Two-photon microscopy is a leading-edge imaging technology and a powerful research tool that combines long wavelength excitation and laser scanning microscopy. Of importance to our work it can enable capture of high resolution three dimensional images of living cells within 3D constructs as well as in-depth penetration of specimens tagged with very specific fluorophores. This technology is now becoming a method of choice for the dynamic imaging of biological and polymeric systems, not otherwise possible by other optical approaches and therefore will underpin a broad number of research programmes in biomaterials and tissue engineering.

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.

The ITRS roadmap for the semiconductor industry has identified semiconducting nanowires as a possible route by whichthe size-scaling of Moore's Law can be extended to yet smaller dimensions. Nanowires could be used both as the logicelements and the memory elements in a future semiconductor technology with device dimensions below 10 nm. The fieldof nanowire research is therefore particularly active at present and can be expected to deliver real applications in themedium to long term.In this fellowship I will address two key issues which must be resolved if nanowire applications are to make an impact inthe electronics sector:(i) How can nanowires be interconnected to form useful circuits?(ii) What unique functional properties can be engineered into nanowires that can be exploited in applications?Experiments to address the first of these issues will focus on using organic scaffold deposition (OSD) for growth of three-dimensional metallic nanowire networks. In particular we will study the growth of magnetic nanowires using OSD with the ultimate aim of creating a three-dimensional magnetic storage medium for high-density computer memory applications.Experiments to address the second issue will concentrate on semiconducting and superconducting nanowires. For semiconducting nanowires we will use the established nanoparticle-seeded molecular beam epitaxy (NS-MBE) technique and extend it to a variety of III-V and II-VI materials. Using NS-MBE we will be able to modulate the properties of the nanowire along its length simply by changing the precursor material during growth. (This technique has already been demonstrated to result in atomically sharp materials interfaces in the InP/InAs system.) NS-MBE therefore gives us a toolkit for studying the role of reduced dimensionality on a number of functional materials and heterostructures, including (for example) dilute magnetic semiconductors and heterostructure photonic devices.Superconducting nanowires will be grown using focussed-ion-beam and OSD techniques. These nanowires, which display a range of new physical phenomena, will be studied for applications as single photon detectors for use in infra-red quantum key distribution systems and as quantum current standards.

To support the development of challenging, difficult to manufacture products, increased reliance is placed on techniques to allow accurate dimensional measurement of parts and components. New measurement systems are needed that provide data quickly with higher levels of accuracy and precision than is currently possible. Currently high accuracy measurements are made using dedicated expensive instrumentation in temperature controlled labs. The wide range of measurement challenges mean there is no single instrument available to suit all needs. In fact, the range of lab based instrument systems required to meet the measurement needs of industry continues to grow. It includes techniques ranging from contact measurements made using a mechanical probe, to non-contact measurements which use light, lasers, or X-ray based measurement methods. The main drawback of these systems is that they are usually slow to set-up, and significant time is required to take measurements. This means that although they are very accurate they are less useful for the control and improvement of challenging manufacturing processes, where data must be collected and analysed quickly. Improved measurement systems are required which provide higher speed measurements, at lower cost, without compromising accuracy. Currently two approaches address this need. One approach uses on machine sensors to provide high-speed measurements, while the other approach is to position instruments closer to the manufacturing environment to reduce the time required to transfer work to the measurement lab. Both approaches have obvious benefits as they provide faster data; however, they are also less accurate as a result of the unwanted disturbances experienced on the factory floor. These limitations result in a trade-off: the user can either have high accuracy, or high speed measurement, but not both at once. The research undertaken within this Fellowship will develop a new way of collecting and effectively processing critical measurement data. Instead of a reliance on high accuracy instruments, this approach will provide a new way of thinking with respect to how measurement systems are designed and implemented. The goal will be to allow different types of lower accuracy data to be combined in a beneficial way. For example, computer simulations of a machine, product, and process will be combined with sensors that monitor environmental conditions. In addition sensors used to take high speed measurements of parts during the manufacturing process itself will be used. Through a collaborative process these data will be combined to provide fast high quality data. To verify and further improve the system a small quantity of accurate feedback data from high accuracy instruments in temperature controlled labs will be used. In effect the approach will be to combine slow accurate data, with fast less reliable data, to produce enhanced accuracy fast measurements. For example, if a batch of high precision components must be produced, the components must also have their geometry verified and corrected if required. On machine sensors may be used to verify geometry, but accuracy is limited due to environmental effects such as temperature and humidity. To compensate for these errors a collaborative measurement system will initially make measurements using both on-machine sensors as well as off-machine lab instruments. It will blend these data sets in addition to data from on-machine environmental monitoring sensors, and computer simulations to correct for errors and therefor enhance the accuracy of the measurements. The system will automatically adapt to changing environmental conditions by triggering the need for more lab-based data which will allow an improved error correction to be made. In this way the system will adapt and optimise the measurement process to suit the current manufacturing conditions.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.