A Finite Element Dual Porosity Approach to Model Deformation-Induced Fluid Flow in Cortical Bone

Fornells, P.; García-Aznar, J.M.; Doblaré, M.

doi:10.1007/s10439-007-9351-5

Cited by 41 publications

(25 citation statements)

References 27 publications

(49 reference statements)

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“…Two recent papers have computationally addressed the question of the two interacting porosities. Fornells et al (2007) considered a mixture theory-based dual porosity model of the PV and the PLC; the model was based on the continuum model of Khalili-Naghadesh & Valliappan (1996). In this model the two porosities are considered to be interacting on the same level as opposed to the model in this paper where the two porosities are arranged hierarchically.…”

Section: Discussionmentioning

confidence: 99%

Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

Cowin

Gailani

Benalla

2009

Phil. Trans. R. Soc. A.

103

113

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The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar-canalicular porosity (PLC) in bone tissue due to cyclic mechanical loading and blood pressure oscillations. The result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells. A formula for the volume of fluid that moves between the PLC and PV in a cyclic loading is obtained as a function of the cyclic mechanical loading and blood pressure oscillations. Formulas for the oscillating fluid pore pressure in both the PLC and the PV are obtained as functions of the two driving forces, the cyclic mechanical straining and the blood pressure, both with specified amplitude and frequency. The results of this study also suggest a PV permeability greater than 10 −9 m 2 and perhaps a little lower than 10 −8 m 2 . Previous estimates of this permeability have been as small as 10 −14 m 2 .

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Section: Discussionmentioning

confidence: 99%

Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

Cowin

Gailani

Benalla

2009

Phil. Trans. R. Soc. A.

103

113

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“…This effect can be attributed mainly to the presence of water in the pores, which is very incompressible, and to its relative difficulty to flow out of the pores upon compression; the gelled state of the SAP results in a somewhat more hindered flow, which translates into somewhat higher linear moduli. This phenomenon is known as poroelasticity, and it is typical of fluid-filled porous media under compression [33,34]. In our experiments the mechanical effect of the filling gel is manifest already at low strains, and persists in the linear deformation region.…”

Section: Discussionmentioning

confidence: 53%

Combining self-assembling peptide gels with three-dimensional elastomer scaffolds

Vallés-Lluch¹,

Arnal-Pastor²,

Martínez‐Ramos³

et al. 2013

Acta Biomaterialia

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ElsevierVallés Lluch, A.; Arnal Pastor, MP.; Martínez Ramos, C.; Vilariño Feltrer, G.; Vikingsson, L.; Castells Sala, C.; Semino, CE.... (2013). Combining self-assembling peptide gels with three-dimensional elastomer scaffolds. Acta Biomaterialia. 9 (12) Abstract: Some of the problems raised by the combination of porous scaffolds and self-assembling peptide (SAP) gels as constructs for tissue engineering applications are for the first time addressed. Scaffolds of poly(ethyl acrylate) and the SAP gel RAD16-I were employed. The in situ gelation of the SAP gel inside the pores of the scaffolds was studied. The scaffold-cum-gel constructs were characterized morphologically, physico-chemically and mechanically. The possibility of incorporating an active molecule (bovine serum albumin, taken here as a model molecule for others) in the gel within the scaffold's pores was assessed, and the kinetics of its release in PBS was followed. Cell seeding and colonization of these constructs was preliminary studied with L929 fibroblasts and checked afterwards with sheep adipose-tissue derived stem cells (ASCs) intended for further preclinical studies. Static (conventional) and dynamically assisted seedings were compared for bare scaffolds and the scaffoldcum-gel constructs. The SAP gel inside the pores of the scaffold significantly improved the uniformity and density of cell colonization of the 3D structure. These constructs could be of use in different advanced tissue engineering applications where, apart from a cell-friendly ECM-like aqueous environment, a larger-scale three-dimensional structure able to keep the cells in a specific place, give mechanical support and/or conduct spatially the tissue growth could be required. COMBINING SELF-ASSEMBLING PEPTIDE GELS WITH 3D ELASTOMER SCAFFOLDSA. AbstractSome of the problems raised by the combination of porous scaffolds and selfassembling peptide (SAP) gels as constructs for tissue engineering applications are for the first time addressed. Scaffolds of poly(ethyl acrylate) and the SAP gel RAD16-I were employed. The in situ gelation of the SAP gel inside the pores of the scaffolds was studied. The scaffold-cum-gel constructs were characterized morphologically, physicochemically and mechanically. The possibility of incorporating an active molecule (bovine serum albumin, taken here as a model molecule for others) in the gel within the scaffold's pores was assessed, and the kinetics of its release in PBS was followed. Cell intended for further preclinical studies. Static (conventional) and dynamically assisted seedings were compared for bare scaffolds and the scaffold-cum-gel constructs. The SAP gel inside the pores of the scaffold significantly improved the uniformity and density of cell colonization of the 3D structure. These constructs could be of use in different advanced tissue engineering applications where, apart from a cell-friendly ECM-like aqueous environment, a larger-scale three-dimensional structure able to keep the cells in a specific place, give mechanical support and/o...

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“…In terms of movement and velocity, the interstitial fluid behaves differently under a cyclic mechanical loading in the PLC from its behavior in the Haversian canal. The difference of the bone fluid behavior stems from the differences in geometry and the intrinsic characteristic of each domain (Fornells et al 2007). On one hand, the Haversian canal is the large-scale porosity with roughly ten orders of magnitude greater permeability (Gardinier et al 2010) that houses blood vessels and in which pressure pulses will decay rapidly.…”

Section: The Anatomy and Physiology Of An Osteonmentioning

confidence: 99%

Analytical basis for the determination of the lacunar–canalicular permeability of bone using cyclic loading

Benalla

Cardoso

Cowin

2011

Biomech Model Mechanobiol

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An analytical model for the determination of the permeability in the lacunar-canalicular porosity of bone using cyclic loading is described in this contribution. The objective of the analysis presented is to relate the lacunar-canalicular permeability to a particular phase angle that is measurable when the bone is subjected to infinitesimal cyclic strain. The phase angle of interest is the lag angle between the applied strain and the resultant stress. Cyclic strain causes the interstitial fluid to move. This movement is essential for the viability of osteocytes and is believed to play a major role in the bone mechanotransduction mechanism. However, certain bone fluid flow properties, notably the permeability of the lacunar-canalicular porosity, are still not accurately determined. In this paper, formulas for the phase angle as a function of permeability for infinitesimal cyclic strain are presented and mathematical expressions for the storage modulus, loss modulus, and loss tangent are obtained. An accurate determination of the PLC permeability will improve our ability to understand mechanotransduction and mechanosensory mechanisms, which are fundamental to the understanding of how to treat osteoporosis, how to cope with microgravity in long-term manned space flights, and how to increase the longevity of prostheses that are implanted in bone tissue.

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A Finite Element Dual Porosity Approach to Model Deformation-Induced Fluid Flow in Cortical Bone

Cited by 41 publications

References 27 publications

Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

Combining self-assembling peptide gels with three-dimensional elastomer scaffolds

Analytical basis for the determination of the lacunar–canalicular permeability of bone using cyclic loading

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