PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation

Lead Research Organisation: University of Cambridge
Department Name: Applied Maths and Theoretical Physics

Abstract

Positron Emission Tomography (PET) is a pillar of modern diagnostic imaging, allowing non-invasive, sensitive and specific detection of functional changes in several disease types. In endocrinology, the precise localisation of small functioning tumours of the pituitary or adrenal glands is crucial for planning curative surgery or radiotherapy. While PET imaging shows good promise for this task, initial studies suggest significant room for improvement, with improved PET imaging and subsequent more accurate localisation opening up the possibility for more adapted therapies. In dementia, the accurate quantification of PET images is key for the early detection of disease. Improved PET imaging may allow for earlier detection of dementia while asymptomatic and increased sensitivity to assess and monitor treatment once appropriate drugs have been found.

In this project mathematicians team up with researchers and clinicians from Addenbrooke's Hospital Cambridge, Dementias Platform UK (DPUK), GE Healthcare and University College London (UCL) for improved diagnosis and localization for tumours in endocrinology and earlier diagnosis of dementia with improved PET imaging. In particular, we investigate modern PET reconstruction approaches based on advanced mathematical methods to increase the PET image resolution and contrast, while keeping computational complexity low, thereby directly benefiting clinical workflow.

Planned Impact

Beneficiaries: This project lives at the interface between applied mathematics, imaging technologies, medical research and clinical practice. As such, it will impact each of these areas.
- Applied Mathematicians: Interdisciplinary research like that, that links mathematical innovation closely with the application, is often desired but not often successfully achieved. This project is one of the few pioneers in this respect. Showcasing, therefore, both interesting mathematical innovation and success in the application domain at the same time, will impact how mathematicians think about research, potentially encouraging them to pursue similar approaches for different problems and as such accelerate impact that mathematics has on other disciplines, society, healthcare and more.
- Imaging Technologies: The mathematical optimisation methods and image reconstruction algorithms developed in this project for PET have several generic elements who are applicable to other imaging problems, e.g. MRI, CT, PAT, etc., and which can benefit those in turn.
- Medical Research and clinical practice: Qualitatively and quantitatively improved PET images can potentially impact the analysis and further understanding of a wide range of diseases, their analysis, diagnosis and treatment.

National Importance: Our proposal fits perfectly within the EPSRC's portfolio and funding strategy, and also connects to other parts of UKRI. It was recognized by a panel of international experts [1] that more focus should be laid on connecting numerical analysis to computation which is a cornerstone of this proposal. With Healthcare Technologies it falls into the EPSRC Optimising Treatment Healthcare Challenge. Dementia is one of the greatest challenges of our time. In 2015 an estimated 850k people in the UK were living with dementia, a number which may rise to 2m by 2050 unless ways to cure or prevent dementia are found [2]. It also accounted for 11.6% of all deaths registered in England and Wales in 2015 making it the leading cause of death [3]. The economic cost of caring to the UK is estimated at more than £23bn in 2014 [4]. To counterfeit this development, it has been noted that "the vast majority of cutting edge biology/health sciences results ... have only been made possible by preceding advances in physics, chemistry, computing, mathematics, materials or engineering" [5]. Moreover, in March 2018 the UK government announced an investment of £40m into the UK Dementia Research Institute [6] which is built to create a new hub of interdisciplinary research for developing new treatments for dementia. An important pillar in our fight again dementia is PET imaging where the UK is world-leading in research and development and several members of UKRI made large infrastructural investments. Most recently, seven PET-MR scanners were purchased as part of the nation wide alliance DPUK "aiming to make the UK leaders in the field of this relatively new technology" [7]. Our aim to improve PET imaging to fight dementia aligns with the MRC priority challenge [8] and helps to "provide solutions to major challenges facing society, in the UK and globally" [8]. As such, this proposal contributes directly to the EPSRC's prosperity outcome Health Nation [8]. Next to EPSRC's vision, this proposal also aligns with STFC's vision as connecting mathematical imaging to its applications helps "to maximise the impact of our knowledge, skills, facilities and resources for the benefit of the United Kingdom and its people" [8].

