skip to content

Journal publications

[86] Moulton, D.E., Sulzer, V., Apodaca, G., Byrne, H.M. & Waters, S.L. Mathematical modelling of stretch-induced membrane traffic in bladder umbrella cells J Theor. Biol. 409:115-132.

[85] Nessler, K.H., Henstock, J.R., El Haj, A.J., Waters, S.L., Whiteley, J.P. and Osborne, J.M. The influence of hydrostatic pressure on tissue engineered bone development. J Theor. Biol. Submitted.

[84] Kimpton, L.S., Whiteley, J.P., Waters, S.L. and Oliver, J.M. Approaches to myosin modelling in a two-phase flow model for cell motility. Physica D. Submitted.

[83] Lang, G.E., Vella, D., Waters, S.L. and Goriely, A. Mathematical modelling of blood-brain barrier failure and edema Math. Med. Biol. Submitted.

[82] Dalwadi, M., Chapman, S.J., Waters, S.L. and Oliver, J.M. On the boundary layer structure near a highly permeable porous membrane J. Fluid Mech. Submitted.

[81] Woolley, T.E., Gaffney, E.A., Oliver, J.M., Waters, S.L, Baker, R.E. and Goriely, A. Global contraction or local growth, bleb shape depends on more than just cell structure J. Theor. Biol. 2015;380:83-97. doi:10.1016/j.jtbi.2015.04.023.

[80] Goriely, A., Geers, M.G.D., Holzapefel, G.A., Jayamohan, J., Jerusalem, A., Sivaloganathan, S., Squier, W., van Dommelen, J.A.W., Waters, S.L. and Kuhl, E. Mechanics of the brain: perspectives, challenges and opportunites Biomech. Mod. Mecanobiol. 2015. doi:10.1007/s10237-015-0662-4.

[79] Lang, G.E., D Vella, D., Waters, S.L. and Goriely, A. Propagation of damage in brain tissue: coupling mechanics of edema and oxygen delivery Biomech. Mod. Mechanobiol. 2015. doi:10.1007/s10237-015-0665-1.

[78] Pearson, N.C., Waters, S.L., Oliver, J.M. and Shipley, R.J. Multiphase modelling of the effect of fluid shear stress on cell yield and distribution in a hollow fibre membrane bioreactor Biomech. Mod. Mechanobiol. Accepted.

[77] Pearson, N.C., R.J. Shipley, R.J., Waters, S.L. and Oliver, J.M. Dispersion-enhanced solute transport in a cell-seeded hollow fibre membrane bioreactor J. Eng. Math. Submitted.

[76] Lang, G., Stewart, P., Vella, D., Waters, S.L. and Goriely, A. Is the Donnan effect sufficient to explain swelling in brain tissue slices? J. Roy. Soc. Int. 2014;11:20140123.

[75] O'Dea, R.D., Nelson, M.R., El Haj, A.J., Waters, S.L. and Byrne, H.M. A multiscale analysis of nutrient transport and biological tissue growth in vitro Math. Med. Biol. Submitted.

[74] Kimpton, L.S., Whiteley, J.P., Waters, S.L. and Oliver, J.M. The effect of membrane regulated actin polymerisation on a two-phase flow model for cell motility IMA J. App. Maths. Submitted.

[73] Woolley, T.E., Gaffney, E.A, Waters, S.L., Oliver, J.M. and Goriely, A. Three mechanical models for blebbing and multi-blebbing IMA J. App. Maths. Submitted.

[72] Chapman, L.A.C., Shipley, R.J., Whiteley, J.P., Ellis, M.J., Byrne, H.M. and Waters, S.L. Optimising cell aggregate expansion in a perfused hollow fibre bioreactor via mathematical modelling PLoS ONE. Submitted.

[71] Reinwald, Y., Leonard, K.H.L, Henstock, J.R., Whiteley, J.P., Osborne, J.M., Waters, S.L., Levesque, P. and El-Haj, A. J. Evaluation of the growth environment of a hydrostatic force bioreactor for preconditioning of tissue engineered constructs Tissue Eng. Part C 2015;21:(1). doi:10.1089/ten.tec.2013.0476.

[70] Kimpton, L.S., Whiteley, J.P., Waters, S.L. and Oliver, J.M. On a poroviscoelastic model for cell crawling J. Math Biol. 2014. doi:10.1007/s00285-014-0755-1.

