Mathematical Modelling of Magnetically Targeted Stem Cell Delivery
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
This project aims to develop mathematical models of a magnetically targeted stem cell delivery technique. The development of an effective method of targeting delivery of stem cells to the site of an injury is a key challenge in regenerative medicine. However, production of stem cells is costly and current delivery methods rely on large doses in order to be effective. Improved targeting through use of an external magnetic field to direct delivery of magnetically-tagged stem cells to the injury site would allow for smaller doses to be used. Developing an accurate mathematical model can reduce required amount of laboratory testing and allow this therapy to reach clinical testing stages faster.
The objective of this project is to create a detailed model of this regenerative medicine therapy containing the dominant features of the underlying continuum mechanics, electrodynamics and mathematical biology. The accuracy of the mathematical model can be verified against real data provided by our collaborators at the University of Birmingham. We aim to use our model in a predicative context to address safety issues critical to the success of the therapy; during experimentation stem cells were found to form dangerous clumps in the body. We will address this issue by including intercellular magnetic and biological forces, through which we aim to determine parameter regimes which offer lower risks of clumps of stem cells leaving the injury site and travelling in the blood system. Furthermore we aim to provide fast and cheap parameter exploration in order to optimise the costly experimental process.
This project will extend existing models to the case of targeting stem cells implanted with magnetic nanoparticles: the majority of models to date consider the case of magnetic nanoparticle transport alone. Secondly we will address the safety issue of clumping not considered for magnetically tagged stem cells, through realistic microscopic magnetic modelling of stem cells implanted with nanoparticles. We will additionally improve biological realism of models by inclusion of additional features of the vessels such as the geometry, through curvature, and the microscale wall structure through inclusion of the porous layer lining the vessels, the glycocalyx.
This project falls into the EPSRC research areas of Mathematical Sciences and Healthcare Technologies, since we aim to optimise a regenerative medicine therapy through the use of mathematical modelling. We are working in collaboration with Prof Alicia El Haj and Dr Hareklea Markides at the University of Birmingham who carry out this therapy in vitro and in vivo. This collaboration allows us to address questions which are relevant and important to the regenerative medicine community.
The objective of this project is to create a detailed model of this regenerative medicine therapy containing the dominant features of the underlying continuum mechanics, electrodynamics and mathematical biology. The accuracy of the mathematical model can be verified against real data provided by our collaborators at the University of Birmingham. We aim to use our model in a predicative context to address safety issues critical to the success of the therapy; during experimentation stem cells were found to form dangerous clumps in the body. We will address this issue by including intercellular magnetic and biological forces, through which we aim to determine parameter regimes which offer lower risks of clumps of stem cells leaving the injury site and travelling in the blood system. Furthermore we aim to provide fast and cheap parameter exploration in order to optimise the costly experimental process.
This project will extend existing models to the case of targeting stem cells implanted with magnetic nanoparticles: the majority of models to date consider the case of magnetic nanoparticle transport alone. Secondly we will address the safety issue of clumping not considered for magnetically tagged stem cells, through realistic microscopic magnetic modelling of stem cells implanted with nanoparticles. We will additionally improve biological realism of models by inclusion of additional features of the vessels such as the geometry, through curvature, and the microscale wall structure through inclusion of the porous layer lining the vessels, the glycocalyx.
This project falls into the EPSRC research areas of Mathematical Sciences and Healthcare Technologies, since we aim to optimise a regenerative medicine therapy through the use of mathematical modelling. We are working in collaboration with Prof Alicia El Haj and Dr Hareklea Markides at the University of Birmingham who carry out this therapy in vitro and in vivo. This collaboration allows us to address questions which are relevant and important to the regenerative medicine community.
People |
ORCID iD |
Sarah Waters (Primary Supervisor) | |
Edwina Yeo (Student) |
Publications

Schamberger B
(2023)
Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales.
in Advanced materials (Deerfield Beach, Fla.)

Yeo E
(2022)
Transport and deposition problems in blood flow


Yeo EF
(2021)
Experimental and mathematical modelling of magnetically labelled mesenchymal stromal cell delivery.
in Journal of the Royal Society, Interface

