Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications

Croll, Tristan I.; Gentz, Silke; Mueller, Kilian Maria Arthur; Davidson, Malcolm R.; O’Connor, Andrea J.; Stevens, Geoffrey W.; Cooper-White, Justin J.

doi:10.1016/j.ces.2005.03.051

Cited by 76 publications

(62 citation statements)

References 36 publications

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“…Croll et al (2005) developed a mathematical model in spherical geometry, dependent only on the radial distance. Here, a one-dimensional Cartesian mathematical model is appropriate for exploring the mechanisms involved in cell proliferation and migration on a vascularising scaffold.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…We denote the cell number density by ρ and the local oxygen concentration by c. Following Croll et al (2005) and Lewis et al (2005), we suppose that the rate of proliferation of the cells is μ(c) and that the rate of oxygen consumption per cell is αμ(c), where α is a constant for low values of cell density. Unlike earlier work, we wish to account for cell crowding in the heterogenous seeding case.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The oxygen diffusion could be modified to account for local cell density, but Croll et al (2005) found this had negligible effect on the results, and so is ignored here.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…We extend the work of Croll et al (2005) and Lewis et al (2005). The additional effects of vascular growth, homogenous and heterogenous seeding, diffusion of cells and critical hypoxic oxygen concentration are considered here.…”

Section: Introductionmentioning

confidence: 98%

“…The curve τ (x) is the boundary between these two regions; it moves at an exponentially decaying rate towards x = 0. Croll et al (2005) developed a model of the oxygen diffusion and cell density in the in vivo A-V loop chamber. A hemi-spherical annular region was considered.…”

Section: Introductionmentioning

confidence: 99%

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Cell Proliferation and Oxygen Diffusion in a Vascularising Scaffold

Landman

Cai

2007

Bull. Math. Biol.

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The supply of oxygen to proliferating cells within a scaffold is a key factor for the successful building of new tissue in soft tissue engineering applications. A recent in vivo model, where an arteriovenous loop is placed in a scaffold, allows a vascularising network to form within a scaffold, establishing an oxygen source within, rather than external, to the scaffold. A one-dimensional model of oxygen concentration, cell proliferation and cell migration inside such a vascularising scaffold is developed and investigated. In addition, a vascularisation model is presented, which supports a vascularisation front which moves at a constant speed. The effects of vascular growth, homogenous and heterogenous seeding, diffusion of cells and critical hypoxic oxygen concentration are considered. For homogenous seeding, a relationship between the speed of the vascular front and a parameter defining the rate of oxygen diffusion relative to the rate of oxygen consumption determines whether a hypoxic region exists at some time. In particular, an estimate of the length of time that a fixed point in the scaffold will remain under hypoxic conditions is determined. For heterogenous seeding, a Fisher-like travelling wave of cells is established behind the vascular front. These findings provide a fundamental understanding of the important interplay between the parameters and allows for a theoretical assessment of a seeding strategy in a vascularising scaffold.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

“…The oxygen diffusion could be modified to account for local cell density, but Croll et al (2005) found this had negligible effect on the results, and so is ignored here.…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Cell Proliferation and Oxygen Diffusion in a Vascularising Scaffold

Landman

Cai

2007

Bull. Math. Biol.

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Soft Tissue Scaffolds

Guan

Stankus

Wagner

2006

Wiley Encyclopedia of Biomedical Engineering

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The effort to develop soft tissues is one of the most demanding and challenging applications in tissue engineering. Soft tissues such as myocardium, blood vessels, skeletal muscle, adipose tissue, and even cartilage often possess large volumes, have high cell densities, and can be mechanically active. 3‐D scaffolds that match the mechanical properties of the tissue that they are replacing are preferred for soft tissue engineering, because such materials might transmit mechanical forces to the developing tissue during in vitro or in vivo development. A well‐defined biodegradation rate is ideal so that host tissue can replace the scaffold and that stress can be transferred from the support scaffold to the new tissue over an appropriate time period. The scaffolds not only serve as a structural support, but also can play an important role in facilitating cell adhesion, growth, and vascularization throughout the scaffold both during in vitro cell culture and in vivo tissue regeneration. Currently used materials meeting these criteria are diverse and include entirely synthetic materials as well as those that are derived from natural sources, and formats that are continuous on a microscale (hydrogels) and those that have defined microporous architectures. Although natural materials have the inherent advantage of bioactivity, they also possess limitations when employed as soft tissue scaffolds that may be overcome with synthetics. Some limitations associated with natural materials include inducement of an immune response that can lead to rapid degradation as well as poor batch‐to‐batch consistencies. Synthetic polymers permit better control over chemical and physical properties leading to tunability in mechanical strength and degradation rate. Surface properties of synthetic materials can also be more easily modified for improved cell attachment or migration. Some disadvantages of synthetic tissue scaffolds consist of potential toxic degradation products and undesired inflammatory responses. In addition, fabrication methods can process materials into scaffolds of desired porosity, morphologies, and anisotropies. The focus of this article will provide a brief overview of the scaffold preparation, properties, and applications of soft tissue scaffolds.

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