A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Modelling the effects of Transforming Growth Factor-β on extracellular matrix alignment in dermal wound repair

We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of transforming growth factor-β (TGFβ.) Our work extends a previously developed model which considers the interactions between fibroblasts and an extracellular matrix composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix directs the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGFβ to alter the properties of the fibroblasts. Thus we are able to simulate experiments which alter the TGFβ profile. Within this model framework we find that most of the known effects of TGFβ, i.e., changes in cell motility, cell proliferation and collagen production, are of minor importance to matrix alignment and cannot explain the anti-scarring properties of TGFβ. However, we find that by changing fibroblast reorientation rates, consistent with experimental evidence, the alignment of the regenerated tissue can be significantly altered. These data provide an explanation for the experimentally observed influence of TGFβ on scarring

The Anti-Bootlegging Provisions: Congressional Power and Constitutional Limitations

Courts and scholars have considered the constitutional validity of 17 U.S.C. § 1101 (civil), and 18 U.S.C. § 2319A (criminal), known together as the anti-bootlegging provisions. These provisions prohibit unauthorized recording, copying, and distribution of live musical performances. The provisions have been challenged in three cases, resulting in five published opinions. Two district court opinions held the provisions unconstitutional, but subsequent opinions vacated those decisions. Notwithstanding a sharp division among copyright scholars, the courts have upheld these provisions. The discussion surrounding them is part of a continuing struggle to ascertain limits on congressional power to regulate copying and distribution of expression. The latest decision in this area, United States v. Martignon, 492 F.3d 140 (2d Cir. 2007), found that Congress had the power to enact § 2319A, but left two major issues unresolved. First, it only considered the constitutionality of the criminal provision, and its analysis cast doubt on the validity of the companion civil provision that was not before the court. Second, Martignon did not consider the free speech challenge to the statute and remanded the case for consideration of that issue. This Article argues that the Constitution firmly supports Congress\u27s power to enact the anti-bootlegging provisions as an exercise of the Commerce Clause, which does not conflict with the Copyright Clause, and does not violate the First Amendment

Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair

We deveiop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a continuous extracellular matrix composed of collagen and a fibrin based blood clot. There are four basic interactions assumed in the model: fibroblasts orient the collagen matrix, fibroblasts produce and degrade collagen and fibrin and the matrix directs the fibroblasts and determines the speed of the cells. Several factors which influence the alignment of collagen are examined and related to current anti-scarring therapies using transforming growth factor ß. The most influential of these factors are cell speed and, more importantly for wound healing, the influx of fibroblasts from surrounding tissue