[1] M. Wright et al., International Review of Mathematical Sciences 2010
[2] Alzheimer's Society UK, 2018
[3] Office of National Statistics, Deaths Registered in England and Wales 2016
[4] F. Lewis et al., Report for Alzheimer's Research UK by OHE Consulting 2014
[5] EPSRC, Maxwell Review 2014
[6] https://mrc.ukri.org/news/browse/40-million-for-uk-dri-hub
[7] MRC Review of PET within The Medical Imaging Research Landscape 2017
[8] RCUK, Spending Plan 2016

Publications

10 25 50
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Arridge S (2019) Solving inverse problems using data-driven models in Acta Numerica

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Arridge SR (2021) (An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

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Benning M (2020) Bregman Itoh-Abe Methods for Sparse Optimisation in Journal of Mathematical Imaging and Vision

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Benning M (2021) Choose Your Path Wisely: Gradient Descent in a Bregman Distance Framework in SIAM Journal on Imaging Sciences

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Brown R (2021) Motion estimation and correction for simultaneous PET/MR using SIRF and CIL in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Buet B (2019) Partial differential equations and variational methods for geometric processing of images in The SMAI journal of computational mathematics

 
Description Positron Emission Tomography (PET) is a pillar of modern diagnostic imaging, allowing non-invasive, sensitive and specific detection of functional changes in several disease types. In endocrinology, the precise localisation of small functioning tumours of the pituitary or adrenal glands is crucial for planning curative surgery or radiotherapy. While PET imaging shows good promise for this task, initial studies suggest significant room for improvement, with improved PET imaging and subsequent more accurate localisation opening up the possibility for more adapted therapies. In dementia, the accurate quantification of PET images is key for the early detection of disease. Improved PET imaging may allow for earlier detection of dementia while asymptomatic and increased sensitivity to assess and monitor treatment once appropriate drugs have been found.

In this project mathematicians team up with researchers and clinicians from Addenbrooke's Hospital Cambridge, Dementias Platform UK (DPUK), GE Healthcare and University College London (UCL) for improved diagnosis and localization for tumours in endocrinology and earlier diagnosis of dementia with improved PET imaging. In particular, we investigate modern PET reconstruction approaches based on advanced mathematical methods to increase the PET image resolution and contrast, while keeping computational complexity low, thereby directly benefiting clinical workflow.
Exploitation Route We envision the findings of this project to be taken forward in various ways:
- Integration of our algorithms in scanner manufactures software: Through our collaboration with GE Healthcare and the open source platform STIR we ensure simple translation of our algorithms to existing software packages.
- Integration of our algorithms in open-source PET software packages: implementation of our algorithms in CIL, a software developed by CCPi Tomographic Imaging, in the course of several hackathons that PET++ has been co-organising with CCP SyneRBI and CCPi. This will allow a wide dissemination of our approaches.
- Clinical use: in our project we are already working on two clinical use cases and we envision to take this forward to other use cases in which higher quality PET imaging can provide a boost to diagnostic or prognostic clinical decisions. This further translation is also be facilitated through collaboration of our project with the EPSRC funded Cambridge Mathematics of Information in Healthcare Hub.
Sectors Digital/Communication/Information Technologies (including Software),Healthcare

URL https://petpp.github.io
 
Description 1. PET++, CCP SyneRBI and CCPi jointly organized two hackathons on algorithms benchmark for medical imaging reconstruction. The goal of the hackathons was to establish a benchmark between the numerous iterative algorithms for CT and PET reconstructions which have been proposed in the recent years, with a focus on randomized algorithms. These hackathons are essential for turning our reconstruction approaches into practical, well-documented and generally usable tools and are an important step towards clinical implementation. 2. Research in PET++ is also featuring in our outreach activities to explain the role of mathematics for tomographic image reconstruction and the role of tomographic imaging in clinical practice. For more details on PET++ activities and findings see https://petpp.github.io/https://petpp.github.io/
First Year Of Impact 2021
Sector Education,Healthcare
Impact Types Societal

 
Description Cambridge Mathematics of Information in Healthcare (CMIH)
Amount £1,295,778 (GBP)
Funding ID EP/T017961/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 07/2020 
End 08/2023
 
Description Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems
Amount £1,240,288 (GBP)
Funding ID EP/V029428/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 05/2021 
End 05/2026
 
