PDE models for cancer invasion

About

The one-day Workshop "PDE models for cancer invasion" will take place at

Mathematical Sciences Research Centre, School of Mathematics and Physics, Queen’s University Belfast

in Emeleus Lecture Theatre on Friday 6 December 2019.

Aims and Scope

Cancer cell invasion of tissue is an essential stage in the development and expansion of tumours and their metastases. Deduction of mathematical models describing this multifaceted process in terms of PDEs and their subsequent analysis and simulations can contribute to a better understanding of the involved biological phenomena and enable predictions about the development and the extent of a tumour. A realistic mathematical modelling of migration of living cancer cells is much more involved than, e.g., that of physical particles. It calls for new classes of models and, as a result, for new approaches in the modelling, analysis, and numerical simulations.

This workshop aims to present recent developments in this area.

Invited Speakers

Raluca Eftimie (University of Dundee)
Kevin Painter (Heriot-Watt University)
Anna Zhigun (Queen’s University Belfast)

Programme

Thursday 5 December

19:00 Conference dinner

Friday 6 December

13:30-14:00 Get together with coffee and sandwiches

14:00-15:00 Talk by Kevin Painter on "Anisotropic PDE models for cell and cancer invasion processes"

Abstract

Many tumours invade in complex and heterogeneous fashion, creating significant difficulties for therapy. An important determinant of invasion is the extracellular environment of the cells which, for many tissues, may be highly anisotropic. In this talk I will discuss the modelling of cell migration in anisotropic tissue environments. Starting from a velocity-jump random walk model for cell movement, I will derive transport and anisotropic PDE models that can be used to describe the macroscopic spread of a population. I will show how the interactions between cells and their environment can lead to complex pattern formation processes and, via exploiting data from DTI imaging, show how the model can be applied to predict the invasion patterns of malignant gliomas, a brain tumour with very poor prognosis.

15:00-16:00 Talk by Raluca Eftimie on "Pattern formation in nonlocal mathematical models for cancer invasion"

Abstract

Cancer invasion is a complex process involving interactions between cancer cells, between cells and extracellular matrix, and between cancer cells and various types of immune cells that can be found inside the tumour microenvironment. These interactions are facilitated by different molecules (e.g., cytokines, chemokines), which can be produced by the cancer cells themselves, or by other cells in the microenvironment. Here we introduce a class of nonlocal mathematical models for cancer proliferation and invasion (models described by hyperbolic and/or parabolic PDEs), and investigate analytically and numerically the spatial and spatio-temporal patterns exhibited by these nonlocal models.

16:00-16:30 Coffee break

16:30-17:30 Talk by Anna Zhigun on "(Non)local models for taxis in cancer cell migration: a rigorous limit procedure"

Abstract

In recent years nonlocal alternatives to the traditional reaction-diffusion-taxis systems for cancer invasion have been proposed in which a local transport flux is replaced by an integral of signal-dependent quantity over a suitable set, typically a ball of a so-called sensing radius r > 0. Terms of this sort allow to describe long-range effects such as cell-cell and cell-tissue adhesions. Some heuristic analysis via local Taylor expansions was performed and led to expect that as r->0 the solutions of these nonlocal models converge to solutions of the corresponding local models. However, to the best of our knowledge no rigorous analytical study of such convergence has as yet been performed. In this talk I will demonstrate a way to close this gap. It relies on a novel reformulation of the involved nonlocality in terms of an integral operator applied directly to the gradient of a signal-dependent quantity. I will show on concrete examples the advantages of the new reformulation. Finally, some numerical simulations in 1D will provide an illustration of the theoretical findings.

The talk is based on a joint work with Maria Krasnianski, Kevin Painter, and Christina Surulescu.

17:30-19:00 Reception and discussions open to all participants

All talks will take place in Emeleus Lecture Theatre.

Registration

The workshop is open to everyone. There are no conference fees but registration is required, klick here.

Travel to Belfast

There is helpful information on the QUB travel web page. Flying to Dublin is sometimes easier (and cheaper) than flying to Belfast. There are regular bus connections from Dublin Airport to Belfast and back (travel time around two hours; check for example Aircoach or Translink buses).

Accommodation

Participants are required to make their own arrangements.

Contact

Please contact the Workshop organiser Anna Zhigun

On the banner: breast carcinoma in a lymph node. An adaptation of https://commons.wikimedia.org/wiki/File:Breast_carcinoma_in_a_lymph_node.jpg

About

Aims and Scope

Invited Speakers

Programme

Registration

Travel to Belfast

Accommodation

Sponsors

Contact