Understanding mechanisms of cortical spreading depression in epilepsy and migraine

Cortical spreading depression (CSD, also known as spreading depolarisation), a neurophysiological phenomenon in the brain consisting of a wave of neuronal hyperactivity followed by excessive depolarisation and a period of electrical silence. About 30% of patients with migraine experience the CSD associated with migraine aura. It is also believed that there exists a link between the CSD and episodes of seizures during epilepsy and that this link is potentially relevant to sudden unexpected death in patients with epilepsy.
Prof. Kirill Volynski's group in the UCL Queen Square Institute of Neurology has recently developed a set of novel methods to record local-field potential data combined with spatio-temporal fluorescence Ca2+ imaging of neuronal activity in awake mice. These data indicate that approximately 25% of seizures were followed by a Ca2+ wave that spreads at a much slower velocity typical of CSD, and this wave is followed by electrical silence. The proposed PhD project will be a direct collaboration with Volynski lab and will complement their experimental research programme funded by the Epilepsy Research UK with biologically constrained mathematical modelling. The main aim of the overall research will be to understand the mechanisms behind the initiation of CSD as well as the mechanistic links between seizures and CSD. In particular, how do seizures that are followed by CSD differ from seizures that are not? How can the cortex transition to CSD directly without passing through a seizure? Can mutations in voltage-gated Ca2+ channels associated with migraine lead to the increased propagation of CSD reaching the brain stem and explaining sudden death?
The PhD project will focus on the development of a modelling framework describing the spatio-temporal electrical signals in neuronal tissue that can support both epileptic seizures and CSD. This will be achieved using integro-differential type models and constrained using the experimental data on electrical and Ca2+ dynamics from UCL.
The context of the research - Cortical spreading depression is a pathological processes that causes malfunction of neuronal networks and plays a crucial role in several conditions such as seizures, ischemia and migraines and its variants. The process is only partially understood because of its complexity and difficulty obtaining direct experimental data. However with the recently available imaging data of Ca2+ dynamics combined with local-field potential recordings in awake mice we can begin to understand the underlying mechanisms and inform the treatments for the linked conditions in the long term.
The aims and objectives of the research - The aim of the project is to develop a novel biologically constrained model of electrical activity in neuronal tissue capable to support epileptic seizures and CSD. This model will help to discriminate between various possible mechanisms linking seizures and CSD as well as it will provide a predictive power for potential novel experiments for validating potential hypotheses.
The novelty of the research methodology - Development of the model will be guided by novel experimental data. Moreover, to our best knowledge, there does not exist a model capable of combining epileptic seizures and CSD using the class of integro-differential equations (or reaction-diffusion type models).
The potential impact, applications, and benefits - The main goal of this overall project is to dissect the mechanisms that predispose cortical neuronal networks to seizures and/or to CSD, using a combination of experimental methods and mathematical/computational modelling. This might provide a significant impact on patients susceptible to epilepsy and migraine and can help of explaining sudden death syndrome in epilepsy patients.
Research area; Healthcare technologies, Mathematical Sciences
External partner - National Hospital for Neurology and Neurosurgery

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.