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A continuum model and a discrete model are developed to capture the population-scale and cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in a confluent cell monolayer. During wound closure, the cell population forms a sustained traveling wave, with close contact between cells behind the wavefront. Cells exhibit(More)
A general mathematical model of cell invasion is developed and validated with an experimental system. The model incorporates two basic cell functions: non-directed (diffusive) motility and proliferation to a carrying capacity limit. The model is used here to investigate cell proliferation and motility differences along the axis of an invasion wave.(More)
Magnetic resonance microscopy (MRM) has been used to study the kinetics of water transport in human eye lenses. Fresh lenses obtained from the Queensland Eye Bank were incubated at 34.5 degrees C in artificial aqueous humour (AAH) containing nutrients and metabolites similar to those that are present in vivo. MR images were acquired over approximately a 20(More)
During development, tissues often undergo rapid physical expansion due to cell proliferation. Continuous and discrete models of one- and two-dimensional tissue growth are developed and applied to observational data of the developing avian gut, where the gut tissue cells undergo dramatic proliferation. The discrete cellular automata model provides results at(More)
Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different(More)
Operator splitting (OS) is a popular and convenient technique used to numerically solve reactive transport problems such as Fisher's equation. Although OS has been widely used to solve Fisher's equation, no characterization of the innate OS error has been presented. Here the exact characteristics of the OS error for travelling wave solutions of Fisher's(More)
The vertebrate enteric nervous system is formed by a rostro-caudally directed invasion of the embryonic gastrointestinal mesenchyme by neural crest cells. Failure to complete this invasion results in the distal intestine lacking intrinsic neurons. This potentially fatal condition is called Hirschsprung's Disease. A mathematical model of cell invasion(More)
Midbrain, hindbrain and vagal neural crest (NC) produced abundant enteric nervous system (ENS) in co-grafted aneural hindgut and midgut, using chick-quail chorio-allantoic membrane grafts, forming complete myenteric and submucosal plexuses. This ability dropped suddenly in cervical and thoracic NC levels, furnishing an incomplete ENS in one or both(More)
Cell proliferation during nervous system development is poorly understood outside the mouse neocortex. We measured cell cycle dynamics in the embryonic mouse sympathetic stellate ganglion, where neuroblasts continue to proliferate following neuronal differentiation. At embryonic day (E) 9.5, when neural crest-derived cells were migrating and coalescing into(More)