[69] Bell, C.G., Byrne, H.M., Whiteley, J.P. and Waters, S.L. Heat or mass transfer at low Peclet number for Brinkman and Darcy flow round a sphere Int. J. Heat Mass Trans. 2014;68:247-258.

[68] Pearson, N., Shipley, R., Waters, S.L., Whiteley, J., Wood, B.D. and Quintard, M. Homogenization via formal asymptotics and volume averaging: how do the two techniques compare? Adv. Water Res. 2013;62:178-206.

[67] O’Keefe, S.G., Moulton, D.E., Waters, S.L. and Goriely. A. Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix Int. J. Nonlin. Mech. 2013;56:94-104.

[66] Pohlmeyer, J., Waters, S.L. and Cummings, L.J. Mathematical model of growth factor driven haptotaxis and proliferation in a tissue engineering scaffold Bull. Math. Biol. 2013;75:(3):393-427.

[65] Pearson, N., Shipley, R.J., Oliver, J.M. and Waters, S.L. Multiphase modelling of the influence of fluid flow and chemical concentration on tissue growth in hollow fibre membrane bioreactors Math. Med. Biol. 2013. doi:10.1093/imammb/dqt015.

[64] Woolley, T.E., Gaffney, E.A., Oliver, J.M., Baker, R.E., Waters, S.L. and Goriely, A. Cellular blebs: pressure-driven, axisymmetric, membrane protrusions Biomech. Mod. Mechanobiol. 2013. doi:10.1007/s10237-013-0509-9.

[63] Bell, C.G., Byrne H.M., Whiteley, J.P. and Waters, S.L. Heat or mass transfer from a sphere in Stokes flow at low Peclet number App. Maths Lett. 2013;26:392-396.

[62] Band, L.R., Oliver, J.M., Waters, S.L. and Riley, D.S. Steady symmetric low-Reynolds-number flow past a film-coated cylinder Eur. J. App. Maths. 2013;24:1-24.

[61] O'Dea, R.D., Osbourne, J.M., El-Haj, A.J., Byrne, H.M. and Waters, S.L. The interplay between tissue growth and scaffold degradation in engineered tissue constructs J. Math. Biol. 2013;67:(5):1199-1225.

[60] O'Dea, R.D., Byrne, H.M. and Waters, S.L. Continuum modelling of in vitro tissue engineering: a review In: L Geris, ed., Computational Modeling in Tissue Engineering 10. Springer Berlin Heidelberg. invited contribution. 2013:229-266.

[59] Kimpton, L.S., Whiteley, J.P, Waters, S.L., King, J.R. and Oliver, J.M. Multiple travelling-wave solutions in a minimal model for cell motility Math. Med. Biol. 2013;30:241-272.

[58] Griffiths, I.M., Bain, C.D., Breward, C.J.W., Chapman, S.J., Howell, P.D. and Waters, S.L. An asymptotic theory for the re-equilibration of a micellar surfactant solution SIAM J. Appl. Math. 2012;72:(1):201-215.

[57] Shakeel, M., Matthews, P.C., Graham, R.S. and Waters, S.L. A continuum model of cell proliferation and nutrient transport in a perfusion bioreactor Math. Med. Biol. 2011;30:21-44.

[56] Shipley, R.J. and Waters, S.L. Fluid and mass transport modelling to drive the design of cell-packed hollow fibre bioreactors for tissue engineering applications Math. Med. Biol. 2011;29:(4):329-359.

[55] Hazel, A.L., Heil, M., Waters, S.L. and Oliver, J.M. On the liquid lining in fluid-conveying curved tubes J. Fluid Mech. 2012;705:213-233.

[54] Griffiths, I.M., Bain, C.D., Breward, C.J.W., Colegate, D.M., Howell, P.D. and Waters, S.L. On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions J. Coll. Int. Sci. 2011;360:662-671.

[53] Whittaker, R.J., Heil, M., Waters, S.L. The energetics of flow through a rapidly oscillating tube with slowly varying amplitude Phil. Trans. Roy. Soc. A. 2011;369:2989-3006.

[52] Shipley, R.J., Davidson, A.J., Chan, K., Chaudhuri, J.B., Waters, S.L., Ellis, M.J. A strategy to determine operating parameters in tissue engineering hollow fiber bioreactors 2011) Biotech. Bioeng.;108:1450-1461.