Yeo EF
(2024)
A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow.
in Biomechanics and modeling in mechanobiology
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509711/1 | 30/09/2016 | 29/09/2021 | |||
2100104 | Studentship | EP/N509711/1 | 30/09/2018 | 29/06/2022 | Edwina Yeo |
EP/R513295/1 | 30/09/2018 | 29/09/2023 | |||
2100104 | Studentship | EP/R513295/1 | 30/09/2018 | 29/06/2022 | Edwina Yeo |
NE/W502728/1 | 31/03/2021 | 30/03/2022 | |||
2100104 | Studentship | NE/W502728/1 | 30/09/2018 | 29/06/2022 | Edwina Yeo |
Description | We have developed two mathematical models for aspects of magnetic drug delivery and related problems in vascular fluid mechanics. These have helped address open questions which biological scientists have about key processes in blood flow and about novel drug delivery techniques. |
Exploitation Route | This will help biological scientists design more effective experiments reducing the number of animal tests required. |
Sectors | Healthcare Manufacturing including Industrial Biotechology Pharmaceuticals and Medical Biotechnology |
Title | Code for Magnetic cell delivery simulations |
Description | Comsol and matlab simulation codes for the transport of stem cells in a channel which deforms as cells aggregate on vessel wall. Datasets for parameter analysis. |
Type Of Material | Computer model/algorithm |
Year Produced | 2020 |
Provided To Others? | Yes |
Impact | Dataset and model was used for journal article, 'Experimental and mathematical modelling of magnetically labelled mesenchymal stromal cell delivery (2021) Author: E. Yeo, H. Markides, A.T. Schade, A.J. Studd, J.M. Oliver, S.L. Waters, A.J. El Haj, Royal Society Interface' |
URL | https://github.com/Edwina-Yeo/Magnetic-Cell-Delivery-Simulations |
Description | Experimental-Modelling Collaboration - Technion |
Organisation | Technion - Israel Institute of Technology |
Country | Israel |
Sector | Academic/University |
PI Contribution | Mathematical modelling of mechanisms of arterial clot formation. |
Collaborator Contribution | Insight into the biological application, experimental data to compare model outcomes to. |
Impact | This collaboration is multidiciplinary. We contribute mathematical modelling, our collaborators are based in biomedical engineering. We have developed a novel mathematical model through this collaboration. |
Start Year | 2019 |
Description | Experimental-Modelling Collaboration - University of Birmingham |
Organisation | University of Birmingham |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | We have developed mathematical models for experimental therapies developed by Professor Alicia El Haj's group at the University of Birmingham, Healthcare Technology Institute. |
Collaborator Contribution | Our collaborators provided insight into the biological application of our model, allowing us to construct relevant mathematical models. They also provided experimental data for us to compare model outputs on. |
Impact | This has resulted in multiple conference presentations and one publication. We have developed two novel mathematical models for this application. The collaboration is multidisciplinary: we delivery mathematical modelling and our partners are researching regenerative medicine. |
Start Year | 2018 |
Description | 3 minute thesis competition |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Postgraduate students |
Results and Impact | Competition aimed at summarising your research to a wider audience. |
Year(s) Of Engagement Activity | 2021 |
Description | Help at Graduate Open day for Research group |
Form Of Engagement Activity | Participation in an open day or visit at my research institution |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Undergraduate students |
Results and Impact | Personal discussions offered with applicants for graduate programs in my research group. |
Year(s) Of Engagement Activity | 2020 |
Description | Oral Presentation at Americal Physical Society, Division of Fluid dynamics Meeting |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Study participants or study members |
Results and Impact | Online 10 minute recorded talk for virtual conference with drop in question time. Lead to discussions with other researchers and students. |
Year(s) Of Engagement Activity | 2020 |
URL | https://ui.adsabs.harvard.edu/abs/2019APS..DFDM03032Y/abstract |
Description | Oral Presentation at Euromech, 'Fluid and solid mechanics for tissue engineering ' Colloqium |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Study participants or study members |
Results and Impact | 20 minute oral presentation to approximately 30 people. Lead to a new collaboration. |
Year(s) Of Engagement Activity | 2019 |
URL | https://604.euromech.org/ |
Description | Oral Presentation at Internal Department Seminar Series |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Study participants or study members |
Results and Impact | 10 minute oral presentation at mathematics department seminar at the 'Oxford Centre for Applied Industrial Mathematics' with following questions. |
Year(s) Of Engagement Activity | 2020 |
URL | https://www.maths.ox.ac.uk/node/37549 |
Description | Oral Presentation at Junior Applied Mathematics Seminar Series |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Postgraduate students |
Results and Impact | Oral presentation on research, with a discussion afterwards ~15 people. |
Year(s) Of Engagement Activity | 2019 |
URL | https://www.maths.ox.ac.uk/node/31813 |
Description | Oral Presentation at Society for Mathematical Biology Annual Conference |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Study participants or study members |
Results and Impact | 20 Minute Oral presentation at a virtual conference, delivered live. With discussions afterwards. |
Year(s) Of Engagement Activity | 2020 |
URL | https://smb2020.org/OTHE_Wednesday_MS1/ |
Description | Outreach activity for school children 'I'm a scientist get me out of here' |
Form Of Engagement Activity | Engagement focused website, blog or social media channel |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Schools |
Results and Impact | Online chat sessions with students about working as a scientist.~ 15 students per session. |
Year(s) Of Engagement Activity | 2019 |
URL | https://hertford19.imascientist.org.uk/profile/edwinayeo/ |
Description | Poster Presentation at Women in Mathematics Symposium ETH |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Study participants or study members |
Results and Impact | Poster presentation to study participants ~25 people. |
Year(s) Of Engagement Activity | 2019 |
URL | https://math.ethz.ch/news-and-events/events/gomath/gomath-2019/symposium.html |
Description | Society for Industrial Applied Mathematics 3 minute Thesis competition presentation |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Postgraduate students |
Results and Impact | 3 minute talk summarising my research to a non technical audience. |
Year(s) Of Engagement Activity | 2021 |
URL | https://www.maths.ox.ac.uk/node/38125 |
Description | Talk at 'Mathematix' engagement session for undergraduates |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Undergraduate students |
Results and Impact | Presentation on my research and life as a PhD students with approximately 10 students. |
Year(s) Of Engagement Activity | 2021 |
Description | Talk at American Physical Society |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Study participants or study members |
Results and Impact | Oral presentation to approximately 20 people at Americal Physical Society with the following discussion with participants. |
Year(s) Of Engagement Activity | 2021 |
URL | https://meetings.aps.org/Meeting/DFD21/Session/T15.10 |