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Utilising mechanistic mathematical models to understand cellular heterogeneity of healthy human tendons #NDORMS-2020/7

About This PhD Project

Project Description

Tendons efficiently transfer force from muscles to the skeleton and are fundamental to all forms of motion. Tendons possess a distinct hierarchical organisation. As well as containing cells they are rich in extracellular matrix that confers its fibrous structure and function. However, age, inflammation, tendinopathies and tendon tears negatively impact these essential structures. For example, tears of the shoulder tendons affect around half of people aged over 65 years, making tendon disease the third most prevalent cause of musculoskeletal pain. No disease modifying drugs exist for tendon disease and surgical approaches for tendon tears fail in 40% of cases despite advances in biomaterial implants. The development of effective treatments for tendon disease requires a step change in our mechanistic understanding of the biophysical processes underpinning tendon physiology and pathobiology.

This project will exploit the reference dataset for healthy tendon cell types arising from an exciting new initiative ``The Tendon Seed Network”, led by Professor Snelling (NDORMS), and develop mechanistic mathematical models to understand the origin of cellular heterogeneity in healthy human tendons. The Tendon Seed Network is a partnership with the Human Cell Atlas and Chan Zuckerberg Initiative. This consortium across 4 international sites is using next generation sequencing approaches to generate a spatial map of healthy tendons. A spatial map will tell us which cell types are present in tendon and where they sit within the tendon anatomy. Maps are being established for healthy tendons from the knee, ankle and shoulder. The Tendon Seed Network will also identify the extracellular matrix surrounding each cell type (the pericellular matrix) and will define the mechanical properties of this pericellular matrix.

The PhD project will focus on generating mathematical models to investigate how spatial cellular heterogeneity is influenced by the interplay between tendon type, single-cell phenotypes and peri-cellular matrix composition. Initial model development will be guided by analysis of the experimental data (e.g. machine learning to identify most relevant covariates and interactions) generating hypotheses for the causal mechanisms underlying the spatial cellular heterogeneity across anatomical sites. Novel multi-physics, multi-scale mechanistic models will be developed that incorporate driving processes on a range of spatial and temporal scales, e,g, cell-cell signaling, cell migration, proliferation and mechanobiology. Ultimately, these mechanistic models will generate new experimentally-testable hypotheses and insights – facilitating identification of entirely novel treatment strategies.

The Research Group

The student will be jointly supervised by Associate Professor Sarah Snelling and Dr Adam Cribbs (NDORMS) and Professor Sarah Waters (Mathematical Institute) . They will based within the interdisciplinary Carr Group at the Botnar Research Centre who work closely with the Cribbs Computational Biology Group. The student will be supported by a team of biologists, engineers, computational biologists, clinicians and mathematicians. They will also be embedded within the Tendon Seed Network providing direct access to an interdisciplinary team of internationally-leading researchers engaged in tendon research.


The student will work within NDORMS and the Mathematical Institute, providing them with an excellent environment to be trained in research at the interface between physical and life sciences. By joining both research environments, the student will be able to take full advantage of all the opportunities for research discussions and collaborations that come with being part of a lively research environment of PhD students and postdoctoral fellows.

Students will also be required to attend regular seminars within both NDORMS and the MI, as well as those relevant in the wider University. Students will be expected to present data regularly in Departmental seminars, at the Carr, Cribbs and Waters group meetings, and to attend external conferences to present their research globally.

Links to supervisor webpages

Subject specific training opportunities are described in more detail below.


The Botnar Research Centre plays host to the University of Oxford's Institute of Musculoskeletal Sciences, which enables and encourages research and education into the causes of musculoskeletal disease and their treatment. Training will be provided in techniques including computational analysis of single cell data and the laboratory methods used to generate spatial maps. The student will not be expected to generate these maps in the laboratory but an understanding of the workflows is regarded as an important aspect of this integrative PhD. A core curriculum of lectures will be taken in the first term to provide a solid foundation in a broad range of subjects including musculoskeletal biology, inflammation, epigenetics, translational immunology, data analysis and the microbiome.

Students will have access to various courses run by the Medical Sciences Division Skills Training Team and other Departments. All students are required to attend a 2-day Statistical and Experimental Design course at NDORMS and run by the IT department (information will be provided once accepted to the programme).

Mathematical Institute:

The student will work directly with Professor Sarah Waters in the development of mechanistic mathematical models. Professor Waters has an extensive track record of successful collaboration with life scientists, clinicians, bioengineers and experimentalists, and particular expertise in the development and solution of novel, mathematical models that provide mechanistic insight into complex biological systems. Within the MI, the student will be able to contribute to, and benefit from, the exciting activities in mathematical biology and medicine within the Oxford Centre for Industrial and Applied Mathematics (OCIAM) and the Wolfson Centre for Mathematical Biology (WCMB), including a programme of research seminars, group meetings, and interdisciplinary workshops. The student will be able to dip into a suite of advanced level mathematical and computational courses as appropriate, including: solid mechanics, perturbation methods, mathematical mechanical biology and finite element methods for partial differential equations.

How to Apply

The Department accepts applications throughout the year but it is recommended that, in the first instance, you contact the relevant supervisor(s) or the Graduate Studies Officer, Sam Burnell (), who will be able to advise you of the essential requirements.

Interested applicants should have, or expect to obtain, a first or upper second-class BSc degree or equivalent in a relevant subject and will also need to provide evidence of English language competence (where applicable).
The application guide and form is found online and the DPhil or MSc by research will commence in October 2020.

Applications should be made to one of the following programmes using the specified course code:
D.Phil in Musculoskeletal Sciences (course code: RD_ML2)
D.Phil in Molecular and Cellular Medicine (course code: RD_MP1)

For further information, please visit


Cytokines in tendon disease: A Systematic Review. Morita W, Dakin SG, Snelling SJB, Carr AJ. Bone Joint Res. 2017 Dec;6(12):656-664.

Profibrotic mediators in tendon disease: a systematic review. Morita W, Snelling SJ, Dakin SG, Carr AJ. Arthritis Res Ther. 2016 Nov 18;18(1):269.

Pattern formation in multiphase models of chemotactic cell aggregation. Green, J; Whiteley, J; Oliver, J; Byrne, H; Waters, S Mathematical medicine and biology : a journal of the IMA issue 3 volume 35 page 319-346

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