[51] Waters, S.L., Alastruey, J., Beard, D.A., Bovendeerd, P.H.M., Davies, P.F., Jayaraman, G., Jensen, O.E., Lee, J., Parker, K.H., Popel, A.S., Secomb, T.W., Sherwin, S.J., Shipley, R.J., Smith N.P. and van de Vosse, F.N. Theoretical models for coronary vascular biomechanics: Progress and challenges Prog. Biophys. Mol. Biol. 2011;104:49-76.

[50] Nelson, M.R., Howard, D., Jensen, O.E., King, J.R., Rose, F.R.A.J., Waters, S.L. Growth-induced buckling of an epithelial layer Biomech. Model. Mechanobiol. 2011;10:883-900.

[49] Lemon, G., Howard, D., Yang, H., Ratchev, S.M., Segal, J.I., Rose, F.R.A.J., Jensen, O.E., Waters, S.L. and King, J.R. Growth of the chorioallantoic membrane into a rapid-prototype model pore system: experiments and mathematical model Biomech. Model. Mechanobiol. 2010;10:539-558.

[48] Green, J.E.F., Waters, S.L., Whiteley, J.P., Edelstein-Keshet, L., Shakesheff, K.M and Byrne, H.M. Non-local models for the formation of hepatocyte-stellate cell aggregates J. Theor. Biol. 2010;267:(1):106-120.

[47] Stewart, P.S., Heil, M., Waters, S.L. and Jensen, O.E. Sloshing and slamming oscillations in collapsible channel flow J. Fluid Mech. 2010;662:288-319.

[46] Whittaker, R.J., Heil, M., Jensen, O.E. and Waters, S.L. A rational derivation of a tube law from shell theory Quart. J. Mech. Appl. Maths. 2010;63:(4):465-496.

[45] Whittaker, R.J., Heil, M., Jensen, O.E. and Waters, S.L. Predicting the onset of high-frequency self-excited oscillations in elastic-walled tubes Proc. Roy. Soc. A. 2010;466:(2124):3635-3657.

[44] Shipley, RJ., Waters, S.L. and Ellis, M.J. Quantifying slip and permeability using crossflow to define operating equations for Poly(vinyl alcohol)-Poly(lactide-co-glycolide) microfiltration membrane-scaffold bioreactors Biotech. Bioeng. 2010;107:(2):382-392.

[43] Stewart, P.S., Waters, S.L. and Jensen, O.E. Local instabilities of flow in a flexible channel: asymmetric flutter driven by a weak critical layer Phys. Fluids. 2010;22:(3):031902.

[42] O'Dea, R.D., Osbourne, J.M., Whiteley, J.P., Byrne, H.M. and Waters, S.L. The influence of bioreactor geometry on engineered tissue construct composition ASME J. Biomech. 2010;132:(5):051006.

[41] Whittaker, R.J., Waters, S.L., Jensen, O.E., Boyle, J and Heil, M. J. The energetics of flow through a rapidly oscillating tube. Part I: General theory J. Fluid Mech. 2010;648:83-121.

[40] Whittaker, R.J., Heil, M., Boyle, J., Jensen, O.E. and Waters, S.L. The energetics of flow through a rapidly oscillating tube. Part II: Application to an elliptical tube J. Fluid Mech. 2010;648:123-153.

[39] O'Dea, R.D., Waters, S.L. and Byrne, H. M. A multiphase model for tissue construct growth in a perfusion bioreactor Maths. Med. Biol. 2010;27:95-127.

[38] Pitt-Francis, J., Pathmanathan, P., Bernabeu, M.O., Bordas, R., Cooper, J., Fletcher, A.G., Mirams, G.R., Murray, P., Osbourne, J.M., Walter, A., Chapman, S.J., Garny, A., van Leeuwen, I.M.M., Maini, P.K., Rodriguez, B., Waters, S.L., Whiteley, J.P., Byrne, H.M., Gavaghan, D.J. Chaste: a test-driven approach to software development for biological modelling Comp. Phys. Comms. 2009;180:2452-2471.

