Mathematical Biology

Mathematical Biology is the application of mathematical modelling to solve problems in biology and physiology. It is one of the fastest growing research areas in mathematics and is contributing significantly to our understanding of the biological world. It also produces new mathematical questions.

The Mathematical Biology Group is a member of the Centre for Mathematics Applied to the Life Sciences, established to promote interdisciplinary research and scholarship in Mathematical Biology. It is a joint centre of the Universities of Glasgow and Strathclyde, under the Synergy agreement. Our research interests are summarised here, but the list is not exhaustive and new projects are being started all the time. For more information and contact details, click on the links below.

Staff

Dr Christina A Cobbold : Reader

Population dynamics of ecological systems; spatial ecology; evolutionary ecology in changing environments

Member of other research groups: Statistics and Data Analytics
Research students: Renato Andrade, Parag Gupta

  • Personal Website
  • Publications
  • Dr Jamie Gabe : Honorary Research Fellow/RA

    Member of other research groups: Geometry and Topology, Algebra

  • Publications
  • Dr Hao Gao : Postdoctoral Research Fellow

    Heart Modelling; biomechancis; MRI; fluid-structure interactions

    Research students: Yingjie Wang, Yalei Yang, Debao Guan, Antesar Mohammed Al Dawoud
    Supervisor: Xiaoyu Luo
    Postgraduate opportunities: Electrophysiological modelling of hearts with diseases

  • Publications
  • Prof Nicholas A Hill : Simson Chair

    Random walk models for movement of micro-organisms and animals; spatial point processes in plant ecology

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Jay MacKenzie, Roxanna Barry, Laura Miller
    Postgraduate opportunities: Optimisation of stent devices to treat dissected aorta, Arterial dissection , Mathematical modelling of the heart and the circulation

  • Personal Website
  • Publications
  • Prof Xiaoyu Luo : Professor of Applied Mathematics

    Biomechanics; fluid-structure interactions; mathematical biology ; solid mechanics

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research staff: Hao Gao, Wenguang Li, Qingying Shu
    Research students: Debao Guan, Xin Zhuan, Ahmed Mostafa Abdelhady Ismaeel, Jay MacKenzie, Yingjie Wang
    Postgraduate opportunities: Mathematical modelling of the heart and the circulation , Arterial dissection

  • Personal Website
  • Publications
  • Dr Benn Macdonald : Research Assistant

    Member of other research groups: Statistics and Data Analytics
    Research student: Hanadi Alzahrani
    Supervisor: Dirk Husmeier

  • Prof Nigel Mottram : Professor of Applied Mathematics

    Modelling of medical devices and blood flow; groundwater flow and the interaction of water resources and plant biomass.

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Postgraduate opportunities: Mathematical Modelling of Liquid Crystal DIsplays, Flow of groundwater in soils with vegetation and variable surface influx, Mathematical Modelling of Active Fluids

  • Dr Raimondo Penta : Lecturer

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Tahani Al Sariri, Laura Miller

  • Personal Website
  • Publications
  • Dr Ariel Ramirez Torres : Lecturer

    My scientific interests range several fields, including multi-scale expansions, non-linear mechanics, composite materials and non-local phenomena, and my research addresses problems of current interest in Homogenisation Theory, Continuum Mechanics, Mathematical Biology and Fractional Calculus. In particular, the focus of my investigations is on the mathematical modelling of biological media and processes that are of importance in real-world problems.

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

  • Dr Radostin Simitev : Reader

    Reaction-diffusion equations; Excitable systems; Mathematical models of cardiac electrical excitation

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Muhamad Bin Noor Aziz, Antesar Mohammed Al Dawoud, Peter Mortensen, Tahani Al Sariri, Jamie Quinn
    Postgraduate opportunities: Electrophysiological modelling of hearts with diseases, Fast-slow asymptotic analysis of cardiac excitation models, Numerical simulations of planetary and stellar dynamos

  • Personal Website
  • Publications
  • Dr Peter Stewart : Senior lecturer

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Roxanna Barry, Ahmed Mostafa Abdelhady Ismaeel, Ifeanyi Onah Sunday
    Postgraduate opportunities: Continuous production of solid metal foams

  • Personal Website
  • Publications
  • Dr Ben Swallow : Lecturer

    Bayesian statistical inference; Markov chain Monte Carlo (MCMC) methods; data integration; model selection; stochastic processes

    Member of other research groups: Statistics and Data Analytics

  • Personal Website
  • Dr Runlian Xia : Lecturer

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics


  • Postgraduates

    Tahani Al Sariri : PhD Student

    Supervisors: Raimondo Penta, Radostin Simitev

  • Roxanna Barry : PhD Student

    Supervisors: Peter Stewart, Nicholas A Hill

  • Muhamad Bin Noor Aziz : PhD Student

    Research Topic: Efficient asymptotic-numerical methods for cardiac electrophysiology
    Supervisor: Radostin Simitev

