Search Results - "Chapman, S. Jonathan"

Mathematical Models of Avascular Tumor Growth by Roose, Tiina, Chapman, S. Jonathan, Maini, Philip K.

“…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…”
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MULTISCALE REACTION-DIFFUSION ALGORITHMS: PDE-ASSISTED BROWNIAN DYNAMICS by FRANZ, BENJAMIN, FLEGG, MARK B., CHAPMAN, S. JONATHAN, ERBAN, RADEK

“…Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian…”
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Mathematical modeling of monoclonal conversion in the colonic crypt by Fletcher, Alexander G., Breward, Christopher J.W., Jonathan Chapman, S.

“…A novel spatial multiscale model of a colonic crypt is described, which couples the cell cycle (including cell division) with the mechanics of cell movement…”
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Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer by Johnston, Matthew D, Edwards, Carina M, Bodmer, Walter F, Maini, Philip K, Chapman, S. Jonathan

“…Colorectal cancer is initiated in colonic crypts. A succession of genetic mutations or epigenetic changes can lead to homeostasis in the crypt being overcome,…”
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Model reduction for slow-fast stochastic systems with metastable behaviour by Bruna, Maria, Chapman, S Jonathan, Smith, Matthew J

“…The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical…”
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ANALYSIS OF BROWNIAN DYNAMICS SIMULATIONS OF REVERSIBLE BIMOLECULAR REACTIONS by LIPKOVÁ, JANA, ZYGALAKIS, KONSTANTINOS C., CHAPMAN, S. JONATHAN, ERBAN, RADEK

“…A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The…”
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On the proportion of cancer stem cells in a tumour by Johnston, Matthew D., Maini, Philip K., Jonathan Chapman, S., Edwards, Carina M., Bodmer, Walter F.

“…It is now generally accepted that cancers contain a sub-population, the cancer stem cells (CSCs), which initiate and drive a tumour’s growth. At least until…”
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Predicting Tumor Location by Modeling the Deformation of the Breast by Gavaghan, David J., Whiteley, Jonathan P., Chapman, S. Jonathan, Brady, J. Michael, Pathmanathan, Pras

“…Breast cancer is one of the biggest killers in the western world, and early diagnosis is essential for improved prognosis. The shape of the breast varies…”
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Diffusion of multiple species with excluded-volume effects by Bruna, Maria, Chapman, S Jonathan

“…Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties…”
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Excluded-volume effects in the diffusion of hard spheres by Bruna, Maria, Chapman, S Jonathan

“…Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core…”
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Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions by Erban, Radek, Chapman, S Jonathan

“…Several stochastic simulation algorithms (SSAs) have recently been proposed for modelling reaction-diffusion processes in cellular and molecular biology. In…”
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Examples of Mathematical Modeling: Tales from the Crypt by Johnston, Matthew D., Edwards, Carina M., Bodmer, Walter F., Maini, Philip K., Chapman, S. Jonathan

“…Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological…”
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ASYMPTOTIC ANALYSIS OF A SYSTEM OF ALGEBRAIC EQUATIONS ARISING IN DISLOCATION THEORY by HALL, CAMERON L., CHAPMAN, S. JONATHAN, OCKENDON, JOHN R.

“…The system of algebraic equations given by $\sum\nolimits_{j = 0,j \ne i}^n {\frac{{\operatorname{sgn} ({x_i} - {x_j})}}{{{\left| {{x_i} - {x_j}} \right|}^a}}}…”
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The two-regime method for optimizing stochastic reaction–diffusion simulations by Flegg, Mark B., Chapman, S. Jonathan, Erban, Radek

“…Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for…”
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Motility-Induced Phase Separation Mediated by Bacterial Quorum Sensing by Ridgway, Wesley J M, Dalwadi, Mohit P, Pearce, Philip, Chapman, S Jonathan

“…We study motility-induced phase separation (MIPS) in living active matter, in which cells interact through chemical signaling, or quorum sensing. In contrast…”
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Influence of correlated antigen presentation on T-cell negative selection in the thymus by Banerjee, Soumya, Chapman, S Jonathan

“…The thymus is the primary organ for the generation of naive T cells, a key component of the immune system. Tolerance of T cells to self is achieved primarily…”
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Diffusion of Finite-Size Particles in Confined Geometries by Bruna, Maria, Chapman, S. Jonathan

“…The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement…”
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Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours by Shipley, Rebecca J, Chapman, S. Jonathan

“…A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed…”
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Reactive boundary conditions for stochastic simulations of reaction-diffusion processes by Erban, Radek, Chapman, S Jonathan

“…Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such…”
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REACTIVE BOUNDARY CONDITIONS AS LIMITS OF INTERACTION POTENTIALS FOR BROWNIAN AND LANGEVIN DYNAMICS by CHAPMAN, S. JONATHAN, ERBAN, RADEK, ISAACSON, SAMUEL A.

“…A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the…”
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