Mathematical approaches for studying form and function of vascular tumours
Prof Helen Byrne (University of Oxford)
Thursday 17th March 14:00-15:00 ZOOM (ID: 924 6361 4209)
Over the past twenty-five years we have witnessed an unparalleled increase in understanding of cancer. This transformation is exemplified by Hanahan and Weinberg's decision in 2011 to expand their original Hallmarks of Cancer from six traits to ten and, very recently, to fourteen! At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testinghypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving its treatment.
Following Hanahan and Weinberg's lead, in this talk I will reflect on how increased access to experimental data is stimulating the application of new theoretical approaches for studying tumour growth. I will focus on three case studies which illustrate how mathematical approaches can be used to characterise and quantify tumour vascular networks, to understand how microstructural features of these networks affect tumour blood flow, and to study the impact of unsteady blood flow on tumour growth.
Asymptotic modeling of nonlinear imperfect solid/solid interfaces
Frederic Lebon (Aix Marseille Universite, France)
Thursday 3rd February 2022 14:00-15:00
Our work focuses on the theoretical and numerical modelling of interfaces between solid structures (contact, friction, adhesion, bonding, etc.). We will present a general methodology based on matched asymptotic theory to obtain families of models including the relative rigidity of the interphase (soft or hard), geometrical or material non-linearities, damage and multiphysics couplings. Numerical results will be presented.
MODELS FOR CELL MIGRATION ASSAYS, INCLUDING PDES WITH NONLINEAR DIFFUSION
Scott McCue (QUT, Brisbane, Australia)
Monday 6th December 2021 11:00-12:00
Experimentalists who study cancer invasion and wound repair often employ simple assays such as the in vitro scratch assay to quantify the combined effects of cell proliferation and cell migration on the collective motion of cells in two dimensions. In turn, these experiments prove to be fruitful for researchers in mathematical biology to test and explore mathematical models for collective cell motion. I will discuss some of these ideas from the perspective of an applied mathematician, making reference to PDE models such as the Fisher-KPP equation as well as discrete processes based on random walk models. Then I will spend some time on a hole-closing model for a two-dimensional wound assay that is based on a PDE with nonlinear degenerate diffusion. The mathematics here is interesting as it involves similarity solutions of the second kind. Finally, I will touch on slightly more complicated PDE models with nonlinear diffusion that can be used to study problems in similar geometries, such as thin tissue growth in printed bioscaffolds.
MODELING THE SKELETAL MUSCLE TISSUE AS AN ANISOTROPIC ACTIVE MATERIAL
Alessandro Musesti (Università Cattolica del Sacro Cuore, Italy)
Thursday 22nd July 2021 14:00-15:20
Abstract: Skeletal muscle tissue is a paradigmatic example of an active
material, for which deformations can occur in absence of loads, given an
external stimulus. After reviewing its main properties, in the talk I
will compare the two main methods used to model such materials, namely
active stress and active strain. In a hyperelastic setting, it will be
shown that a simple shear produces different stresses in the two
approaches; hence, active stress and active strain produce contrasting
results in shear, even if they both fit uniaxial data. Our results show
that experimental data on the stress-stretch response on uniaxial
deformations are not enough to establish which activation approach
better capture the activation mechanics. A further study of other
deformations, such as simple shears, would be important in order to
develop a realistic model of an active material.