University of Glasgow

School of Mathematics & Statistics










                                  - 275 HS Prof Nick Hill Maths


Professor Nick Hill


Simson Professor of Mathematics

Research interests

Mathematical Biology
Biological Fluid Mechanics
Soft Tissue Mechanics

Telephone (internal)


Telephone (UK)

(0141) 330 4258

Telephone (International)

+44 141 330 4258

Telephone (Secretary)

(0141) 330 2940






Research Students

My main research interests are in mathematical modelling of systems in biology, physiology, and biological fluid dynamics - see below.

SofTMech EPSRC Centre for Multiscale Soft Tissue Mechanics
I am a Co-investigator and Executive Director of the 2.4M SofTMech Centre, which is an initiative to accelerate the development soft-tissue modelling by constructing a generic mathematical multiscale framework, and of SofTMechMP a 1.5M International Centre-to Centre Network with MIT and Politecnico di Milano.
The specific SofTMech research projects that I am working on include mathematical and computational modelling of the coronary circulation in the beating heart, parameter estimation for personalised circulation models, and integrating multiscale mechanobiology of individual cells and soft tissue, such as myocytes and the myocardium.

I am an Associate Editor for the Journal of Mathematical Biology and for Mathematical Medicine & Biology, a Fellow of the Institute of Mathematics and its Applications,
and a member of the London and Edinburgh  Mathematical Societies.

contact me for details of current opportunites for PhD projects.   

Google Scholar Publications Profile   ReseacherID Publications List

Bioconvection & swimming micro-organisms

Bioconvection is the spontaneous formation of patterns by active suspensions of swimming micro-organisms such single-celled algae and bacteria. The cells swim in preferred directions due external stimuli such as light (phototaxis) or gravity through being bottom-heavy (gravitaxis). As postdoc at the University of Cambridge and later as a lecturer at the University of Leeds, I developed the first theories of bioconvection due to gyrotaxis and phototaxis, and carried out some of the first quantitative experiments both on pattern wavelengths and on the swimming responses of individual cells. Detailed numerical simulations have shown how the fully-developed nonlinear patterns evolve in time. I made a theoretical advance in the extending the concept of generalised Taylor dispersion to estimate diffision coefficients for gyrotactic cells in flows. I run a small experimental lab at the University of Glasgow and continue to develop mathematical theory for this paradigm for biological complexity, which has grown into a major research area in fluid mechanics.

Recently, Prof Martin Bees (York) and I supervised a PhD student, developing the use of wavelets to analyse bioconvection patterns in our Biofluid Dynamics Laboratory. Current projects with Dr Andrew Baggaley (Newcastle) include gyrotaxis and the suppression of Lagrangian chaos in laminar and turbulent 3D flows, and bioconvection in rotating cylinders with application to biofuels.

Key publications:

Pedley, T.J., Hill, N.A. & Kessler, J.O.  "The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms.'' Journal of Fluid Mechanics, 195, pp. 223-238, 1988.

Hill, N.A., Pedley, T.J. & Kessler, J.O.  "Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth.'' Journal of Fluid Mechanics, 208, pp. 509-543, 1989.

Kessler, J.O., Hill, N.A. & Haeder, D.-P.  "Orientation of swimming flagellates by simultaneously acting external factors.'' Journal of Phycology, 28, 816-822, 1992.

Hill, N.A. & Vincent, R.V.  "A simple model and strategies for orientation in phototactic micro-organisms.'' Journal of Theoretical Biology, 163, pp. 223-235, 1993.

Vincent, R.V. & Hill, N.A. "Bioconvection in a suspension of phototactic algae.'' Journal of Fluid Mechanics, 327, pp. 343-371, 1996.

Hill, N.A. & Haeder, D.-P. A Biased Random Walk Model for the Trajectories of Swimming Micro-Organisms. Journal of Theoretical Biology, 186, 503-526 (1997). 

