91 citations · 658 across the 28 of their papers we have counts for
29 papers
Dimension-dependent continuum limits in tissue mechanics
Matthew J Simpson, Pascal R Buenzli
Continuum descriptions of epithelial tissue mechanics can replace expensive individual-based simulations with tractable macroscopic models, yet the link between cell-scale forces a…
Mechanical cell interactions on curved interfaces
Pascal R. Buenzli, Shahak Kuba, Ryan J. Murphy +1
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional s…
Random walk models for the propagation of signalling molecules in one-dimensional spatial networks and their continuum limit
Adel Mehrpooya, Vivien J. Challis, Pascal R. Buenzli
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the co…
Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion
Matthew J Simpson, Keeley M Murphy, Scott W McCue +1
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion…
Pushing coarse-grained models beyond the continuum limit using equation learning
Daniel J. VandenHeuvel, Pascal R. Buenzli, Matthew J. Simpson
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processe…
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework
Yifei Li, Pascal R. Buenzli, Matthew J. Simpson
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study populatio…