Fluid Mechanics

Fluid mechanics is the study of how fluids move. Newtonian fluids are described by the Navier–Stokes equations, and there are various formulations for non-Newtonian fluids. Modelling approaches may include direct numerical simulations, asymptotic approaches, and the solution of model problems in simplified domains.

Fluid mechanics modelling can be used to help understand a wide range of problems. Problems brought to Mathematics in Medicine Study Groups which have involved such modelling are listed below.

Problems

Targeting stem cells following i.v. injection using magnetic particle based approaches: (A problem studied at the UK MMSG: Keele 2012); Prof Alicia El Haj (Institute for Science & Technology in Medicine, Keele University); Mr Thomas Kwan (ISTM, Keele University)
Mathematical modelling of airway smooth muscle cell proliferation and apoptosis in asthma: (A problem studied at the UK MMSG: Reading 2011); Dr Charlotte Billington (Division of Therapeutics & Molecular Medicine, University of Nottingham); Professor Ian Hall (Therapeutics and Molecular Medicine, University of Nottingham); Dr Anthony Holmes (NC3Rs)
Definition of a periodicaly distributed 'porosity gradient' in functionally graded materials to be used as bone scaffolds: (A problem studied at the UK MMSG: Strathclyde 2010); Dr Carmen Torres-Sánchez (Mechanical Engineering, Heriot-Watt University)
Comparing placentas from normal and abnormal pregnancies: (A problem studied at the UK MMSG: Strathclyde 2010); Dr Alexander Heazell (Maternal and Fetal Health Research Centre, University of Manchester)
Mathematical modelling of the normal swallow: (A problem studied at the UK MMSG: Strathclyde 2010); Mrs Carol Fairfield (Department of Clinical Language Sciences, University of Reading)
Sodium flux during haemodialysis: (A problem studied at the Canadian MMSG: Toronto 2009); Dr Sushrut Waikar (Renal Division, Brigham and Women's Hospital)
Intramantle pressure gradients favoring hydrocephalus development following disruption of integrin-matrix interactions: (A problem studied at the Canadian MMSG: Toronto 2009); Dr. Miles Johnston (Sunnybrook Health Sciences Centre)
Multiscale modelling of bioreactors for growing bone tissue: (A problem studied at the UK MMSG: Loughborough 2008); Mr Norazharuddin Abdullah (Engineering Science, University of Oxford); Dr Diganta Das (Chemical Engineering, Loughborough University)
Modelling of the growth of engineered orthopaedic tissue in zero force and variable load environments: (A problem studied at the UK MMSG: Loughborough 2008); Dr Nikolay Nikolaev (Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University); Mr Henk Versteeg (Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University); Prof David Williams (Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University)
Solid–fluid interaction in force and energy transmission in shaken baby syndrome: (A problem studied at the UK MMSG: Loughborough 2008); Dr Donal McNally (Institute of Biomechanics, University of Nottingham)
Continuous non-invasive blood-pressure measurements: (A problem studied at the UK MMSG: Southampton 2007); Dr Tony Birch (Neurological Physics Group, Southampton University Hospitals NHS Trust)
Photonic and microfluidic strategies for bioanalysis applications: (A problem studied at the UK MMSG: Southampton 2007); Dr Tracy Melvin (Optoelectronics Research Centre, University of Southampton)
Implants for osteochondral repair using cell printing: (A problem studied at the UK MMSG: Southampton 2007); Dr Jos Malda (University Medical Center, University of Utrecht)
Measuring intra-disc pressures in the spine from MRI images: (A problem studied at the UK MMSG: Southampton 2007); Ms Angela Darekar (University of Southampton); Dr Hamid Rassoulian (Medical Physics Group, Southampton University Hospitals NHS Trust)
Representation of spectrum in the auditory system: (A problem studied at the UK MMSG: Nottingham 2006); Dr Chris Sumner (MRC Institute of Hearing Research, University of Nottingham)
