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
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.
Please 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
A
grand challenge in physiological mathematics that
colleagues and I are working on is to develop a full
biomechanical model of the whole circulation including the
arteries, veins and heart to help in the diagnosis and
treatment of cardiovascular disease. An important step
forward has been our 2014 paper, which presents the first
multiscale mathematical and computational model for the
propagation of the pressure pulse throughout the pulmonary
circulation. We are using this to study diseases such as
Pulmonary Hypertension, and are currently working with
Prof Dirk Husmeier (Statistics, Glasgow) on parameter
estimation for personalised models of the pulmonary
circulation in patients.
We have linked the systemic arteries to a full
biomechanical model of the left ventricle of the heart
developed by Prof Xiaoyu Luo (Glasgow). This is
internationally-leading research that only our group at
Glasgow is equipped to undertake.
Key publications:
Olufsen,
M.S., Hill, N.A., Vaughan, G.D.A., Sainsbury, C. and
Johnson, M. (2012) Rarefaction and blood pressure in
systemic and pulmonary arteries. Journal of Fluid
Mechanics, 705,
pp. 280-305. ISSN 0022-1120
(doi:10.1017/jfm.2012.220).
Qureshi,
M. Umar, Vaughan, Gareth D.A., Sainsbury, Christopher,
Johnson, Martin, Peskin, Charles S., Olufsen, Mette S.
& Hill, N.A. (2014) Numerical simulation of blood flow
and pressure drop in the pulmonary arterial and venous
circulation. Biomechanics and Modeling in
Mechanobiology, 13 (5), pp. 1137-1154. ISSN
1617-7959 (doi:10.1007/s10237-014-0563-y).
Qureshi, M. Umar & Hill, N.A. (2015) A
computational study of pressure wave reflections in the
pulmonary arteries. Journal of Mathematical Biology, online
publication (doi:10.1007/s00285-015-0867-2).
Chen,
W. W., Gao,
H., Luo,
X. Y., and Hill,
N. A. (2016) Study of
cardiovascular function using a coupled left ventricle
and systemic circulation model. Journal
of Biomechanics, (doi:10.1016/j.jbiomech.2016.03.009)
(PMID:27040388)
(Early Online Publication)
Noe, U., Chen, W.W., Filippone, M., Hill, N.A. and
Husmeier, D. (2016)
Inference in a
Partial Differential Equations Model of Pulmonary
Arterial and Venous Blood Circulation using Statistical
Emulation. In: 13th International Conference on
Computational Intelligence Methods for Bioinformatics and
Biostatistics, Stirling, UK, 01-03 Sep 2016.
Paun,
L., Haider, M.,
Hill,
N. , Olufsen, M., Qureshi,
M., Papamarkou,
T. and Husmeier,
D. (2017) Parameter
Inference in the Pulmonary Blood Circulation. RSS 2017
Annual Conference, Glasgow, Scotland, 04-07 Sep 2017.
Paun,
L. M., Qureshi, M. U.,
Colebank, M., Haider, M. A., Olufsen,
M. S., Hill,
N. A. and Husmeier,
D. (2017) Parameter
Inference in the Pulmonary Circulation of Mice. In:
32nd International Workshop on Statistical Modelling,
Groningen, Netherlands, 03-07 Jul 2017, pp. 190-195.
