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 student: Renato Andrade

  • Personal Website
  • 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, Assessing risk of heart failure with cardiac modelling and statistical inference

  • 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

  • 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: Assessing risk of heart failure with cardiac modelling and statistical inference

  • 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

    My research interests are in the mathematical modelling of real-world systems, generally focussing on those that include the dynamics of non-Newtonian fluids. I am particularly interested in anisotropic fluids such as liquid crystals, where viscoelasticity is an important consideration, as is their behaviour under electric fields.

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Postgraduate opportunities: Flow of glacial ice sheets over deformable material, Viscous fingering instabilities: control and flow-structure interaction, 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, Parag Gupta, 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, Gordon McNicol, Ifeanyi Onah Sunday
    Postgraduate opportunities: Predicting patterns of retinal haemorrhage, Theoretical modelling of cell response to external cues, Radial foam fracture, 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
    Research student: Stephen Jun Villejo

  • Personal Website

  • 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

    Supervisor: Radostin Simitev

  • Debao Guan : PhD Student

    Supervisors: Xiaoyu Luo, Hao Gao

  • 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

    Predicting patterns of retinal haemorrhage (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology, Statistics and Data Analytics, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

    Retinal haemorrhage (bleeding of the blood vessels in the retina) often accompanies traumatic brain injury and is one of the clinical indicators of `shaken baby syndrome'. This PhD project will give you the opportunity to develop a combination of mathematical and statistical models to help explain the onset of retinal haemorrhage. You will devise and implement image processing algorithms to quantify the pattern of bleeding in clinical images of haemorrhaged retinas. In addition, you will develop a mathematical model for pressure wave propagation through the retinal circulation in response to an acute rise in intracranial pressure, to predict the pattern of retinal bleeding and correlate to the images. Cutting-edge pattern recognition methods from Machine Learning and Bayesian modelling will be used to infer characteristic signatures of different types of brain trauma. These will be used to help clinicians in characterising the origin of traumatic brain injury and diagnosing its severity. This is an ideal project for a postgraduate student with an interest in applying mathematical modelling, image analysis and machine learning to predictive healthcare. The project will give you the opportunity to join a cross-disciplinary Research Hub that aims to push the boundaries of quantitative medicine and improve clinical decision making in cases of suspected non-accidental head injury using innovative mathematical and statistical modelling.

     

    Assessing risk of heart failure with cardiac modelling and statistical inference (PhD)

    Supervisors: Dirk Husmeier, Hao Gao, Xiaoyu Luo
    Relevant research groups: Mathematical Biology, Statistics and Data Analytics

    In recent years, we have witnessed impressive developments in the mathematical modelling of complex physiological systems. However, parameter estimation and uncertainty quantification still remain challenging. This PhD project will give you the opportunity to join an interdisciplinary research team to develop new methodologies for computational modelling and inference in cardio-mechanic models. Your ultimate objective will be to contribute to paving the path to a new generation of clinical decision support systems for cardiac disease risk assessment based on complex mathematical-physiological models. You will aim to  achieve patient-specific calibration of these models in real time, using magnetic resonance imaging data. Sound uncertainty quantification for informed risk assessment will be paramount. This is an ideal PhD project for a postgraduate student with a strong applied mathematics and statistics or Computer Science background who is interested in computational mechanics and adapting cutting-edge inference and pattern recognition methods from Machine Learning and Bayesian modelling to challenging cardio-mechanic modelling problems. The project will give you the opportunity to join a cross-disciplinary Research Hub that aims to push the boundaries of quantitative medicine and improve cardio-vascular healthcare by bringing cutting-edge mathematical and statistical modelling into the clinic.

     

    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. 

     

     

    Theoretical modelling of cell response to external cues (PhD)

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

    Cells and tissues respond to mechanotransductive and biochemical cues. These external cues interact with protein signaling pathways within the cell and can trigger changes in size, structure, binding and differentiation. This project will use theoretical modelling to examine the response of an array of cells to various external mechanical and biochemical cues, considering how these cues can be tailored to optimize a particular outcome. The model will couple the mechanical components of the cell (nucleus, cytoskeleton,…) to internal protein expression pathways (Myosin II, MLCK,…) and the properties of the external stimuli. The model will take the form of coupled differential equations which will be solved using both analytical and numerical methods.

    This model will be validated against experimental data in two main ways, including examining the response of the array to small amplitude mechanical vibration (‘nanokicking’) to predict its influence on the behavior of the array over long timescales. The model will also be used to understand growth factor delivery using PODS® technology developed by Cell Guidance Systems to predict the optimal spatial arrangement of PODS® relative to the array and the resulting temporal and spatial profiles of both the growth factor and the cell growth and proliferation.

    This project is part of the LifETIME Centre for Doctoral Training

    https://lifetime-cdt.org/projects-2/

    and involves collaboration with Prof Matt Dalby (Institute of Molecular, Cell and Systems Biology) and industrial partner Cell Guidance Systems. Applicants must apply to the CDT (details on the website) to be considered for this project.

     

    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

     

     

    Electrophysiological modelling of hearts with diseases (PhD)

    Supervisors: Radostin Simitev, Hao Gao
    Relevant research groups: Mathematical Biology

    How to Apply: Please refer to the following website for details on how to apply: http://www.gla.ac.uk/research/opportunities/howtoapplyforaresearchdegree/. 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. 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.