Bees, M.A. & Hill, N.A. Wavelengths of Bioconvection Patterns. Journal of Experimental Biology, 200, 1515-1526, (1997).

Bees, M.A. & Hill, N.A. Linear Bioconvection in a Suspension of Randomly Swimming, Gyrotactic Micro-Organisms. Physics of Fluids A 10, No. 8, 1864-1881 (1998).

Kessler, J.O., Hill, N.A., Strittmatter, R. & Wiseley, D. Sedimenting Particles and Swimming Micro-Organisms in a Rotating Fluid. Advances in Space Research, 21, 1269-1275 (1998). 

Bees, M.A. & Hill, N.A. Non-Linear Bioconvection in a Deep Suspension of Gyrotactic Swimming Micro-Organisms. Journal of Mathematical Biology 38, No.2, 135-168 (1999).

Ghorai, S. & Hill, N.A. "Development and stability of gyrotactic plumes in bioconvection.'' Journal of Fluid Mechanics, 400, pp. 1-31, 1999.

Ghorai, S. & Hill, N.A. "Periodic arrays of gyrotactic plumes in bioconvection.'' Physics of Fluids, 12, No. 1, pp. 5-22, 2000.

Hill, N.A. & Plumpton, L.A. "Control strategies for the polarotactic orientation of the micro-organism Euglena gracilis.'' Journal of Theoretical Biology, 203, pp. 357-365, 2000.

Ghorai, S. & Hill, N.A. "Wavelengths of gyrotactic plumes in bioconvection.'' Bulletin of Mathematical Biology, 62, pp. 429-450, 2000.

Roberts, A., Hill, N.A. & Hicks, R. "Simple mechanisms organise orientation of escape swimming in embryos and hatchling tadpoles of Xenopus laevis.'' Journal of Experimental Biology, 203, pp. 1869-1885, 2000.

Hill, N.A. & Bees, M.A. "Taylor dispersion of gyrotactic swimming micro-organisms in a linear shear flow.'' Physics of Fluids, 14, pp. 2598-2605, 2002.

Ghorai, S. & Hill, N.A. "Axisymmetric bioconvection in a cylinder.'' Journal of Theoretical Biology, 219, pp. 137-152, 2002. 

Codling, E.A., Hill, N.A., Pitchford, J.W. & Simpson, S.D. "Random walk models for the movement and recruitment of reef fish larvae.'' Marine Ecology Progress Series, 279, pp. 215-224, 2004. 

Codling, E.A. & Hill, N.A. "Sampling rate effects on measurements of correlated and biased random walks.'' Journal of Theoretical Biology, 233, pp. 573-588, 2005. 

Codling, E.A. & Hill, N.A. "Calculating spatial statistics for velocity jump processes with experimentally observed reorientation parameters.'' Journal of Mathematical Biology, 51(5), 527-556, 2005. 

Hill, N.A. & Pedley, T.J. "Bioconvection.'' Fluid Dynamics Research, 37, pp. 1-20, 2005. 

Ghorai, S. & Hill, N.A. "Penetrative phototactic bioconvection.'' Physics of Fluids, 17, 074101, 2005. 

Ghorai, S. & Hill, N.A. "Gyrotactic bioconvection in three dimensions.''  Physics of Fluids, 19, 054107, 2007. 

Ghorai, S., Panda, M.K. & Hill, N.A. "Bioconvection in a suspension of isotropically scattering phototactic algae." Physics of Fluids, 22, 071901, 2010, DOI: 10.1063/1.3457163.


Ghorai, S., Singh, R. & Hill, N.A. "Wavelength selection in gyrotactic bioconvection." Bulletin of Mathematical Biology, 2015, DOI: 10.1007/s11538-015-0081-9.

Heath Richardson, S.I., Baggaley, A.W. & Hill, N.A. "Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows."
Physical Review Fluids 3 (2), 023102, 2018.