Description Predicting Dementia: Optimising and translating AI to improve prognosis and clinical pathways
Amount £764,285 (GBP)
Funding ID 221633/Z/20/Z 
Organisation Wellcome Trust 
Sector Charity/Non Profit
Country United Kingdom
Start 02/2022 
End 01/2025
 
Description rapiD and secuRe AI imaging based diaGnosis, stratification, fOllow-up, and preparedness for coronavirus paNdemics (DRAGON)
Amount € 11,542,642 (EUR)
Funding ID Grant Agreement (GA) No: 101005122 
Organisation European Commission 
Department Innovative Medicines Initiative (IMI)
Sector Public
Country Belgium
Start 09/2020 
End 09/2023
 
Description 21st ECMI Conference on Industrial and Applied Mathematics (ECMI 2021) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The series of European Consortium for Mathematics in Industry (ECMI) conferences are devoted to enforcing the interaction between academy and industry, leading to innovations in both fields. These events have attracted leading experts from business, science, and academia, and have promoted the application of novel mathematical technologies to industry. We hope that ECMI 2021 will further enhance multidisciplinary research and development both in academia and industry, leading to the formulation of challenging real-life problems, where mathematics may provide significant new insights and at the same time may be inspired by those interactions.
Year(s) Of Engagement Activity 2021
URL https://ecmiindmath.org/2020/11/22/21st-ecmi-conference-on-industrial-and-applied-mathematics/
 
Description 91st GAMM Annual Meeting 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The Annual Meeting of the International Association of Applied Mathematics and Mechanics, the GAMM 2020@21.
Year(s) Of Engagement Activity 2021
URL https://jahrestagung.gamm-ev.de/jahr2020-2021/annual-meeting/
 
Description BIRS Women in Inverse Problems 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The objective of this workshop is to bring together women in the broad and vibrant field of Inverse Problems. Both established as well as early career researchers will come together to discuss their recent research achievements. This workshop will facilitate professional networking and create mentoring opportunities for women researchers. The ultimate goal is to help broaden female participation in research careers in particular in the field of Inverse Problems, as well as to create new research collaborations.
Year(s) Of Engagement Activity 2021
URL https://www.birs.ca/events/2021/5-day-workshops/21w5035
 
Description CANADIAN APPLIED AND INDUSTRIAL MATHEMATICS SOCIETY 2021 Annual Meeting 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Each year CAIMS/SCMAI hosts an annual meeting for all members. This meeting is one of the central activities of CAIMS and has been held for over 30 years. The annual meeting covers all areas of applied and industrial mathematics with high profile speakers invited to give keynote addresses on currently active thematic areas.
Year(s) Of Engagement Activity 2021
URL https://uwaterloo.ca/canadian-applied-industrial-math-society-annual-meeting-2021/
 
Description Computational Mathematics and Machine Learning 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The aim of this workshop is to formulate a plan for future developments within the area of computational science and engineering (CSE) making use of machine learning techniques. We will discuss the impact that machine learning has already made or will make on computational mathematics, and how the ideas from computational mathematics, particularly numerical analysis, can be used to help understanding and better formulating machine learning models. In the annex, the state of the art is provided in more detail. The question is: which research directions are most promising? What should we concentrate on? How can we combine physics-based and data-based techniques? Can we formulate joint projects? Or maybe a joint organisation for the discussion and dissemination of new developments?

In this workshop, we will address the following two very important questions: (1) How machine learning has already impacted and will further impact computational mathematics, scienti?c computing and computational science? (2) How computational mathematics, particularly numerical analysis, can impact machine learning? To accomplish the aforementioned aim, in this workshop, we review what has been learned on these two issues.

