8 citations · 10 across the 13 of their papers we have counts for
13 papers
Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations
Carles Falcó, Rebecca M. Crossley, Martina Conte +1
We consider a minimal pressure-based model of heterogeneous cell populations consisting of proliferative and non-proliferative cells with different mobilities. The model is formula…
Kinetic and mean-field modeling of muscular dystrophies
Tommaso Lorenzi, Horacio Tettamanti, Mattia Zanella
We present a new class of models for assessing the cell dynamics characterising muscular dystrophies. The proposed approach comprises a system of integro-differential equations for…
Derivation and quasi-invariant asymptotics of phenotype-structured integro-differential models
Emanuele Bernardi, Tommaso Lorenzi, Andrea Tosin
Building upon kinetic theory approaches for mass-varying multi-agent systems, we develop a modelling framework for phenotype-structured populations that makes it possible to bridge…
A phenotype-structured reaction-diffusion model of avascular glioma growth
Francesca Ballatore, Xinran Ruan, Chiara Giverso +1
We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into…
On a phenotype-structured phase-field model of nutrient-limited tumour growth
Tommaso Lorenzi, Giulia Pozzi, Andrea Signori
Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type wh…
Pattern formation within phenotype-structured chemotactic populations
Tommaso Lorenzi, Kevin J. Painter
Populations can become spatially organised through chemotaxis autoattraction, wherein population members release their own chemoattractant. Standard models of this process usually…
Heterogeneously structured compartmental models of epidemiological systems: from individual-level processes to population-scale dynamics
Emanuele Bernardi, Tommaso Lorenzi, Mattia Sensi +1
We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-sp…
Trait-structured chemotaxis: Exploring ligand-receptor dynamics and travelling wave properties in a Keller-Segel model
Viktoria Freingruber, Tommaso Lorenzi, Kevin J. Painter +1
A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derive…
Phenotype-structuring of non-local kinetic models of cell migration driven by environmental sensing
Tommaso Lorenzi, Nadia Loy, Chiara Villa
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migrati…
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…
Phenotype structuring in collective cell migration:a tutorial of mathematical models and methods
Tommaso Lorenzi, Kevin J Painter, Chiara Villa
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be…
Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the `go-or-grow' hypothesis
Rebecca M. Crossley, Kevin J. Painter, Tommaso Lorenzi +2
A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models ofte…
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…