Heath Richardson, S.I., Hill, N.A. & Baggaley, A.W.  "Shape-dependent clustering of gyrotactic swimmers in direct numerical simulations of turbulent flows." Under review, 2019.

Arterial disease and soft tissue mechanics


I have pioneered the application of constitutive models of the arterial wall to understand and predict the pathology of abdominal aortic aneurysms, which are a life-threatening condition. The model incorporates the mechanics of the microstructural components including elastin and collagen, and describes how the loss of elastin and its replacement by much stiffer collagen leads to the growth of the aneurysm. The fact that collagen fibres are laid down with a preferred strain was shown to play a fundamental role in the progression of the disease. A recent paper considers tearing of the arterial wall as part of a fundamental study into the biomechanics of arterial dissection. My work with Prof Xiaoyu Luo on the mathematical modelling of soft tissue mechanics has also helped to identify causes of buckling of the iris of the eye during surgery to remove cataracts and has influenced changes in surgical procedure.


Key publications:

Watton, P.N., Hill, N.A. & Heil, M. "A mathematical model for the growth of the abdominal aortic aneurysm.'' Biomechanics and Modeling in Mechanobiology, 3, pp. 98-113, 2004. 

Watton, P.N. & Hill, N.A. "Evolving mechanical properties of a model of abdominal aortic aneurysm.'' Biomechanics and Modeling in Mechanobiology, 8: 25-42, 2009, DOI: 10.1007/s10237-007-0115-9.

Lockington, D., Luo, X.Y., Wang, H.M., Hill, N.A. & Ramaesh, K. "Mathematical and computer simulation modelling of intracameral forces causing pupil block due to air bubble use in Descemet's Stripping Endothelial Keratoplasty: the mechanics of iris buckling." Clinical and Experimental Ophthalmology, 40(2), 182-186, 2012.

Wang, L., Roper, S.M., Luo, X.Y. & Hill, N.A. (2015) Modelling of tear propagation and arrest in fibre-reinforced soft tissue subject to internal pressure. Journal of Engineering Mathematics
, 95(1), pp. 249-265. (doi:10.1007/s10665-014-9757-7).

Qi, N., Gao, H., Ogden, R.W., Hill, N.A., Holzapfel, G.A, Han, H. & Luo, X.Y. (2015) Investigation of the optimal collagen fibre orientation in human iliac arteries. Journal of the Mechanical Behavior of Biomedical Materials,
52, pp. 108-119. (doi:10.1016/j.jmbbm.2015.06.011) (PMID:26195342).

Goodman, M.E., Luo, X.Y. & Hill, N.A. (2016) A mathematical model on the feedback between wall shear stress and intimal hyperplasia. International Journal of Applied Mechanics, 8(7), 1640011. (doi:10.1142/S1758825116400111).

Wang, L., Roper, S. M., Hill, N. A., and Luo, X.
Y. (2017) Propagation of dissection in a residually-stressed cylindrical model of a large artery. Biomechanics and Modeling in Mechanobiology,
16(1), pp. 139-149. (doi:10.1007/s10237-016-0806-1) (PMID:27395061).

Wang, L., Hill, N. A. , Roper, S. M. and Luo, X. (2018) Modelling peeling- and pressure-driven propagation of arterial dissection. Journal of Engineering Mathematics, 109(1), pp. 227-238. (doi:10.1007/s10665-017-9948-0)

Qi, N., Lockington, D., Wang, H., Hill, N. A. , Ramaesh, K. and Luo, X. (2018) Modelling floppy iris syndrome and the impact of phenylephrine on iris buckling. International Journal of Applied Mechanics, 10(5), 1850048. (doi:10.1142/S1758825118500485)

Li, B., Roper, S. M. , Wang, L., Luo, X. and Hill, N.A. (2019) An incremental deformation model of arterial dissection. Journal of Mathematical Biology, 78(5), pp. 1277-1298. (doi:10.1007/s00285-018-1309-8) (PMID:30456652) (PMCID:PMC6453878)

The circulation of blood