32 citations · 92 across the 10 of their papers we have counts for
11 papers
Spatial segregation across travelling fronts in individual-based and continuum models for the growth of heterogeneous cell populations
José A. Carrillo, Tommaso Lorenzi, Fiona R. Macfarlane
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells prefe…
Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion
Tommaso Lorenzi, Fiona R. Macfarlane, Kevin J. Painter
We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from `fully mesenchymal' to `ful…
The impact of phenotypic heterogeneity on chemotactic self-organisation
Fiona R Macfarlane, Tommaso Lorenzi, Kevin J Painter
The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phe…
Individual-based and continuum models of phenotypically heterogeneous growing cell populations
Fiona R Macfarlane, Xinran Ruan, Tommaso Lorenzi
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells h…
A single-cell mathematical model of SARS-CoV-2 induced pyroptosis and the effects of anti-inflammatory intervention
Sara J Hamis, Fiona R Macfarlane
Pyroptosis is an inflammatory mode of cell death that can contribute to the cytokine storm associated with severe cases of coronavirus disease 2019 (COVID-19). The formation of the…
A hybrid discrete-continuum approach to model Turing pattern formation
Fiona R Macfarlane, Mark AJ Chaplain, Tommaso Lorenzi
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The rel…
From a discrete model of chemotaxis with volume-filling to a generalised Patlak-Keller-Segel model
Federica Bubba, Tommaso Lorenzi, Fiona R Macfarlane
We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result…
Discrete and continuum models for the evolutionary and spatial dynamics of cancer: a very short introduction through two case studies
Tommaso Lorenzi, Fiona R. Macfarlane, Chiara Villa
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynami…
Quantitative predictive modelling approaches to understanding rheumatoid arthritis: A brief review
Fiona R Macfarlane, Mark AJ Chaplain, Raluca Eftimie
Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion,…
A stochastic individual-based model to explore the role of spatial interactions and antigen recognition in the immune response against solid tumours
Fiona R Macfarlane, Mark AJ Chaplain, Tommaso Lorenzi
Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against so…
Bridging the gap between individual-based and continuum models of growing cell populations
Mark AJ Chaplain, Tommaso Lorenzi, Fiona R Macfarlane
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These…