D. L. Sean McElwain

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K e y w o r d s F i s h e r ' s equation, Human peritoneal mesothelial cells, Invasion waves. I N T R O D U C T I O N Severa l a u t h o r s have p r o p o s e d t h a t c o n s t a n t profile, c o n s t a n t speed t r ave l l i ng waves p lay an i m p o r t a n t role in a n u m b e r of m ed i ca l app l ica t ions . For example , in e p i d e r m a l w(More)
Many solid tumour growth models are formulated as systems of parabolic and/or hyperbolic equations. Here an alternative, two-phase theory is developed to describe solid tumour growth. Versions of earlier models are recovered when suitable limits of the new model are taken. We contend that the multi-phase approach represents a more general, and natural,(More)
Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method(More)
Spreading cell fronts are essential features of development, repair and disease processes. Many mathematical models used to describe the motion of cell fronts, such as Fisher's equation, invoke a mean-field assumption which implies that there is no spatial structure, such as cell clustering, present. Here, we examine the presence of spatial structure using(More)
Moving cell fronts are an essential feature of wound healing, development and disease. The rate at which a cell front moves is driven, in part, by the cell motility, quantified in terms of the cell diffusivity D, and the cell proliferation rate λ. Scratch assays are a commonly reported procedure used to investigate the motion of cell fronts where an initial(More)
Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch(More)
Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate(More)