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.
Information about
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
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
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
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
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
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
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
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
Dr Xin Zhuan : Research Associate
Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
Supervisor: Xiaoyu Luo
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
Andrew Brown : PhD Student
Research Topic: Multiscale Modelling of Tissue Tearing
Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
Supervisors: Nicholas A Hill, Raimondo Penta, Steven Roper
Ahmed Mostafa Abdelhady Ismaeel : PhD Student
Supervisors: Peter Stewart, Xiaoyu Luo
Sathish Kumar : PhD Student
Research Topic: Optimisation of stent devices to treat dissected aorta
Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
Supervisor: Nicholas A Hill
Mikolaj Kundegorski : PhD Student
Supervisor: Colin Torney
Gordon McNicol : PhD Student
Research Topic: A mathematical model for nanokicking
Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
Supervisor: Peter Stewart
Antesar Mohammed Al Dawoud : PhD Student
Research Topic: Mathematical modelling of electrophysiology in hearts with
healed myocardial infarction scar
Supervisors: Radostin Simitev, Hao Gao
Mathematical Biology - Example Research Projects
Efficient asymptotic-numerical methods for cardiac electrophysiology (PhD)
Supervisors: Radostin Simitev
Relevant research groups: Mathematical Biology, Continuum 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 Biology, Continuum 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 Biology, Continuum 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 Biology, Continuum 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 Biology, Continuum 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.

Host-parsitoid coinvasion
Integrodifference models of host-parasitoid interactions give rise to a wide range of travelling wave dynamics
Mountain pine beetle attack
In collaboration with entomologists we are using mathematical models to give insight into mountain pine beetle adaptation to changing temperatures
Intrinsic dynamics of a cardiac excitation model
The electrical properties of the cardiac myocytes are described by multi-component reaction-diffusion equations
Bioconvection patterns
Bioconvection patterns, as seen from above, due to hydrodynamic instabilities induced by the biased swimming motion of many negatively buoyant unicellular green algae