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

Sodium flux during hemodialysis: (A problem studied at the Canadian MMSG: Toronto 2009); Dr Sushrut Waikar (Renal Division, Brigham and Women's Hospital)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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 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)
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)
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)
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)
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)