A hyperbolic curvature flow for biological tissue growth

Most biological tissues are sensory, dynamic materials. They undergo

changes in their geometry and in their material properties during growth

and remodelling processes. In this talk, I will focus on a recent

mathematical model of curvature-controlled tissue growth based on a

spatio-temporal cell population model. In this model, geometry modulates

cells collectively through the evolving space available to the population

of cells. The influence of curvature on the collective crowding or

spreading of cells growing new tissue leads to a type of hyperbolic

curvature flow (with curvature-dependent normal acceleration) for the

evolution of the tissue interface. Depending on the strength of lateral

diffusion, the model exhibits complex growth patterns such as undulating

motion, efficient smoothing of irregularities, and the generation of

cusps. While some of these growth patterns can be understood analytically,

such as the shock structure in the zero-diffusion and infinite-diffusion

limits, the transition between undulating motion and efficient smoothing

that occurs at intermediate diffusion remains an open problem.

* Bio

Pascal is a lecturer in Mathematical Biology at Queensland University of

Technology (QUT), Brisbane, Australia. He has been an Australian Research

Council Early Career Research Award (ARC DECRA) Fellow (2013-2017), and

previously held appointments at Monash University (School of Mathematical

Sciences) and at the University of Western Australia (Engineering

Computational Biology Group). He holds a PhD in Theoretical Physics

(Statistical Mechanics) from the Swiss Federal Institute of Technology

Lausanne (EPFL) and a MSc in Physics from the Swiss Federal Institute of

Technology Zurich (ETHZ).

His research interests include mathematical biology, mechanobiology,

complex systems, and stochastic processes.