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Full-Text Articles in Physical Sciences and Mathematics
A Mathematical Model Of Collagen Lattice Contraction, J. C. Dallon, Emily J. Evans, H Paul Erhlich
A Mathematical Model Of Collagen Lattice Contraction, J. C. Dallon, Emily J. Evans, H Paul Erhlich
Faculty Publications
Two mathematical models for fibroblast-collagen interaction are proposed which reproduce qualitative features of fibroblast populated collagen lattice contraction in time. Both models are force based and model the cells as individual entities with discrete attachment sites however the collagen lattice is modeled differently for each model. In the collagen lattice model the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fiber model the nodes are not triangulated, are less interconnected, and the collagen fibers are modeled as a string of nodes. Both models suggest that the overall increase in stress of …
A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich
A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich
Faculty Publications
Bellaes introduction of the fibroblast populated collagen lattice (FPCL) (1) has facilitated the study of collagen-cell interactions. As a result of the numerous modifications of the casting of FPCL's, the in vivo applications of these in vitro findings has been confusing. Here experimental FPCL contraction findings are viewed in regard to three proposed mechanisms responsible for lattice contraction. The cellular mechanisms responsible for generating FPCL contraction are: cell contraction, cell tractional forces related to cell locomotion, and initial cell elongation and spreading.
A Mathematical Model For Spatially Varying Extracellular Matrix, J. C. Dallon, J. A. Sherratt
A Mathematical Model For Spatially Varying Extracellular Matrix, J. C. Dallon, J. A. Sherratt
Faculty Publications
Orientation of extracellular matrix fibers in the skin is a key ingredient of tissue appearance and function, and differences in fiber alignment are one of the main distinctions between scar tissue and normal skin. In this paper, the authors develop a mathematical model for alignment of collagen fibers and the fibroblast cells that remodel them; the model extends previous work in which spatial variation was excluded. Numerical simulations of the model are presented, which show spatial variations in alignment over long transients, but with spatially uniform behavior in the long term. This is investigated further via asymptotic analysis, using the …
A Mathematical Model For Fibroblast And Collagen Orientation, J. C. Dallon, J. A. Sherratt
A Mathematical Model For Fibroblast And Collagen Orientation, J. C. Dallon, J. A. Sherratt
Faculty Publications
Due to the increasing importance of the extracellular matrix in many biological problems, in this paper we develop a model for fibroblast and collagen orientation with the ultimate objective of understanding how fibroblasts form and remodel the extracellular matrix, in particular its collagen component. The model uses integro-differential equations to describe the interaction between the cells and fibers at a point in space with various orientations. The equations are studied both analytically and numerically to discover different types of solutions and their behavior. In particular we examine solutions where all the fibroblasts and collagen have discrete orientations, a localized continuum …