Păun, L. M., Qureshi, M. U., Colebank, M., Hill, N. A. , Olufsen, M. S., Haider, M. A. and Husmeier, D. (2018) MCMC methods for inference in a mathematical model of pulmonary circulation. Statistica Neerlandica, 72(3), pp. 306-338. (doi:10.1111/stan.12132)
Umar Qureshi, M., Colebank, M. J., Paun, L. M., Ellwein, L., Chesler, N., Haider, M. A., Hill, N. A. , Husmeier, D. and Olufsen, M. S. (2019) Hemodynamic assessment of pulmonary hypertension in mice: a model based analysis of the disease mechanism. Biomechanics and Modeling in Mechanobiology, 18(1), pp. 219-243. (doi:10.1007/s10237-018-1078-8) (PMID:30284059)
Duanmu, Z., Chen,
W., Gao,
H. , Yang, X., Luo,
X. , Wang, T. and Hill,
N. A. (2019) A one-dimensional
hemodynamic model of the coronary arterial tree. Frontiers
in Physiology, 10, 853. (doi:10.3389/fphys.2019.00853)
Pain and strain in the human gall bladder
With
Professor Xiaoyu Luo, I have demonstrated that gall
bladder pain in the absence of gall stones or other
anomalies is strongly correlated with regions of high
strain in the wall of the gall bladder during emptying,
and that this can be diagnosed using non-invasive
ultrasound scans. This
is important clinically because the NHS carries out many
operations each year to remove gall bladders but these are
successful in ending pain in only 50% of cases.
Key publications:
Li, W.G., Luo, X.Y., Johnson, A.G., Hill, N.A., Bird,
N. & Chin, S.B. "One-dimensional models for the human
biliary system.'' ASME Journal of Biomechanical
Engineering, 129, pp. 164-173,
2007.
Luo, X.Y.,
Li, W., Bird, N., Chin, S.B., Hill, N.A. & Johnson,
A.G. "On the mechanical behaviour of the human biliary
system.'' World J.
of Gastroenterology, 13(9): 1384-1392, 2007.
Li, W.,
Luo, X.Y., Hill, N.A., Smythe,
A., Chin, S.B., Johnson, A.G. & Bird, N. "Correlation
of Mechanical Factors and Gallbladder Pain.'' Computational and
Mathematical Methods in Medicine, Vol. 9, 27-45,
2008.
Li, W.G., Luo X.Y., Chin S. B., Hill N.A.,
Johnson, A.G. & Bird N.C. "Non-Newtonian Bile Flow in
Elastic Cystic Duct: One- and Three-Dimensional
Modelling." Annals
of Biomedical Engineering, 36(11), 1893-1908, 2008, DOI: 10.1007/s10439-008-9563-3.
Li, W.G.,
Luo, X.Y., Hill, N.A., Ogden, R.W., Smythe,
A., Majeed, A. & Bird, N.
"A
mechanical model for CCK induced acalculous
gallbladder pain." Annals
of Biomedical Engineering, 39, 786-800, 2011, DOI
10.1007/s10439-010-0205-1.
Li, W.G., Luo, X.Y., Hill, N.A., Ogden, R.W., Tian, T., Smythe, A., Majeed, A.W. & Bird, N. "Cross-bridge apparent rate constants of human gallbladder smooth muscle." J Muscle Res Cell Motil, 32 (3), 209-220, 2011, DOI 10.1007/s10974-011-9260-y.
Li,
W.G., Luo, X.Y., Hill, N.A., Ogden, R.W., Smythe, A., Majeed, A.W. and Bird, N. (2012)
A quasi-nonlinear analysis of the anisotropic behaviour
of human gallbladder wall. Journal of
Biomechanical Engineering, 134 (10). p. 101009. ISSN
0148-0731 (doi:10.1115/1.4007633).
Li, W.G., Hill,
N.A., Going, J. and Luo, X.Y. (2013) Breaking analysis of
artificial elastic tubes and human artery. International Journal
of Applied Mechanics, 5 (3). p. 1350024. ISSN
1758-8251 (doi:10.1142/S1758825113500245).
Li, W.G., Hill,
N.A., Ogden, R.W., Smythe,
A., Majeed, A.W., Bird, N.
& Luo, X.Y. (2013) Anisotropic behaviour of human
gallbladder walls. Journal
of the Mechanical Behavior of Biomedical Materials,
20,
pp. 363-375. ISSN 1751-6161
(doi:10.1016/j.jmbbm.2013.02.015).