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Mathematical modelling of problems in physics and biology

The department of Mathematics and Statistics at the University of Limerick invites you to a seminar

Speaker:                     Vladimir Zubkov (School of Computing, Engineering and Mathematics, University of Brighton).

Time and location:     Friday14th September, at 4p.m. in Room A2-002

Title:                           Mathematical modelling of problems in physics and biology

Abstract: The research focuses on the application of numerical and asymptotic methods for Mathematical Biology and Fluid Dynamics. Initially, my research focused on fluid dynamics. My current research interest has been related to the mathematical modelling of the human tear film in the context of dry eye pathology and to the mathematical modelling of the kidney morphogenesis.

We have formulated and explored a model describing the spatial distribution of tear film osmolarity across the ocular surface of a human eye during one blink cycle, incorporating detailed fluid and solute dynamics.

We also have considered a mathematical model of kidney morphogenesis. Mammalian kidneys are vital organs that filter wastes such as urea from the blood. Kidney development is initiated by the outgrowth of a ureteric bud (UB) of epithelial cells into a population of mesenchymal cells. Interactions between the epithelial and mesenchymal cells coordinate the processes of cell proliferation and branching, leading to the formation of a highly branched structure known as the urinary collecting system. While models of fluid and solute transport within the mature kidney have been developed, little attention has been devoted to kidney morphogenesis.

We considered a mathematical model of growing kidney in culture medium, where the epithelium is modelled as a continuous medium with elastic boundary using Navier-Stokes equations. Studying stability of growing kidney with the use of analytical and numerical methods, we explained the archetypal mechanism of branching. We have also formulated a spatially-averaged mathematical model of kidney morphogenesis in which the time evolution of key cell populations is described by a system of ordinary differential equations. The mathematical model and its predictions were validated against experimental data collected from developing mouse kidneys.

If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email  and Clifford Nolan (061 202766),

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (, centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.