42 citations · 47 across the 8 of their papers we have counts for
9 papers
Biological Modelling with Nonlocal Advection Diffusion Equations
Kevin J Painter, Thomas Hillen, Jonathan R Potts
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods g…
Weakly nonlinear analysis of a two-species non-local advection-diffusion system
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection…
Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent pa…
Local and Global Existence for Non-local Multi-Species Advection-Diffusion Models
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has be…
Direction-Dependent Turning Leads to Anisotropic Diffusion and Persistence
Nadia Loy, Thomas Hillen, Kevin John Painter
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool…
Non-Local Cell Adhesion Models: Steady States and Bifurcations
Andreas Buttenschön, Thomas Hillen
In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type…
Nonlocal Adhesion Models for Microorganisms on Bounded Domains
Thomas Hillen, Andreas Buttenschön
In 2006 Armstrong, Painter and Sherratt formulated a non-local differential equation model for cell-cell adhesion. For the one dimensional case we derive various types of adhesive,…
A Stochastic Model for the Normal Tissue Complication Probability (NTCP) in Radiation Treatment of Cancer
Theresa Stocks, Thomas Hillen, Jiafen Gong +1
The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth death…
Mathematical Analysis of a Kinetic Model for Cell Movement in Network Tissues
Thomas Hillen, Peter Hinow, Zhi-An Wang
Mesenchymal motion describes the movement of cells in biological tissues formed by fiber networks. An important example is the migration of tumor cells through collagen networks du…