The Extracellular Matrix: How to model structure complexity
CECAM-HQ EPFL, LAUSANNE, SWITZERLAND
The extracellular environment being essentially everything that is not cells is universal across biology and, specifically for this workshop, within the human body. It is a key contributor to many human biological processes, for example, embryonic development and cancer cell invasion. It is, however, a highly complex structure which can be difficult to describe within a mathematical model. This workshop will introduce the extracellular matrix (ECM) as a mathematical structure, within which specific components such as matrix fibres can be modelled explicitly, in contrast to the traditional approach in which the ECM is described by a density or continuum. There are many examples of mathematical models incorporating ECM as a density, for example, in liver fibrosis , tumour growth , and in wound healing . It is well-known that cells interact with ECM and feedback between the two changes both cell behaviours and ECM structure. Having a deeper understanding of cell-ECM interactions is vital to our understanding of biological processes. To truly understand these interactions we need to build multiscale models which take the individual ECM components into account. Agent-based cell models (ABMs) are now a common tool, where the ECM is usually incorporated by considering background diffusion within the environment so that cell-ECM interactions are modelled using hybrid ABMs. Rarely in such a case can the physics and mechanics of cell-ECM interactions be fully taken into account. Multiscale models that consider fibres from a continuum perspective , and as rods in an ABM  have been explored, whilst there have been recent advancements in considering groups of spherical agents to represent fibres in an ABM . Our interest lies in fully defining ECM structures as additional agents within an ABM to allow the physical and mechanical interactions to be accurately captured and analysed in order to indicate their true contribution to the system. ECM mediated processes such as cell durotaxis and topotaxis are modelled more accurately in this way . Organisers Robyn Shuttleworth and Cicely Macnamara are part of a team developing a PhysiCell add-on (PhysiMESS) which allows ECM structures to be treated as additional agents and allows the user to define the physics of cell-ECM structure interactions. We anticipate that the interdisciplinary projects developed at the workshop would use the capabilities of both PhysiCell and PhysiMESS to create detailed models of key biological processes.
(Please note that a reference could not be retrieved below, so we will add it here:  Friedman, A., Hao, W., Mathematical Modelling of Liver Fibrosis, Math. Biosci. and Eng., 14(1) (2017). DOI: 10.3934/mbe.2017010)
Robyn Shuttleworth (University of Saskatchewan) - Organiser
Lisanne Rens (Delft University of Technology) - Organiser
Cicely Macnamara (University of Glasgow) - Organiser