  • Debao Guan : PhD Student

    Supervisors: Xiaoyu Luo, Hao Gao

  • Parag Gupta : PhD Student

    Research Topic: Mathematical modelling of infection dynamics of Animal African trypanosomiasis, an economically important livestock disease.
    Supervisor: Christina A Cobbold

  • Ahmed Mostafa Abdelhady Ismaeel : PhD Student

    Supervisors: Peter Stewart, Xiaoyu Luo

  • Mikolaj Kundegorski : PhD Student

    Supervisor: Colin Torney

  • Mx Jay MacKenzie : PhD Student

    Supervisors: Nicholas A Hill, Xiaoyu Luo

  • Laura Miller : PhD Student

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisors: Raimondo Penta, Nicholas A Hill

  • Antesar Mohammed Al Dawoud : PhD Student

    Research Topic: Mathematical modelling of electrophysiology in hearts with healed myocardial infarction scar
    Supervisors: Radostin Simitev, Hao Gao

  • Peter Mortensen : PhD Student

    Supervisor: Radostin Simitev

  • Ionut Paun : PhD Student

    Supervisors: Colin Torney, Dirk Husmeier

  • Xin Zhuan : PhD Student

    Research Topic: Heart tissue remodelling under stress
    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisor: Xiaoyu Luo


  • Postgraduate opportunities

    Fast-slow asymptotic analysis of cardiac excitation models (PhD)

    Supervisors: Radostin Simitev
    Relevant research groups: Mathematical Biology

    Mathematical models of cardiac electrical excitation describe processess ocurring on a wide range of time and length scales. 

     

     

    Electrophysiological modelling of hearts with diseases (PhD)

    Supervisors: Radostin Simitev, Hao Gao
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology

    SofTMechMP is a new International Centre to Centre Collaboration between the SofTMech Centre for Multiscale Soft Tissue Mechanics (www.softmech.org) and  two world-leading research centres, Massachusetts Institute of Technology (MIT) in the USA and Politecnico di Milano (POLIMI) in Italy, funded by the EPSRC. Its exciting programme of research will address important new mathematical challenges driven by clinical needs, such as tissue damage and healing, by developing multiscale soft tissue models that are reproducible and testable against experiments.

    Heart disease has a strong negative impact on society. In the United Kingdom alone, there are about 1.5 million people living with the burden of a heart attack. In developing countries, too, heart disease is becoming an increasing problem. Unfortunately, the exact mechanisms by which heart failure occurs are poorly understood. On a more optimistic note, a revolution is underway in healthcare and medicine - numerical simulations are increasingly being used to help diagnose and treat heart disease and devise patient-specific therapies. This approach depends on three key enablers acting in accord. First, mathematical models describing the biophysical changes of biological tissue in disease must be formulated for any predictive computation to be possible at all. Second, statistical techniques for uncertainty quantification and parameter inference must be developed to link these models to patient-specific clinical measurements. Third, efficient numerical algorithms and codes need to be designed to ensure that the models can be simulated in real time so they can be used in the clinic for prediction and prevention.

    The goals of this project include designing more efficient algorithms for numerical simulation of the electrical behaviour of hearts with diseases on cell, tissue and on whole-organ levels. The most accurate tools we have, at present, are so called monolithic models where the differential equations describing constituent processes are assembled in a single large system and simultaneously solved, While accurate, the monolithic approaches are  expensive as a huge disparity in spatial and temporal scales between relatively slow mechanical and much faster electrical processes exists and must be resolved. However, not all electrical behaviour is fast so the project will exploit advances in cardiac asymptotics to develop a reduced kinematic description of propagating electrical signals. These reduced models will be fully coupled to the original partial-differential equations for spatio-temporal evolution of the slow nonlinear dynamic fields. This will allow significantly larger spatial and time steps to be used in monolithic numerical schemes and pave the way for clinical applications, particularly coronary perfusion post infarction. The models thus developed will be applied to specific problems of interest, including

    (1) coupling among myocyte-fibroblast-collagen scar;

    (2) shape analysis of scar tissue and their effects on electric signal propagation;

    (3) personalized 3D heart models using human data.

     The project will require and will develop knowledge of mathematical modelling, asymptotic and numerical methods for PDEs and software development and some basic knowledge of physiology.  Upon completion you will be a mature researcher with broad interdisciplinary education. You will not only be prepared for an independent scientific career, but will be much sought after by both academia and industry for the rare combination of mathematical and numerical skills. 

