34 citations · 226 across the 27 of their papers we have counts for
8 papers · 1 filter
Mechanical models of pattern and form in biological tissues: the role of stress-strain constitutive equations
Chiara Villa, Mark A. J. Chaplain, Alf Gerisch +1
Mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems and describe the physical interactions between cells and t…
A mathematical study of the influence of hypoxia and acidity on the evolutionary dynamics of cancer
Giada Fiandaca, Marcello Delitala, Tommaso Lorenzi
Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spa…
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…
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…
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…
Effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors
Alexander Lorz, Tommaso Lorenzi, Jean Clairambault +2
Histopathological evidence supports the idea that the emergence of phenotypic heterogeneity and resistance to cytotoxic drugs can be considered as a process of adaptation, or evolu…