In vitro bone growth responds to local mechanical strain in three-dimensional polymer scaffolds

Baas, Elbert; Kuiper, Jan Herman; Yang, Ying; Wood, Mairead A.; Haj, Alicia J. El

doi:10.1016/j.jbiomech.2009.10.016

Cited by 47 publications

(46 citation statements)

References 30 publications

(29 reference statements)

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“…Such an approach is used by El Haj and coworkers within a bioreactor system that comprises a cell-seeded poly(L-lactic acid) (PLLA) scaffold (depicted in Figure 2(a)), through which culture medium is perfused (El Haj et al, 1990;Baas et al, 2010). We employ data obtained from µCT scans of such a PLLA scaffold to define our periodic microscale domain Ω ; in this context, the microscale growth embodied by (3.30) represents ECM deposition and/or mineralisation on the pore surface by a cell population seeded within the scaffold.…”

Section: Microscale Geometrymentioning

confidence: 99%

“…Figure 2(b) indicates a typical two-dimensional section of the scaffold, together with our chosen computational domain. The porosity of such a scaffold is Φ f = 0.9 (Baas et al, 2010) and we choose the relative areas of Ω f and Ω s in our computational domain to reflect this. When such a scaffold is seeded with human bone cells and cultured for four weeks, deposition of extracellular materials and subsequent mineralisation reduce the porosity by approximately 2% to Φ f ≈ 0.88 (data omitted; see Baas et al (2010) for details).…”

Section: Microscale Geometrymentioning

confidence: 99%

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A multiscale analysis of nutrient transport and biological tissue growthin vitro

et al. 2014

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In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenisation method to accommodate explicitly the influence of the underlying microscale structure of the material, and its evolution, on the macroscale dynamics. Such methods have been widely used to study porous and poroelastic materials; however, a distinguishing feature of biological tissue is its ability to remodel continuously in response to local environmental cues. Here, we present the derivation of a model broadly applicable to tissue engineering applications, characterised by cell proliferation and extracellular matrix deposition in porous scaffolds used within tissue culture systems, which we use to study coupling between fluid flow, nutrient transport and microscale tissue growth. Attention is restricted to surface accretion within a rigid porous medium saturated with a Newtonian fluid; coupling between the various dynamics is achieved by specifying the rate of microscale growth to be dependent upon the uptake of a generic diffusible nutrient. The resulting macroscale model comprises a Darcy-type equation governing fluid flow, with flow characteristics dictated by the assumed periodic microstructure and surface growth rate of the porous medium, coupled to an advection-reaction equation specifying the nutrient concentration. Illustrative numerical simulations are presented to indicate the influence of microscale growth on macroscale dynamics, and to highlight the importance of including experimentally-relevant microstructural information in order to correctly determine flow dynamics and nutrient delivery in tissue engineering applications.

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Section: Microscale Geometrymentioning

confidence: 99%

Section: Microscale Geometrymentioning

confidence: 99%

A multiscale analysis of nutrient transport and biological tissue growthin vitro

et al. 2014

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“…On the basis of the results stated in Sections 3.1 & 3.2, we now proceed with the stability and error analysis of the DGFEM defined in (5). To this end, following the work presented in [40], we begin by defining the following extensions of the forms B Diff (·, ·) and F Diff (·): …”

Section: Error Analysis Of the Dgfemmentioning

confidence: 99%

“…The fine mesh which accurately describes Ω is generated based on image data supplied by Prof. El Haj & Dr. Kuiper. Here, only a coarse model has been employed; a more detailed description of the scaffold geometry is presented in the articles [4,5]. However, even for this 'coarse' model, the underlying fine finite element mesh consists of 15.8 million elements.…”

Section: Example 2: Flow Past a 3d Scaffold Geometrymentioning

confidence: 99%

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Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains

Antonietti

Cangiani

Collis

et al. 2016

Lecture Notes in Computational Science and Engineering

118

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The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of standard mesh generators, employing simplices or tensor product elements, for example, naturally leads to very fine finite element meshes, and hence the computational effort required to numerically approximate the underlying PDE problem may be prohibitively expensive. As an alternative approach, in this article we present a review of composite/agglomerated discontinuous Galerkin finite element methods (DGFEMs) which employ general polytopic elements. Here, the elements are typically constructed as the union of standard element shapes; in this way, the minimal dimension of the underlying composite finite element space is independent of the number of geometrical features. In particular, we provide an overview of hp-version inverse estimates and approximation results for general polytopic elements, which are sharp with respect to element facet degeneration. On the basis of these results, a priori error bounds for the hp-DGFEM approximation of both second-order elliptic and first-order hyperbolic PDEs will be derived. Finally, we present numerical experiments which highlight the practical application of DGFEMs on meshes consisting of general polytopic elements.

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Contribution of Physical Forces on the Design of Biomimetic Tissue Substitutes

Ermis¹,

Baran²,

Dursun³

et al. 2014

Bio‐inspired Materials for Biomedical Engineering

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In vitro bone growth responds to local mechanical strain in three-dimensional polymer scaffolds

Cited by 47 publications

References 30 publications

A multiscale analysis of nutrient transport and biological tissue growthin vitro

A multiscale analysis of nutrient transport and biological tissue growthin vitro

Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains

Contribution of Physical Forces on the Design of Biomimetic Tissue Substitutes

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