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, Scott Richardson
    Research students: Andrew Brown, Sathish Kumar, 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: 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 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
    Postgraduate opportunities: Multiscale modelling of liquid crystal-filled porous media

  • 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

  • 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

  • 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 student: Stephen Jun Villejo

  • Personal Website
  • 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

  • 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

  • Ionut Paun : PhD Student

    Supervisors: Colin Torney, Dirk Husmeier


  • 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. 

     

     

    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.

     

    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.