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 Liuyang Feng : Research Associate

    Supervisor: Xiaoyu Luo

  • Dr Hao Gao : Postdoctoral Research Fellow

    Heart Modelling; biomechancis; MRI; fluid-structure interactions

    Research staff: Debao Guan
    Research students: Yingjie Wang, Yalei Yang, Antesar Mohammed Al Dawoud
    Supervisor: Xiaoyu Luo

  • Publications
  • Dr Debao Guan : Research Associate

    Supervisors: Xiaoyu Luo, Hao Gao

  • 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 staff: Jay MacKenzie, Laura Miller, Scott Richardson
    Research students: Andrew Brown, Sathish Kumar, Roxanna Barry
    Postgraduate opportunities: A coupled cardiovascular-respiration model for mechanical ventilation

  • 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: Liuyang Feng, Hao Gao, Debao Guan, Wenguang Li, Qingying Shu, Xin Zhuan, Jay MacKenzie
    Research students: Ahmed Mostafa Abdelhady Ismaeel, Yingjie Wang

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

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

  • Mx Jay MacKenzie : Research Associate

    Supervisors: Nicholas A Hill, Xiaoyu Luo

  • Dr Laura Miller : EPSRC Postdoctoral Fellow

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

  • Dr Peter Mortensen : Research Associate

    Supervisor: Radostin Simitev

  • 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
    Research student: Parna Mandal

  • Dr Ionut Paun : Research Associate

    Supervisors: Colin Torney, Dirk Husmeier

    Dr Raimondo Penta : Lecturer

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

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

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

  • Dr Scott Richardson : Research Associate

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisors: Andrew Baggaley, Nicholas A Hill

  • Prof Radostin Simitev : Professor of Applied Mathematics

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

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research staff: Peter Mortensen
    Research students: Muhamad Bin Noor Aziz, Parag Gupta, Antesar Mohammed Al Dawoud, Tahani Al Sariri, Jamie Quinn
    Postgraduate opportunities: Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD), Fast-slow asymptotic analysis of cardiac excitation models, Numerical simulations of planetary and stellar dynamos, Efficient asymptotic-numerical methods for cardiac electrophysiology, Stellar atmospheres and their magnetic helicity fluxes, 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: Mathematical models of vasculogenesis, A coupled cardiovascular-respiration model for mechanical ventilation , 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 students: Stephen Jun Villejo, Chenglei Hu

  • Personal Website
  • Dr Xin Zhuan : Research Associate

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisor: Xiaoyu Luo


  • Postgraduates

    Mathematical Biology - Example Research Projects

    Efficient asymptotic-numerical methods for cardiac electrophysiology (PhD)

    Supervisors: Radostin Simitev
    Relevant research groups: Mathematical BiologyContinuum Mechanics

    The mechanical activity of the heart is controlled by electrical impulses propagating regularly within the cardiac tissue during one's entire lifespan. A large number of very detailed ionic current models of cardiac electrical excitability are available.These realistic models are rather difficult for numerical simulations. This is due not only to their functional complexity but primarily to the significant stiffness of the equations.The goal of the proposed project is to develop fast and efficient numerical methods for solution of the equations of cardiac electrical excitation with the help and in the light of newly-developed methods for asymptotic analysis of the structure of cardiac equations (Simitev & Biktashev (2006) Biophys J; Biktashev et al. (2008), Bull Math Biol; Simitev & Biktashev (2011) Bull Math Biol)

    The student will gain considerable experience with the theory of ordinary and partial differential equations, dynamical systems and bifurcation theory, asymptotic and perturbation methods,numerical methods. The applicant will also gain experience in computerprogramming, scientific computing and some statistical methods for comparison with experimental data.

    Electrophysiological modelling of hearts with diseases (PhD)

    Supervisors: Radostin Simitev
    Relevant research groups: Mathematical BiologyContinuum Mechanics

    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.

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

    Supervisors: Radostin Simitev
    Relevant research groups: Mathematical BiologyContinuum Mechanics

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

    Mathematical models of vasculogenesis (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Mathematical BiologyContinuum Mechanics

    Vasculogenesis is the process of forming new blood vessels from endothelial cells, which occurs during embryonic development. Viable blood vessels facilitate tissue perfusion, allowing the tissue to grow beyond the diffusion-limited size. However, in the absence of vasculogenesis, efforts to engineer functional tissues (eg for implantation) are restricted to this diffusion-limited size. This project will investigate mathematical models for vasculogenesis and explore mechanisms to stimulate blood vessel formation for in vitro tissues. The project will involve collaboration with Department of Biological Engineering at MIT, as part of the SofTMechMP project.

    A coupled cardiovascular-respiration model for mechanical ventilation (PhD)

    Supervisors: Peter Stewart, Nicholas A Hill
    Relevant research groups: Mathematical BiologyContinuum Mechanics

    Mechanical ventilation is a clinical treatment used to draw air into the lungs to facilitate breathing, used in treatment of premature babies with respiratory distress syndrome and in the treatment of severe Covid pneumonia. The aim is to oxygenate the blood while simultaneously removing unwanted by-products. However, over-inflation of the lungs can reduce the blood supply to the gas exchange surfaces, leading to a ventilation-perfusion mis-match. This PhD project will give you the opportunity to develop a mathematical model to describe the coupling between blood flow in the pulmonary circulation and air flow in the lungs (during both inspiration and expiration). You will devise a coupled computational framework, capable of testing patient-specific ventilation protocols. This is an ideal project for a postgraduate student with an interest in applying mathematical modelling and image analysis 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 using innovative mathematical and statistical modelling.