In our work in the current edition of the CMIH we have built up a strong pool of researchers and collaborations across the board from mathematics, statistics, to engineering, medical physics and clinicians. Our work has also confirmed that imaging data is a very important diagnostic biomarker, but also that non-imaging data in the form of health records, memory tests and genomics are precious predictive resources and that when combined in appropriate ways should be the source for AI-based healthcare of the future. Following this philosophy, the new CMIH brings together researchers from mathematics, statistics, computer science and medicine, with clinicians and relevant industrial stakeholder to develop rigorous and clinically practical algorithms for analysing healthcare data in an integrated fashion for personalised diagnosis and treatment, as well as target identification and validation on a population level. We will focus on three medical streams: Cancer, Cardiovascular disease and Dementia, which remain the top 3 causes of death and disability in the UK. Whilst applied mathematics and mathematical statistics are still commonly regarded as separate disciplines there is an increasing understanding that a combined approach, by removing historic disciplinary boundaries, is the only way forward. This is especially the case when addressing methodological challenges in data science using multi-modal data streams, such as the research we will undertake at the Hub. This holistic approach will support the Hub aims to bring AI for healthcare decision making to the clinical end users.

Models of complex chemical processes such as combustion or atmospheric chemistry assume that the molecules taking part are thermalized, that is that their energy is characterized by the temperature of the system. Chemical activation (CA) occurs when the energy released by a reaction is channelled into the products and they have an energy greater than would be thermally predicted. How does the reactivity of these activated species compare with their thermalized equivalents? What is the significance of CA? How can CA be incorporated into chemical models of complex systems? These are the questions at the heart of our project: Complex Chemistry and Chemical Activation (C3A). Aspects of CA have been known about for more than 100 years, indeed 2022 marks the centenary of the Lindemann Mechanism, the first theory proposed to explain the pressure dependence of some chemical reactions. Models of CA have grown in sophistication, yet uncertainties in key processes (energy transfer, calculation of densities of states) limit the accuracy of kinetic and thermodynamic predictions from such systems. Addressing the uncertainties in these aspects of current models through new experimental data and developments in fundamental models is one strand of C3A. More recently, work in this group and elsewhere has shown that systems which were thought to be adequately modelled by thermalized reagents, such as abstraction reactions (e.g. OH + HCHO), do need to considered in the context of chemical activation. In a 2018 review, Klippenstein states: 'These studies ultimately led us to the realization that at combustion temperatures, the foundational assumption of thermalization prior to reaction is not always valid, and further that its breakdown significantly affects key combustion properties' (Proceedings of the Combustion Institute, 36, p77). These phenomena are not limited to combustion; plasma chemistry and the atmospheric chemistry of Earth and other planets provide other important examples of applications. C3A is a collaboration between leading groups from Leeds and Oxford, both with interests in experiments and theory. C3A will generate a wealth of new experimental data, which in combination with theoretical interpretation, will allow us to assess the significance of CA in real systems and provide the tools to allow CA to be accurately incorporated into chemical models of of these processes. The impact of C3A to industry will be facilitated by collaborations with Shell, Dassault Systemes and AirLabs. Such models are essential tools for understanding important questions from current highly practical issues (how can combustion systems be optimized to minimize CO2 emissions and improve air quality) to future questions (biofuels for aviation, novel methods of renewable energy storage such as ammonia generation and combustion) to important, fundamental questions such as modelling the atmospheres of hot-Jupiter exo-planets or the interstellar medium. The accurate assessment and incorporation of CA into such models will significantly enhance their reliability and predictive value.

Soft tissue related diseases (heart, cancer, eyes) are among the leading causes of death worldwide. Despite extensive biomedical research, a major challenge is a lack of mathematical models that predict soft tissue mechanics across subcellular to whole organ scales during disease progression. Given the tremendous scope, the unmet clinical needs, our limited manpower, and the existence of complementary expertise, we seek to forge NEW collaborations with two world-leading research centres: MIT and POLIMI, to embark on two challenging themes that will significantly stretch the initial SofTMech remit: A) Test-based microscale modelling and upscaling, and B) Beyond static hyperelastic material to include viscoelasticity, nonlinear poroelasticity, tissue damage and healing. Our research will lead to a better understanding of how our bodies work, and this knowledge will be applied to help medical researchers and clinicians in developing new therapies to minimise the damage caused by disease progression and implants, and to develop more effective treatments. The added value will be a major leap forward in the UK research. It will enable us to model soft tissue damage and healing in many clinical applications, to study the interaction between tissue and implants, and to ensure model reproducibility through in vitro validations. The two underlying themes will provide the key feedback between tissue and cells and the response of cells to dynamic local environments. For example, advanced continuum mechanics approaches will shed new light on the influence of cell adhesion, angiogenesis and stromal cell-tumour interactions in cancer growth and spread, and on wound healing implant insertion that can be tested with in vitro and in vivo systems. Our theoretical framework will provide insight for the design of new experiments. Our proposal is unique, timely and cost-effectively because advances in micro- and nanotechnology from MIT and POLIMI now enable measurements of sub-cellular, single cell, and cell-ECM dynamics, so that new theories of soft tissue mechanics at the nano- and micro-scales can be tested using in vitro prototypes purposely built for SofTMech. Bridging the gaps between models at different scales is beyond the ability of any single centre. SofTMech-MP will cluster the critical mass to develop novel multiscale models that can be experimentally tested by biological experts within the three world-leading Centres. SofTMech-MP will endeavour to unlock the chain of events leading from mechanical factors at subcellular nanoscales to cell and tissue level biological responses in healthy and pathological states by building a new mathematics capacity. Our novel multiscale modelling will lead to new mathematics including new numerical methods, that will be informed and validated by the design and implementation of experiments at the MIT and POLIMI centres. This will be of enormous benefit in attacking problems involving large deformation poroelasticity, nonlinear viscoelasticity, tissue dissection, stent-related tissue damage, and wound healing development. We will construct and analyse data-based models of cellular and sub-cellular mechanics and other responses to dynamic local anisotropic environments, test hypotheses in mechanistic models, and scale these up to tissue-level models (evolutionary equations) for growth and remodelling that will take into account the dynamic, inhomogeneous, and anisotropic movement of the tissue. Our models will be simulated in the various projects by making use of the scientific computing methodologies, including the new computer-intensive methods for learning the parameters of the differential equations directly from noisy measurements of the system, and new methods for assessing alternative structures of the differential equations, corresponding to alternative hypotheses about the underlying biological mechanisms.

