As quality of life constantly improves, the average lifespan will continue to increase. Underlining this improvement is the vast amount of the UK government's support to NHS (£133.5 billion in year 2011/12) and the UK pharmaceutical industry's R&D large investment (4.9 billion to R&D in year 2011/12). The expectation of quality healthcare is inevitably high from all stakeholders. Fortunately recent advances in science and technology have enabled us to work towards personalised medicine and preventative care. This approach calls for a collective effort of researchers from a vast spectrum of specialised subjects. Advances in science and engineering is often accompanied by major development of mathematical sciences, as the latter underpin all other sciences. The UoL Centre will consist of a large and multidisciplinary team of applied and pure mathematicians, and statisticians together with healthcare researchers, clinicians and industrialists, collaborating with 15 HEIs and 40 NHS trusts plus other industrial partners and including our strongest groups: MRC Centre in Drug Safety Science, Centre for Cell imaging (CCI for live 3D and 4D imaging), Centre for Mathematical Imaging Techniques (unique in UK), Liverpool Biomedical EM unit, MRC Regenerative Medicine Hub, NIHR Health Protection Research Units, MRC Hub for Trials Methodology Research. Several research themes are highlighted below: Firstly, an improved understanding of the interaction dynamics of cells and tissues is crucial to developing effective future cures for cancer. Much of the current work is in 2D, with restrictive assumptions and without access to real data for modelling. We shall use the unparalleled real data of cell interactions in a 3D setting, generated at UoL's CCI. The real-life images obtained will have low contrast and noise and they will be analysed and enhanced by our imaging team through developing accurate and high resolution imaging models. The main imaging tools needed are segmentation methods (identifying objects such as cells and tissues regions in terms of sizes, shapes and precise boundaries). We shall propose and study a class of new 3D models, using our imaging data and analysis tools, to investigate and predict the spatial-temporal dynamics. Secondly, better models of how drugs are delivered to cells in tissues will improve personalised predictions of drug toxicity. We shall combine novel-imaging data of drug penetration into 3D experimental model systems with multi-scale mathematical models which scale-up from the level of cells to these model systems, with the ultimate aim of making better in-vitro to in-vivo predictions. Thirdly, there exist many competing models and software for imaging processing. However, for real images that have noise and are of low contrast, few methods are robust and accurate. To improve the modelling, applied and pure mathematicians team up to consider using more sophisticated tools of hyperbolic geometry and Riemann surfaces and fractional calculus to meet the demand for accuracy, and, applied mathematicians and statisticians will team up to design better data fidelity terms to model image discrepancies. Fourthly, resistance to current antibiotics means that previously treatable diseases are becoming deadly again. To understand and mitigate this, a better understanding is needed for how this resistance builds up across the human interaction networks and how it depends on antibiotic prescribing practices. To understand these scenarios, the mathematics competition in heterogeneous environments needs to be better understood. Our team links mathematical experts in analysing dynamical systems with experts in antimicrobial resistance and GPs to determine strategies that will mitigate or slow the development of anti-microbial resistance. Our research themes are aligned with, and will add value to, existing and current UoL and Research Council strategic investments, activities and future plans.

Molecular sciences, such as chemistry, biophysics, molecular biology and protein science, are vital to innovations in medicine and the discovery of new medicines and diagnostics. As well as making a crucial contribution to health and society, industries in this field provide an essential component to the economy and contribute hugely to employment figures, currently generating nearly 500,000 jobs nationally. To enable and facilitate future economic growth in this area, the CDT will provide a cohort of researchers who have training in both aspects of this interface who will be equipped to become the future innovators and leaders in their field. All projects will be based in both molecular and medical sciences and will focus on unmet medical needs, such as understanding of disease biology, identification of new therapeutic targets, and new approaches to discovery and development of novel therapies. Specific problems will be identified by researchers within the CDT, industrial partners, stakeholders and the CDT students. The research will be structured around three theme areas: Biology of Disease, Molecule and Assay Design and Structural Biology and Computation. The CDT brings together leading researchers with a proven track record across these areas and who have pioneered recent advances in the field, such as multiple approved cancer treatments. Their combined expertise will provide supervision and mentorship to the student cohort who will work on projects that span these research themes and bring their contributions to bear on the medical problems in question. The student cohort approach will allow teams of researchers to work together on joint projects with common goals. Projects will be proposed between academics, industrial partners and students with priority given to those with industrial relevance. The programme of research and training across the disciplines will equip graduates of the CDT with an unprecedented background of knowledge and skills across the disciplines. The programme of research and training across the disciplines will be supplemented by training and hands-on experiences of entrepreneurship, responsible innovation and project management. Taken together this will make graduates of the CDT highly desirable to employers, equip them with the skills they need to envisage and implement future innovations in the area and allow them to become the leaders of tomorrow. A structured and highly experienced management group, consisting of a director, co-directors, theme leads and training coordinators will oversee the execution of the CDT with the full involvement of industry partners and students. This will ensure delivery of the cohort training programme and joint events as well as being accountable for the process of selection of projects and student recruitment. The management team has an established track record of delivery of research and training in the field across industry and academia as well as scientific leadership and network training coordination. The CDT will be delivered as a single, fully integrated programme between Newcastle and Durham Universities, bringing together highly complementary skills and backgrounds from the two institutions. The seamless delivery of the programme across the two institutions is enabled by their unique connectivity with efficient transport links and established regional networks. The concept and structure of the CDT has been developed in conjunction with the industrial partners across the pharmaceutical, biotech and contract research industries, who have given vital steer on the desirability and training need for a CDT in this area as well as to the nature of the theme areas and focus of research. EPSRC funding for the CDT will be supplemented by substantial contributions from both Universities with resources and studentship funding and from industry partners who will provide training, in kind contribution and placements as well as additional studentships.