     

    Arterial dissection (PhD)

    Supervisors: Nicholas A Hill, Steven Roper, Xiaoyu Luo
    Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

    Location:

    School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

    Civil and Environmental Engineering, Politecnico di Milano.Supervisors:

    Prof Nicholas HIll   (lead, UofG, Mathematics),

    Dr Steven Roper   (UofG, Mathematics),

    Prof Xiaoyu Luo   (UofG, Mathematics),

    Prof Anna Pandolfi   (Structural Mechanics, Politecnico di Milano)

     

     

    Scholarship details:

     

    Eligibility: A three-and-a-half year, fully-funded PhD scholarship open to UK/EU applicants

     

     

    Project Description:

     

     

    SofTMechMP is a new International Centre to Centre Collaboration between the SofTMech Centre for Multiscale Soft Tissue Mechanics (www.softmech.org) and  two world-leading research centres, Massachusetts Institute of Technology (MIT) in the USA and Politecnico di Milano (POLIMI) in Italy, funded by the EPSRC. Its exciting programme of research will address important new mathematical challenges driven by clinical needs, such as tissue damage and healing, by developing multiscale soft tissue models that are reproducible and testable against experiments.

    This PhD project will focus on the application of our new theories of tissue damage to arterial dissection, using mathematical and computational modelling. Arterial dissection is a tear along the length of an artery that fills with high pressure blood and often re-enters the lumen. In the case of the aorta, this is life-threatening, as the dissection often propagates upstream and compromises the aortic valve. The objectives of the project are to predict the propagation and arrest of the dissection in patient-specific geometries, and to help to assess the benefits and risks of treatments including the placement of stents.

     

    The student will develop expertise in multiscale hyperelastic continuum models, and in the numerical methods to solve the governing equations in physiological geometries. The student will have the opportunity to visit and work with our collaborators at MIT and POLIMI, and with our clinical and industrial partners, and will be part of a large dynamic group of researchers at the University of Glasgow.

     

    Upon completion you will be a mature researcher with broad interdisciplinary education. You will not only be prepared for an independent scientific career, but will be much sought after by both academia and industry for the rare combination of mathematical and numerical skills. 

     

    Application will be through the University of Glasgow Postgraduate Admissions:

     

     

    https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

    For further information please contact:

    Professor Nicholas A Hill FIMA

    Executive Director - SofTMech

    Senate Assessor on Court

    School of Mathematics & Statistics

    Tel: 0141 330 4258

    Nicholas.Hill@glasgow.ac.uk

     

     

    Optimisation of stent devices to treat dissected aorta (PhD)

    Supervisors: Nicholas A Hill
    Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

    Location:

     

    School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

     

    Chemistry, Materials and Chemical Engineering, Politecnico di Milano,

     

    Terumo Aortic, Newmains Ave, Inchinnan, Glasgow

     

    Supervisors:

    Prof Nicholas Hill (lead, UofG, Mathematics),

    Dr Robbie Brodie (Terumo Aortic),

    Dr Sean McGinty (UofG, Biomedical Engineering),

    Prof Francesco Migliavacca,   (Industrial Bioengineering, Politecnico di Milano)

     

     

    Scholarship details:

    Eligibility: A three-and-a-half year, fully-funded PhD scholarship open to UK/EU applicants

    Project Description: 

    SofTMechMP is a new International Centre to Centre Collaboration between the SofTMech Centre for Multiscale Soft Tissue Mechanics (www.softmech.org) and  two world-leading research centres, Massachusetts Institute of Technology (MIT) in the USA and Politecnico di Milano (POLIMI) in Italy, funded by the EPSRC. Its exciting programme of research will address important new mathematical challenges driven by clinical needs, such as tissue damage and healing, by developing multiscale soft tissue models that are reproducible and testable against experiments.

    This PhD project will focus on the application of our new theories of tissue damage and growth and remodelling to the design of stents by Terumo Aortic to treat aortic dissection, using mathematical and computational modelling. An aortic dissection is a tear along the length of vessel that fills with high pressure blood and often re-enters the lumen. This is life-threatening, as the dissection often propagates upstream and compromises the aortic valve. The objectives of the project are to help to develop and optimise the next generation of stents by predicting their performance in patient-specific geometries, and to minimise the medium- to long-term risks due to remodelling of the arterial wall.

    The student will develop expertise in multiscale hyperelastic continuum models, and in advanced numerical methods to solve the governing equations in physiological geometries. The student will have the opportunity to visit and work with our collaborators at MIT and POLIMI, and with our clinical partners, and will be part of a large dynamic group of researchers at the University of Glasgow and Terumo Aortic, a world-leading company in the design and manufacture of medical devices.

