School
of Mathematics & Statistics 













Name 
Professor Nick Hill 

Position 

Research interests 
Mathematical
Biology 

Telephone (internal) 
4258 

Telephone ( 
(0141) 330 4258 

Telephone (International) 
+44 141 330 4258 

Telephone (Secretary) 
(0141) 330 2940 

Email 
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
Coinvestigator and Executive Director of the £2.4M SofTMech
Centre, which is an initiative to accelerate the
development softtissue modelling by constructing a
generic mathematical multiscale framework, and of
SofTMech^{MP} a £1.5M
International Centreto 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.
Please contact
me for details of current opportunites for
PhD projects.
Google
Scholar
Publications Profile ReseacherID
Publications List
Bioconvection & swimming microorganisms
Bioconvection is the spontaneous formation of
patterns by active suspensions of swimming microorganisms
such singlecelled algae and bacteria. The cells swim in
preferred directions due external stimuli such as light
(phototaxis) or gravity through being bottomheavy
(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
fullydeveloped 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
microorganisms.'' Journal of Fluid Mechanics,
195, pp. 223238, 1988.
Hill, N.A., Pedley, T.J.
& Kessler, J.O. "Growth of bioconvection
patterns in a suspension of gyrotactic
microorganisms in a layer of finite depth.'' Journal
of Fluid Mechanics, 208, pp. 509543, 1989.
Kessler, J.O., Hill, N.A. & Haeder,
D.P. "Orientation of swimming flagellates by
simultaneously acting external factors.'' Journal of
Phycology, 28, 816822, 1992.
Hill, N.A. & Vincent, R.V. "A
simple model and strategies for orientation in phototactic microorganisms.'' Journal
of Theoretical Biology, 163, pp. 223235, 1993.
Vincent, R.V. & Hill, N.A. "Bioconvection in a suspension of phototactic algae.'' Journal
of Fluid Mechanics, 327, pp. 343371, 1996.
Hill, N.A. & Haeder,
D.P. A Biased Random Walk Model for the Trajectories of
Swimming MicroOrganisms. Journal of Theoretical
Biology, 186, 503526 (1997).
Bees, M.A. & Hill, N.A. Wavelengths of Bioconvection Patterns. Journal
of Experimental Biology, 200, 15151526, (1997).
Bees, M.A. & Hill, N.A. Linear Bioconvection in a Suspension of
Randomly Swimming, Gyrotactic
MicroOrganisms. Physics of Fluids A 10, No. 8,
18641881 (1998).
Kessler, J.O., Hill,
N.A., Strittmatter, R. &
Wiseley, D. Sedimenting Particles and Swimming
MicroOrganisms in a Rotating Fluid. Advances in Space
Research, 21, 12691275 (1998).
Bees, M.A. &
Hill, N.A. NonLinear Bioconvection
in a Deep Suspension of Gyrotactic
Swimming MicroOrganisms. Journal of Mathematical
Biology 38, No.2, 135168 (1999).
Ghorai, S. & Hill, N.A.
"Development and stability of gyrotactic
plumes in bioconvection.'' Journal
of Fluid Mechanics, 400, pp. 131, 1999.
Ghorai, S. & Hill, N.A. "Periodic arrays of gyrotactic plumes in bioconvection.'' Physics of
Fluids, 12, No. 1, pp. 522, 2000.
Hill, N.A. & Plumpton,
L.A. "Control strategies for the polarotactic
orientation of the microorganism Euglena gracilis.'' Journal of
Theoretical Biology, 203, pp. 357365, 2000.
Ghorai, S. & Hill, N.A. "Wavelengths of
gyrotactic plumes in bioconvection.'' Bulletin of
Mathematical Biology, 62, pp. 429450, 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. 18691885, 2000.
Hill, N.A. & Bees, M.A. "Taylor
dispersion of gyrotactic
swimming microorganisms in a linear shear flow.'' Physics
of Fluids, 14, pp. 25982605, 2002.
Ghorai, S. & Hill, N.A.
"Axisymmetric bioconvection
in a cylinder.'' Journal of Theoretical Biology,
219, pp. 137152, 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. 215224, 2004.
Codling, E.A. & Hill, N.A. "Sampling rate effects on
measurements of correlated and biased random walks.'' Journal
of Theoretical Biology, 233, pp. 573588,
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), 527556, 2005.
Hill, N.A. & Pedley, T.J.
"Bioconvection.'' Fluid
Dynamics Research, 37, pp. 120, 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/s1153801500819.
Heath Richardson, S.I., Baggaley, A.W. & Hill, N.A.
"Gyrotactic suppression and emergence of chaotic
trajectories of swimming particles in threedimensional
flows." Physical Review
Fluids 3 (2), 023102, 2018.
Heath Richardson,
S.I., Hill, N.A. & Baggaley,
A.W. "Shapedependent 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 lifethreatening 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. 98113, 2004.
Watton, P.N. & Hill, N.A. "Evolving mechanical
properties of a model of abdominal aortic aneurysm.'' Biomechanics
and Modeling in Mechanobiology,
8: 2542, 2009,
DOI: 10.1007/s1023700701159.
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), 182186,
2012.
Wang, L., Roper, S.M., Luo, X.Y. & Hill, N.A. (2015)
Modelling of tear propagation and arrest in
fibrereinforced soft tissue subject to internal pressure.
Journal of Engineering Mathematics, 95(1), pp. 249265. (doi:10.1007/s1066501497577).
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. 108119. (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 residuallystressed cylindrical model of
a large artery. Biomechanics
and Modeling in Mechanobiology, 16(1), pp. 139149. (doi:10.1007/s1023701608061)
(PMID:27395061).
Wang, L., Hill,
N. A. , Roper,
S. M. and Luo,
X. (2018) Modelling peeling
and pressuredriven propagation of arterial dissection.
Journal
of Engineering Mathematics, 109(1), pp.
227238. (doi:10.1007/s1066501799480)
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. 12771298. (doi:10.1007/s0028501813098) (PMID:30456652) (PMCID:PMC6453878)
The circulation of blood