By 2020, the advanced composite market is predicted to be worth around £17 billion, with automotive the second largest growth sector (after wind energy) but still falling far short of its enormous growth potential; the high cost of production for advanced composite products is still a major obstacle to their wider exploitation. Government legislation on the reduction of emissions is an important driver across the transport sector and one way to achieve prescribed targets is through the substitution of relatively heavy metallic components with highly optimised light-weight advanced polymer composite parts. Consequently, there is an urgent need to address the economic viability of manufacturing with advanced polymer composites and realise their full weight and fuel saving potential. The proposed project aims to contribute to this overarching goal by introducing an ambitious low-cost route to manufacturing highly optimised advanced composite structures. The ability to produce 'steered-fibre laminates' containing non-linear fibre paths, creates a step change in the design space for advanced composite structures. The designer is able to reposition stress concentrations away from holes and inserts, improve a laminate's resistance to buckling and failure, and to enhance a laminate's dynamic response to vibrations. Ultimately this can lead to lighter, more optimised structures for use in the aerospace and automotive sectors, enhancing fuel efficiency and contributing to the broader goals of reduced cost and lower emissions across the transport sector. The aim of the proposed project is to implement and demonstrate a novel and disruptive manufacture process that can produce low-cost high-quality steered-fibre laminates, without use of expensive, capital intensive automated fibre placement machines (the current solution). The new process is best described as 2-D forming; in order to support this novel manufacture process, a custom-designed suite of computer aided design and manufacture software will be developed. Computational tools for digital manufacturing are essential if 2-D forming is to be successfully achieved without inducing severe wrinkling and buckling of the deforming biaxial sheet. Reducing cost will effectively bring fibre-steering technology to a broader range of applications, increasing its economic impact and bringing new manufacturing capabilities to a wider industrial base, with the UK leading the way in this important area of manufacturing.

There have recently been impressive developments in the mathematical modelling of physiological processes. As part of a previously EPSRC-funded research centre (SofTMech), we have developed mathematical models for the mechanical and electrophysiological processes of the heart, and the flow in the blood vessel network. This allows us to gain deeper insight into the state of a variety of serious cardiovascular diseases, like hypoxia (a condition in which a region of the body is deprived of adequate oxygen supply), angina (reduced blood flow to the heart), pulmonary hypertension (high blood pressure in the lungs) and myocardial infarction (heart attack). A more recent extension of this work to modelling blood flow in the eye also provides novel indicators to assess the degree of traumatic brain injury. What all these models have in common is a complex mathematical description of the physiological processes in terms of differential equations that depend on various material parameters, related e.g. to the stiffness of the blood vessels or the contractility of the muscle fibres. While knowledge of these parameters would be of substantial benefit to the clinical practitioner to help them improve their diagnosis of the disease status, most of the parameters cannot be measured in vivo, i.e. in a living patient. For instance, the determination of the stiffness and contractility of the cardiac tissue would require the extraction of the heart from a patient and its inspection in a laboratory, which can only be done in a post mortem autopsy. It is here that our mathematical models reveal their diagnostic potential. Our equations of the mechanical processes in the heart predict the movement of the heart muscle and how its deformations change in time. These movements can also be observed with magnetic resonance image (MRI) scans, and they depend on the physiological parameters. We can thus compare the predictions from our model with the patterns found in the MRI scans, and search for the parameters that provide the best agreement. In a previous proof-of-concept study we have demonstrated that the physiological parameters identified in this way lead to an improved understanding of the cardiac disease status, which is important for deciding on appropriate treatment options. Unfortunately, the calibration procedure described above faces enormous computational costs. We typically have a large number of physiological parameters, and an exhaustive search in a high-dimensional parameter space is a challenging problem. In addition, every time we change the parameters, our mathematical equations need to be solved again. This requires the application of complex numerical procedures, which take several minutes to converge. The consequence is that even with a high-performance computer, it takes several weeks to determine the physiological parameters in the way described above. It therefore appears that despite their enormous potential, state of the art mathematical modelling techniques can never be practically applied in the clinical practice, where diagnosis and decisions on alternative treatment option have to be made in real time. Addressing this difficulty is the objective of our proposed research. The idea is to approximate the computationally expensive mathematical model by a computationally cheap surrogate model called an emulator. To create this emulator, we cover the parameter space with an appropriate design, solve the mathematical equations in parallel numerically for the chosen parameters, and then fit a non-linear statistical regression model to this training set. After this initial computational investment, the emulator thus created gives predictions for new parameter values practically instantaneously, allowing us to carry out the calibration procedure described above in real time. This will open the doors to harnessing the diagnostic potential of state-of-the art mathematical models for improved decision support in the clinic.