[37] Lemon, G., Howard, D., Tomlinson, M.J., Buttery, L.D., Rose, F.R.A.J., Waters, S.L. and King, J.R. Mathematical modelling of tissue-engineering angiogenesis Math. Biosci. 2009;221:101-120.

[36] Cummings, L.J., Sawyer, N.B.E., Morgan, S.P., Rose, F.R.A.J. and Waters, S.L. Tracking large solid constructs suspended in a rotating bioreactor: a combined experimental and theoretical study Biotech. Bioeng. 2009;104:(6):1224-1234.

[35] Stewart, P.S., Waters, S.L. and Jensen, O.E. Local and global instabilities of flow in a flexible-walled channel Eur. J. Mech. B. 2009;28:(4):541-557.

[34] Band, L.R., Riley, D.S., Matthews, P.C., Oliver, J.M. and Waters, S.L. Annular thin-film flows driven by azimuthal variations in interfacial tension Quart. J. Mech. Appl. Math. 2009;62:(4):403-430.

[33] Band, L.R., Cummings, L.J., Waters, S.L. and Wattis, J.A.D. Modelling crystal aggregation and deposition in the catheterised lower urinary tract J. Math Biol. 2009;59:(6):809-840.

[32] Green, J.E.F., Waters, S.L., Shakesheff , K.M. and Byrne, H.M. A mathematical model of liver cell aggregation in vitro Bull. Math. Biol. 2009;71:906-930.

[31] van Leeuwen, I.M.M, Mirams, G.R., Walter, A., Fletcher, A., Murray, P., Osborne, J., Varma, S., Young, S.J., Cooper, J., Pitt-Francis, J., Momtahan, L., Pathmanathan, P., Whiteley, J.P., Chapman, S.J., Gavaghan, D.J., Jensen, O.E., King, J.R., Maini, P.K., Waters, S.L. and Byrne, H.M. An integrative computational model for intestinal tissue renewal Cell Prolif. 2009;42.

[30] Whittaker, R., Booth, R., Dyson, R., Bailey, C., Parsons Chini, L., Naire, S., Payvandi, S., Rong, Z., Woollard, H., Cummings, L. J., Waters, S.L., Mawasse, L., Chaudhuri, J., Ellis, M., Michael, V., Kuiper, N. and Cartmell, S. Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor J. Theor. Biol. 2009;256:533-546.

[29] Siggers, J.H., Waters, S.L., Wattis, J.A.D. and Cummings, L.J. Flow dynamics in a stented ureter Math. Med. Biol. 2009;26:(1):1-24.

[28] O'Dea, R.D., Waters, S.L. and Byrne, H.M. A two-fluid model for tissue growth within a dynamic flow environment Eur. J. Appl. Math. 2008;19:607-634.

[27] Guerreiro-Lucas, L.A, Pop, S.R., Machado, M.J.C. Ma, Y.L., Waters, S.L., Richardson, G., Saetzler, K., Jensen, O.E. and Mitchell, C.A. Experimental and theoretical modelling of blind-ended vessels within a developing angiogenic plexus Microvasc. Res. 2008;76:(3):161-168.

[26] Fenner, J., Brook, B., Clapworthy, G., Coveney, P., Feipel, V., Gregersen, H., Hose, R., Kohl, P., Lawford, P., McCormack, K., Pinney, D., Thomas, R., Van Sint Jan, S., Waters, S., Viceconti, M. The EuroPhysiome, STEP and a roadmap for the Virtual Physiological Human Phil. Trans. A. 2008;366:(1878):2979-2999.

[25] Brook, B.S and Waters, S.L. Mathematical challenges in integrative physiology J. Math. Biol. 2008;56:893-896.

[24] Heil, M. and Waters, S.L. How rapidly oscillating collapsible tubes extract energy from a viscous mean flow J. Fluid Mech. 2008;601:199-227.

[23] Waters, S.L., Heaton, K., Siggers, J.H., Bayston, R., Bishop, M., Cummings, L.J.,Grant, D.M., Oliver, J.M. and Wattis, J.A.D. Ureteric stents: investigating flow and encrustation Proc. IMechE Part H: J. Eng. Med. 2008;222, H4:551-561.

[22] Siggers, J.H. and Waters, S.L. Unsteady flows in pipes with finite curvature J. Fluid Mech. 2008;600:133-165.

