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Assessing deficiencies in ultradian glucose regulation using delay differential equations (Advert Reference: RDF20/EE/MPEE/HUARD)

  • Full or part time
  • Application Deadline
    Friday, January 24, 2020
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

Glucose regulation in humans operates in an oscillatory way in non-diabetic individuals. In particular, it has been observed that rhythms in the ultradian regime, which is repeating several times in the course of one day, occur in reaction to various patterns of glucose stimuli and are less effectively controlled in diabetic patients. Several mathematical models have been created in the last few decades to understand the mechanisms responsible for these oscillations and study how diabetic deficiencies affect these processes. Following the pioneering work of J. Sturis and his team in the 1990’s, the analysis of models of differential equations that incorporate time delays representing pancreatic insulin secretion and hepatic glycogenesis has provided significant insights into the glucose-insulin dynamics.

The main objective of this new project consists in extending the current model by taking into account the non-constant nature of insulin secretion and thus consider state-dependent delays. Such varying behaviour has been evidenced in early phases of Type-2 diabetes and results in a loss of entrainment of the ultradian oscillations. Through a novel and more complete model, we aim to uncover new indicators of deficiencies in the glucose-insulin feedback loop and provide tools for restoring an accurate regulation.

The characterisation of periodic solutions described by delay differential equations pose significant mathematical challenges for which tools from complex analysis, functional analysis as well as numerical solutions will be employed. Some familiarity with these disciplines would be an advantage. Furthermore, the project may also provide an opportunity to develop links with clinicians and researchers in the healthcare sector.

The principal supervisor for this project is Dr Benoit Huard. The second supervisor will be Dr Antonio Moro.

Please note eligibility requirement:
• Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
• Appropriate IELTS score, if required.
• Applicants cannot apply for this funding if currently engaged in Doctoral study at Northumbria or elsewhere.

For further details of how to apply, entry requirements and the application form, see

Please note: Applications that do not include a research proposal of approximately 1,000 words (not a copy of the advert), or that do not include the advert reference (e.g. RDF20/EE/MPEE/HUARD) will not be considered.

Deadline for applications: Friday 24 January 2020

Start Date: 1 October 2020

Northumbria University takes pride in, and values, the quality and diversity of our staff. We welcome applications from all members of the community. The University holds an Athena SWAN Bronze award in recognition of our commitment to improving employment practices for the advancement of gender equality.

Funding Notes

The studentship is available to Home/EU/Worldwide students where a full stipend, paid for three years at RCUK rates (for 2019/20, this is £15,009 pa) and full fees.


B. Huard, J. Easton, M. Angelova, Investigation of stability in a two-delay model of the ultradian oscillations in glucose–insulin regulation, Communications in Nonlinear Science and Numerical Simulation, 26 (2015) 211–222.

B. Huard, A. Bridgewater, M. Angelova, Mathematical investigation of diabetically impaired ultradian oscillations in the glucose–insulin regulation,418 (2017) 66–76.

Bridgewater, A., Stringer, B., Huard, B. and Angelova, M., 2019, April. Ultradian rhythms in glucose regulation: A mathematical assessment. In AIP Conference Proceedings (Vol. 2090, No. 1, p. 050010). AIP Publishing.

A. Bridgewater, B. Huard, M. Angelova, Amplitude and frequency variation in nonlinear glucose dynamics with multiple delays via periodic perturbation, Accepted Oct 2019, Journal of Nonlinear Science.

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