34 citations · 226 across the 27 of their papers we have counts for
10 papers · 1 filter
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…
Evolutionary dynamics in vascularised tumours under chemotherapy
Chiara Villa, Mark A. J. Chaplain, Tommaso Lorenzi
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-d…
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…
Modelling the emergence of phenotypic heterogeneity in vascularised tumours
Chiara Villa, Mark A. J. Chaplain, Tommaso Lorenzi
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of…
A structured population model of clonal selection in acute leukemias with multiple maturation stages
Tommaso Lorenzi, Anna Marciniak-Czochra, Thomas Stiehl
Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain un…
Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments
Aleksandra Ardaševa, Robert A. Gatenby, Alexander R. A. Anderson +3
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading thr…
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…
Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks
Tommaso Lorenzi, Camille Pouchol
We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual species whose phenotypic fitness landscape is characterised by multi…
From individual-based mechanical models of multicellular systems to free-boundary problems
Tommaso Lorenzi, Philip J. Murray, Mariya Ptashnyk
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteris…
Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes
Mark A. J. Chaplain, Chiara Giverso, Tommaso Lorenzi +1
We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity…