Sample thesis topics

Below are sample topics available for prospective postgraduate research students. These sample topics do not contain every possible project, they are aimed at giving an impression of the breadth of different topics available. Most prospective supervisors would be more than happy to discuss projects not listed below.

Funded projects are projects with project-specific funding. Funding for other projects is usally available on a competitive basis.

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.

 

Topological full groups and continuous orbit equivalence (PhD)

Supervisors: Xin Li
Relevant research groups: Geometry and Topology, Analysis, Algebra

This proposed PhD project is part of a research programme whose aim is to develop connections between C*-algebras, topological dynamics and geometric group theory which emerged recently.

More specifically, the main goal of this project is to study topological full groups, which are in many cases complete invariants for topological dynamical systems up to continuous orbit equivalence. Topological full groups have been the basis for spectacular developments recently since they led to first examples of groups with certain approximation properties, solving long-standing open questions in group theory. The goal of this project would be to systematically study algebraic and analytic properties of topological full groups. This is related to algebraic and analytic properties of topological groupoids, the latter being a unifying theme in topological dynamics and operator algebras. A better understanding of the general construction of topological full group -- which has the potential of solving deep open questions in group theory and dynamics -- goes hand in hand with the study of concrete examples, which arise from a rich variety of sources, for instance from symbolic dynamics, group theory, semigroup theory or number theory.

Another goal of this project is to develop a better understanding of the closely related concept of continuous orbit equivalence for topological dynamical systems. This new notion has not been studied in detail before, and there are many interesting and important questions which are not well-understood, for instance rigidity phenomena. Apart from being interesting on its own right from the point of view of dynamics, the concept of continuous orbit equivalence is also closely related to Cartan subalgebras in C*-algebras and the notion of quasi-isometry in geometric group theory. Hence we expect that progress made in the context of this project will have an important impact on establishing a fruitful interplay between C*-algebras, topological dynamics and the geometry of groups.

The theme of this research project has the potential of shedding some light on long-standing open problems. At the same time, it leads to many interesting and feasible research problems.

 

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.

 

Electrophysiological modelling of hearts with diseases (PhD)

Supervisors: Radostin Simitev, Hao Gao
Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology

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. 

 

Arterial dissection (PhD)

Supervisors: Nicholas A Hill, Steven Roper, Xiaoyu Luo
Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

Location:

School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

Civil and Environmental Engineering, Politecnico di Milano.Supervisors:

Prof Nicholas HIll   (lead, UofG, Mathematics),

Dr Steven Roper   (UofG, Mathematics),

Prof Xiaoyu Luo   (UofG, Mathematics),

Prof Anna Pandolfi   (Structural Mechanics, Politecnico di Milano)

 

 

Scholarship details:

 

Eligibility: A three-and-a-half year, fully-funded PhD scholarship open to UK/EU applicants

 

 

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.

This PhD project will focus on the application of our new theories of tissue damage to arterial dissection, using mathematical and computational modelling. Arterial dissection is a tear along the length of an artery that fills with high pressure blood and often re-enters the lumen. In the case of the aorta, this is life-threatening, as the dissection often propagates upstream and compromises the aortic valve. The objectives of the project are to predict the propagation and arrest of the dissection in patient-specific geometries, and to help to assess the benefits and risks of treatments including the placement of stents.

 

The student will develop expertise in multiscale hyperelastic continuum models, and in the numerical methods to solve the governing equations in physiological geometries. The student will have the opportunity to visit and work with our collaborators at MIT and POLIMI, and with our clinical and industrial partners, and will be part of a large dynamic group of researchers at the University of Glasgow.

 

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. 

 

Application will be through the University of Glasgow Postgraduate Admissions:

 

 

https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

For further information please contact:

Professor Nicholas A Hill FIMA

Executive Director - SofTMech

Senate Assessor on Court

School of Mathematics & Statistics

Tel: 0141 330 4258

Nicholas.Hill@glasgow.ac.uk

 

 

Optimisation of stent devices to treat dissected aorta (PhD)

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

Location:

 

School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

 

Chemistry, Materials and Chemical Engineering, Politecnico di Milano,

 

Terumo Aortic, Newmains Ave, Inchinnan, Glasgow

 

Supervisors:

Prof Nicholas Hill (lead, UofG, Mathematics),

Dr Robbie Brodie (Terumo Aortic),

Dr Sean McGinty (UofG, Biomedical Engineering),

Prof Francesco Migliavacca,   (Industrial Bioengineering, Politecnico di Milano)

 

 

Scholarship details:

Eligibility: A three-and-a-half year, fully-funded PhD scholarship open to UK/EU applicants

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.

This PhD project will focus on the application of our new theories of tissue damage and growth and remodelling to the design of stents by Terumo Aortic to treat aortic dissection, using mathematical and computational modelling. An aortic dissection is a tear along the length of vessel that fills with high pressure blood and often re-enters the lumen. This is life-threatening, as the dissection often propagates upstream and compromises the aortic valve. The objectives of the project are to help to develop and optimise the next generation of stents by predicting their performance in patient-specific geometries, and to minimise the medium- to long-term risks due to remodelling of the arterial wall.

The student will develop expertise in multiscale hyperelastic continuum models, and in advanced numerical methods to solve the governing equations in physiological geometries. The student will have the opportunity to visit and work with our collaborators at MIT and POLIMI, and with our clinical partners, and will be part of a large dynamic group of researchers at the University of Glasgow and Terumo Aortic, a world-leading company in the design and manufacture of medical devices.

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. 

 

 ----------------------------------------------------------------------------------------------------------------------------------

 

Application will be through the University of Glasgow Postgraduate Admissions:

 

https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

 

For further information please contact:

 

Professor Nicholas A Hill FIMA

Executive Director - SofTMech

Senate Assessor on Court

School of Mathematics & Statistics

Tel: 0141 330 4258

Nicholas.Hill@glasgow.ac.uk

 

 

Mathematical modelling of the heart and the circulation (PhD)

Supervisors: Nicholas A Hill, Xiaoyu Luo
Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

 

Location:

 

School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

 

Supervisors:  Xiaoyu Luo and Nick Hill

 

Cardiovascular disease is the leading cause of disability and death in the UK and worldwide. The British Heart Foundation (BHF) estimates it has a £19B annual economic impact.Structural impairment such as mitral regurgitation and myocardial infarction are heart diseases that, even when treated in time, can lead to diastolic heart failure with preserved ejection fraction, for which there is no recommended treatment options.   Mathematical modelling of the heart can advance our understanding of heart function, and promises to support diagnosis and develop new treatments.

This PhD project will focus on developing mathematical descriptions of the whole heart and its interactions with the circulation, using a combination of one-dimensional and lumped parameter models.  State-of-the-art structured-tree models will be used for systemic, pulmonary and coronary circulations.  The objectives of the project are to identify how the heart functions under different pathological diseases and what treatment options may be effective.  The student will develop expertise in fluid and solid mechanics modelling, as well as insights into mathematically-guided clinical translation.   The project will be performed in the research environment of SofTMech (www.softmech.org) where extensive collaborations with clinicians and international research groups are forged.  The student will have the opportunity to visit and work with our collaborators, including our clinical and industrial partners, and will be part of a large dynamic group of researchers at the University of Glasgow. 

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.   

 

Application will be through the University of Glasgow Postgraduate Admissions: 

 

https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

 

 

 

For further information please contact:

 

 

 

Professor Nicholas A Hill FIMA

 

Executive Director - SofTMech

 

Senate Assessor on Court

 

School of Mathematics & Statistics

 

Tel: 0141 330 4258

 

Nicholas.Hill@glasgow.ac.uk

 

 

 

 

 

Quantum spin-chains and exactly solvable lattice models (PhD)

Supervisors: Christian Korff
Relevant research groups: Algebra, Integrable Systems and Mathematical Physics

Quantum spin-chains and 2-dimensional statistical lattice models, such as the Heisenberg spin-chain and the six and eight-vertex models remain an active area of research with many surprising connections to other areas of mathematics.

Some of the algebra underlying these models deals with quantum and Hecke algebras, the Temperley-Lieb algebra, the Virasoro algebra and Kac-Moody algebras. There are many unanswered questions ranging from very applied to more pure topics in representation theory and algebraic combinatorics. For example, recently these models have been applied in combinatorial representation theory to compute Gromov-Witten invariants (enumerative geometry) and fusion coefficients in conformal field theory (mathematical physics).

 

Integrable quantum field theory and Y-systems (PhD)

Supervisors: Christian Korff
Relevant research groups: Algebra, Integrable Systems and Mathematical Physics

The mathematically rigorous and exact construction of a quantum field theory remains a tantalising challenge. In 1+1 dimensions exact results can be found by computing the scattering matrices of such theories using a set of functional relations. These theories exhibit beautiful mathematical structures related to Weyl groups and Coxeter geometry.

In the thermodynamic limit (volume and particle number tend to infinity while the density is kept fixed) the set of functional relations satisfied by the scattering matrices leads to so-called Y-systems which appear in cluster algebras introduced by Fomin and Zelevinsky and the proof of dilogarithm identities in number theory.

 

Continuous production of solid metal foams (PhD)

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

Porous metallic solids, or solid metal foams, are exceedingly useful in many engineering applications, as they can be manufactured to be strong yet exceedingly lightweight. However, industrial processing methods for producing such foams are problematic and unreliable, and it is not currently possible to control the porosity distribution of the final product a priori.


This project will consider a new method of solid foam production, where bubbles of gas are introduced continuously into a molten metal flowing through a heat exchanger; foaming and solidification then occur almost simulatanously, allowing the foam structure to be controlled pointwise. The aim of this project is to construct a simple mathematical model for a gas bubble moving in a liquid filled channel ahead of a solidification front, to predict optimal conditions whereby the gas bubble is drawn toward the phase boundary, hence forming a porous solid.


This project will require some background in fluid mechanics and a combination of analytical and numerical techniques for solving partial differential equations.

 

Radial foam fracture (PhD)

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

Gas-liquid foams are a useful analgoue of crystalline atomic solids. 2D foam fracture has been used to study the mechanisms of fracture in metals. A two-dimenisonal network model (formed from a large system of differential equations) has recently been produced to study foam fracture in a rectangular channel which is pressurised along one edge. This model has helped to explain the origin of the velocity gap (a range of inadmissable steady fracture velocities), observed both in foam fracture experiments and in atomistic simulations of brittle fracture. This project will apply this network modelling approach to study radial foam fracture in a Hele-Shaw cell, to mimick recent experiments. This system has strong similarity to radial Saffmann-Taylor fingering, where fingering has been observed when a less viscous fluid displaces a more viscous fluid in a confined geometry. This project will involve studying systems of ordinary and partial differential equations using both numerical and analytical methods.

 

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.

 

Topological full groups and continuous orbit equivalence (PhD)

Supervisors: Xin Li
Relevant research groups: Geometry and Topology, Analysis, Algebra

This proposed PhD project is part of a research programme whose aim is to develop connections between C*-algebras, topological dynamics and geometric group theory which emerged recently.

More specifically, the main goal of this project is to study topological full groups, which are in many cases complete invariants for topological dynamical systems up to continuous orbit equivalence. Topological full groups have been the basis for spectacular developments recently since they led to first examples of groups with certain approximation properties, solving long-standing open questions in group theory. The goal of this project would be to systematically study algebraic and analytic properties of topological full groups. This is related to algebraic and analytic properties of topological groupoids, the latter being a unifying theme in topological dynamics and operator algebras. A better understanding of the general construction of topological full group -- which has the potential of solving deep open questions in group theory and dynamics -- goes hand in hand with the study of concrete examples, which arise from a rich variety of sources, for instance from symbolic dynamics, group theory, semigroup theory or number theory.

Another goal of this project is to develop a better understanding of the closely related concept of continuous orbit equivalence for topological dynamical systems. This new notion has not been studied in detail before, and there are many interesting and important questions which are not well-understood, for instance rigidity phenomena. Apart from being interesting on its own right from the point of view of dynamics, the concept of continuous orbit equivalence is also closely related to Cartan subalgebras in C*-algebras and the notion of quasi-isometry in geometric group theory. Hence we expect that progress made in the context of this project will have an important impact on establishing a fruitful interplay between C*-algebras, topological dynamics and the geometry of groups.

The theme of this research project has the potential of shedding some light on long-standing open problems. At the same time, it leads to many interesting and feasible research problems.

 

Numerical simulations of planetary and stellar dynamos (PhD)

Supervisors: Radostin Simitev
Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

Using Fluid Dynamics and Magnetohydrodynamics to model the magnetic fields of the Earth, planets, the Sun and stars. Involves high-performance computing. 

 

 

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.

 

Electrophysiological modelling of hearts with diseases (PhD)

Supervisors: Radostin Simitev, Hao Gao
Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology

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. 

 

Arterial dissection (PhD)

Supervisors: Nicholas A Hill, Steven Roper, Xiaoyu Luo
Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

Location:

School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

Civil and Environmental Engineering, Politecnico di Milano.Supervisors:

Prof Nicholas HIll   (lead, UofG, Mathematics),

Dr Steven Roper   (UofG, Mathematics),

Prof Xiaoyu Luo   (UofG, Mathematics),

Prof Anna Pandolfi   (Structural Mechanics, Politecnico di Milano)

 

 

Scholarship details:

 

Eligibility: A three-and-a-half year, fully-funded PhD scholarship open to UK/EU applicants

 

 

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.

This PhD project will focus on the application of our new theories of tissue damage to arterial dissection, using mathematical and computational modelling. Arterial dissection is a tear along the length of an artery that fills with high pressure blood and often re-enters the lumen. In the case of the aorta, this is life-threatening, as the dissection often propagates upstream and compromises the aortic valve. The objectives of the project are to predict the propagation and arrest of the dissection in patient-specific geometries, and to help to assess the benefits and risks of treatments including the placement of stents.

 

The student will develop expertise in multiscale hyperelastic continuum models, and in the numerical methods to solve the governing equations in physiological geometries. The student will have the opportunity to visit and work with our collaborators at MIT and POLIMI, and with our clinical and industrial partners, and will be part of a large dynamic group of researchers at the University of Glasgow.

 

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. 

 

Application will be through the University of Glasgow Postgraduate Admissions:

 

 

https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

For further information please contact:

Professor Nicholas A Hill FIMA

Executive Director - SofTMech

Senate Assessor on Court

School of Mathematics & Statistics

Tel: 0141 330 4258

Nicholas.Hill@glasgow.ac.uk

 

 

Optimisation of stent devices to treat dissected aorta (PhD)

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

Location:

 

School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

 

Chemistry, Materials and Chemical Engineering, Politecnico di Milano,

 

Terumo Aortic, Newmains Ave, Inchinnan, Glasgow

 

Supervisors:

Prof Nicholas Hill (lead, UofG, Mathematics),

Dr Robbie Brodie (Terumo Aortic),

Dr Sean McGinty (UofG, Biomedical Engineering),

Prof Francesco Migliavacca,   (Industrial Bioengineering, Politecnico di Milano)

 

 

Scholarship details:

Eligibility: A three-and-a-half year, fully-funded PhD scholarship open to UK/EU applicants

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.

This PhD project will focus on the application of our new theories of tissue damage and growth and remodelling to the design of stents by Terumo Aortic to treat aortic dissection, using mathematical and computational modelling. An aortic dissection is a tear along the length of vessel that fills with high pressure blood and often re-enters the lumen. This is life-threatening, as the dissection often propagates upstream and compromises the aortic valve. The objectives of the project are to help to develop and optimise the next generation of stents by predicting their performance in patient-specific geometries, and to minimise the medium- to long-term risks due to remodelling of the arterial wall.

The student will develop expertise in multiscale hyperelastic continuum models, and in advanced numerical methods to solve the governing equations in physiological geometries. The student will have the opportunity to visit and work with our collaborators at MIT and POLIMI, and with our clinical partners, and will be part of a large dynamic group of researchers at the University of Glasgow and Terumo Aortic, a world-leading company in the design and manufacture of medical devices.

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. 

 

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Application will be through the University of Glasgow Postgraduate Admissions:

 

https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

 

For further information please contact:

 

Professor Nicholas A Hill FIMA

Executive Director - SofTMech

Senate Assessor on Court

School of Mathematics & Statistics

Tel: 0141 330 4258

Nicholas.Hill@glasgow.ac.uk

 

 

Mathematical modelling of the heart and the circulation (PhD)

Supervisors: Nicholas A Hill, Xiaoyu Luo
Relevant research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

 

Location:

 

School of Mathematics and Statistics, University of Glasgow, Glasgow, UK,

 

Supervisors:  Xiaoyu Luo and Nick Hill

 

Cardiovascular disease is the leading cause of disability and death in the UK and worldwide. The British Heart Foundation (BHF) estimates it has a £19B annual economic impact.Structural impairment such as mitral regurgitation and myocardial infarction are heart diseases that, even when treated in time, can lead to diastolic heart failure with preserved ejection fraction, for which there is no recommended treatment options.   Mathematical modelling of the heart can advance our understanding of heart function, and promises to support diagnosis and develop new treatments.

This PhD project will focus on developing mathematical descriptions of the whole heart and its interactions with the circulation, using a combination of one-dimensional and lumped parameter models.  State-of-the-art structured-tree models will be used for systemic, pulmonary and coronary circulations.  The objectives of the project are to identify how the heart functions under different pathological diseases and what treatment options may be effective.  The student will develop expertise in fluid and solid mechanics modelling, as well as insights into mathematically-guided clinical translation.   The project will be performed in the research environment of SofTMech (www.softmech.org) where extensive collaborations with clinicians and international research groups are forged.  The student will have the opportunity to visit and work with our collaborators, including our clinical and industrial partners, and will be part of a large dynamic group of researchers at the University of Glasgow. 

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.   

 

Application will be through the University of Glasgow Postgraduate Admissions: 

 

https://www.gla.ac.uk/postgraduate/howtoapplyforaresearchdegree/

 

 

 

For further information please contact:

 

 

 

Professor Nicholas A Hill FIMA

 

Executive Director - SofTMech

 

Senate Assessor on Court

 

School of Mathematics & Statistics

 

Tel: 0141 330 4258

 

Nicholas.Hill@glasgow.ac.uk

 

 

 

 

 

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

 

 

Mathematical Modelling of Liquid Crystal DIsplays (PhD)

Supervisors: Nigel Mottram
Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems

In the modern world, Liquid Crystal Displays are all around us - from your TV and mobile phone, to the small display on your washing machine. Within these displays are thin layers of liquid, which react to an applied electric field to switch between different states. These states have different molecular configurations, and it is how these molecular arrangements interact with liqht that make them crucial to display technologies. The mathematical modelling of these molecular arrangements, using a continuum mechanics approach, has been essential to the development of LCDs over the last thirty years.

In this project we will consider the mathematical modelling of novel types of displays, based on confined regions of liquid crystal and effects such as flexoelectricity and defect latching. As well as the development of these models, and the derivation of the resulting partial differential equations, this project will involve analytic and numerical methods for solving the equations.

The results of this proect will lead to a deeper understanding of liquid crystals in confinement but will also help display device manufacturers understand how to improve current and new displays.

Contact nigel.mottram@glasgow.ac.uk for more details

 

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.

 

Modality of mixtures of distributions (PhD)

Supervisors: Surajit Ray
Relevant research groups: Statistics and Data Analytics

Finite mixtures provide a flexible and powerful tool for fitting univariate and multivariate distributions that cannot be captured by standard statistical distributions. In particular, multivariate mixtures have been widely used to perform modeling and cluster analysis of high-dimensional data in a wide range of applications. Modes of mixture densities have been used with great success for organizing mixture components into homogenous groups. But the results are limited to normal mixtures. Beyond the clustering application existing research in this area has provided fundamental results regarding the upper bound of the number of modes, but they too are limited to normal mixtures. In this project, we wish to explore the modality of non-normal distributions and their application to real life problems

 

 

Statistical Analyis of Medical images: Application to tumour detetection from PET imaging (PhD)

Supervisors: Surajit Ray
Relevant research groups: Statistics and Data Analytics

Positron-emission tomography (PET) is a nuclear medicine functional imaging technique that is used to observe metabolic processes in the body and is often used for tumour detection. Unlike CT or MRI scans PET scans are more reliable as the target the metabolic process but are very expensive. There are only 5 PET scanners in the whole of Scotland and around 30 in England. Further, very limited information from the images is used by the radiologists to hand segment the tumour. It is often challenging to extract the tumour alone from the background of healthy tissues and image noise. In this project, we will explore existing methods for automatic segmentation of tumor based on PET images and develop a technique to implement automatic segmentation on anonymized PET images obtained at Gartnavel Hospital.