EVENT: Applied Mathematics Seminar

Tissue growth, renewal, and shape adaptation are common traits to many biological tissues and biomaterials. These traits involve changes in tissue geometry and in bulk material properties that are due to modelling processes (tissue generation/destruction) and remodelling processes (tissue renewal). As a result, tissues are made up of different "patches" (adjacent regions of different ages and different material properties) within evolving boundaries. Examples include bone tissues, which adapt their shape and have heterogeneous mineral densities reflecting the history of microcrack repairs; extracellular matrix modelling and remodelling, which gives cells control over local stress fields; wound repair; and cancer invasion, which breaks down normal tissue boundaries and affects their function.

In this talk, I will present recent applications of mathematical models that take into account bulk balance due to tissue maturation, as well as nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces. These applications include the evolution of mechanical memories recorded in bone's in-built circuitry of cells (osteocytes), the generation of stochastic inclusions during tissue growth, collisions with evolving surfaces, and curvature-dependent surface evolutions. These mathematical models are particularly applied to the evolution of bone tissues, but have implications in other systems with evolving boundaries, such as sedimentation, 3D printing, etching, and adsorption.