Optimisation of fluid distribution inside a porous construct: (A problem studied at the UK MMSG: Nottingham 2006); Dr Sarah Cartmell (Institute of Science and Technology in Medicine, University of Keele); Mr Vipin Michael (Institute of Science and Technology in Medicine, University of Keele)
The swollen and sunken optic disc: (A problem studied at the UK MMSG: Nottingham 2006); Mr Alexander Foss (Queen's Medical Centre, University of Nottingham)
In vivo delivery of gene therapy to tumours: (A problem studied at the UK MMSG: Oxford 2005); Dr Kerry Fisher (Clinical Pharmacology, University of Oxford); Dr Len Seymour (Clinical Pharmacology, University of Oxford)
Using micro-nanostructures to deliver genes and drugs to skin for immunotherapeutic applications: (A problem studied at the UK MMSG: Oxford 2005); Dr Mark Kendall (The PowderJect Centre for Gene and Drug Delivery Research, University of Oxford)
Modelling the development and formation of biofilms: (A problem studied at the UK MMSG: Oxford 2005); Prof Judith Armitage (Department of Biochemistry, University of Oxford)
Ions in solutions and protein channels: (A problem studied at the UK MMSG: Oxford 2005); Prof Robert Eisenberg (Department of Molecular Biophysics and Physiology, Rush University Medical Center)
Bacterial proteins that knock out cell defences: Cruise missiles or cannonballs?: (A problem studied at the UK MMSG: Oxford 2005); Dr Gail Preston (Department of Plant Sciences, University of Oxford)
How can we model the water transport through the kidney?: (A problem studied at the UK MMSG: Oxford 2005); Dr Susan Franks (Computational Toxicology, Health and Safety Laboratory)
Drug release from polymer coated stents: (A problem studied at the UK MMSG: Strathclyde 2004); Simon Kennedy (Physiology and Pharmacology, University of Strathclyde)
Post-reattachment retinal detachment: (A problem studied at the UK MMSG: Strathclyde 2004); Alistair Fitt (School of Mathematics, University of Southampton)
The impact of substrate on the measurement of DNA complex morphology: (A problem studied at the UK MMSG: Nottingham 2002); Dr Stephanie Allen (School of Pharmaceutical Sciences, University of Nottingham)
Hydrocephalus shunts: Modelling pressure and volume changes in the brain: (A problem studied at the UK MMSG: Nottingham 2002); Dr Roger Bayston (School of Medical and Surgical Sciences, University of Nottingham)
Odontogenic cysts: Comparing the growth of radicular cysts and keratocysts: (A problem studied at the UK MMSG: Nottingham 2002); Dr Gabriel Landini (The School of Dentistry, University of Birmingham)
Atherosclerotic plaque rupture: (A problem studied at the UK MMSG: Nottingham 2002); Prof Alan Moody (Academic Radiology, University of Nottingham)
The effect of ureteric stents on urine flow: Is there a better shape?: (A problem studied at the UK MMSG: Nottingham 2001); Mr Stuart Graham (Institute of Urology and Nephrology, University College London)
Curvature of the spine: Hydrostatic pressure as an indicator of scoliosis: (A problem studied at the UK MMSG: Nottingham 2001); Ms Susan Bibby (Physiology Laboratory, University of Oxford); Dr Jill Urban (Physiology Laboratory, University of Oxford)
Effects of a new anti-tumour drug, fibrinogen E-fragment, in vivo: differential effects on the outer versus the inner areas of tumours: (A problem studied at the UK MMSG: Nottingham 2000); Prof Claire Lewis (Medical School, University of Sheffield)
Blunt traumatic aortic injury: (A problem studied at the UK MMSG: Nottingham 2000); Dr Mike Neale (Transport Research Laboratory, Crowthorne)
Magnetically-targeted drug and gene delivery: (A problem studied at the UK MMSG: Nottingham 2000); Dr Jon Dobson (Department of Biomedical Engineering and Medical Physics, University of Keele)
Mathematical modelling of profiled haemodialysis: (A problem studied at the UK MMSG: Nottingham 2000); Dr Steve Baigent (Centre for Nonlinear Dynamics and Its Applications, University College London); Prof Robert Unwin (Middlesex Hospital)

Meetings

ASM Growth in Asthma Follow-up Meeting 2012: (A meeting in the UK MMSG series.)
Neurons Follow-up Meeting 2010: (A meeting in the UK MMSG series.)