[21] Sawyer, N.B.E., Worrall, L.K., Crowe, J.A., Waters, S.L., Shakesheff, K. M., Rose, F.R.A.J and Morgan, S.P. In situ monitoring of 3D in vitro cell aggregation using an optical imaging system Biotech. Bioeng. 2008;100:159-167.

[20] Lemon, G., Waters, S.L., Rose, F.R.A.J. and King, J.R. Mathematical modelling of human mesenchymal stem cell proliferation and differentiation inside three-dimensional artificial porous scaffolds J.Theor. Biol. 2007;249:543-553.

[19] Pop, R., Richardson, G., Waters, S.L. and Jensen, O.E. Shock formation and nonlinear dispersion in a microvascular capillary network Math. Med. Biol. 2007;24:379-400.

[18] Cummings, L.J. and Waters, S.L. Tissue growth in a rotating bioreactor. Part II: Flow and nutrient transport problems Math. Med. Biol. 2007;24:169-208.

[17] Heil, M. and Waters, S.L. Transverse flows in rapidly oscillating, elastic cylindrical shells J. Fluid Mech. 2006;547:185–214.

[16] Preston, S.P., Waters, S.L., Jensen, OE., Heaton, P.R. and Pritchard, D.I. T-cell motility in the early stages of the immune response modelled as a random walk amongst targets Phys. Rev. E 2006;74:011910.

[15] O’Dea, R.D. and Waters, S.L. Flow and solute uptake in a twisting tube J. Fluid Mech. 2006;562:173-182.

[14] Weekley, S.J., Waters, S.L. and Jensen, O.E. Transient elastohydrodynamic drag on a particle moving near a deformable wall Quart. J. Mech. Appl. Math. 2006;59:277-300.

[13] Waters, S.L., Cumings, L.J., Shakesheff, K.M. and Rose, F.R.A.J. Tissue growth in a rotating bioreactor. Part I: Mechanical stability Math. Med. Biol. 2006;23:311-337.

[12] Siggers, J.H. and Waters, S.L. Steady flows in pipes with finite curvature Phys. Fluids 2005;17:077102.

[11] Waters, S.L. and Cummings, L.J. Coriolis effects in a rotating Hele-Shaw cell Phys. Fluids 2005;17:148101.

[10] The effect of ureteric stents on urine flow: Reflux. Cummings, L.J, Waters, S.L., Wattis, J.A.D. and Graham, S.J J. Math. Biol. 2004;49:56-82.

[9] Waters, S.L. A mathematical model for the laser treatment of heart disease J. Biomech. 2004;37:281-288.

[8] Wei, H.H., Waters, S.L., Lui, S.Q. and Grotberg, J.B. Flow in a wavy-walled channel lined with a poroelastic layer J. Fluid Mech. 2003;492:23-45.

[7] Waters, S.L. and Guiot, C. Flow in an elastic tube subject to prescribed forcing: a model of umbilical venous flow J. Theor. Med. 2002;3:287-298.

[6] Waters, S.L. and Grotberg, J.B. The influence of soluble surfactant on the propagation of a liquid plug along a rigid tube Phys. Fluids. 2002;14:(2):471-480.

[5] van Meerveld, J. and Waters, S.L. Numerical computation of the steady secondary flow in a tube with time--dependent curvature Q. J. Mech. Appl. Maths. 2001;54:631-640.

[4] SL Waters. Solute uptake through the walls of a pulsating channel J. Fluid Mech. 2001;433:193-208.

[3] PD Howell, SL Waters and JB Grotberg. The propagation of a liquid bolus along a liquid-lined flexible tube J. Fluid Mech. 2000;406:309-335.

[2] SL Waters and TJ Pedley. Oscillatory flow in a tube of time-dependent curvature: Part I. Perturbation to flow in a stationary curved tube J. Fluid Mech. 1999;383:327-352.

[1] Lynch, D.G., Waters, S.L. and Pedley, T.J. Flow in a tube with non-uniform, time-dependent curvature: governing equations and simple examples J. Fluid Mech. 1996;323:237-265.


Book chapters

[1] Siggers, J.H., Cummings, L.J., Waters, S.L. and Wattis, J.A.D. The effect of ureteric stents on urine flow. Biofilms: persistence and ubiquity. Contributions made at the Seventh Meeting of the Biofilm Club held at Greynog Hall, Powys, 7th-9th September 2005.