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: Andrew Brown, Sathish Kumar, Jay MacKenzie, Roxanna Barry, Laura Miller
    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: 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
    Research student: Parna Mandal
    Postgraduate opportunities: Mathematical Modelling of Liquid Crystal Displays, Mathematical Modelling of Active Fluids, Multiscale modelling of liquid crystal-filled porous media, Flow of glacial ice sheets over deformable material, Viscous fingering instabilities: control and flow-structure interaction

  • 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, Andrew Brown
    Postgraduate opportunities: Multiscale modelling of liquid crystal-filled porous media

  • 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

  • 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 students: Muhamad Bin Noor Aziz, Parag Gupta, Antesar Mohammed Al Dawoud, Peter Mortensen, Tahani Al Sariri, Jamie Quinn
    Postgraduate opportunities: Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD), Electrophysiological modelling of hearts with diseases, Fast-slow asymptotic analysis of cardiac excitation models, Numerical simulations of planetary and stellar dynamos, 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 , 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

  • 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

  • Debao Guan : PhD Student

    Supervisors: Xiaoyu Luo, Hao Gao

  • 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

  • Mx Jay MacKenzie : PhD Student

    Supervisors: Nicholas A Hill, Xiaoyu Luo

  • 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

  • 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 - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology, Statistics and Data Analytics

    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 involves collaboration with Prof Matt Dalby (Institute of Molecular, Cell and Systems Biology).

     

    Mathematical models of vasculogenesis (PhD)

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

    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.

     

    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

     

     

    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.

     

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

    Supervisors: Peter Stewart, Nicholas A Hill
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Mathematical Biology

    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.

     

    Bayesian statistical data integration of single-cell and bulk “OMICS” datasets with clinical parameters for accurate prediction of treatment outcomes in Rheumatoid Arthritis (PhD)

    Supervisors: Mayetri Gupta
    Relevant research groups: Mathematical Biology, Statistics and Data Analytics

    In recent years, many different computational methods to analyse biological data have been established: including DNA (Genomics), RNA (Transcriptomics), Proteins (proteomics) and Metabolomics, that captures more dynamic events. These methods were refined by the advent of single cell technology, where it is now possible to capture the transcriptomics profile of single cells, spatial arrangements of cells from flow methods or imaging methods like functional magnetic resonance imaging. At the same time, these OMICS data can be complemented with clinical data – measurement of patients, like age, smoking status, phenotype of disease or drug treatment. It is an interesting and important open statistical question[1] how to combine data from different “modalities” (like transcriptome with clinical data or imaging data) in a statistically valid way, to compare different datasets and make justifiable statistical inferences.

    In this PhD project (jointly supervised with Dr. Thomas Otto and Prof. Stefan Siebert from the Institute of Infection, Immunity & Inflammation), you will explore how to combine different datasets using Bayesian latent variable modelling, focusing on clinical datasets from Rheumatoid Arthritis. Single cell data has been generated from rheumatoid arthritis patients[2] from synovial and blood samples. This will be combined with rich clinical datasets from cohorts like SERA [3], RAMAP[4] and others, that all have transcriptomics data (bulk RNA-Seq from blood and some tissues). All these datasets are already curated and stored in a tranSMART database. In the different datasets, the patients were treated with different drugs and their response or the lack of it, was recorded over time.

    Our overall aim is to build a Bayesian statistical framework and methodology that can combine these different data types in a latent space in a statistically justifiable way, with the goal of more accurate prediction of clinical outcomes than can be achieved with a single (or fewer types of) dataset alone.  The secondary aim is to develop robust and efficient Bayesian computational methodologies to fit these models on ultra-high-dimensional, complex datasets to make valid inferences, build user-friendly, publicly available computational software (in R) implementing these methods, and compare them to other currently available computational tools, both in simulated and real datasets.

    Some questions of interest are: (1) determining if it is possible to differentiate from the single cell data the different phenotypes (active RA, remission) in the clinical data; (2) explore if in the latent space, it is possible to combine the different modalities when including further datasets from the IMID-Bio-UK dataset as well as imaging data; (3) exploring our methods in the context of Rheumatoid Arthritis with Psoriasis Arthritis- which are two immune mediated inflammatory diseases with distinct pathways but also similarities- can our proposed methods (a) confirm existing findings (b) highlight novel shared signatures between the two diseases?

    Applicant criteria

    The successful candidate should have a strong training and background in theoretical, methodological and applied Statistics, expert skills in relevant statistical software or programming languages (such as R, Python/C/C++, or MATLab), and also have a deep interest in developing knowledge in cross-disciplinary topics in genomics, sequencing technology, and inflammatory disease, during the PhD. The candidate will be expected to consolidate and master an extensive range of topics in modern Statistical theory and applications during their PhD, including advanced Bayesian modelling and computation, latent variable models, machine learning, and methods for Big Data. The candidate is expected to have excellent interpersonal and communication skills (oral and written) and to be enthusiastic and comfortable interacting and communicating with researchers in other disciplines, especially in biology and medicine.

    Funding Notes

    The successful candidate will be considered for funding to cover domestic tuition fees, as well as paying a stipend at the Research Council rate (estimated £15,609 for Session 2021-22) for four years.

    References:

    1. Adossa N,  Khan S, Rytkönen KT, Elo LL: Computational strategies for single-cell multi-omics integration. Comput. Struct. Biotechnol 2021, 19: 2588-2596.
    2. Alivernini S, MacDonald L, Elmesmari A, Finlay S, Tolusso B, Gigante MR, Petricca L, Di Mario C, Bui L, Perniola S et al: Distinct synovial tissue macrophage subsets regulate inflammation and remission in rheumatoid arthritis. Nat Med 2020, 26(8):1295-1306.
    3. Dale J, Paterson C, Tierney A, Ralston SH, Reid DM, Basu N, Harvie J, McKay ND, Saunders S, Wilson H et al: The Scottish Early Rheumatoid Arthritis (SERA) Study: an inception cohort and biobank. BMC Musculoskelet Disord 2016, 17(1):461.
    4. Cope AP, Barnes MR, Belson A, Binks M, Brockbank S, Bonachela-Capdevila F, Carini C, Fisher BA, Goodyear CS, Emery P et al: The RA-MAP Consortium: a working model for academia-industry collaboration. Nat Rev Rheumatol 2018, 14(1):53-60.