    Upon completion you will be a mature researcher with broad interdisciplinary education. You will not only be prepared for an independent scientific career, but will be much sought after by both academia and industry for the rare combination of mathematical and numerical skills. 

     

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    Application will be through the University of Glasgow Postgraduate Admissions:

     

    https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

     

    For further information please contact:

     

    Professor Nicholas A Hill FIMA

    Executive Director - SofTMech

    Senate Assessor on Court

    School of Mathematics & Statistics

    Tel: 0141 330 4258

    Nicholas.Hill@glasgow.ac.uk

     

     

    Mathematical modelling of the heart and the circulation (PhD)

    Supervisors: Nicholas A Hill, Xiaoyu Luo
    Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

     

    Location:

     

    School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

     

    Supervisors:  Xiaoyu Luo and Nick Hill

     

    Cardiovascular disease is the leading cause of disability and death in the UK and worldwide. The British Heart Foundation (BHF) estimates it has a £19B annual economic impact.Structural impairment such as mitral regurgitation and myocardial infarction are heart diseases that, even when treated in time, can lead to diastolic heart failure with preserved ejection fraction, for which there is no recommended treatment options.   Mathematical modelling of the heart can advance our understanding of heart function, and promises to support diagnosis and develop new treatments.

    This PhD project will focus on developing mathematical descriptions of the whole heart and its interactions with the circulation, using a combination of one-dimensional and lumped parameter models.  State-of-the-art structured-tree models will be used for systemic, pulmonary and coronary circulations.  The objectives of the project are to identify how the heart functions under different pathological diseases and what treatment options may be effective.  The student will develop expertise in fluid and solid mechanics modelling, as well as insights into mathematically-guided clinical translation.   The project will be performed in the research environment of SofTMech (www.softmech.org) where extensive collaborations with clinicians and international research groups are forged.  The student will have the opportunity to visit and work with our collaborators, including our clinical and industrial partners, and will be part of a large dynamic group of researchers at the University of Glasgow. 

    Upon completion you will be a mature researcher with broad interdisciplinary education. You will not only be prepared for an independent scientific career, but will be much sought after by both academia and industry for the rare combination of mathematical and numerical skills.   

     

    Application will be through the University of Glasgow Postgraduate Admissions: 

     

    https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

     

     

     

    For further information please contact:

     

     

     

    Professor Nicholas A Hill FIMA

     

    Executive Director - SofTMech

     

    Senate Assessor on Court

     

    School of Mathematics & Statistics

     

    Tel: 0141 330 4258

     

    Nicholas.Hill@glasgow.ac.uk

     

     

     

     

     

    Mathematical Modelling of Active Fluids (PhD)

    Supervisors: Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Mathematical Biology

    The area of active fluids is currently a “hot topic” in biological, physical and mathematical research circles. Such fluids contain active organisms which can be influenced by the flow of fluid around them but, crucially, also influence the flow themselves, i.e. by swimming. When the organisms are anisotropic (as is often the case) a model of such a system must include these inherent symmetries. Models of bacteria and even larger organisms such as fish have started to be developed over the last ten years in order to examine the order, self-organisation and pattern formation within these systems, although direct correlation and comparison to real-world situations has been limited.

    This project will use the theories and modelling techniques of liquid crystal systems and apply such modelling techniques to the area of anisotropy and self-organisation derived from active agents. The research will involve a continuum description of the fluid, using equations similar to the classical Navier-Stokes equations, as well as both the analytical and numerical solution of ordinary and partial differential equations.

    Contact nigel.mottram@glasgow.ac.uk for more details

     

     

    Flow of groundwater in soils with vegetation and variable surface influx (PhD)

    Supervisors: Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Mathematical Biology

    Groundwater is the water underneath the surface of the earth, which fills the small spaces in the soil and rock, and is extremely important as a water supply in many areas of the world. In the UK, groundwater sources, or aquifers, make up over 30% of the water used, and a single borehole can provide up to 10 million litres of water every day (enough for 70,000 people).

    The flow of water into and out of these aquifers is clearly an important issue, more so since current extraction rates are using up this groundwater at a faster rate than it is being replenished. In any specific location the fluxes of water occur from precipitation infiltrating from the surface, evaporation from the surface, influx from surrounding areas under the surface, the flow of surface water (e.g. rivers) into the area, and the transpiration of water from underground directly into the atmosphere by the action of rooted plants.

    This complicated system can be modelled using various models and combined into a single system of differential equations. This project will consider single site depth-only models where, even for systems which include complicated rooting profiles, analytical solutions are possible, but also two- and three-dimensional models in which the relatively shallow depth compared to the plan area of the aquifer can be utilised to make certain "thin-film" approximations to the governing equations.

    Contact nigel.mottram@glasgow.ac.uk for more details