Novel Topological Approaches to Positron Imaging and Medical Physics

My PhD project titled "Novel Topological Approaches to Positron Imaging and Medical Physics" focuses on developing innovative approaches for positron imaging and medical physics using topology-based techniques. The project's primary objective is to develop a topology-based Positron Emission Particle Tracking algorithm called TopoloPEPT. This algorithm will improve the accuracy and efficiency of positron tracking and reconstruction of tracer trajectories. TopoloPEPT will employ topological methods to analyse the complex and high-dimensional data generated by positron imaging, leading to a better understanding of particulate processes.

The project will also involve applying topological data analysis (TDA) to medical fields, such as structural MRI scans, to identify diseases using topological statistics. TDA will enable the development of novel methods for analysing and visualising medical data, leading to more accurate and precise diagnoses of diseases such as cancer and neurodegenerative disorders.

Moreover, the project will explore the application of TDA to industrial fields, such as aerospace and engineering, to improve industrial processes. The internships with Rolls Royce will provide opportunities to apply the skills developed through the project to real-world use cases, improving engine performance and reliability.
The PhD project will also involve validating simulation systems such as computational fluid dynamics and the discrete element method using TopoloPEPT. The algorithm's ability to validate simulation systems will improve the accuracy and reliability of these simulations, leading to better predictions of physical systems' behaviour.

In summary, the "Novel Topological Approaches to Positron Imaging and Medical Physics" project aims to develop innovative methods and algorithms that leverage topology-based techniques for positron imaging and medical physics. The project will involve developing TopoloPEPT, applying TDA to medical fields and industrial uses, validating simulation systems, and working with industrial partners such as Rolls Royce. This project will contribute to the development of new tools and approaches that can be applied in both medical and industrial contexts, leading to significant improvements in healthcare and industrial processes.

1. Our primary impact will be by supplying the UK knowledge economy with skilled multidisciplinary researchers, equipped with the technical and transferable skills to establish the UK as pre-eminent in topology-based future technologies. The training they receive will make them proficient in the demands of the translation of academic science (with a broad background in condensed matter physics, materials science and applied electromagnetics) to industry, with direct experience from internship and industry engagement days. With their exposure to both theoretical research (including modelling and big data-driven problems) and experimental practice, our graduates will be ideally equipped to tackle research challenges of the future and communicate to a broad audience, ready to lead teams made up of diverse specialised components. The potential impact of our researchers will be enhanced by a broad programme of transferable skills, focusing on innovation, entrepreneurship and responsible research. Beneficiaries here will include the students themselves as they embark on future careers intertwining academic research and industry, as well as the other sectors listed below.

2. The research undertaken by students in the CDT will have impact on the future direction of topological science. Related disciplines, including physics, materials science, mathematics, and information technology will benefit from the cross-disciplinary fertilisation it will enable. The CDT will not only provide an interface between research in physical sciences and engineering, but also provide a route for academia to interact effectively with industry. This will help organise researchers from different disciplines to collaborate around the needs of future technology to design materials based on topological properties.

3. Our research will enable industries to set the direction of topological research around the needs of commercial research and development, leading to wealth generation for the UK, and to influence the mindset of the next generation of future technologists. Specifically, topological design has the promise to revolutionise devices and materials relevant to communications, microwave and terahertz technologies, optical information processing, manufacturing, and cybersecurity. Through partnership with organisations from the wider knowledge sector, we will deepen the relationship between academic research and disciplines including IP law and scientific software development.

4. Our CDT will also have impact on the wider academic community. New specialist courses and training in transferable skills will be developed utilising cutting-edge multimedia technologies. Our international research collaborators, including prominent global laboratories, will benefit from placements and research visits of the CDT students. Our interdisciplinary research, combining the needs of academia and industry will be an exemplar of the effectiveness of the CDT model on an international stage.

5. The wider community will benefit from our organised public engagement activities. These will include direct interaction activities, such as demonstrating at the Birmingham Thinktank Science Centre, the Royal Society Summer Exhibition, local schools and community centres.