Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory

Abdalrahman, Tamer; Scheiner, Stefan; Hellmich, Christian

doi:10.1016/j.jtbi.2014.10.011

Cited by 36 publications

(45 citation statements)

References 105 publications

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“…On the other hand, solvent molecules can move preferentially along the 1-direction (characterized by ani-sotropic diffusion coefficient D11) as a result of synergic interactions of the water molecules at the interface with the calcium, hydroxyl, and phosphate ions of the HAP surface. Our study demonstrates and quantifies the anisotropic behaviour of fluid in bone nanostructures, which is an important area of bone biophysics (Lemaire et al 2015a;Abdalrahman et al 2015) and, therefore, gives new insights into the mechanisms controlling the motion of solvent mol-ecules in confined spaces.…”

Section: Resultsmentioning

confidence: 82%

Anisotropic diffusion of water molecules in hydroxyapatite nanopores

et al. 2017

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New insights into the dynamical properties of water in hydroxyapatite (HAP) nanopores, a model system for the fluid flow within nanosize spaces inside the collagen-apatite structure of bone, were obtained from molecular dynamics simulations of liquid water confined between two parallel HAP surfaces of different sizes (20 Å ≤ H ≤ 240 Å). Calculations were conducted using a coreshell interatomic potential for HAP together with the extended simple point charge model for water. This force field gives an activation energy for water diffusion within HAP nanopores that is in excellent agreement with available experimental data. The dynamical properties of water within the HAP nanopores were quantified in terms of the second-order water diffusion tensor. Results indicate that water diffuses anisotropically within the HAP nanopores, with the solvent molecules moving parallel to the surface twice as fast as the perpendicular direction. This unusual dynamic behaviour is linked to the strong polarizing effect of calcium ions, and the synergic interactions between the water molecules in the first hydration layer of HAP with the calcium, hydroxyl, and phosphate ions, which facilitates the flow of water molecules in the directions parallel to the HAP surface.

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Section: Resultsmentioning

confidence: 82%

Anisotropic diffusion of water molecules in hydroxyapatite nanopores

et al. 2017

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“…Classical phenomenological relations such as the Kozeny–Carman equation, have linked bone porosity to permeability together with some phenomenological constant characteristic for the bone sample morphology (Arramon and Nauman, 2001, Bear, 1972) . Other more sophisticated techniques use semi-analytical tools to estimate pore-scale fluid flow properties which can then be upscaled to obtain (apparent) bone permeability estimates (Abdalrahman et al, 2015) . Two interesting findings were revealed by Abdalrahman et al Firstly, the constant appearing in the Kozeny–Carman equation is a function of bone porosity and bone specific surface (Abdalrahman et al, 2015) .…”

Section: Introductionmentioning

confidence: 99%

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

et al. 2017

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In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens.For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 −8 m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

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“…Recent developments in continuum homogenization theories extended to infinitely many material phases related to all orientations in Euclidean space (Fritsch et al 2009(Fritsch et al , 2013Abdalrahman et al 2015) could be successfully applied to diffusivity upscaling. The corresponding results allow for improved representation of water-to-cement ratio-dependent and hydration-dependent diffusivity of cement paste.…”

Section: Discussionmentioning

confidence: 99%

“…Derivation of A pore has been dealt with in great detail in (Abdalrahman et al 2015), based on Eshelby's famous inhomogeneity problem (Eshelby 1957), see also the work of Dormieux and Kondo (2005), eventually yielding…”

Section: Representative Volume Element For Diffusive Transport In Cemmentioning

confidence: 99%

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Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

et al. 2017

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Chloride ingress into concrete is a major cause for material degradation, such as cracking due to corrosion-induced steel reinforcement expansion. Corresponding transport processes encompass diffusion, convection, and migration, and their mathematical quantification as a function of the concrete composition remains an unrevealed enigma. Approaching the problem step by step, we here concentrate on the diffusivity of cement paste, and how it follows from the microstructural features of the material and from the chloride diffusivity in the capillary pore spaces. For this purpose, we employ advanced self-consistent homogenization theory as recently used for permeability upscaling, based on the resolution of the pore space as pore channels being oriented in all space directions, resulting in a quite compact analytical relation between porosity, pore diffusivity, and the overall diffusivity of the cement paste. This relation is supported by experiments and reconfirms the pivotal role that layered water most probably plays for the reduction of the pore diffusivity, with respect to the diffusivity found under the chemical condition of a bulk solution.Keywords Diffusion · Homogenization · Chlorides · Multiscale modeling · Layered water List of Symbols Mathematical operators divDivergence operator, applied to a vector field div Divergence operator, applied to a second-order tensor field grad Gradient operator on the microscopic observation scale of pore space

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Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory

Cited by 36 publications

References 105 publications

Anisotropic diffusion of water molecules in hydroxyapatite nanopores

Anisotropic diffusion of water molecules in hydroxyapatite nanopores

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

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