We will discuss some of the most important progress that has been made on the foregoing two issues, and where new developments should take place. This workshop will be considered a success if we have been able to put things into a perspective that will help to integrate machine learning with computational mathematics, and produced (at the end of the workshop) a sound plan for future research directions in several of the areas mentioned in Section 4. We will identify the most promising research directions, networking activities, as well as building of new collaborations between participants.
Year(s) Of Engagement Activity 2021
URL https://www.lorentzcenter.nl/computational-mathematics-and-machine-learning.html
 
Description Deep Learning and Inverse Problems (NeurIPS Workshop) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact This virtual workshop aims at bringing together theoreticians and practitioners in order to chart out recent advances and discuss new directions in deep learning-based approaches for solving inverse problems in the imaging sciences and beyond.
Year(s) Of Engagement Activity 2021
URL https://deep-inverse.org/index.html
 
Description Eighth International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact SSVM is a biannual meeting within the area of Computer Vision and Image Analysis. SSVM focuses especially on multiscale analysis of image content, partial differential equations, geometric and level-set methods, variational methods, and optimization.
Year(s) Of Engagement Activity 2021
URL https://ssvm2021.sciencesconf.org/
 
Description IEEE International Symposium on Biomedical Imaging 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The IEEE International Symposium on Biomedical Imaging (ISBI) is a scientific conference dedicated to mathematical, algorithmic, and computational aspects of biological and biomedical imaging, across all scales of observation. It fosters knowledge transfer among different imaging communities and contributes to an integrative approach to biomedical imaging.
Year(s) Of Engagement Activity 2021
URL https://biomedicalimaging.org/2021/
 
Description INTERACT 2021 "Sense, Feel, Design" 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The theme of INTERACT 2021 "Sense, Feel, Design" highlights the new challenges of interaction design. Technology is today more and more widespread, pervasive and blended in the world we live in. On one side, devices that sense humans' activities have the potential to provide an enriched interaction. On the other side, the user experience can be further enhanced by exploiting multisensorial technologies. Not only the traditional human senses of vision and hearing, but also senses of touch, smell, and taste, as well as emotions are to be taken into account when designing for future interactions.
INTERACT 2021 represents the right venue to debate such new challenges. Another hot topic of this edition is Human-AI Interaction, focusing on the design of human-centered intelligent systems.
Year(s) Of Engagement Activity 2021
URL https://www.interact2021.org/
 
Description Mathematics of deep learning 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Aiming to derive a mathematical foundation of deep learning, this programme addresses theoretical questions in two realms:
(1) Theoretical foundations of deep learning independent of a particular application.
(2) Theoretical analysis of the potential and the limitations of deep learning for mathematical methodologies, in particular, for inverse problems and partial differential equations.

The main goal of this programme is to achieve substantial progress in developing a theoretical foundation of deep learning. For this, the programme will for the first time gather the top experts from various areas of mathematics and of the theory of machine learning, including computer scientists, physicists, and statisticians in one place, initiating collaborations across intra- and interdisciplinary boundaries and thereby generating unprecedented research dynamics.
Year(s) Of Engagement Activity 2021
URL https://www.newton.ac.uk/event/mdl/
 
Description Mathematisches Forschungsinstitut Oberwolfach - Geometric Numerical Integration 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects.
Year(s) Of Engagement Activity 2021
URL https://publications.mfo.de/handle/mfo/3860
 
Description Mathematisches Forschungsinstitut Oberwolfach - Mini-Workshop: Deep Learning and Inverse Problems 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Machine learning and in particular deep learning offer several
data-driven methods to amend the typical shortcomings of purely analytical approaches. The mathematical research on these combined models is
presently exploding on the experimental side but still lacking on the theoretical point of view. This workshop addresses the challenge of developing
a solid mathematical theory for analyzing deep neural networks for inverse
problems.
Year(s) Of Engagement Activity 2021
URL https://publications.mfo.de/handle/mfo/3633
 
Description Woudschoten Conference 2021 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The Woudschoten conference has a long and rich history, dating back to the first edition in 1976, and it has featured many of the great names in numerical analysis and scientific computing. Since its establishment in the early days of `approximation and discretization' - the two themes of the first edition of the conference -- the Woudschoten conference has provided an introduction to and overview of groundbreaking developments in scientific computing and numerical analysis. The conference is attended by essentially all Dutch and Flemish researchers in numerical analysis and scientific computing, from PhD students to full professors, and including industrial researchers. By virtue of its unique format and its informal setting, the conference does not only provide insight and inspiration to the Dutch-Flemish numerical-mathematics community, but it also plays a central role in retaining coherence in the community.
Year(s) Of Engagement Activity 2021
URL https://wsc.project.cwi.nl/woudschoten-conferences/2021-conference