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- John R Collier, Nicholas A. M. Monk, Philip K. Maini, Julian Lewis
- Journal of theoretical biology
- 1996

In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition--a type of cell-cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbors from doing… (More)

- Tomás Alarcón, Helen M. Byrne, Philip K. Maini
- Journal of theoretical biology
- 2003

Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this paper we aim to address this shortcoming by developing a mathematical model which shows how blood flow and red blood cell heterogeneity influence the growth of… (More)

- Maksim V. Plikus, Julie Ann Mayer, +4 authors Cheng-Ming Chuong
- Nature
- 2008

In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult life, and are an important model for organ regeneration. Hair stem cells located in the follicle bulge are regulated by the surrounding microenvironment, or niche.… (More)

- Edmund J. Crampin, EA Gaffney, Philip K. Maini
- Bulletin of mathematical biology
- 1999

We investigate the sequence of patterns generated by a reaction-diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction-diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence… (More)

- Christian A. Yates, Radek Erban, +5 authors David J. T. Sumpter
- Proceedings of the National Academy of Sciences…
- 2009

Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending… (More)

- Tomás Alarcón, Helen M. Byrne, Philip K. Maini
- Multiscale Modeling & Simulation
- 2005

We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between cancerous and normal tissue, cell division, apoptosis, vascular endothelial growth factor release, and the coupling between these processes. Simulations of the… (More)

- Leeanne Olsen, Jonathan A. Sherratt, Philip K. Maini
- Journal of theoretical biology
- 1995

The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic component of full-thickness excisional dermal wound healing. The underlying biomechanics of wound contraction, however, are not fully understood, and little is known… (More)

- Tiina Roose, S. Jonathan Chapman, Philip K. Maini
- SIAM Review
- 2007

This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical… (More)

- Philip K. Maini, Donald L. S. McElwain, David I. Leavesley
- Tissue engineering
- 2004

The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over components of the extracellular matrix. Results were interpreted in terms of Fisher's equation, which includes terms for the modeling of random cell motility… (More)

Abstract. A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for… (More)