Scientific background

I studied for my D.Phil (Ph.D) under Dr Peter Howell and Dr Chris Breward at the Oxford Centre for Industrial and Applied Mathematics. My project was based on an industrial coating process used within the paper industry, where I modelled the pigment-containing fluid flows involved. I used techniques from fluid mechanics and asymptotic methods; in particular exploiting the geometry of the flow to simplify the governing equations. This project was sponsored by ArjoWiggins via a CASE studentship, and therefore involved a high degree of multidisciplinarity including spending time on-site with them and discussions with their scientists.

CPIB research

My main role within CPIB was to model the mechanical aspects of root growth, at both cellular and organ scale. I use mathematical modelling techniques such as asymptotic analysis to formulate models which can be tackled analytically, in addition to giving mathematical back up to the hyperelastic models which are solved using finite element methods. In particular, we wish to incorporate the mechanical anisotropy of the call wall, which has been mainly neglected in previous models of plant cells.

My plant work is focused on cell growth within the elongation zone of the root, in which the cell undergoes rapid anisotropic expansion; increasing in length around 30 fold whilst displaying minimal radius change.   Growth is driven by high internal turgor pressure causing viscous stretching of the cell wall.  Cellulose microfibrils embedded within the wall give strongly anisotropic mechanical properties, which are under biochemical control and are modified by the cell during growth.  We have derived and analysed the governing system for this process (Dyson and Jensen 2010).  Representing the cell as a thin axisymmetric fibre-reinforced viscous sheet between rigid end plates, we performed a systematic reduction of the governing equations, under simple sets of assumptions about fibre and wall properties, to derive the governing system. This extension of the Trouton model for extensional flow of a Newtonian fluid to a fibre-reinforced fluid was in itself a novel and challenging piece of mathematics, which may have other applications to other areas as well as plant growth. We found variants of the traditional Lockhart equation, which relates the axial cell growth rate to the internal pressure and is currently used by many plant biologists to model growth.  The model provides insights into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and shows how either dynamical changes in wall material properties or passive fibre reorientation may suppress cell elongation.

Current Position

Rosemary Dyson is now a Lecturer in the School of Mathematics, University of Birmingham. She continues to work closely with CPIB.