advection. The continuum multicomponent model on the macroscale finally leads to a coupled system of partial differential equations (PDE). In contrast, the hepatic metabolism on the microscale (cell level) was modeled via a coupled system of ordinary differential equations (ODE). Again, we recall the constitutive relations for cell metabolism level. A finite element implementation of this framework is used to provide an illustrative example, describing the spatial and time-depending perfusion-metabolism processes in liver lobules that integrates perfusion and metabolism of the liver.

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Modeling sample/patient‐specific structural and diffusional responses of cartilage using DT‐MRI

Cited by 35 publications

References 56 publications

A poroplastic model of structural reorganisation in porous media of biomechanical interest

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability

Modeling function–perfusion behavior in liver lobules including tissue, blood, glucose, lactate and glycogen by use of a coupled two-scale PDE–ODE approach

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