Benjamin L. Vaughan

Influence of the Hydrodynamic Environment on Quorum Sensing in Pseudomonas aeruginosa Biofilms

We provide experimental and modeling evidence that the hydrodynamic environment can impact quorum sensing (QS) in a Pseudomonas aeruginosa biofilm. The amount of biofilm biomass required for full QS induction of the population increased as the flow rate increased.

A mechanochemical model of striae distensae

Striae distensae, otherwise known as stretch marks, are common skin lesions found in a variety of clinical settings. They occur frequently during adolescence or pregnancy where there is rapid tissue expansion and in clinical situations associated with corticosteroid excess. Heralding their onset is the appearance of parallel inflammatory streaks aligned perpendicular to the direction of skin tension. Despite a considerable amount of investigative research, the pathogenesis of striae remains obscure. The interpretation of histologic samples - the major investigative tool - demonstrates an association between dermal lymphocytic inflammation, elastolysis, and a scarring response. Yet the primary causal factor in their aetiology is mechanical; either skin stretching due to underlying tissue expansion or, less frequently, a compromised dermis affected by normal loads. In this paper, we investigate the pathogenesis of striae by addressing the coupling between mechanical forces and dermal pathology. We develop a mathematical model that incorporates the mechanical properties of cutaneous fibroblasts and dermal extracellular matrix. By using linear stability analysis and numerical simulations of our governing nonlinear equations, we show that this quantitative approach may provide a realistic framework that may account for the initiating events.

The Influence of Fluid Flow on Modeling Quorum Sensing in Bacterial Biofilms

In this paper, we study quorum sensing in Pseudomonas aeruginosa biofilms. Quorum sensing is a process where bacteria monitor their population density through the release of extra-cellular signalling molecules. The presence of these molecules affects gene modulation leading to changes in behaviour such as the release of virulence factors. Here, we use numerical methods to approximate a 2-D model of quorum sensing. It is observed that the shape of the biofilm can have a profound effect on the onset of quorum sensing. This has serious repercussions for experimental observations since biofilms of the same biomass but different shapes can produce quite different results.

A MODIFIED OSTER-MURRAY-HARRIS MECHANICAL MODEL OF MORPHOGENESIS ∗

There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83--125]. We revisit the Oster--Murray--Harris model and find that, due to the infinitesimal displacement assumption made in the original version of this model, there is a restriction on the types of boundary conditions that can be prescribed. We derive a modified form of the model which relaxes the infinitesimal displacement assumption. We analyze the dynamics of this model using linear and multiscale nonlinear analysis and show that it has the same linear behavior as the original Oster--Murray--Harris model. Nonlinear analysis, however, predicts that the modified model will allow for a wider range of parameters where the solution evolves to a bounded steady state. The results from both analyses are verifi...

A Poroelastic Model Describing Nutrient Transport and Cell Stresses Within a Cyclically Strained Collagen Hydrogel

In the creation of engineered tissue constructs, the successful transport of nutrients and oxygen to the contained cells is a significant challenge. In highly porous scaffolds subject to cyclic strain, the mechanical deformations can induce substantial fluid pressure gradients, which affect the transport of solutes. In this article, we describe a poroelastic model to predict the solid and fluid mechanics of a highly porous hydrogel subject to cyclic strain. The model was validated by matching the predicted penetration of a bead into the hydrogel from the model with experimental observations and provides insight into nutrient transport. Additionally, the model provides estimates of the wall-shear stresses experienced by the cells embedded within the scaffold. These results provide insight into the mechanics of and convective nutrient transport within a cyclically strained hydrogel, which could lead to the improved design of engineered tissues.

Propagation of an Air Finger Into a Fluid Filled Bifurcation

The occlusion of pulmonary airways can be caused by many respiratory diseases such as respiratory distress syndrome. It is believed that these occluded airways are reopened by the propagation of an air finger. The mechanics of airway reopening have been studied in-depth for an individual airway [1,2] without considering the frequent branching of pulmonary airways. The presence of a bifurcation leads to the question of whether the propagating air finger will clear both branches of the airway or will propagate through a single branch, leaving the other branch occluded. The propagation of a finite length liquid plug through a fixed bifurcation has been studied experimentally [3, 4]. We wish to develop a numerical model for the propagation of an air finger through bifurcating channel filled with a viscous fluid. In this model, the air finger is driven by a pressure difference between the parent channel and the two daughter branches. The presence of an additional pressure difference between the two branches can cause unsymmetrical splitting of the air finger and, above a critical pressure difference, prevent the clearance of both branches.Copyright