Mathematical modelling of anisotropy in fibrous connective tissue

Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.; Dallon, John C.

doi:10.1016/s0025-5564(99)00005-x

Cited by 49 publications

(32 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to this previous work, we are not primarily concerned with "broblast orientation as such, but rather on how this a!ects the orientation of the "brous network. The work which most closely relates to the modelling in this paper is that which examines alignment of the extracellular matrix (Olsen et al, 1998(Olsen et al, , 1999Dallon & Sherratt, 1998;Barocas & Tranquillo, 1997). Each of these represents very di!erent approaches to modelling similar systems.…”

Section: Introductionmentioning

confidence: 99%

“…Each of these represents very di!erent approaches to modelling similar systems. Olsen et al (1998) model the system with reaction di!usion equations where the species can take one of two orthogonal directions, while Olsen et al (1999) use a related model including the long-range mechanical forces within the "brous network. Dallon & Sherratt (1998) formulate the long-range angular interactions as integro-di!erential equations, ignoring spatial variation, and in Barocas & Tranquillo (1997) the extracellular matrix is treated as a biphasic medium with viscoelastic properties which both orients, and is oriented, by the cells.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Modelling of Extracellular Matrix Dynamics using Discrete Cells: Fiber Orientation and Tissue Regeneration

Dallon

Sherratt

Maini

1999

Journal of Theoretical Biology

126

117

View full text Add to dashboard Cite

Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the factors involved in orientation and alignment. Within this framework, cells are considered as discrete objects, while the matrix is modelled as a continuum. Using numerical simulations, we investigate the e!ect on alignment of changing cell properties and of varying cell interactions with collagen and "brin. Academic Press

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Extracellular Matrix Dynamics using Discrete Cells: Fiber Orientation and Tissue Regeneration

Dallon

Sherratt

Maini

1999

Journal of Theoretical Biology

126

117

View full text Add to dashboard Cite

show abstract

“…Other models account for ECM deposition or degradation, and allow fibre orientation to bias cell movement (e.g. Chauviere et al (2007); Hillen (2006); Olsen et al (1999);Painter (2009)), but assume the forces exerted by the cells do not affect fibre orientation.…”

Section: Deformation Changes Fibre Alignmentmentioning

confidence: 99%

An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

et al. 2015

View full text Add to dashboard Cite

Mechanical interactions between cells and the fibrous extracellular matrix (ECM) in which they reside play a key role in tissue development. Mechanical cues from the environment (such as stress, strain and fibre orientation) regulate a range of cell behaviours, including proliferation, differentiation and motility. In turn, the ECM structure is affected by cells exerting forces on the matrix which result in deformation and fibre realignment. In this paper we develop a mathematical model to investigate this mechanical feedback between cells and the ECM. We consider a three-phase mixture of collagen, culture medium and cells, and formulate a system of partial differential equations which represents conservation of mass and momentum for each phase. This modelling framework takes into account the anisotropic mechanical properties of the collagen gel arising from its fibrous microstructure. We also propose a cell-collagen interaction force which depends upon fibre orientation and collagen density. We use a combination of numerical and analytical techniques to study the influence of cell-ECM interactions on pattern formation in tissues. Our results illustrate the wide range of structures which may be formed, and how those that emerge depend upon the importance of cell-ECM interactions.

show abstract

“…Barocas and Tranquillo 1997), wound healing (cf. Olsen et al 1999), and soft tissue growth and remodeling (cf. Driessen et al 2003).…”

Section: Introductionmentioning

confidence: 99%

A theoretically-motivated biaxial tissue culture system with intravital microscopy

Humphrey

Wells

Baek

et al. 2007

Biomech Model Mechanobiol

View full text Add to dashboard Cite

Many cell types produce, remodel, and degrade extracellular matrix in response to diverse stimuli, including mechanical loads. Much is known about the molecular biology and biochemistry of the deposition and degradation of collagen, the primary structural constituent of the extracellular matrix in many tissues, yet there has been little modeling of the associated mechanobiology. For example, we do not have quantitative descriptions, or rules, for the kinetics of collagen turnover as a function of altered mechanical loading and we do not know what governs the orientation and pre-stretch at which new fibers are incorporated within extant tissue. In this paper, we use a constrained mixture theory for growth and remodeling of planar soft tissues to motivate a new experimental approach for investigating competing hypotheses on, for example, how new collagen is aligned by synthetic cells. In particular, because stress and strain fields can be homogeneous in a central region of a biaxially tested tissue, and because biaxial testing admits diverse protocols wherein equal stresses can be imposed in the presence of unequal strains or stresses can be maintained in the absence of strain, we report simulations that illustrate the potential utility of biaxial culture studies. Finally, we describe the associated design of a computer-controlled system that allows intravital microscopic quantification of collagen density, orientation, and cross-linking at various stages during the adaptation of a native tissue or the development of a tissue engineered equivalent, each subjected to well controlled biaxial loads.

show abstract

Mathematical modelling of anisotropy in fibrous connective tissue

Cited by 49 publications

References 42 publications

Mathematical Modelling of Extracellular Matrix Dynamics using Discrete Cells: Fiber Orientation and Tissue Regeneration

Mathematical Modelling of Extracellular Matrix Dynamics using Discrete Cells: Fiber Orientation and Tissue Regeneration

An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

A theoretically-motivated biaxial tissue culture system with intravital microscopy

Contact Info

Product

Resources

About